ENGINEERING RESEARCH INSTITUTE
THE UNIVERSITY OF MICHIGAN
ANN ARBOR
APPLICATION OF NUCLEAR ENERGY TO TRANSPORTATION
Progress Report No. 6
PRELIMINARY NUCLEAR HEAT POWERPLANT ENGINE STUDIES
F/. G. HAMMITT
E. M,. 1ROWER
R. K. FU`'
J. L. SUMMERS
Approved by:
H. A. OHLGREN
Project 2427
CHRYSLER CORPORATION
DETROIT, MICHIGAN
April 1956

TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS - PART I iv
LIST OF ILLUSTRATIONS - PART II v
LIST OF TABLES - PART I viii
LIST OF TABLES - PART II ix
1.0 ABSTRACT 1
2.0 INTRODUCTION 3
3.0 OB3JE'CTIVES 5
4.0 ACKNOWLEDGEMENTS 6
PART I. GENERALIZED HEAT ENGINE STUDIES FOR NUCLEAR POWERPLANTS 7
1.0 GENERAL THERMODYNAMIC PARAMETERS 7
1,1l Application to Nuclear Powerplant 7
1.2 General Discussion of Thermodynamic Factors 7
2.0 SPECIFIC CYCLE ARRANGEMENTS 16
2.1 Gas Turbine Cycle 16
2.2 Steam Cycle 17
2~3 Binary Vapor Cycles 17
3-0 COMPARISON OF VARIOUS CYCLES 33
4.0 FUTURE WORK 36
5.0 CONCLUSIONS 37
6.0 BIBLIOGRAPHY 38
7.0 APPENDIX 39
7.1 Assumptions for Steam Cycle Efficiencies 39
7.2 Liquid Metal Turbine Design Characteristics 42
7.3 Trinary Na-Hg-H20 Cycle. Sample Calculations
and Assumptions 42
7~4 Estimation of Effect of Turbine Efficiency
on Ideal Trinary Na-Hg-H20 Cycle.
Corrections to Na Data 47
7.5 Effect of Finite Temperature Differential
Between Various Portions of Binary and
Trinary Cycles 49
ii

Table of Contents, Continued
Page
7o6 Effect of Temperature Differential in
Extraction Feed Heaters 50
PART IIo GAS TURBINE DETAILED STUDIES FOR NUCLEAR POWERPLANTS 51
1.0 GENERAL THERMODYNAMIC FEATURES OF GAS TURBINE CYCLE 51
1.1 Approach to Ideal Efficiency 51
1.2 Selection of Basic Cycle 51
1.3 General Relations with Perfect Gas 53
2.0 OPERATING PARAMETER VARIATION EFFECTS ON EFFICIENCY
FOR PERFECT GAS 56
2.1 Basic Cycle 56
2.2 Results of Theoretical Performance Calculations 56
3.0 EFFECT OF PLANT SIZE AND REAL WORKING FLUID ON
OTHER PLANT PARAMETERS 79
3.1 General Considerations 79
3.2 Gas Properties 80
303 Turbomachinery Types Considered 81
3.4 Methods of Efficiency Estimation 82
3.5 Results and Tabulations 118
4.0 FUTURE WORK 127
500 CONCLUSIONS 128
6.0 NOMENCLATURE 129
7.0 BIBLIOGRAPHY 131
8.0 APPENDIX 132
8.1 Derivation of Thermal Efficiency Equations 132
8.2 Velocity Vector Diagram Calculations 134
8.3 Effects of Gas Turbine Plant Size. Sample
Calculations 136
804 Number of Compressor Stages for Air and
Helium if Velocities are Equal 151
111

LIST OF ILLUSTRATIONS - PART I
Page
Figure 1. Temperature-Entropy Diagrams for Various Cycles 8
Figure 2. Simple Gas Turbine Cycle 10
Figure 3. Regenerative Gas Turbine Cycle 11
Figure 4. Temperature-Entropy Diagrams for Various Steam
Cycles with Extraction 13
Figure 5. Thermal Efficiency of a Regenerative Air Cycle
with Reheater and Intercooler 18
Figure 6a. Sodium-Mercury-Steam Extraction Trinary Cycle I
Temperature-Entropy Diagram 21
Figure 6b. Sodium-Mercury-Steam Extraction Trinary Cycle II
Temperature-Entropy Diagram 22
Figure 6c. Sodium-Mercury-Steam Ideal Extraction Trinary
Cycle Temperature-Entropy Diagram 23
Figure 7. Sodium-Steam Binary Extraction Cycle TemperatureEntropy Diagram 24
Figure 8. Sodium-Air Binary Extraction - Reheat Cycle
Temperature-Entropy Diagram 25
Figure 9. Mercury-Steam Binary Extraction Cycle
Temperature-Entropy Diagram 28
Figure 10. Mercury-Steam Binary Non-Extraction Cycle
Temperature-Entropy Diagram 29
Figure 11. Maximum Feasible Efficiency vs. Temperature
Various Heat Engine Cycles 34
iv

LIST OF ILLUSTRATIONS - PART II
Page
Figure 1. Schematic Flow Diagram of the Basic Gas Turbine
Cycle 57
Figure 2. Schematic Flow Diagram of the Basic Gas Turbine
Cycle without Recuperator 57
Figure 3. Schematic Flow Diagram of the Basic Gas Turbine
Cycle without Intercooler 58
Figure 4. Schematic Flow Diagram of the Basic Gas Turbine
Cycle without Recuperator or Intercooler 58
Figure 5. Schematic Flow Diagram of the Basic Gas Turbine
Cycle with Reheater 59
Figure 6a. Thermal Efficiency of a Gas Turbine Cycle with
Various Cycle Arrangements. Basic Cycle 60
Figure 6b. Thermal Efficiency of a Gas Turbine Cycle with
Various Cycle Arrangements. Basic Cycle without
Recuperator 61
Figure 6c. Thermal Efficiency of a Gas Turbine Cycle with
Various Cycle Arrangements. Basic Cycle without
Intercooler 62
Figure 6d. Thermal Efficiency of a Gas Turbine Cycle with
Various Cycle Arrangements. Basic Cycle without
Recuperator and Intercooler 63
Figure 6e. Thermal Efficiency of a Gas Turbine Cycle with
Various Cycle Arrangements. Basic Cycle with
Reheater 64
Figure 7a. Thermal Efficiency of a Basic Gas Turbine Cycle
with Recuperator Effectiveness = 0.93 65
Figure 7b. Thermal Efficiency of a Basic Gas Turbine Cycle
with Recuperator Effectiveness = 0.75 66
Figure 7c. Thermal Efficiency of a Basic Gas Turbine Cycle
with Recuperator Effectiveness = 0.50 67
Figure 8a. Thermal Efficiency of a Basic Gas Turbine Cycle
with Frictional Pressure Losses = 0.07 68
Figure 8b. Thermal Efficiency of a Basic Gas Turbine Cycle
with Frictional Pressure Losses = 0.12 69
v

List of Illustrations - Part II., Continued
Page
Figure 8c. Thermal Efficiency of a Basic Gas Turbine Cycle
with Frictional Pressure Losses = 0.20 70
Figure 9a. Thermal Efficiency of a Basic Gas Turbine Cycle
with Turbine Efficiency = Compressor Efficiency =
0.85 71
Figure 9b. Thermal Efficiency of a Basic Gas Turbine Cycle
with Turbine Efficiency = Compressor Efficiency =
0.80 72
Figure 9c. Thermal Efficiency of a Basic Gas Turbine Cycle
with Turbine Efficiency = Compressor Efficiency =
0.75 73
Figure 10. Thermal Efficiency of a Basic Gas Turbine Cycle
with Ratio of Specific Heats Varied 76
Figure 11. Thermal Efficiency at Optimum Pressure Ratio as a
Function of the Ratio of Specific Heats. Basic
Gas Turbine Powerplant with Regenerator and
Intercooler 77
Figure 12. Air Compressor Efficiency at Standard Temperature
and Pressure at Inlet vs. Volumetric Flow Rate 83
Figure 13a. Velocity Vector Diagrams for Air and Helium.
Compressor Diagram 85
Figure 13b. Velocity Vector Diagrams for Air and Helium.
Turbine Diagrams 86
Figure 14. Reynold's Number for Air Compressor Blade Passage
at Stand.ard Temperature and Pressure vs.
Volumetric Flow Rate 93
Figure 15a. Turbine Diameter for Air Power Plants of Various
Turbine Horsepower. T1 = 1500 F 94
Figure 15b. Turbine Diameter for Air Power Plants of Various
Turbine Horsepower. T1 = 1200 F 95
Figure 15c. Turbine Diameter for Air Power Plants of Various
Turbine Horsepower. T1 = 900 F 96
Figure 16a. Turbine Diameter for Helium Power Plants of Various
Turbine Horsepower. T1 = 1500 F 103
Figure 16b, Turbine Diameter for Helium Power Plants of Various
Turbine Horsepower. T1 = 1200 F 104
vi

List of Illustrations - Part II, Continued
Page
Figure 16c. Turbine Diameter for Helium Power Plants of Various
Turbine Horsepower. T1 = 900 F 105
Figure 17. Blade Loss Coefficient as a Function of Reynold's
Number and Angle of Turn 108
Figure 18a. Turbine Efficiency for Air Power Plants of Various
Turbine Horsepower. T1 = 1500 F 112
Figure 18b. Turbine Efficiency for Air Power Plants of Various
Turbine Horsepower. T1 = 1200 F 113
Figure 18c. Turbine Efficiency for Air Power Plants of Various
Turbine Horsepower. T1 = 900 F 114
Figure 19a. Turbine Efficiency for Helium Power Plants of Various
Turbine Horsepower. T1 = 1500 F 115
Figure 19b. Turbine Efficiency for Helium Power Plants of Various
Turbine Horsepower. T1 = 1200 F 116
Figure 19c. Turbine Efficiency for Helium Power Plants of Various
Turbine Horsepower. T1 = 900 F 117
Figure 20a. Thermal Efficiency vs. Plant HP, Using Air as
Working Fluid. T1 = 1500 F 119
Figure 20b. Thermal Efficiency vs. Plant HP, Using Air as
Working Fluid. T1 = 1200 F 120
Figure 20c. Thermal Efficiency vs. Plant HP, Using Air as
Working Fluid. T1 = 900 F 121
Figure 21a. Thermal Efficiency vs. Plant HP, Using Helium
as Working Fluid. T1 = 1500 F 122
Figure 21b. Thermal Efficiency vs. Plant HP, Using Helium
as Working Fluid. T1 = 1200 F 123
Figure 21c. Thermal Efficiency vs. Plant HP, Using Helium
as Working Fluid. T1 = 900 F 124
Figure 22. Small Turbine Velocity Diagram 147
vii

LIST OF TABLES - PART I
Page
Table I. Vapor Pressures for Various Fluids at Several
Temperatures 26
Table II. Tabulated Efficiencies of Binary and Trinary
Vapor Cycles at 1500 F Inlet, 70 F Cooling Water 27
Table III. Effect of Turbine Efficiency on Trinary Cycles 32
Table IV. Sonic Velocity of Liquid Metal Vapors at 1500 F 42
* 11

LIST OF TABLES - PART II
Page
Table I. Assumed Component Efficiencies for the Basic Gas
Turbine Cycle 52
Table II. Gas Turbine Cycle Thermal Efficiency Relations 54
Table III. Tabulation of Cycle Conditions Presented in Report 74
Table IV. Thermodynamic Assumptions for Plant Design Calculations 80
Table V. Calculations for Gas Turbine Powerplant
Air - 60,000 HP 87
Table VI. Calculations for Gas Turbine Powerplant
Air - 20,000 HP 88
Table VII. Calculations for Gas Turbine Powerplant
Air - 6,oo000o HP 89
Table VIII. Calculations for Gas Turbine Powerplant
Air - 2,000 HP 90
Table IX. Calculations for Gas Turbine Powerplant
Air - 600 HP 91
Table X, Calculations for Gas Turbine Powerplant
Helium - 60,000 HP 98
Table XI. Calculations for Gas Turbine Powerplant
Helium - 20,000 HP 99
Table XII. Calculations for Gas Turbine Powerplant
Helium - 6,000 HP 100
Table XIII. Calculations for Gas Turbine Powerplant
Helium - 2,000 HP 101
Table XIV. Calculations for Gas Turbine Powerplant
Helium - 600 HP 102
Table XV. Required Number of Compressor and Turbine Stages
for Increased Pressure Ratios 106
ix

1.0 ABSTRACT
This report includes a preliminary overall appraisal of the various
conceivable heat engine cycles which might be used with a nuclear powerplant,
as well as a detailed investigation of the gas turbine cycle in this application - particularly from the viewpoint of the turbomachineryo The report is
divided into Part I and Part II, with Part I comprising the overall investigation and Part II the gas turbine study.
Part I.
It is the function of this portion of the report to review in a
preliminary fashion all heat engine cycles feasible for use in nuclear powerplants. It is concluded that the gas turbine type, the steam type, and the
binary or trinary vapor cycle type include all the modes of design which are
presently practical. These cycles are reviewed primarily with respect to
attainable thermal efficiency as a function of source and receiver temperature.
It is concluded that within the range of source temperature up to
1500 F, the highest efficiencies may be obtained with the binary or trinary
cycle (about 59% at 1500 F), with a maximum of about 45% for the gas turbine
and about 49% for the steam cycle (Figure 11)o It is further concluded that
the development of a 1500 F gas turbine plant with an efficiency approaching
this figure, except for very large outputs, is less difficult than the development of either the steam or binary plant for the same temperature.
The machinery requirements of a binary plant are examined briefly,
and it is concluded that inherently no insuperable problem is involved. The
possibility of the utilization of sodium, mercury, or possible other fluids
as direct reactor coolant in a boiling-type reactor concurrent with its use
as a heat engine fluid for the high temperature portion of a binary vapor
cycle is discussed.
A listing of anticipated future efforts to compliment the work herein
reported is included.
Part IIo
This portion of the report is concerned with a detailed investigation
of the gas turbine cycle as it may be applied to nuclear powerplantso It includes a theoretical "perfect gasv" investigation, and also a detailed study of
the effects of power output, pressure, and temperature on the overall plant
efficiency in terms of t he variamtion of turbomachinery component efficiencies.
The "sperfect gas"t studies are applied to both monatomic and diatomic gases,
while both air and helium were considered in the machinery studies.
1

A "basic cycle", consisting of a highly effective regenerator, a
single intercooler, a heat source and sink, and a compressor and turbine is
considered~ This type of cycle was chosen rather than a "simple cycle" (no
intercooler or regenerator) because of higher efficiencies, though sacrificing
size and weight considerations to some extent. The conceivable variations in
component efficiencies and cycle arrangement from the "basic cycle" were considered, and thus a method for estimating the attainable efficiency for any
other cycle arrangement provided,
For the "perfect gas" study, it was noted that, for given temperature limitations and cycle arrangement, the plant thermal efficiency is affected only by the ratio of specific heats and the pressure ratio. Under these
assumptions, monatomic gases differ in attainable efficiency from diatomic,
but the gas molecular weight has no effect. Diatomic gases appear somewhat
superior in this respect. It is shown that the result may be somewhat misleading since, in some instances, monatomic gases may show certain superior
qualities which may allow the attainment of a given level of component efficiency at reduced cost.
For the machinery studies with air and helium, the variations in
turbomachinery efficiency, size, and type with output, fluid, temperature, and
pressure were investigated for the "basic cycle". Constant heat exchanger
effectivenesses were assumed. All significant results are tabulated, plotted
and discussed. In combination with the Tfperfect gas"' study, these efficiency
results may be used to estimate the attainable efficiency with other cycle
arrangements.
The arnticipated course of future work is outlined.
2

2 0 h1NlRODUSCTION
A nuclear reactor, as presently conceived, is essentially a heatproducing device. If usable power is to be generated, it is necessary, under
present day technology to convert this heat through a suitable means to mechanical and/or electrical energy. Thus a "eheat engine"" of some sort is required.. Although very considerable experience and knowledge exists relating to heat
engines as used in conventional fossil-fueled powerplants, the step to nuclear
energy introduces many new factors and variables into the overall desigri It
requires a reappraisal of the existing practice in order to adapts successfully
to the new boundary conditionso If nuclear powerplants are to be successfully
applli.ed to tranrsportation. devices, where size and weight become of paramount
importance, it is necessary that the energy level be raised considerably above that obtained in present day nuclear plants, and even above that common
to fossil-fueled units.
In general it is necessary to consider various new working fluids
and cycles, and also to reconsider the conventional ones in the light of higher
temperatures, exposure to radiation, possible inaccessibility of machinery,
stringent sealing requirements, unusual relations between fuel costs and capital costs, etco As is well knomn, the suitability of the various conceivable
heat engine devices depends upon the avail.able souree and receiver temperatures,
the size of the plant (i.e power output), and various other factors involving
type of application, particular type and arrangement of the reactor, etco
A general appraisal of the possible working fluids for heat engine
cycles (which comprise the only presently known practical large scale devices
for the conversion of heat energy into mecharnial energy) shows that these are
either of the single phase type in -the working range (as a gas) or exhibit
phase change within the cycle range (as water). There is also, of course, the
possibility of advantageously combirnig fluids of the same or dif:ferent types
in this respect into the same cycle.
The present report reviews the various possible cycles from the
standpoint of attainable efficiencyo The cycles'being considered are the gas
turoine, the steam, asnd the binary (or trinary) vapor cycles which utilize
combinations of a low vapor pressure fluid for the high temperature portion
of the cycle and water or gas for the lower temperature portion.
In addi'tion, detailed studies of the gas turbine cycle are included.
These consider "perfect gas'" cycles, and also real fluid cycles, in which the
influences on efficiency of the plant output,9 pressure level, temperature, an.d
working fluid as they affect the turbomLachinery are considered.
3

The work reported covers the preliminary phases and progress of
these investigations~ Major items remaining to be considered are:
a) Additional working fluid combinations and further
refinement of those studies presently underway,
b) Evaluation of probable developmental difficulties
for the various cycles,
c) Radioactivity effects on working fluid and machinery,
d) Effects on gas turbine cycle of heat exchanger
component variations,
e) Overall economic optimization of nuclear powerplants
for typical applications,
f) Control problems of an integrated nuclear-gasturbine powerplanto
4b

3.0 OBJECTIVES
The work herein reported is being undertaken in partial fulfillment of the contract between the University of Michigan and the Chrysler
Corporation. The general objective of this work is the examination of
possible heat engine cycles as components of nuclear powerplants, particularly
with respect to those features by which the imposed boundary conditions for
this type of plant may alter the previously established design philosopieso
A specific objective is the investigation in detail of the gas turbine cycle
for application to a nuclear powerplant.
5

4.0 ACKNOWLEDGEMENTS
The authors wish to express their appreciation to Professor H. A.
Ohlgren for his aid and suggestions in the preparation of this report, and
to Philip Allen, William Becmnan and Jacques Boegli for their assistance
with the calculations.
The authors also wish to thank Robert Thomas and Ronald Hanson who
drafted the figures and Mrs. Autumn Jenkins for her secretarial help.

PART I. GENERALIZED HEAT ENGINE STUDIES FOR NUCLEAR POWERPLANTS
1.0 GENERAL THERMODYNAMIC PARAMETERS
1.1 Application to Nuclear Powerplant
For the successful utilization of a nuclear powerplant, heat generated by nuclear fission in the core of the reactor must be converted in as
large a proportion as possible into useful mechanical work. This realizable
proportion is largely controlled by the temperature ratio available to the
heat engine: i.e., the ratio of the maximum absolute temperature available to
the heat engine fluid to the minimum absolute temperature at which heat may be
rejected to the environment.* The minimum temperature is a function of the
application and of ambient conditions. For example, it may be as low as 60 F
for a plant located in proximity to a suitable supply of cooling water. On
the other hand, it may be as high as 300-400 F in cases where an adequate
cooling medium may not be' available.
The upper temperature limit is fixed by the nuclear reactor. Depending on the choice of reactor type, it may assume a wide range of values.
Because increased maximum temperature, and hence increased heat engine temperature ratio**, leads to the conversion of a greater proportion of the heat energy produced in the reactor to useful work, there exists a large scale effort
to increase the maximum available temperature for the existing reactor types,
and to investigate those apparently capable of higher temperatures. For this
reason it is necessary to examine the various heat engine alternatives and to
outline, from the viewpoint of thermodynamic efficiency, those most suitable
for various ranges of temperature. With this information in hand, it becomes
possible to intelligently consider the other factors involved in the selection
of a suitable arrangement for a given application.
1.2 General Discussion of Thermodynamic Factors
As is well known from the Second Law of Thermodynamics, the greatest
thermal efficiency which is possible for a heat engine cycle operating between
prescribed temperature limits is that of the Carnot cycle (Figure la), where
heat is received and rejected at constant temperatures, equal respectively to
the prescribed upper and lower cycle temperature limits, and where expansion
and compression are accomplished isentropically. This maximum efficiency may
be expressed as
*i The general relations are well illustrated in Reference 11.
3* It should be emphasized that this efficiency increase is generally a function
of temperature ratio and not simply of additional temperature. Thus the
possible efficiency increase for a fixed temperature increase becomes less
for higher temperatureso
7

3 2
(a.) CARNOT CYCLE
V 2 P2
/ /
3 4 / a2 /I
/ /
(b.) ERIRLISON CYCLE
I I TEMPERAURE-ENTROPY DAGRAMS
T4 / I I
T /~
3/ -1 / 2
(c.) STIRLING CYCLE
OF VARIOUS CYCLES

Ith Tin - Tout Where T refers to the absolute
in temperature scale.
The Ericsson and Stirling cycles (Figures lb and lc) are also theoretically capable of attaining the maximum possible thermal efficiency between
prescribed temperature limits. In the first case the isentropics of the Carnot cycle are replaced by constant pressure, and in the second case by constant volume processes. In both cases heat is received and rejected along
constant temperature lines as in the Carnot cycle. Here it is necessary to
postulate a regenerator so that heat rejected along 1-2 may be reabsorbed along
3-4. Thus it is implied that the working fluid be such that the specific heat
is not a function of temperature or pressure. (An example of such a fluid is,
of course, a perfect gas.)
Although it is not possible to duplicate these ideal processes with
actual machinery, they may be approached. In general, the degree by which
the ideal overall efficiency is approximated is controlled by the
1) approach to constant temperature heat admission and
rejection from the cycle at the maximum and minimum
temperatures available respectively; and by the
2) degree by which irreversibilities can be eliminated
from the cycle.
With these basic considerations in mind, one can examine the feasible
real cycles and postulate certain general statements as to their attainable
efficiencies.
1.2.1 Gas Turbine Cycle
To attain theoretically the ideal Carnot efficiency with the
gas turbine type cycle, there are two alternatives. If the "simple"'
cycle is considered (Figure 2a), consisting of heat source, expander,
heat sink*, and compressor, the ideal efficiency can be attained only by
infinite pressure ratio. In this case, the heat addition and rejection
may be at relatively constant temperature compared to the overall temperature spread (Figure 2b). This alternative is often used for aircraft
type powerplants where space and weight are of great importance, and
large heat exchangers prohibitive.
On the other hand, ideal efficiency may be attained with the
regenerative type cycle with an infinite number of reheat and expan.slion
stages. This cycle is illustrated in Figure 3b, where the arrangement
~ In an "open" cycle, this component effectively becomes the infinte mixing
medium of the atmosphere. Thus thermodynamically there is no difference
between open and closed gas turbine cycles.
9

HEAT EXCHANG ER
FROM
NUCLEAR
REACTOR
COMPRESSOR - NETU
HEAT SINK
to.) FLOW DIAGRAM.PI
T HEAT IN
P2
HEAT OUT
(b.) TEMPERATURE-ENTROPY DIAGRAM WITH A
HIGH PRESSURE RATIO
FIG. 2 SIMPLE GAS TURBINE CYCLE
o10

I N T E R g 0'. - Ez
H~EATR SINK
(a FLOW DIAGRAM WITH REHEATER AND INTERCOOLER.
~~~~~T T
p1I p2
4 I P2
3 2
3- -
FIG. 3 REGENERATIVuE GAS TURBINE CYCLE
11

closely approaches the previously described Ericsson cycle. The same
result would be approached by a regenerative cycle with no reheat or
intercooling but with a pressure ratio approaching zero (Figure 3c) since
here heat addition and rejection are accomplished at substantially constant pressures (compared to the overall range). Practically, this is
not a particularly useful approach because the work output per unit mass
of fluid would be very small and the required mass flow rates and machinery sizes excessive.
A combination of these approaches, i.e. a cycle, with perhaps
one reheat and one intercooler stage, and with a highly effective regenerator appears desirable either for
1) an elevated-pressure closed cycle large output
plant (pressure ratio small so that all components
can be at reasonably high pressure to reduce machinery and heat exchanger sizes), or
2) small output plants where the reduced flow rates
do not allow sufficiently high turbomachinery
efficiencies to profit fully from a high pressure
ratio cycle, and the large flow rate per output
is not embarassing.
1.2.2 Steam Cycle
The ordinary saturated steam cycle (Figure 4a) approaches the
Carnot cycle in so far as the main portion of the heat is added along the
constant temperature boiling line (and the expansion and compression are
isentropic). If extraction feed water heating is employed, the approach
is closer, since, in the limiting case, all net heat to the cycle is
supplied along the constant temperature boiling line, and all net heat
rejected in the constant temperature condensing process.
Thus, in many cases, surprisingly high efficiencies are obtained with a very limited maximum temperature with this type of cycle
(Army Package Reactor reports an overall thermal efficiency of 19.3%
with 407 F peak temperature. Reference 1). It has found general acceptance with the initial types of nuclear power reactors where only moderate temperatures were possible because of the types of reactors employed.
Actually, of course, the turbine efficiency is severely penalized by the necessity for handling a mixture of steam and water droplets
(involving, as well as destructive erosion, the inefficient momentum
transfer between the slow moving droplets and the steam). It has been
found desirable in past experience with fossil-fueled plants to utilize
superheater-cycles (Figure 4b) so that the expansion may be entirely
12

T
I -l
(a) SATURATED STEAM CYCLE
S
(b) SUPERHEATED STEAM CYCLE
T
S
(c) SUPERCRITICAL STEAM CYCLE
FIG. 4. TEMPERATURE-ENTROPY DIAGRAMS FOR VARIOUS
STEAM CYCLES WITH EXTRACTION
13

with dry steam. This affords an arrangement whereby the temperature
level of the cycle can be raised without increasing the pressure level.
Thermodynamically it does not take the maximum advantage of a given
available temperature. However, for a given pressure level, it is superior in efficiency to the saturated cycle because of the increased
temperature ratio, and also the increased turbine efficiency which can
be attained. The pressure level, with a steam cycle, has perhaps more
influence on the machinery cost and feasibility than the temperature.
Therefore, a superheater is an economic advantage.
If the water is to be vaporized in the saturated region, the
maximum boiling temperature and pressure must necessarily be less than
the critical temperature and pressure (705 F and 3206 psia). Since the
boiling temperature is so limited, the desirable superheat (or combination
of reheat and superheat) temperature is also limited. In other words,
if the superheat temperature, for a cycle of a given pressure level is
raised beyond a certain point, the result is rejection of heat from superheated steam at a temperature in excess of the condensing temperature.
From the viewpoint of efficiency, this is not desirable.
It is as a result of these conditions, that supercritical cycles
(Figure 4c) have been considered and utilized (reference 2) since advancing metallurgy has allowed the use of higher and higher maximum temperatures and pressures. With the supercritical arrangement it is possible
to utilize effectively, from the thermodynamic viewpoint, whatever maximum temperature may be metallurgically feasible. However, higher temperae
tures necessitate higher pressures, reaching the range of 5,000-10,000
psig (reference 2). This may become economically and mechanically inconvenient. Also, from the viewpoint of the ideal cycle, the heat is not
added substantially at the maximum temperature, since no constant temperature addition is possible. Of course, the situation is improved considerably by extraction feed water heating.
1. 23 6irn.ary VLapOr Cyle
The necessity for very high steam pressures as more elevated
temperatures become feasible, makes apparent the advantage of a fluid in
which high temperature is not accompanied by high vapor pressure. Such a
fluid can be expanded through a turbine and condensed at a temperature
at which its vapor pressure (and density) reaches a minimum for feasible
turbomachine operation, but which is convenient for the addition of heat
to a moderate pressure and temperature steam cycle.
These considerations led to the installation of several mercurysteam binary cycle central station plants in this country in the years
prior to World War II. The maximum temperature employed was only 958 F,
but the thermal efficiency (boiler losses excluded) was 44%, accomplished
14

with a maximum pressure of only 365 psig (reference 3). This temperature
is too low for an advantageous recourse to a supercritical cycle.
Aside from the advantage of reduced pressure over the corresponding steam cycle, there is the further advantage of increased efficiency over the same limits of available temperature. This can be
explained theoretically on the basis that heat addition to the binary
cycle (with several extraction points) is substantially at a constant
temperature equal to the maximum cycle temperature, since the mercury is
used in a saturated cycle. On the other hand, in the superheated steam
cycle with which the binary cycle must be compared (since a saturated
steam cycle at 1000 F is not possible) the heat is added at a mean temperature substantially less than the maximum available (i.e. at a tempera,
ture corresponding to the boiling temperature at the existing pressure,
say 550 F in this case).
15

2.0 SPECIFIC CYCLE ARRANGEMENTS
2.1 Gas Turbine Cycle
As previously indicated there are two possible approaches to the
attainment of high efficiency in a gas turbine cycle. These are:
1) The utilization of very high pressure ratio and the
consequent elimination of bulky heat transfer equipment such as a regenerator, and
2) The utilization of heat exchange equipment of maximum
effectiveness including a regenerator, compressor intercoolers, and reheat stages.* This automatically
leads to the selection of a moderate pressure ratio
since the maximum efficiency occurs at such a value
(see Figure 6a of Part II for example).
It can be shown that, with attainable component efficiencies, a
higher cycle efficiency is feasible with the second arrangement, i.e. low
pressure ratio and maximum utilization of heat exchangers. The interrelations
of these efficiencies, the degree of their attainability, and the various
alternative arrangements with various working fluids, are examined in detail
in Part II of this report. For the present purpose, a cycle including a
regenerator, a single intercooler, and a single reheat stage has been selected
to give approximately the maximum gas turbine cycle efficiency, which may
practically be obtained, as a function of temperature. This is not to say
that such an efficiency represents an optimum economic design in all cases -
only that if generous weight, space and financial allowance may be made for
each component, this overall efficiency is obtainable for the imposed temperature limitations. For the purposes of the report, these temperature limitations are largely a function of reactor design and ambient environmental
conditions.
The derivation for the thermal efficiency relation which was used
for this cycle is shown in Part II (Section 8.1) and the assumed values of
component efficiencies (Table III, Part II)o Although these values are
actually functions of the power level, pressure level, working fluid, temperature, etc. (these interrelations are examined in Part II), the values selected
for this computation are believed to be fairly realistic assumptions. To
* Heat source and sink, necessary to all heat engine cycles, are not included
in this discussion since from the viewpoint of the cycle they do not allow
any freedom of choice. As a piece of physical equipment, the heat sink
exists in the closed cycle gas turbine, but, of course, not in the open.
16

estimate the optimum efficiency for the given temperature level, curves were
plotted of efficiency against pressure ratio (Figure 5). The values shown
for the gas turbine cycle of Figure 11 represents the optimums.
A cycle utilizing a reciprocating compressor and/or expander for the
purposes of this report is also considered to be a gas turbine cycle. Such a
design might find application for low output power, in cases where the higher
component efficiencies for low flow rates of the reciprocating machinery
would be advantageous, and where the space-weight penalty not important. A
very real thermodynamic advantage of an internal combustion engine is that
high fluid temperatures are possible because of the intermittent nature of the
process. This situation cannot be realized in a cycle which depends on steadystate heating as in a nuclear reactor. However, the possibilities of an intermittent critical reactor in a reciprocating device have been considered by the
Baldwin Locomotive Company and others.
2.2 Steam Cycle
The steam cycle efficiencies plotted in Figure 11 for the various
temperatures are based on existing commercial plants as reported in the literature. For the low temperature ranges, they involve simple saturated cycles
(references 1 and 3). As the maximum temperature is increased, superheat,
reheat, and extraction cycles are utilized where desirable (reference 3). For
the very high temperature ranges, supercritical plants were considered, including both design studies and projected plants (references 2, 3, and 4).
The detailed assumptions and sources for this data are shown in the Appendix
(Section 7.1).
As is well known, the applicability and the attainable efficiency of
high temperature and pressure steam cycles depends very strongly on the power
range. For example, it is shown in reference 4 that for a given inlet temperature the pressure for optimum heat rate increases with plant output. Also the
desirability of very high temperatures and pressures exists only in fairly
large plants, because of the small volume flow rates to the turbine. On the
other hand, if only moderate temperature is available, the saturated steam
cycle may well be the most suitable choice down to quite low power ranges
(reference 1 - considers a plant of 2500 hp output). However, in general,
for fairly standard temperature and pressure conditions, it appears that the
steam cycle is most suitable for power outputs in excess of 10,000 hp.
2,3,Binary Vapor Cycles
2.3.1 General Factors
As previously mentioned the required pressure for an efficient
high temperature steam cycle becomes extremely excessive. This is of
particular importance in the relatively low power ranges where the steam
17

- - - - -' - - - - t- - - --
Q4 - -f m -m -mltm —-
-- _ >T=120C - - - - F
0.3 t;;;
0.2 -...
z -
- 0.1 -/ - m
=Id
00 ~ ---... — ------- -- -. -..-.L L L H eH
O 1 3 4 5 6 7 8 9 10
PRESSURE RATIO
FIG. 5. THERMAL EFFICIENCY OF A REGENERATIVE
AIR CYCLE WITH REHEATER & INTERCOOLER
"BASIC'8CYCLE WITH REHEAT
*SEE TABLE 3, PART i
18

volume flow rate is not sufficient to allow an efficient turbine design.
Hence, the desirability of utilizing a fluid for which the vapor pressure
at a given elevated temperature is still moderate, is apparent. For these
reasons, several mercury-vapor and steam binary cycle central station
plants were constructed in this country and performed at extremely high
thermal efficiency (reference 3) at temperatures, high at that time (about 950 F) but today relatively moderate.
The efficiency of the mercury-steam cycle in the 950 F temperature range is considerably in excess of that of either the steam cycle
or the gas turbine cycle for the same temperature. Hence, it appears
desirable to consider seriously cycles of this type for higher temperatures, which may eventually become available through advancing reactor
technology. As was mentioned 6efore, (Section 1.2`.3)there is good theoretical justification for the expectation of extremely favorable efficiencies
in the very high temperature range.
2.3.2 Working Fluids: Machinery and Nuclear Factors
In spite of its high efficiency, the mercury-steam cycle has not
enjoyed very extensive application apparently because of the mechanical
difficulties of sealing, pumping, etc. However, there have been very
great efforts expended in the last few years toward the development of
liquid metal pumps and seals in connection with the nuclear effort. It
is believed that a great many of the mechanical difficulties which existed
at the time of the original designs have been overcome.
Although the past operating experience with the binary vapor
cycle has been restricted to the mercury and water combination, there are
other possibilities for the high temperature fluid which may be more suitable in some applications. For example, sodium or sodium-potassium alloy
may be considered. Sodium has a much lower vapor pressure at a given
temperature than mercury, and would become applicable for maximuam tenperatures of at least the order of 1500 F. In this temperature range the vapor
pressure of mercury becomes quite excessive.
The principle difficulty with sodium lies in its extremely low
vapor pressure at temperatures suitable for transfer of the heat to the
water cycle. However, it turns out that the low pressure turbine blading
to handle sodium vapor at 1000 F is of the same order as steam turbine
blading operating to 2-" Hg condenser pressure (Appendix, Section 7.2).
Since the sonic velocity of the sodium vapor would lie between that of
steam and air, no difficulty should accrue to the turbine design on this
account. The general practicability of liquid metal vapor turbines has
been demonstrated over the years by the performance of the steam-mercury
plants.
19

The question of low vapor pressure at high temperature raises
the possibility of a trinary cycle wherein the sodium portion would serve
as a topping cycle to a mercury binary arrangement. Such a cycle is shown
on the T-S diagram of Figure 60 Another possibility which would lead to
a somewhat reduced efficiency would be the use of a sodium-steam binary
cycle lFigure 7) in which the sodium plant exchanged heat with a superheated. steam cycle operating to about 1200 F-. This involves a considlerable irreversibility in the heat transfer since a large portion of
the heat to the steam cycle would be delivered across a large temperature
differential. Another possible combination is a sodium topping cycle
discharging its heat to a gas turbine. This is shown in the T-S diagram
of Figure 8.
As a compromise between the low vapor pressure of sodium and
the high vapor pressure of mercury, there are the possibilities of sodium-potassium alloyX- or pure potassium. There are possibilities of other
metals also for which exploratory calculations have been conducted by
other agencies. However, since detailed thermodynamic data were available only for sodium and mercury, the preliminary calculations reported
herein consider only these two fluids. The vapor pressures for various
fluids at several temperatures are listed in Table I along with the
applicable references.
Sodium as a direct reactor coolant in some such device as a
sodium-boiler reactor is conceivable. Because of the high intensity gamma
radiation from sodium, the sodium portion of the machinery would require
extensive shielding. Since the pressure rises in the sodium are small,
it appears that either electromagnetic pumping equipment or jet ejectors
would be completely suitable, allowing a hermetically sealed system except for the turbine~ The ejectors have the advantage of serving also
as direct mixing heat exchangers and. thus eliminating the necessity of
closed type heaters.
A cycle of this type could transfer its heat to either a conventional water system or to a gas turbine system. In either case, the
efficiency is quite high. Since the density of the sodium working fluid
is low, the system might be quite adaptable to relatively small size
ulitz, Calculations have been performed for the sodium-mercury-steam
cycle, for the sodium-steam cycle, and for the sodium-gas-turbine cycle,
These are shown on T-S diagrams in Figures 6, 7 and 8 respectively, The
results of all the binary and trinary cycles are tabulated in Table II
where, for purposes of comparison, the best steam and gas turbine cycles
are also shown.
* In this case the concentrations in the gas phase would depend on the partial
pressures existing at the temperature, and would not be a choice of the
designer.
20

PUMPs/ =.5U
FLOW RATES BASED ON
UNITY WATER FLOW.
ENTHALPY PER BTU/LB
OF FLUID..808 \ p 9.3
1500 h= 398 h -223 0
h = 2230
SODIUM SATURATION
CURVE
SODIUM TURBINE =:.80
1340 h 30.013
~~~~~~1340 | ~ ~~~~~~~~~h =2120.794
1240 h=-320 0400
102 0' - h - 31.7 _ _ _ _ _ p-h=20407 h
o753 | MERCURY STURATION_ 9t=1220 OF.013
1140 ------— h 290 MERCURY TURNE83
740
1020 h=31.7 h - -- p=207 h=1850
MERCURY SATURATION 9.20 h = 156
Iz CURVE /
4h13 t -1 - -— e.230h: p195 MERCURAM TURBINE:.83
3go00 hz27.9 \
c0n-c __.0_... h- 151.3
8.98
cr 1.h3 p= 45
2 800 h h=24.8143
a./ t=780 OF
79 |h 7 —_.25 _ 70 _J h-':84
p 18.9
700OVRALL EFFICIENCY 00 h=21.7
21h=13
7.05
7.0 p =6.6
p6= 1275 h= 127
WATER SATURATION
CURVE -00.14.6 p= 360
434 ~~ h=413 / h= 1249 STEAM TURBINE r/:.85
300 h:270 -- 4':090
h= 1131
764.094 p = 11.5
P00 h=168 =~.....
670
79 _.... p = I" H9
ENTROPY —S
OVERALL EFFICIENCY =.600
21

PUMPs -.50
FLOW RATES BASED ON
UNITY WATER FLOW.
ENTHALPY PER BTU/LB
OF FLUID.
1500 h:398 /_.788 p — 9.3
1500 r - - h.398
h= 2230
SODIUM SATURATION
CURVE
SODIUM. TURBINE.75.013
1340 h2- 3h50
775
0045
~~~~~~~~~~35t=1220 OF _0 h25
//735,,,~~~~ z-22 Oh=161
1140 h- 2 90. 013h
h=260 22 -722
1040
L | CURVE y/ 1
90 0 I
0. i /t8~~~~~.89
cr 1.715 \ " p=45
6 800 h 24.8 -
37.17 h4l362
700 h2 p=18.9
600 L 8.5 _/6.980 \ p6.6
3005 1 -----— ~,, -~ ~-=1275 h=128
257005 h582 i C _ _ _v1.000 h = 18179.8
WATER SATURATION
CURVE
434 h:TE41E3 R UE -E Y1249 STEAM TURBINE =-.85
300 h=270 - h-=27090 -- -
le: 8.891131
200 ~h.h 168 l _ \.5
7 9 4 - — 60 PI H
ENTROPY-S
OVERALL EFFICIENCY x.588
tEM PERATURE-NTROPY DIAGRAM
22

PUMPs =.50
FLOW RATES BASED ON
UNITY WATER FLOW.
ALL TURBINES 100% EFFICIENT.
ENTHALPY PER BTU/LB
OF FLUID.,756, p= 9.3
1500 l ~- h= ~398 / >.756 ~h=2230
SODIUM SATURATION
CURVE 75.013
13 40 h = 350:W 900~2090
/.743
1240 - h 320.013\
575 h:582 ~27 =1990
730
1140 - h:290 /.014
h=1880.716 p=.25
I828 hh=26C // h=31.27 =07 \ h:1765
MERCURY SATURATION 8.33 h- 155.
LA CURVE \
o //8.33
W 900 h= 27.9 - 5
h = 145.5
8.12 \
1v 0 h: 24.8 - D.22 p =45
w 800 h 24.36.8
I6J / / 7:90
700 h=21.7
22 =1 27.5
600 h 18.5
575 h-=582 p=1275 h -118.5
WATER SATURATION -/, =1
CURVE
434 h-413 1__t084
h=824
300 )- -- h- 27 t - <*0 h =997.723
=68 -.100 p=11.5
200 /- \ h:871.623.623 j pIN Hg
79 h 4 7
ENTROPY -S
OVERALL EFFICIENCY =,671
23

SODIUM SATURATION
CURVE.683 p=9.5
1500 h=-398
h =2230
/683 SODIUM TURBINE =.80.011
1340 h=350 h2120.672.012
1240 h —-320 h=2035
1140 h —=290 h=1943
/.48 \ \
h = 2.6480 p=.25
1020 P h=1850
FLOW RATES BASED ON
I g / I UNITY WATER FLOW.
WATER SATURATION CURVE ENTHALPY-BTU PER LB
OF FLUID.
| p L tP - 593
I- P~~~~~~~~~~~~~~~~~~~~~h= I1333.5
6 00 h:= 617. - STEAM TURBINE, 2.85
48 5 t h-:470 g- - - t \ PUMP, =.50
/.866.113 8 p-145.5
3 5 6.......23288
/ 754.100 \ p=17.2
220: 188.1 -1-1 -
h= 1 123
/.653 i..653 =I \ pl Hg
79 h=47 h:957
ENTROPY —-S
OVERALL EFFICIENCY =.516
FIG. 7 SODIUM- STEAM BINARY EXTRACTION CYCLE
TEMPERATURE -ENTROPY DIAGRAM

SODIUM SATURATION.0878 _\ _p=9.3
1500- h:398
h=2230
/ /08'78 i SODIUM TURBINE:.80
1340 h=350- h =2120.0015
1240 h:320 h P \M\ h: 2 035
/f0849 \\PUMP,:5O.0015
1140 -- h=29 h-1943
~,,,,.0834 psP25
1040 h-260 h-1850
I O 20 vr\,5 z / \ /hz850
1020
LL. 10 J \
0
875 AIR TURBINE.89
8/2 7/ AIR EXPANSICOMPRESSOR:.89
181
90
REGE TR COMPRESSION RATIOTROPY
EXPANSION RATIO -1.07 FOR AIR
REGENERATOR EFF. C.93 FOR AIR
AIR EXPANSION RATIO C 4.0
ENTHALPY PER BTU/LB. OF FLUID.
233 FLOW RATES BASED ON UNITY
90
ENTROPY -S
OVERALL EFFICIENCY =.486
TEMPERATURE-ENTROPY DIAGRAM
25

TABLE I. VAPOR PRESSURES FOR VARIOUS FLUIDS AT SEVERAL TEMPERATURES
Temperature Vapor Pressure
Fluid OF psia Reference
-----. -- -- ---- —,"..',.....,:'i,
Mercury 600 6.64 5
900 95 4
1200 509.5
1500 2000
Sodium 600.01 6
9oo.1
1200 1.0
1500 9.0
1620 14.7
Potassium 1400 14.7 7
Rubidium 1270 14.7
Mercury, due to its high neutron capture cross-section, is not
in general a desirable reactor moderator or coolant. However, it can be
used as coolant for a fast reactor (Los Alamos Clementine) where high
capture cross-sections are not so disadvantageous. Potassium, and perhaps other suitable fluids which may be determined, could be used with
varying degrees of success directly in a reactor. The mercury cycles
which were calculated are shown in the T-S diagrams of Figures 9 and 10.
2,3.3 Thermodynamic Calculations
In order to achieve optimum efficiency with cycles of these
types, it is necessary that irreversibilities in the heat transfer be
eliminated as far as possible. This has been approached by including
three extraction "feed water"' heaters for both the liquid metal and the
steam portions. To take maximum advantage of the obtainable efficiency
with steam turbines operating with dry steam, the lowest liquid metal
extraction is used to superheat the steam. An efficiency of 0.85, including reheat factor, was used. This was based on current figures for
large plant steam turbine efficiency. A liquid metal vapor turbine
efficiency of 0.80, including reheat factor, was used. This reduced
value is assumed because of the unknown performance, and operation in the
saturated region. - In the case of the sodium-mercury-steam cycle a mercury turbine efficiency of 0.83 was used because of the superheat afforded by a sodium extraction.
Several cycle arrangements with the mercury steam cycle were
26

TABLE IIo TABULATED EFFICIENCIES OF BINARY AND TRINARY
VAPOR CYCLES AT 1500 F INLET, 70 F COOLING WATER
(l" Hg cond.)
Cycle Description T-S Diagram Efficiency
1) Mercury-Steam, Extraction Figo 9.588
Mercury Turbine Eff. - o80
Steam Turbine Eff. -.85
Steam Superheated
2) Mercury-Steam, Non-Extraction Fig. 10.550
Mercury Turbine Eff -.80
Steam Turbine Eff. -.85
Steam Superheated
3) Sodium-Mercury-Steam, Extraction Fig. 6.588
Sodium Turbine Eff, -.75
Mercury Turbine Eff. -.80
Steam Turbine Eff. -.85
Mercury and Steam Superheated
4) Sodium-Mercury-Steam, Extraction Fig. 6.600
Sodium Turbine Eff. -.80
Mercury Turbine Eff. -.83
Steam Turbine Eff. -.85
Mercury and Steam Superheated
5) Sodium-Mercury-Steam, Extraction Fig. 6 671
Sodium Turbine Eff. - 1.00
Mercury Turbine Eff. - 100
Steam Turbine Eff. - 1.00
No Superheat
6) Sodium-Steam, Extraction Fig. 7.518
Sodium Turbine Eff. -.80
Steam Turbine Effo -.85
Steam Superheated
7) Sodium-Air, Extraction Fig. 8.486
Sodium Turbine Eff. - 080
Air Turbine Eff. -.89
Air Compressor Eff. -.89
Regenerator Effectiveness - 093
Precooler Terminal At - 20 F
Compression to Expansion
Ratio - 1.07
8) Supercritical Steam Cycle.485
7000 psig - 1500 F
Reference 4
9) Gas Turbine Cycle - 1500 F.448
Regenerator, Reheat, Intercooler
27

MERCURY SATURATION
CURVE
62000 PUMP =.50
1500 h=46
FLOW RATES ARE BASED
ON UNITY WATER FLOW.
| |14.55 \ \ ENTHALPY PER BTU/L.
OF FLUID.
p=590
4.29 h154
1230 h=38 t = 1200 OF
h=1625
10.26 r P6
p=200
1000 h: 31
Io MERCURY TURBINE =.80
a: 9.46 CURVE.. |f h= 124
_ 700 h=21.7
w
FIG ~. 900
h = 1490
486 h =472
1.00
I.00 1p=60
392 -h=362.090...... h= 144.910
293 -h=25.085
p p=16.064 h S 1229
2 16 --— h=184
STEAM TURBINEs=.85.761.761 p SI" HQ
79 h447 h. 1029
ENTROPYmS
OVERALL EFFICIE NCY z:,590
28

MEERCURY SATURATION
CURVE
p=2000
15.88 h = 167
1500 h 46 -
150 88
p=590:.67h154
1230 t =h38 3 1200 OF
SUPERHEATER p 6s0
h=1625
o | MERCURY TURBINE ~.80
_~O~ / / 1 } \ ~~~~~FLOW RATES ARE BASED
ON UNITY WATER FLOW.
I /p.8 It \PUMP411.50
12.21 h'110
500 h = 15.3
486 h=472
1.00
/ / 1 0h a 1203 \ ENTHALPY PER BTU/LB.
OF FLUI.
WATER SATURATION
CURVE
STEAM TURBINE 1Z85
1.0 p a I' HI
~~~~~~79 hz3~~~47 - ~h=1029
ENTROPY — S
OVERALL EFFICENCY =.550
FIG.IO MERCURY-STEAM BINARY NON-EXTRACTION CYCLE
TEMPERATURE - ENTROPY DIAGRAM
29

investigated in the course of the study. However, it was determined that
the arrangement shown in Figure 9 is most suitable. Three extraction
points for the mercury and also for the steam are assumed, with the lowest
mercury extraction used to superheat steam. The calculated thermal efficiency (considering no reactor losses) is 59o0% for 1500 F inlet and 79 F
condensate temperature. This can be compared to a similar cycle, which
had been calculated without extractions (Figure 10) wherein it was determined that thermal efficiency under the same conditions is 55.0%.
Thus, the improvement due to the extraction heaters is 1.07.
Two trinary sodium-mercury-steam cycles were calculated with
three extractions in each phase but with slightly differing turbine
efficiencies (Figures 6a and 6b; the thermal efficiencies were 60.0% and
58.8%). Using the extraction sodium cycle discussed above, cycles involving
1) sodium topping to steam cycle (Figure 7), and
2) sodium topping to gas turbine cycle (Figure 8)
were calculatedo The resulting efficiencies for 1500 F inlet and 70 F
cooling water (giving 80 F steam condensate and 90 F air compressor inlet) were.518 and.486 respectively. The latter cycle, when compared
with the regenerative gas turbine cycle with reheat and intercooler shows
an efficiency improvement of 8.4% (3-. points). The former is about 2
points better than the corresponding super critical steam cycle and 7
points better than the gas turbine (14%)o
To more clearly illustrate the basic relations involved, a
simplified trinary cycle involving saturated Na, Hg, and H 0 portions
with ideal turbines was calculated, This is shown on the T-S diagram of
Figure 6co The overall cycle efficiency was.694 compared to the Carnot
efficiency of.725. However, if the individual portions are compared
with the Carnot efficiency for that portion the results are as belowO
Fluid Ratio: Calculated to Carnot Efficiency
Na 1.024
Hg.985
H20 o 943
It is noted that the sodium portion shows an efficiency in excess of that of the ideal heat engine. The only possible conclusion is
that the degree of refinement of the sodium thermodynamic data as plotted
and listed (reference 6) is not adequate (linear extrapolation over large
ranges were necessary for this calculation). It is assumed that the
ratios of calculated to ideal efficiency for the mercury and steam cycle
are probably typical. Therefore the sodium portion efficiency has been
reduced by.985/1.024 =.962. On the basis that this correction should
be applied to the heat input to the overall cycle, the efficiency becomes.671. This is a very conservative assumption since an equally defensible procedure would be reduction of Na work only by this ratio.
30

Estimates of the effect of turbine losses were made (method
of calculation is shown in Section 7.4.2 of the Appendix). The results
are shown in Table III.
It will be noted from Table III that losses in the sodium turbine have very little effect on the overall cycleo Losses in the mercury
turbine have slightly more, and losses in the steam turbine are most important. This is explained by the fact that losses in the topping turbines
result in additional heat to the lower turbines, and some of the loss is
thus recouped. This factor is often used in steam turbine design where
inefficient initial stages are employed to drop the pressure and temperature in a minimum number of stages to values which may be more economically handled. Therefore, an inefficient liquid metal turbine is not an
important handicap to a cycle of this type.
The approximate results agree very closely with the superheat
trinary cycle shown in Figure 6a where turbine efficiencies of 0.80,
0o83, and 0.85 (including reheat) were used for the sodium, mercury,
and steam respectively~ This cycle showed an overall efficiency of 60.0%
as compared with 60.4% for the approximation in Table III. An additional
cycle with efficiencies of.75,.80, and.85 was calculated (Figure 6b).
The efficiency decreased by only 1.2 points to 58.8%. This confirms
the expectation that the efficiency of the liquid metal turbines is not
of great importance.
The effect of the irreversible heat transfer across the temperature drop between the various portions of the trinary cycle was estimated
(Section 7.5 of Appendix). It is noted that the efficiency is decreased
about 1.0 points on this account. The effect of a temperature differential
in the extraction heaters also was estimated (Section 7.6 of Appendix).
This involves an overall efficiency loss of only 0.4% (0.2 points) and is
thus quite negligible (no temperature differential at this point was
assumed in the calculations).
in the calculation of the sodium cycles it was assumed that the
sodium did not dimerize to form Na2. However, it is indicated in reference
6 that there is a likelihood of such an effect at high temperatures. It
is shown that the number of moles of a given mass quantity of sodium will
be decreased by about 15% at 1500 F equilibrium on account of this effect.
If this is the case, there will be heat liberated during the expansion in
the turbine, so that the process will not approach an isentropic, and the
cycle efficiency will be somewhat reduced. This effect will be further
investigated as the work progresses.
Sample calculations, analytical procedures and assumptions for
the one of sodium-mercury-steam extraction cycles are included in the
Appendix (Seetion 7.3). The results of all these calculations are tabulated in Table IIo
31

TAKBLE III. EFFECT OF TURBINE EFFICIENCY ON TRINARY CYCLES
Cycle Conditions* Cnt Cor
Na Turbine 1o00 O700.725 ~,671
1) Hg Turbine - 100
H20 Turbine - 1.00
Na Turbine - 80.679.725.652
2) Hg Turbine 100
H20 Turbine - 1.00
Na Turbine -.80.657.725.631
3) Hg Turbine -.83
H20 Turbine - 1o00
Na Turbine -.80.630.725.604
4) Hg Turbine -.83
H20 Turbine - o85
Trinary Cycle I - Superheat
Na Turbine.8G0 626.725.600
5) Hg Turbine.83
H20 Turbine -.85
Tr.nary Cycle II - Superheat
Na Turbine -.75.613.725.588
6) Hg Turbine -.80
H20 Turbine -.85
* All cycles refer to inlet temperature of 1500 F and condensing temperature
of 79 Fo Cycles 1, 2, 3, and 4 do not employ superheat. The values were
estimated as explained in Section 7.4.2 to show the effect of varying
turbine efficiency.
32

3~0 COMPARISON OF VARIOUS CYCLES
The estLnated attainable cycle efficiencies are plotted against
temperature for the gas turbine cycle, steam cycle, and binary vapor cycle
in Figure 11o In all cases, a cooling medium temperature of 70 F has been
assumed. On this basis, the steam and binary vapor cycles, considering the
good condensing for heat transfer coefficients, condense to 1'" of Hg or 79 F,
whereas for the gas turbine cycles, a minimum gas temperature of 90 F was assumed.
The efficiency values are based upon an effective'"boiler efficiency"
of 100%. In other words, no loss comparable to "stack loss" is assessed to the
nuclear reactor plant.* This is not to say that 100% of the energy actually
released in fission will find its way to the heat engine cycle. Actually,
there will be heat losses in and through the shielding, the neutrino loss,
and the conventional heat transfer losses in the primary loop, if the reactor
is not cooled directly by the working fluid. However, this is a function of
the particular design and can be applied to any desired case,
The assumed component efficiencies which enter into the overall cycle
efficiency calculations are believed to be attainable in large power output
installations where weight and space are not a factor per se. The quoted efficiencies for a given cycle temperature are thus somewhat in excess of the
values applying to a transportation device where it may be desirable to com*
promise efficiency to some extent in exchange for size, weight, and perhaps
cost advantages.
It will be noted from the curve of Figure 11 that the attainable
efficiency of the gas turbine cycle, for a given temperature, is inferior to
that of either the steam or the binary-vapor cycles over the entire temperature
range. There is no doubt, however, that for the higher temperatures (1400 F
to 1500 F and above) where the proper utilization of the available temperature requires extreme pressures and considerable auxiliary equipment for the
steam cycle, that the gas turbine is the more suitable of the two in many
applications. An obvious point in case is the aircraft powerplant. Thus,
it appears that the developmental effort connected with producing a 1500 F
gas turbine plant with an efficiency approaching that shown would be much less
than that involved in producing a steam plant for these temperatures and efficiencies, except perhaps in. extremely large output ranges.**
* It is for this reason that (by a factor of about,85) the values given for
the steam and binary vapor cycles are higher than usually noted. This consideration does not affect the open cycle gas turbine since it is an internal combustion device,
** As shown in reference 4, the supercritical steam cycle is limited to fairly
large power ranges because of the low volumetric steam flow rate in the high
pressure positions. This difficulty does not affect the closed cycle gas
turbine or the binary cycles to the same extent.
33

.8.7.6.5
~~~W S A~~~~~~~~
z
x /
LU..
a /,0~~ 1 ~I) 0 CALCULATED REGENERATIVE, REHEAT
".3 MAXIMUM EFFICIENCY POINTS
2) X CALCULATED STEAM CYCLE POINTS,REFERENCE 3 (VARIATION FROM DIFFERENT
PRESSURE LEVEL AT SAME TEMPERATURE )'
3) I CALCULATED STEAM CYCLE POINTS, REFER-.2 1 / ENCE 5, VARIATION PER NOTE 2
4) * APDA STEAM PLANT, REFERENCE 9
5) 0 BNL STEAM PLANT REFERENCE 10
6) V PHILO SUPERCRITICAL STEAM PLANT,
REFERENCE 2.1 7) V CALCULATED HG-H20 OR NA-HG-H20 POINTS
REFERENCE 3 AND APPENDIX 3
8) S KEARNY HG-H20 PLANT
500 600 700 800 900 1000 1100 1200 1300 1400 1500
TEMPERATURE - OF
FIG. II MAXIMUM FEASIBLE EFFICIENCY VS TEMPERATURE
VARIOUS HEAT ENGINE CYCLES
COOLING WATER AT 70~ F
34

The developmental -effort involved in a binary type plant is no
doubt large, but its true- extent cannot well be estimated without more detailed
engineering studieso In its favor, of course, is the absence of high pressure. As shown in the curve of Figure 11, the attainable efficiency from a
binary or trinary cycle is considerably in excess of that for either the gas
turbine or steam cycle, and follows quite closely to the Carnot efficiency which
is plotted as a reference. It is apparent that this will be the case for any
temperature if a fluid or fluids with a suitable liquid-vapor phase relation
can be found, so that heat addition can be at an approximately constant temperature equal to the maximum temperature available. As higher reactor temperatures become feasible, it appears that the possibilities of cycles of this
type must be given serious consideration, especially in view of the possibility
of integrating the coolant and heat engine fluids, as in the previously discussed sodium boiler reactor. As previously shown, a sodium topping cycle
of this sort may be combined with a low temperature gas turbine cycle to give
an overall efficiency in excess of the ordinary gas turbine cycle over the
same temperature rangeo
35

4,0 FUTURE WORK APPLYING TO PART I
Preliminary work on the basic thermodynamics of the various possible cycle arrangements has been completed, as here reported. Additional
efforts, continuing from this basis, becomes desirable. Such work will include the following'
a) Investigation of various possible working fluids from
the viewpoint of radioactivity effects; i.e. the degree
of machinery shielding, accessibility considerations,
etco which are involved;
b) Further consideration to other possible working fluids
in addition to those discussed in this report;
c) Further consideration of the binary type cycles from
the viewpoint of evaluating probable developmental
difficulties and costs;
d) Consideration of possible combinations other than
those already investigated.
Considering the combined possibi.lities of a direct-boiling liquid metal reactor and the extremely high efficiencies of the'binarywvapdr cycle, this
arrangement seems likely to represent one logical path for future developments.
36

5. 0 CONCTLUSIONS
A broad investigation of various conceivable heat engine cycles and
working fluid combinations has been conducted. Their attainable thermal efficiencies as a function of temperature have been calculated. The results are
plotted in Figure 11, and tabulated for 1500 F in Table II. These overall
efficiency values are consistent with component efficiencies which are generally attainable in large scale plants where efficiency is of primary importance. They represent a maximum envelope curve for the given cycle and temperature.
The results show that the binary and/or trinary vapor cycles have
an efficiency advantage of about 33% (15 points) over the optimum gas turbine
and about 23% (11 points) over the steam cycle for an inlet temperature of
1500 F. The combined sodium-vapor-gas turbine cycle has an advantage of 8.5%
over the simple gas turbine at 1500 F (3.8 points). Efficiency-wise the gas
turbine is somewhat inferior to the other alternatives at any except extremely
high temperatureso The gas turbine cycle efficiencies shown apply roughly to
any diatonmic gas as working fl.uid. Monatomic gases show a slightly reduced
efficiency for equal component efficiencies~
It is believed that the high temperature highly efficient gas turbine is more easily attainable development-wise, especially in small sizes,
than the alternatives presented. In many applications where weight and space
are a factor, and capital cost of especial importance, it is no doubt the most
suitable selection. However, there appears the strong possibility that a
development of a boiling liquid metal reactor combined with a binary-vapor
cycle or a vapor-gas-turbine combination cycle might achieve efficiencies and
operating economies which are in excess of those attainable by other methodso
37

6 0o BIBLIOGRAPHY
lo Kasschou, Kenneth, Army Package Power Reactor, Preprint 30, Nuclear
Engineering and Science Congress, December, 1955.
2. Fiala, S. N,, First Commercias Supercritical Pressure Steam-Electric
Generating Unit for Philo Plant, ASME Paper Noo 55-A-1370
3. Kent's Mechan11cal Engineers Handbook, 12th Edition - Power Volume,
Section 8, 1950, John Wiley and Sons, New York.
4. Downs JO Eo, Margins for Improvement of the Steam Cycle, ASME Paper
No. 55-SA-76.
5. Sheldon, L. A., Thermodynamic Properties of Mercury Vapor, ASME
Paper No. 49-A-30.
6. Inatomi, To Ho, and Parrish, W. C., Thermodynamic Diagrams for Sodium,
North American Aviation Report SR 62, 13 July 1950.
7. Atomic Energy Commission, Department of Navy, Liquid Metals Handbook,
NAVEXOS-P-733 (Rev.), June, 1952o
8. Atomic Power Development Associates, Developmental Fast Breeder Power
Reactor (Brochure).
9. Sengstakin., D, Jo, and Durham, E., The Liquid Metal Fuel Reactor
Central..Station Power, Preprint 39, Nuclear Engineering and Science
Congress, December, 1955.
10. Keenan, Joseph H. and Keyes, Frederick G., Thermodynamic Properties
of Steam, 1936, John Wiley and Sons, New York.
11. Ohlgren, H. A., Weber, E., Hammitt, F. G., Initial Approaches to Systems
Analyses of Nuclear Heat-Power Engines, Progress Report No. 5 to
Chrysler Corporation, February, 1956.
38

7~0 APPENDIX - PART I
7.1 Assuptions for Steam Cycle Efficiencies (Figre 11).
7.1.1 Low and Moderate Temperature Steam Plants
Operating data for low and moderate temperature steam plants
was abstracted from various portions of the literature. The data utilized and. the sources are shown below,
7..1.1o Kent's Mechanical Engineers Handbook - Power, JO Kenneth
Salisbury, 12th Edition, Reference 3.
Table XXIV, Section 8 (Part II) presents data calculated for various
cycles under the following conditions:
1) Overall turbine efficiency 82%
2) Moisture at turbine exhaust (full load) 11%
3) Terminal difference on feedwater heaters of 5 to
20 F for feed temperatures of 100 to 525 F
4) Steam generator efficiency (including air preheater
if used) 85%
5) Pressure drop between boiler and turbine, bleed
points and heaters, reheater piping and reheater 10%
6) Radiation loss - Bleed point to heater 2%
Reheat lines 3%
7) Normal auxiliary power allowances, with 20
kw-hr/ton as power for pulverizing coal
8) Feed water heated in equal temperature steps to
75-80% saturation
9) Final vacuum 29" Hg
It was assumed that five feed water heaters would be used. It was
also assumed that there were no heat losses between the reactor
and the working fluid. This is not actually the case. Factors such
as reactor shielding losses, heat transfer loop losses, etc. exist.
However, they depend on the specific design and are usually not
large. Thus, to provide an equal basis for the comparison of the
various heat engine cycles it was determined to assume zero losses
39

of this type. Therefore, the nuclear plant efficiency is determined by dividing the conventional plant efficiency by the steam
generator efficiency which is 0O85 for these cases.
Heat Rate Conventional Nuclear Plant
Cyccl Conditions Btu/kw-hr Plant Eff. Eff.
40Q psia, 800 F 12,400.275.323
600 psia, 900 F 11,590.294.346
1200 psia, 1000 F 10,220.334.393
3226 psia, 1000 F 9,550.358 o422
7.1.1.2 Additional Sources
7.1.1.2.1 Liquid Metal Fuel Reactor steam plant. Reference 9.
Calculated data is given for a steam plant designed in connection with an LMFR-type reactor which operates with steam at 1265
psia and 900 F.
Abstracting the heat balance of Figure 6, Reference 9.
Heat Input to Cycle - 1,915,080 (1438.3 - 458 5)
1875 x 106
Work Output 209,130 x 3413 729 x 106
o98
(.98 is generator efficiency. )
Efficiency - 29 =.389
1875,1J.1.2.2 Army Package Power Reactor - Reference 1
Cycle conditions call for 407 F, 200 psia, steam conditions.
Anticipated overall efficiency is 19o25%.
7o1.1.2.3 Kent's Mechanical Engineering Handbook. Reference 30
Table 17, pp. 8-73.
This table gives the calculated non-extraction ideal turbine
heat rates for various conditions. In the use of these points
the following assumptions were made:
1) Improvement in heat rate due to five feed water heaters
as given in Figure 43, Section 8 (Part II) of Reference
3;
40

2) Auxiliary losses are 5%;
3) Turbine efficiency is 0.85o
Then for an 800 psig, 650 F cycle.
Efficiency = 3413 x 685 x 1l115 x e95/8757 = o352.
For a 200 psig, 650 F cycle:
Efficiency = 3413 x o85 x 1.09 x o95/10140 =.296
7.1.2 Supercritical Steam Cycles
I71_.2.1 Reference 4 data.
Calculated data for supercritical steam cycles ranging from 1050 F
to 1450 F, and from 4000 psia to 10,000 psia are given. It is
shown that for large capacity plants (1000 MW, 300 MW, and 150 MW
are discussed) the desirable pressure at a given temperature is
greater. It is also shown that larger plants for the same temperature and for optimized pressure are capable of higher efficiencies. A steam generator efficiency of ~89 was used in the calculations and thus the reported efficiency must be corrected by this
ratio to give the corresponding value for a nuclear plant. All
losses ascribable to an operating plant were considered and evaluated for the various caseso The data used in the plot of Figure 11
is shown and reduced below.
Heat Rate Conventional Nuclear
Cycle Conditions Btu/kw-hr Plant Eff. Plant Eff.
4,000 psia-1050 F, 150 MW 9050.378.425
4,000 psia-1050 F, 300 MW 8820.387.435
6,000 psia-1250 F, 300 MW 8320.411.462
7,000 psia-1450 F, 300 MW 7970.429.482
10,000 psia-1450 F,1000 MW 7770.440.494
In all cases condenser pressure is 14' Hgo
7o 1o,2o2 Philo Plant Operating Data (Reference 2).
This plant is to utilize steam at 1150 F, 4500 psia and to operate to
1" Hg condenser pressure~ The full load output is 125 MW. The final
anticipated heat balance shows an overall thermal efficiency, as a
fossil-fueled unit of 3413/8530 =.400~ Since the steam generator
41

efficiency is.896, the corresponding nuclear plant efficiency
would be.400/.896 =.446.
7.2 Liquid Metal Turbine Design Characteristics
72So l Success:ful turbine design for high efficiency operation requires
that the Mach Number of the flow relative to the blading be subsonic.
Thus, if the sonic velocity for a particular fluid is very low with respect to the conventional working fluids, turbine design might be seriously circumscribed. The approximate sonic velocities for various of
the possible liquid metal vapors are listed in Table IV below. It will
be noted that with the exception of mercury they do not differ tremendously from air. However, mercury turbines have been constructed and
operated satisfactorily.
TABLE iV. SONIC VELOCITY OF LIQUID METAL VAPORS AT 1500 F
C
Fluid Molecular Wt. ft/sec 1500 F
Na 23 2350
K 39 1800
Rb 85.5 1220
Hg 201 795
Air 29 2090
H20 18 2650
7T2o2 Sodium Turbine - Low Pressure Blading
Assume t - 1040 F in condenser, This is the value used in the
calculations. Then p =.20 psi (Reference 6). This is the equivalent
of about.4 in Hgo Sodium flow rates are about similar to steam rates
for the same power output (see Figures 6 and 7). Thus the low pressure
stage of such a turbine would be about comparable to the low pressure
stage of a steam turbine in a plant of the same power rating, condensing
at "1 Hg, or twice the flow capacity of a steam turbine condensing to
1" Hg.
7 3 Trinary Na-Hg-H20 Cycleo Sample Calculations and Assumptions
7.3.1 Sample Calculations and Assumed Values
Two Na-Hg-H20 trinary cycles, a Na-H20, a Na-Air, and two
Hg-H20 cycles were computed~ The results are shown in Figures 6, 7, 8,
9, and 10, and tabulated in Table IL,

The calculating methods are the same for all the cycleso The
trinary cycle of Figure 6 - Cycle II is chosen as an example for illustration.
The following assumptions were made for this cycle~
Turbine Efficiencieso
Na Turbine.75
Hg Turbine.80
H20 Turbine.85
Condenser Back Pressure:
H20 li Hg
Maximum Temperatureo
Na 1500 F
Cycle Arrangement:
Nao 3 extraction points. Saturated cycle,
IHg 3 extraction points. Superheated by one of
Na extractions o
H20: 3 extraction points. Superheated by one of
Hg extractionso
Pump Work:
Pump efficiency 050
No credit for pump work input,
Extraction Feed Heaters:
Zero temperature and pressure differentials (see
Section 7,4 for comment).
The thermodynamic points were computed from the data of references 5 and 6 for sodium and mercury respectively. No dimerization was
assumed. Steam data was taken from Reference 10. The expansion lines
were computed on the basis of the assumed efficiencies, considering the
drops between extraction points individually. No further credit for
turbine reheat was assumedo
For the steam expansion line, for example, the first drop (between the steam chest and first extraction) is computed in the following
43

manner,
S1 s2 1o 5214 t 780 F, h 1362.35, P= 1275
1 2 1 1 1
p = 360
2
h2 = 1228.9
Ahl = 1362o35 - 1228.9 = 133145
1 2
ahl2 =.85 x 133.45 = 113.43
h2 = 1362.35 - 113.43 = 1248.92
t2 497.9 F
S2= 1o5426
The locations for the extraction points were selected on the
basis of a more or less equal division of the feed water enthalpy rise.
The extraction quantities were computed on the basis of a simple heat balance. For example, the highest steam extraction becomes:
x (1248.92 - 412.67) = (1 - x) (412.67 - 269.59),
x = 143.o8/979~ 33 = o01461o
In this manner the other extractions were computed and the
corresponding flow rates through the turbine.
Then the work from the steam cycle becomeso
W 113.43 +J 0o8539 x 118.382 + 0.7638 x 102.483 +
o0.6696 x 144o15 = 113,43 + 101086 + 78.274 + 96.520
389.31 Btu/lb-H20.
The extraction quantities anxd work for the Na and Hg were computed in similar mannero The only difference in procedure involves the
additional extraction flows for superheating of the subsequent fluids
which must be included in these caseso
The matching of flow quantities between the various fluids is
accomplished as a simple heat balance~ The stea- m cycle flow was used
as a basis, and it was assumed that 1.0 units H 0 was the quantity of
flow through the H20 steam generator. The Hg ffow necessary to superheat
44

this steam was computed, as previously mentioned, along with one of the
extraction flows. The quantity of Hg to boil the H20 is computed in a
heat balance as shown below..Hg cond, 1179.8 - 412.67 6979
# - H20 boil 128.437 - 18.513
The cycle points which correspond to the enthalpy values used may be
noted from Figure 6b.
The same procedure was utilized to relate the flow quantities
in the Na and Hg cycles. All work and heat units were then referred
back to Btu/lb of water boiled.
On this basis the contributions to the total work from the Na,
Hg, and H20 portions of the cycle are,
Na 263 Btu/lb H20 boiled
Hg 262.84 " ft It
IE20 389. 31 t It
Total 915 Btu/lb H20 boiled
The heat input to the cycle is that quantity of heat necessary
to heat the Na from the highest feedwater heater exit point to the saturated vapor condition corresponding to 1500 Fo This quantity becomes
Qin = 0.7877 (2225 - 350) = 1480 Btu/lb H20 boiled.
Then the cycle efficiency would be, considering pump work
Work = 908 00613
Heat In 1480
As explained in Section 7.3, this result is reduced by a
factor of.96 to account for an apparent discrepancy in the Na data.
As is explained in that section, this is a very conservative assumption,
since a factor of.99 would be equally defensible.
713.2 Comments on Assumptions
The cycle calculations were somewhat shortened by the following
approximat ions ~
1) No credit. for pump work reducing heat input;
2) No temperature and pressure differentials in feed water heaters;
3) No allowance for pump suppression head following each heater;
45

4) No allowance for radiation losses;
5) Uniform but very low pump efficiency assumption applied to all
cases;
6) Division of turbine expansion lines into four portions only,
thus neglecting some of the existing reheat;
7) Use of only three feed heaters in each portion. A larger number would inc:rease efficiency to some extent.
It will be noted that assumptions 1, 5, 6, and 7 tend to reduce cycle efficiency while the remainder cause it to increase. However,
all of these effects are quite small and it is believed that they fairly
closely cancel each other. The final application of a factor of 0.96
to the overall efficiency is very likely to be highly conservative.
Thus the final cycle result, for turbines of the stated efficiency, is
believed to be conservative.
7.3.2.1 Turbine Efficiencies
For trinary cycle II, turbine efficiencies of.75, -80,.85 ( including reheat effect beyond the four divisions of the expansion line for each fluid.) were selected for Na, Hg, and H20
respectively. For cycle I, values of.80,.83, and.85 respectively were usedo
For the Hg-H20 cycles (Figures 9 and 10) turbine efficiencies of.80 and o85 for Hg and H20 respectively were used (including reheat as above). In general the attainable efficiency is
a function of the flow rate and hence depends on the size plants.
No evaluation of attainable efficiency for given cases was made,
but the values used apply generally to fairly large installations.
The high temperature liquid metal turbine efficiency has been
assumed lowest because of the unknown characteristics of the working fluid and the fact that it must operate with saturated vapor.
The intermediate turbine in the trinary cycles has been assumed
to be somewhat more efficient because it utilizes superheated vapor.
7.3.2.2 Liquid Metal Cycle Pump Desis
7.3,.2.2.1 Mercury Cycles
Consider a 60,000 KW binary plant. As shown in these
calculations the water flow rate is about 60 lb/sec about 60 lb/sec and the mercury flow rate about 850 lb/sec. Then the respective flows are
about 550 GP. for the mercury pump and 420 GPM for water. Thus
46

the pumping requirements will be of the same order of magnitude.
7.3,2..0 2 Sodium Cycle
The sodium flow rates are similar to those for the
water portion of the cycle since the enthalpies and densities
are similar. However, the total pressure rise in the sodium
cycle is only about 15 psi. Thus the possibility of electromagnetic or jet pumps is strongly suggested.
7,4 Estimatimton of Effect of Turbine Efficiency on Ideal Trinary Na-Hg-H20
Cycle. Correc:oo:s to Na Data,
7a4.1 Ideal Trinary Cycle
Utilizing the same temperatures, and thermodynamic data, which
were used in the calculation for Trinary Cycle I explained in Section 2.3,
a trinary cycle was computed using 100% turbine efficiency for the three
turbines. The other assumptions and the calculations procedure was as
per Section 7.3 except that superheat was not used for any of the fluidso
The resulting efficiencies were compared to the Carnot efficiency for
each portion. The results are as listed below~
Cycle ic i/i0c 1/ corrected
Na.2395.234 1.024.985
Hg.280.284.985 --
H20.452.479.943
Overall.700.725.966.928
7.4.1.1 Correction to Na Data
It is obvious that the Na data (reference 6) is not sufficient for these calculationso It is assumed that sodium and mercury
should. give cycle efficiencies about equally proportionate to the
Carnot efficiency. Therefore, it has been assumed in all calculations that the heat input to the Na portion (which is of course the
total input to the cycle) must be increased by.985/1.024 = 0.962.
An equally defensible assumption would be that the heat input to
the sodium cycle is correct but that the work output is reduced by
this ratio. Then the effective reduction of the overall efficiency
would. be only about 0099. The true situation probably lies between
these extremeso
47

7-4k 2 Effect of Changing of Turbine Efficiencies
The ideal trinary cycle discussed in Section 744.1 was used as
a basis for the determination of the effect of changing of the various
turbine efficiencies o
As a first step, the Na turbine efficiency was decreased from
100% to 80%. This has the effect of decreasing work output from the Na
portion of the cycle,'but increasing work outputs (i.e. flow rate/Na
flow rate) of the Hg and H20 portions since more heat becomes available
in the Na conden.ser. On this basis, the heat/per unit Na flow rate to
the Hg portion is increased by a factor of 1.06 and the Na turbine work
decreased by o80o
Originally (all turbines at 100%) the work output was
_Na ~DH_~_ +,;I2.0 = 32,300
10,880 9720 1.1700
and with the above corrections this becomes
Na Hg H20
1.0,880 x.80 + 1.0o o6 (9720 + 11?700) 3,400
Thus, since heat input to the Na cycle is unchanged (Na flow rate unchanged.), the cycle efficiency becomes (uncorrected for Na data).700 (31,400/32,300). ~679
a reduction of only.021 for a turbine efficiency reduction of.200
In ad.dition, as a second step, the Hg turbine efficiency was
reduced to ~83~ By a similar analysis, the cycle efficiency becomes
o.657, a further reduction of.022 for a Hg turbine drop of.17.
Finally, the steam turbine efficiency was reduced to.85, This
has the effect of reducing overall cycle efficiency to.63, a drop of.027 for an H20 turbine drop of.15. It will be noted that this final
result, derived approximatel.y, matches very closely the more exact result of Trinary Cycle II (Figure 6b) where the same turbine efficiencies
were used, but where the Hg and H20 cycles were superheated. This result
is to be expected in that the superheat does not inherently improve the
thermodynamic situation in this case since it is only a matter of intracycle heat transfer~ The superheat is justified, actually, as a means of
increasing attainable turbine efficiency.
48

7.5 Effect of Finite Teperature Differential Between, Various Portions of
Binary and Triznary Cyles
Consider as an example a binary Carnot cycle versus a simple Carnot
cycle as sketched below.
T'M1...T
T T
4 --
t —-s4 --— H
S S
In either arrangement the heat input to the cycle is TA1 S.l In
the binary cycle, heat, in amount T2 A S1l must be transferred across the
temperature differential AT to become the heat input to the lower portion of
the cycle, T3A S4.
By continuity, T2S AS 1 T3A S4o Since T2> T3, AS4> AS1. Heat
in amount T4A S4 is rejected:from the binary cycle and T4 A S1 from the simple
cycle. The heat rejected from the binary cycle is greater than that rejected
from the simple cycle by the ratio AS4/A S1 = T2/T3. Since heat inputs to
the cycles were equal, the work output and efficiency of the binary cycle are
less than for the simple cycle.
The amount of this reduction can be estimated for a typical example.
Suppose 1Carnot.609 T2 = 1500 R, and AT - 30 F. Then T2 = 1500/1470 = 1.02
Heat In. Heat Out 1 eat Out
Heat Tm. Heat In
In this case
Heat Out.4
HE~~~~~~~eat nOut
If Heat Out is increased in proportion to T2/ (i.e. 102), Heat Out is increased by the same factor. Thus Heat In' becomes 1 -.40 x 1.02 =.592
49

Thius, for this type of cycle, there is an efficiency loss of about
1 point for every 30 F additionlIa temperature differential between the portions.
inherently, then, the trinary cycle is perhaps 1 point less efficient than a
comparable binary arrangement.
7.6 Effect of Temperature Differential in Extraction Feed Heaters
As stated in Section 7.3, no temperature differential was assumed
for the feed heaters. Practically, this case might be attained for the sodium
cycle by the use of sodium ejectors rather than feed pumps, since the pressure differential is very low. However, for the mercury and steam cycles it
is only an approximation. A rough estimate of the magnitude of the discrepancy
introduced by this approximation is made in this section.
Suppose we assume a 20 F differential for each feed heater. Roughly
we may assume that *the effect is similar for any of the portions of the trinary cycle. This effect is the reduction of turbine work caused by a removal
of a portion of the working fluid at a temperature 20 F greater than implied
by the zero temperature differential assumption which was made.
Say we consider the portion of one of the Hg cycles in a trinary
cycle between the second and third. extractions as typical. In this region
of the turbine expansion line there is a Ah of approximately 1.7 Btu/lb
corresponding to a aZt of 20 Fo The flow extracted at this point for feed
water heating is 0189 out of a total flow of 8.89 or.021 of the total. Since
the total turbine enthalpy drop is about 37 Btu/lb, the loss on this account
is proportionately.7 x.021.0ooo0096
37
Since there are three extractions per fluid the total proportionate loss is about 0.003 and is thus quite negligible.
5o

PART II. GAS TURBINE DETAILED STUDIES FOR NUCLEAR POWERPLANTS
1.0 GENERAL THERMODYNAMIC FEATURES OF GAS TURBINE CYCLE.1 Approach'to Id.eal Efficiency
For the appraisal of any thermodynamic heat engine cycle, it is
first desirable to investigate its degree of approach to the ideal heat engine
cycle efficiency'which, according to the Second Law of Thermodynamics, sets
the maximum possible efficiency for given temperature limits. This situation
is examined in some. detail in Part I
It is concluded. that the gas turbine type cycle can approach the
ideal effi.c:iency limitation either through the utilization of the "simple
cycle" (Figure 2 of Part I) with a pressure-ratio approaching infinity or
through an ideal regenerative cycle (Figure 3 of Part I) which approaches'the Ericsson cycle. This latter involves an infinite number of reheat and
also intercooler stages in the ideal. case. Practically, of course, a compromise somewhere between these two extremes is required.
In past practice with fossil-fueled gas turbine plants, the first
possibility, i.eo the use of a high pressure ratio with no heat exchanging
equipment, has been applied to cases where size and weight of plant were of
more importance than efficiency. A case in point is the aircraft gas turbine
plant. However, where efficiency assumes proportionately more importance,
as for most land-based and. marine applications, plants utilizing highly effective heat transfer equipment and a rather low pressure ratio seem more suitable. If practically attainable component efficiencies and effectivenesses
are assumed, it may be shown that plants designed according to the latter
philosophy cran achieve considerably higher thermal efficiency values for
any imposed temperature limitations. This fact is illustrated graphically
by a comparison of Figures 6e and 6d. Figure 6e is a plot of thermal efficiency against pressure ratio for a plant including regenerator, intercooler,
and reheater, as well as the universally required heat sink and source. It
is noted that, in this case, the maximum thermal efficiency values for source
temperatures of 900, 1200, and 1500 F respectively are 25.0, 34.7, and 41.5.
On the other hand, Figure 6d shows the maximum efficiency against pressure
ratio for a plant with no regenerator, intercooler, or reheater. Here it is
noted that the maximum efficiency values occur for considerably higher pressure
ratios (about 5.5 instead of 3,5 for 1200 F). However, the maximum efficiency
values are only 12.8, 19.3, and 24.6, at the same temperatures.
1.2 Selection of Basice Cycle
High efficiency appears essential for any but perhaps airborne
51

nuclear powerplanlts. There:fore, it -was decided to base the study on the cycle
arrangement whic.h is cwapable of the higher efficiency. As explained in the
last secti.on, the choice of the regenerative type cycle is di.ctated. A basic
arrangement (see Fi.gure:1.) is assumed whi.ch includes regenerator, intercooler,and
heat source and si.,lnk, as well, as turbine and compressor. (Thermodynamically
the decl.sion as to whether the turbinre would be divided into a power and compressor drbi-re turbin.e ran.d the.-decision as -to whether the cycle is open or
closed is of no sigrifi:c-tanceo ) This cycle was used. as a basis from which the
effects of the possible variations in component arrangement, efficiencies,
and. effectiveness could be evaluated. For this "basic cycle",'the assumptions
listed. in. Tabl.e I] were made.
TABLE i ASSUMED CO.MYONE.f' E.FFICI..ENCIES FOR THE BASIC GAS TURBINE CYCLE
Turb ine Effi eie.ny 857%
Compressor F, ffi:L:iency 85%
Regenerator E:f fectiven.ess 93%
Ratio of Compressor Pressure Ratio to Turbine Expansion Ratio 1.07
Cooling Medium Temperature 70 F
Mi:ni'mum FLuid Temperature 90 F
These values are believed'to be attainable in large scale plants
where e:ffi.iency is of cWonsiderable import compared to capital cost. The relations'betweenL the relati:re importances of capital cost and efficiency depend
on the part.icular appli.cation arLd. no general statements may be made. For a
nuclea:r plant these relatliors may differ considerably from a fossil.fueled
plant. They depend very strongly on'the type of reactor because of the influencees of fabrication a-nd reprocessing costs fo:r the fuel elements, as well
as the price of uranium~ A further study of this situation seems a logical
exteansLion to the work which. has been alread.y accomplished:.
A closed cycle type installation is assumed in the selection of
~these component efficiencies. This is apparenit in the case of the regeneratoro It is believed t;hat, for a fail.rly l.arge plant operating at elevated
pressure, that considering the cornsequent increase in heat transfer coefficien'ts, a regenerator e:ffecetiveness of 0.93 is reasonable. This is particularly the case for plants util.izing helium instead of air, where there is a further improvement in heat transfer.
In. general, the turbine efficiency will exceed to some extent the
compressor effi.ciency, and each of these values will increase for large flow
rates. This increase is somewhat obviated with the closed cycle, elevatedpressure pl.at, since the turbomachi.nery volume flow rates may be too low for
optimum effici.ency in an optimized plant. This is the case because the presue level. se.l.eetion for an optimum plant design may be i.nfluenced more strongly
52

by the regenerator requirements than by the turbo-machinery. It is believed
that the selection of a rather high regenerator effectiveness with more moderate turbomachinery eff.ciencies may represent a reasonable compromise for
the closed.-cycle plant. Therefore, an assumption of 0.85 for turbine and
compressor efficiency has been made for the "basic cycle." It is not implied
that the turbine and compressor efficiencies are equal at 0.85, but that they
achieve values (turb:ine somewhat higher than compressor) which are the equivalent, so far as the overall cycle efficiency is concerned.
1.3 General. Relations with Perfect Gas
The calculations reported in this section are based on the assumption of a perfect gas. There is no question of a mixture of combustion products
with the working fl.uid for a nuclear plant as in the case of the conventional
open-cycle fossl.!..fueled. gas turbine. Therefore, the perfect gas assumptions
are believed to be fairly close to the actual case. The relations for the
thermal efficiency of the basic cycle and. for the various permutations of this
cycle which were studied. are derived in the Appendix (Section 8.1) and listed
in. Table 1:,
It will be noted from the expressions for the thermal efficiency
listed in Table:Ii that the thermal efficiency is not a function of the working fluid, The only characteristic of a perfect gas working fluid which is
involved in the expression for the theoretical cycle thermal efficiency is the
ratio of specific heats. Thus, as far as the perfect gas assumption is applicable,a ce:rt.:L -thermal efficiency is attainable with any diatomic (k = 1.4),and
another with any monatomic (k = 1.66) gas, assuming no change in the attainable
component efficiencies and effectivenesses. This is, of course, not the general case since the optimum heat exchanger designs for a given application
strongly depend on many c.haracteristics of the gas not considered in this type
of analysis, and. the optimum turbomachine design depends on such factors as
the Mach number arad Reynold.'s number.
Under the assumption of a perfect gas working fluid and constant
component efficiencies and effectivenesses, it can be shown that for any given
temperature limits the attainable thermal efficiency increases as the ratio
of specific heats decreases. This is illustrated in Figure 11 where thermal
efficiency at optimum pressure ratio is plotted against the ratio of specific
heats. The same effect is also evident from an examination of Figure 6, where
in all cases the maximum thermal efficiency for the k = 14 value exceeds by
one or two points that of the k =- 1.66 value. Thus, under the assumptions of
this study, gases such as air or nitrogen are inherently capable of higher
cycle thermal efficiencies than helium or argon. On this basis, gases with
a still lower k value such as carbon dioxide would be even more suitable. As
far as actual machinery design is concerned this may not be the case. The
machinery required. to extract the required efficiencies and effectivenesses
from the heavier gases may be more extensive than that required for helium,
so that the optimized plant for a given application may well show a higher
53

TABLE II. GAS TURBINE CYCLE THERMAL EFFICIENCY RELATIONS
Cycle Arrangement Thermal Efficiency Equation
-T 2 yR/2
Basic Cycle th TRT 1 - (p ] - (pR _ 1)
TR{ 1 - R+ RT [ 1 -(T pPR)-Y + 1R- 1 (PRy/2 -)
TRT [1 - (%PR)-Y] 2 (pRy/2 -1)
Basic Cycle Without Recuperator th 2
TR-! (p R/2 + n -1)
Ic c
TRnT [ 1 - (npPR)-j (PRY _1
Basic Cycle Without Intercooler t = T Pc
th1 { 1 R + TRTT [ 1 - (TpPR)-7]} + TR 1 (PRY + -1)
TRfT [ 1 - (rpPR)-7] - (PRY -1)
Basic Cycle Without Intercooler nth = Y
and Recuperator TR- _(PR + c 1)
2BTTR [ 1- (PR) y/2] 2 (pRY/2 _1)
Basic Cycle With Reheat =
th
TR{ + RT[(ppR)']} + R (pRY7/ +R_') + TR[1-( _ > 2 ]
Note: Symbols are defined in Section 6.

overall efficiency with helium as working fluid than air. It is felt that this
situation deserves further examination and will be considered at greater length
in a continuing investigation.
55

2, 0 OPERATING- PARAMETER VARIATION EFFECTS ON EFFICIENCY FOR PERFECT GAS
2.1 Basic Cycle
As was explained in Section 1lO,0 a "basic cycle" was postulated,
consisting of a compressor with a single intercooler, a turbine, a regenerator,
and a heat source and sink (:Figure 1i) Along with the "basic cycle", four
other cycles, including the elements as listed below, were considered.
a. Compressor with single intercooler, turbine, heat source and sink,
(i.e. n.o regenerator)o (Schematic Figure 2, performance Figure 6b).
b. Compressor, turbine}regenerator, heat source and sink, (i.e. no
intercooler). (Schematic Figure 3, performance Figure 6c).
c. Compressor, turbine, heat source and sink, (i.e. no intercooler
or regenerator)> (Schematic Figure 4, performance Figure 6d).
d. Compressor with single intercooler, turbine with single reheater,
regenerator, heat source and sink. (Schematic Figure 5, performance Figure 6e).
The "basic cycle'" is also used as a basis for the determination of
the effect on thermal efficiency of changing each of the significant cycle
parameters individually with all other factors held constant. From the data
presented it is possible to estimate the efficiency of any gas turbine cycle.
The estimate is obtai.ned by correcting the "basic cycle" efficiency value
by the proportionate efficiency change caused by each of the cycle parameter
variations involved0 The data is plotted in all cases as a function of pressure ratios and thus the optimum pressure ratio for given conditions can be
selected from the curves~ Also, the proportionate loss of efficiency to be
expected from operation (as perhaps at part load) at pressure ratios other
than the optimum may be estimated~ In all cases, data is presented for both
a monatomic and a diatomic gas (i.e. for k values of 1.66 and 1.4 respectively) and for inlet temperatures of 1500 F, 1200 F, and 900 F. The cycle diagrams are presented in Figures 1 through 5, and the performance curves in
Figures 6 through 9. Listed in Table III are the various cycle conditions
which are presented in this report0
2.2 Results of Theoretical Performance Calculations
Several important points are apparent from this study. At 900 F,
25% is approximately the maximum obtainable efficiency. This value corresponds to the cycle with a reheater. Without a reheater, the approximate
maximum is 23 5%. At 1200 F the maximum thermal efficiency with reheater
approaches 35% and without reheater 341/
56

HEAT EXINTERCOOLER CHANGER
FROM
_NUCEAR
To
CO PR OR TURBINE!.T
HEAT SINK
FIG. I SCHEMATIC FLOW DIAGRAM OF THE BASIC GAS TURBINE
CYC LE
HEAT EXCHANGER
INTERCOOLER FROM!I M NUCLEAR
REACTOR
Te
COM OR 1 TURBINE
1 - T.
HEAT Sl NK
FIG. 2 SCHEMATIC FLOW DIAGRAM OF THE BASIC GAS TURBINE
CYCLE WITHOUT RECUPERATOR
57

HEAT EXCHANGER
FROM
NUCLEAR
REACTOR
T,' I~~T9 RECUPERATOR' izVr~mB~~ m T4
HEAT SINK
FIG.3 SCHEMATIC FLOW DIAGRAM OF THE BASIC GAS TURBINE CYCLE WITHOUT INTERCOOLER
HEAT EXCHANGER
FROM
NUCLEAR
REACTOR
COMPRESSOR TURBINE
HEAT SINK
FIG. 4 SCHEMATIC FLOW DIAGRAM OF TH1E BASIC GAS TURBINE CYCLE WITHOUT RECUPERATOR OR
INTERCOOLER
58

HEAT EX-"
CHANGER
I NTERCOOLER FROM RE
FROM REHEAT
FIG. SENUCLEAR FROM
T+I ~~VV!REACTOR RICTi
Ti T,'lA
T8 T2
COMPRE SOR TUR NE
T, RECUPERATOR
T1T
HEAT SINK
FIG. 5 SCHEMATIC FLOW DIAGRAM OF THE BASIC GAS TURBINE CYCLE WITH REHEATER
59

0 1 2 3 4 5m 6 7 8 9 10
_ -~ __' — =;O,_=
0.4 - -----
/., _ > _mL_ =_ ==
II7I = = =======
0 -
0.3 - - ---
c~~~~~~~~~~~~~~~~,,
/,. s
C.) ~ ~ I 0. I, -x
IL
1H 2e 3i (
PRESSURE RAT IO
FIG. 6=. THERMAL EFFICIENCY OF A GAS TURBINE CYCLE WITH
VARIOUS CYCLE ARRAN GE MENTS.~'BASIC SCYCLE
*~SEE TABLE 3, PART II.
~~~~~0.2 r =====
>_ _ -- i =\ == =
mF \ ~ AX
0 Oi * "e
w ) i. xb.
J! i 1PRE1-RE- - \ 1
FIG 6a HRA FIIEC OF! GA TUBN YCEWT
u~~~~~AtOSCCEARNEET.I
I- ~ BSI YL
*SEE TABLE 3, PART n~~~~~~~~~~ii
O O!''~~~~~6

O 2 3 4 5 6 7 8 9 10
0.4 -
~~~,0.3
0.2 - -
03 2 3 4 z}=F 6 7 8 3 E'3
1JEHX 3;du L
0.2
YE0- - - - - - - - -: —
*SEE TABLE 3) PART I
61
0 3 4 5 7 8 9 10~'&
___1PESUERAI
FI. b- HEML FFCENY FA ASTRBNECCL\WT
n- ~ ~ ~ AIOSCCEARAGMNS

0 1 2 3 -
- -4
0.4 — 7 - -7 -- - 7 --
~~o. /3E1 +
— 7- -
I IA..+ \'o...
__~~......,.... _
ltz -,, --
___~~~-7 i _ _= —=== -
--
LiiNg - - -...-.. -
Qj- - m -v -St
IL — 22 2
=~~~ S + \' 4Sx r'
0.'..~
21~~~~~~~~~6
Lii
I0 2 ~3 4 5 6 7 8 9 tO
PRESSURE: RAT IO
FIG. 6c. THERMAL EFFICIENCY OF A GAS TURBINE CYCLE WITH
VAR IOUS CYCLE ARR ANGEM E NTS'IBASIC YCYCLE WITHOUT INTERCOOLER
iSEE TABLE 3, PART II
62

0 I 2 3 4 5 6 7 8 9. 9
0.4,
0..
0.3 -.i - - - -
0.2
I_.
w I I I
0 0.1
2. 3 5 6 7 9
PRESSURE RATIO
FIG. 6d. THERMAL EFFICIENCY OF A GAS TURBINE CYCLE WITH
VARIOUS CYCLE ARRANGEMENTS.
"BASIC"*CYCLE WITHOUT RECUPERATOR AND INTERCOOLER'SEE TABLE 3, PART II
63

0 2 3 4 5 6 7 8 9 10
0.4
0.3 -
0. -- - -
z,- - -I
U. -
0. 2 3 4 5 6 9.. 1.
PRESSURE RATIO
FIG. 6e. THERMAL EFFICIENCY OF A GAS TURBINE CYCLE WITH
VARIOUS CYCLE ARRANGEMENTS.
"'BASICCYCLE WITH REHEATER
0-3:*SEE TABLE-3, PART 11
[O 1...... 4! 6 ]! [ "%et I _)....
PR... ES SU.ERA.1
FIG. 66. THERMAL EFFICIENCY OF A GAS TURBINE CYCLE WITH~~~~~~~~~~~~~~~~~~~~~~~~~~.,AIU,YL RAGMNS
U~~BSCCCE IHRHAE
I~ ~~~~* E AL-,dPR
o.~~~~~~~~~6

IEld'~ 3918V1 33S
~6'0 - SS3N3AI.33.333 8t1O.lV3dnD38 H1IM
3"10. 3NIB8n.l S9VO*,,O1SV8,, V O AON31I13 3 -W1"V3HI'DL 91J
01.t.V 38nss3ld
01 6 8 1 9 S ~, I 0
I - m - -- - - - I -I-I-I -m0.--
I1 1
_-Pm
z,m,, I~'o 9!'9.~~~~~~~ l \
0~1 6 9~.~ 9 ~~G~! ",0
=- I= == ~i I ",=\'it_ ===
1H<H3+H He~~~~~~~~~~

O I 2 3 4 5 6 7
0.4
0.3
O. _ —_ = ==== =_
0.
zz,, 0.1 R
FIG. 7b THERMAL EFFICIENCY OF A BASIC" GAS TUR3INE CYCLE
WITH RECUPERATOR EFFECTIVENESSwO075
II*EaE I
WITH RECUPERATOR I 0.75
- Z,~~~~~~~~0

0 1 2 3 4 15 6 7 8'O.4
0.4
0.2- - - -_- -= -= - 150 k:1.
0.1
LL
U0 - - - - - - -
0.PRESSURE RATIO
* SE EE TABLE 3, PART I
FIG.7c. THERMAL EFFICIENCY /ABc G TURBINE CYCLE
iii ~E IAL IPIT If
o o i~~~~~~~6

0 1 2 3 4 5 6 7 8
==.
0. 3
-~~~~~~~~~~~- I- &/.\IIIIII.l
=~~ ~,: —I,.,TT - ITTT1
~
0.2
I-
U
==-... "T " I ~_ITI
U 0.1
__- I. "I
==:I:... === T "' 1.''X 1,1
F = = == I I'~.4'.,,
=
S~~~~ I_ i\'cL 1 " 1{,.2
zU 2 3 45 7I i
~
PR E SSUR E RAT IO
FIG. 8a. THERMAL EFFICIENCY OF A "BASIC"<AS TURBINE CYCLE
WNITH FRICTIONAL PRESSURE LOS SES - 0.07
SEE TABLE 3, PART \.
68: — -~I00- - \
~~~~*ETAL3, PART f.,, "..~~~~6

0. - - - 4 6 - - 0
I<F<TI~~~~~~~~~~~~I rnnrnI i 1III I
0..3
0.4 i ii i
0.2~~ -/ -' - -- m - -
IL
~_ = L I I\=
IL
w. _ i Ir I'_. e = = _=
-J
0 — 11 - —. — -4,. -
PRESSURE RATIO
FIG.Bb. THERMAL EFFICIENCY OF ASUBASICSI*GAS TURBINE CYCLE
WITH FRICTIONAL PRESSURE LOSSES-O.I2
*~SEE TABLE 3, PART i
69... 11 l" — -x
I @g@+ @ 33t @33~~~~~,
i ol t ~~~~~1 " L~'WN 1~Z
W~~~~~~~~~~...." L'i
o ~ ~~1 3 r 8 44 1;~~~~~ SE!AL 3~lI', PAR D:
u ~....\ 9

~'m Tl I I I I IlHi I I J"<
O.s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.
~~~~~~~~~~~~~~~.4
0.4.,, _ _,
0. 4 _ _ _ _ _ _ _ _ _ _ _ _ _ T l
-- ==========
__=~~~~~~~~~~ _ _ = ===., = = -,
z~ ===zZsSt=== ===
0.3 == -1 ==..... -, ==,= _ _,_o
- = _, -,,_ —-
[.II I! / I I I3 i3!-', [,
=== =-: - /f!~ = == == === i
02 _1 __-!/! I_ _ _ I!!!I....
=-: = =T= ===== -] _= I!!
I o.,
PR
Z ~ ~ ~ ~~~XE TAL 3, PAR,
13~ ~ ~~~~~~7
-I/,"-,., o I
-~.
PL~~
F16.8c. THERMAL EFFICIENCY OF A"BASIC~~~-qk''A UBN YL
0~~~~~~~7

O 1
0.4
0.4 /, - - -- -1
0.3
0U 0.
_ _ 10
PRESSURE RATIO
FIG. 9o THERMAL EFFICIENCY OF A "BASIC" S*GAS TURBINE CYCLE
WITH TURBINE EFFICIENCY= COMPRESSOR EFFICI ENCY=.85
* SEE TABLE 3, PARIET D
_ ~ -_.
tF~~~~~ ~ H HH
> ==== = ==S = = = = == == === =~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.==2=== ===== == -
Z~~ ~~,= ====, L ==._
S == = = == = = = === = ==
=2u HgL~~~~~~~~~~~~~~~
O~ ~ ~ ~,L~~.....
z~~~RESR N-o. %~
FIG. 9a THERMAL EFFICIENCY OF A"BASIC"*GAS TURBINE CYCLE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r
WIT TUBIN EFICINC=CMRSO EFIENY08
-— ~~~~~*E O.BL )......,
-' X~~~~~~~~~7

- - 2 3 -
0.4
0.3
0.2
I FlbHi3 H 3HE 3I
U -- — =
03 -
- PESSURE I RATIO
FLYC
IWI TB EFi #i #iCu
t! I I —-- - -~.",
0 1' 3 4 5 7 8 9 -)
PRESSUR E RATIO
FIG. 9b THERMAL EFFICIENCY OF A"BASIC"I*GAS TURBINE CYCLE
WITH TURBINE EFFICIENCY=COMPRESSOR EFFICIENCY= 0.80
~SEE TABLE 3, PART Z
72

0 - 2 3 - 5 -6 71 - - - -
- -
=0.3 - = - - - - -m
0.4 - __
C _= - _ =
03 - -=- - - - -
La~~~~~~,~. -,:-'o-0
o o~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~,
QT~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
i J - = - =~~J — == -_ === === — _1 m- A - -mIr)~~~~~~~~~~
0.2 _=_. _ _ __3 4 5 6 7 8 9 10
u.I L- \X
x/. ~"~'
PRESSURE RATIO
FIG. 9c. THERMAL EFFICIENCY OF A "BASIC"I:AS TURBINE CYCLE
WITH TURBINE EFFICIENCY= COMPRESSOR EFFICIENCY= 0.75
* SEE TABLE 3. PART II
73

TABLE III.o TABULATION OF CYCLE CONDITIONS PRESENTED IN REPORT
Component" Ef ficiency and Effectiveness Results'Duct & Heat in
__Cycle Diagr Turbine Compressor Recuperator Intercooler Exch. Losses Reheat k Figure
Basic Cycle - Figure 1.85.85.93 Yes.07 No 1.4 6a
1.66
Basic Cycle - without
Recuperator - Figure 2.85.85 No Yes.03 No 1o4 6b
1.66
Basic Cycle - without
Intercooler - Figure 3.85 ~85.93 No.05 No 1.4 6c
1,66
Basic Cycle - without
Intercooler & Recuperator- Figure 4.85.85 No No.01 No 1.4 6d
1.66
Basic Cycle - with Reheat
Figure 5.85.85.93 Yes o09 Yes 1.4 6e
1.66.
Basic Cycle - Figure 1.85.85.93 Yes.07 No 1o4 7
~75 1.66.50
Basic Cycle - Figure 1.85.85..93 Yes.07 No 104 8.12 1.66.20
Basic Cycle - Figure 1.85.85 93 Yes.07 No 1.4 9.80.80 1.66.75.75
Basic Cycle - Figure 1.75 o75.93 Yes ~ 07 No 1.33 10
1.4
1.5
1'66

At 1500 F however, the relation is reversed and the efficiency is
42% with reheat and 44% without.* It will be noted that these values are
greatly in excess of those for the cycles without a regenerator. For example, with an intercooler but without regenerator or reheater, the approximate
obtainable maximum efficiencies at 900 F, 1200 F, and 1500 F. respective inlet
temperatures are 13.5, 20.0, and 25.0. These values are obtained at a much
greater pressure ratio than is optimum for the regenerative cycles. The
optimum pressure ratios for the cycles with regenerator are in the order of
2.5 to 4.0 whereas for the non-regenerative cycle they are in the order of
5-10.
In all the cycles which are plotted, it is seen that a greater increase in thermal efficiency is realized for the temperature increase from
900 F to 1200 F than for the increase from 1200 F to 1500 F. This result
is to be expected since it will be noted from the tabulated thermal efficiency functions in Table II that thermal efficiency is a function of temperature ratio across the cycle and not simply of temperature difference.
In considering the suitability of various gases for working fluids
in such a cycle it has been noted in Section 1 that the molecular weight of
the gas does not enter into the determination of the efficiency. The only
effect of using various "perfect gases" with fixed component efficiencies
is through the ratio of specific heats. This is relatively minor. Consequently, all diatomic gases are equal in efficiency and also all monatomic
gases. The monatomic gas optimum efficiency is always a few points less than
that of the diatomic gas. In fact, (Figure 10), optimum thermal efficiency
increases consistently with decreasing ratio of specific heats. Of course,
as was previously mentioned, these results may be misleading, since for a
given physical heat exchanger component, the effectiveness may be higher
with helium, for example, than with air, because of superior heat transfer
properties. Then, for this case, the cycle efficiency with the monatomic
gas may be superior to that with the diatomic gas.
The advantage of a diatomic over a monatomic gas decreases as the
inlet temperature is increased. At 900 F, the thermal efficiency decreases
from 23.5% with a diatomic gas in one case (Figure 6a) to 21.5% for the
monatomic, and at 1500 F, from 42% for diatomic to 41% for monatomic.gases.
The optimum pressure ratio increases as the maximum thermal efficiency increases. However, the extent of the increase is greater with a
diatomic gas than with a monatomic gas. The cycle efficiency for a monatomic gas also tends to decrease more rapidly at pressure ratios above the
optimum than for a diatomic gas. Thus the monatomic gas cycle does not
allow as broad an operating range at high efficiency as does the diatomic.
* However, in all cases, reheat will considerably reduce mass flow rates.
75

O 1 2 3_1
O ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.4
0.4 -= - = - =
*'(
03 l I I I l l L I I l I I I I. I.]
I F I.I I....
~9-I A-I -. ~ ".
r 4 _ -
uJ — r -= ~== ===
0.2L__L_ r;-.- - _ - --
w~~~~~4~ ~~~'-4, -~,, -.
-'r, ( _~0.- - - ~_- *;,- ~ _~ __
PR ESSURE RATIlO
fIG. 10 THERMAL EFFICIENCY OF A "'BASIC" GAS TURBINE CYCLE
WITH RATIO OF SPECIFIC HEATS VARIED.
* SEE TABLE 3, PART 11
— ~,~,76

IrT
I I
I Wl I I IIII X I IM
101111 I 17 I I I
U JR
I kill I I...
UTX
Li I A. Hill
It& 11 I Hill Ti I I -I I I I I lei I
Ud I M I I
I EFf- I I I Ill I I 7t I I
I lu. I W I I I I I II I I I I I I I I
jui 1 4111 11 I Ill
1.1I Ljp:I M w ill I I I I I 11111 Ill I I I I M
I I P a Q I I I I I I LI I
I I ivp. M 99 1 1 1 1 I
irm 1 1
111144 It
Ull.a HIM I 1111
I" U
WIM 11 I I Ilf"
I A ll I I
I Ill I to F L If
1 U 1 1 Li _L
J.
I I f I WI
UP I
111 A ll
itt I Ifill I I Ill L I I I
I 11 I Hill I I
A ll I Ill
1W I I I I
40 11 1 1 1 LLM I L H I I I F
f9 I I I I I NH — I
I I law I I 11 I L I I I Hill I I I I I
11 I.X I I I& I I 11 Hill Ill I I IIII
H I I*H -1 I I I I
11 ri In I -1
rt I
AM
I I M I I I I
IQ1W I I I I
I I 111111- I I l F
Hill 11111ML
I UL
FF 1111111IF - I I I - I J —- I
to CM

It would appear for this reason that the monatomic cycle would be at a
somewhat greater disadvantage compared to the diatomic in off-design conditions (as part load.) t;h.an for the design condition; i.e. if part load were
to be achieved by reducing mathinery speed rather than the alternate possibilLty for a closed cycl.e plant of reducing the operating pressure level by
refmoving gas from the sys, tem.
It will: be noted. that he optimum pressure ratio also increases
with reduced heat exchanger effectiveness. Figure 7 shows the effect as regenerator effectiventess. i.s reduced. from.93 to.75 to.50. In fact the
optimum pressure rati.o for the 1500)i) F.^>ycl.,e w: thout regenerator (Figure 6b)
is over 10, while it is onr.l.y 4,2 for the 1.500 F regenerative cycle with reheat and 302 for the regenera't-rAe cycle without reheat. It is only 2.3 for
this cycle at 900 F (F7iguire 6a)o.
78

3,0 EFFECT OF PIANT SIZE AND REAL WORKING FLUID ON OTHER PLANT PARAMETERS
3.1 General Considerations
The data presented in FigSures 1 through 10 and discussed in detail
in Sections 1 and 2, Part II of this report are based on perfect gas relations
and certain component ef.ficiencies and effectivenesses. These are assumed
to be typical regardless of plant size or actual working fluid. They are
then arbitrarily varied to ascertain the corresponding change in overall
plant thermal effi.cienc(yo
It is the purpose of the work reported in this section to attempt
to evaluate the actual effiL.ciency values which may most probably be obtained
under various conditions of plant size, working fluid, operating pressure
level, and available source and sink temperature. To date this work has
been concerned mainly with the variation of turbine and compressor efficiency
as a function of the above parameters and the corresponding effect on the
overall plant efficiency. It appears useful to examine the heat exchanger
components in the same way, including the interrelations of capital cost
and operating cost for specific applicationso Such an investigation will
involve the cost of uranium processing, fuel rod fabrication, etc.
The present work has assumed given effectiveness levels for the
heat exchangerso It is obviously possible to attain any desired effectiveness for such a component, the only question being one of the balance of
capital cost, wEt-i hj and "fuel" cost. The situation is somewhat different
with respect to the turbomachineryo There is an approximate ceiling on the
efficiency for a given application depending on flow rates, Mach numbers,
Reynold's numbers, and the state of the art for this type of machinery, It
is desirable in anlmost all cases to approach this ceiling value fairly
closely; ioe. to utilize a sufficient number of stages at proper speeds,-etc.v
Possible excepti.ons are air-borne devices where size and weight may be f
especially overbearing importance compared to efficiency. This latter is
particularly true of a nuclear plant, since in many cases, a reduction in
thermal. efficiency of the heat engine device will not increase the size of
the reactor, or decrease the range of the vehicle or missile. It will only
result in an increase in the replacement fuel costs. In many cases this
would be of no importance whatsoever.
Efforts have been made to evaluate the ceiling value for turbomachinery effi.ciencies as it is affected by size of plant, working fluid,
temperature, and pressure. The evaluation has been conducted for a closed
cycle arrangement (l'basic cycle"), which includes a compressor with a single intercooler, a turbine, a regenerator, and a heat source and sink. To
the present time the evaluation has included air and helium as working
fluids for plants ranging in size from 600 to 60,000 horsepower, for inlet
79

temperatures from 1.500 F to 600 F, and for operating pressure levels, i.oe
compressor discharge pressure, from 45 to 1000 psia. In the future the
study will expand to include carbon dioxide. Air, helium, and carbon dioxide were chosen for the initial work since they cover a wide range of
molecula:r weight with the corresponding variation of the other applicable
quantities (sonic velocity, specific heat, ratio of specific heats, density,
viscosity, etc,)
In. order to simpli:fy the calculations to some extent, a pressure
ratio of 3.0 Vwas selected. for all. the conditions. This is fairly close to
the optimum:for the`bas-c.e cycle"' w:ith high heat exchanger component effectivenesses for the entire range of temperatures for both diatomic and monatomic
gases, as illustrated in Figure 6ao The other cycle constants which were
assumed for the study are listed in Table IV.
TAB.LE IV.o TBERMODYNAMI:. ASStUTEAIONS FOR PLANT DESIGN CALCULATIONS
Regenerator Effectiveness O0 93
Ratio of Compressor Pressure Ratio to Turbine Expansion
Rat; io 1 07
Cooling Medium Temperatumre 70 F
Minimum Working Fl.uid Temperature 90 F
Compressor Pressure Ratio 3.0
Insulation and AuxilLiary Losses 3%.The results of the study may be used to estimate the probably efficiency of plants in which the cyele constants differ somewhat from those
chosen. This can be accomplished through the use of Figures 7 through 9,
where the loss of efficiency:from the "basic cycle" optimum, chargeable to
various changes in the cycle parameters considered separately, is illustrated.
3o 2 Gas Prot:i.es
The air properties utilized in the study are as given in reference
1. References 1 and 2 we:re used for the viscosity datao These data consider the variation inr the specific heat with temperature, but assume that
the properties are constant with pressure, If the variations with pressure
as presented in references 3 and 4 are considered, it is found that over the
range of interest to this study the effect is negligible, ie.o the thermal
efficiencies which are comEputed from the air properties as corrected for
pressure variation are very close to those computed directly from the tables
of reference 1o
For helium, perfect gas data was used. Extreme-case cycle efficiencies computed on thi.s basis were compared with efficiencies computed from
80

the data given in reference 5 and it was found that the difference was negligible Viscosity data for helium was taken from reference 2.
3~3 Turbomachinery Types Considered
The type of turbomachinery to be selected for a given application
depends ono
1) flow rate,
2) efficiency desired,
3) temperature,
4) type of fluid (corrosive, lubricating qualities, abrasive
qualities, necessity for seal integrity, etc )
5) pressure level,
6) variation from design point.
In the selection of components for a gas turbine plant, flow rate
and off-design performance are of the greatest importance. For a nuclear gas
turbine plant, there may be introduced complications involving the necessity
for absolute sealing if the fluid is radioactive, the necessity of preventing
any admixture of lubricant and fluid, and the necessity for remote maintenance. In any closed cycle plant, if the fluid is other than air, there is
the necessity for a very good sealing arrangement on the basis of the replacement cost of the fluid, For air, it becomes simply a matter of auxiliary power to operate the make-up compressor.
For the present, only the fluid-dynamic flow path design has been
considered. The study will be expanded to consider the mechanical difficulties which will be involved if radioactive working fluids are to be utilized.
However, the fluid-dynamic flow-path considerations dictate the choice of
axial flow machinery for the large sizes, both for compressors and turbines
for the attaining of optimum efficiency values. In general as the volume
flow is decreased, because of low power requirements or high pressure levels
at moderate power, the possibility of a centrifugal compressor and/or turbine exists. (For sufficiently small output, the centrifugal compressor
efficiency surpasses that of the axial flow machine. ) Because of its more
stable operating conditions over a broader range, it may become the logical
choice for small plants. If very small flow rates are to be considered,
there is in fact the possibility that positive displacement machinery may
show to advantage in certain applications. If weight and space are not
important, it is certainly true that the efficiencies in small sizes of such
a device (reciprocating or rotating) may be superior to the centrifugal or
axial machines. However, in a closed cycle nuclear plant there may be
81

added difficulties of sealing and of preventing any contamination of the
working fluid from lubricationO
The same considerations of applicable type of machine versus flow
rate may be applied. also to the turbine. However, due to the favorable
direction of the pressure gradient in the boundary layer, turbine design is
not nearly so sensitive a matter as is compressor design. Hence, it is
belibeved. that an axial flow type can be used for the entire range, This is
not to say that centripedal or centrifugal turbines, or even positive displacement expanders, may not be more applicable for certain situations, but
only that the axial-.:flow turbine efficiency will be typical, and not too far
from the optimum.
For the cycle evaluations herein reported, axial-flow, centrifugal,
and positive displacement (as the Lysholm type) compressors were considered
in the applicable flow rangeo Axial-flow turbine designs were considered
throughout. It was assumed that a turbine of this type, with 100% arc of
admission, was feasible to a wheel diameter of 5 inches with a 5/8 inch
blade height, Because of the necessity of high efficiency in this type of
plant, no partial admission designs were deemed suitable. Thus the operating pressure level for the minimum output plant considered is based on
reasonable volume flow requirements for such a turbineo
3.4 Methods of Effiaiency Estimation
Efficienrcies were estimated for the compressors and turbines primarily on. the basis of correcting the handbook values as quoted for given
flow rates with air at nominal pressures, according to the Reynold's number
and Mach number effect. This takes account of both pressure and working
fluid variation from the air machines, For the relatively large machines
the data was abstracted from reference 6 for axial, centrifugal, and positive displacemnent Lysholm type compressors. This data was plotted as shown
in Figure!12 and extrapolated. into the low ranges according to data available from private sourcesO It is assumed that the efficiency of air compressors, with the fixed pressure ratio of 3 and drawing suction from atmospheric air follows the curve shown. While there are no doubt examples
of numerous machines which vary substantially from these values, it is
believed that the curve is typical and certainly illustrates the correct
trend. A division between the ranges of axial, centrifugal, and positive
displacement machines was made. This is more or less arbitrary but follows
the information of reference 6. It is assumed that the actual efficiencies
obtainable with axial and centrifugal machines of a given size is a function
of the Reynold's number and the Mach number but that these parameters have
no effect on the efficiency of the positive displacement machine. It is
believed that the assumptions are well substantiated by experimental results.
82

N) 0) 1 0) iOD (D ) * ( CO b (D - N) L a) to.85.84
09
t~~~~~~~~~~~~~~~~~~~~~~~~~~~i.81~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.81.7.79.7
102 10 1
VO LUMETRI C FLOW RATE -- CFM

3Al.4,l Axial Flow Compressors
To correct the efficiencies from the values applying to air
at standard temperature and pressure suction, the Reynold's number and
Mach number for the standard air case as well as the actual case under
consideration must be computed and compared. To accomplish this, certain assumptions with respect to the compressor design must be made.
It is assumed that symmetrical staging will be used as a typical although
not necessarily optimum solution, with a pressure ratio per stage of
1082 for air. The vector diagram is illustrated in Figure 13. Using
typical blading angles, the axial velocity becomes 200 ft/sec, which is
again a reasonably typical value. It is assumed that the hub/tip diameter ratio is 0.75 and that the ratio of blade height to blade spacing
measured perpendicular to the flow stream is 0.500 of the blade height.
Then the hydraulic diameter of the blading flow path becomes 0o667 x blade
height. (On the basis that the guidance of flow need not be as close
in the turbine as in the compressor, a blade height to passage width
ratio of 0.48 was assumed for the turbines This is believed to be in
the direction of optimization since the frictional loss becomes less
with the reduced blading surface area )
From these relations the compressor wheel dimensions were
computed and are tabulated for the various plants in Tables V thro,ugh
IXo The Reynold's numbers for each condition (all dimensions and computations refer to the first stage for both compressor and turbine),
based on relative blading velocity and passage hydraulic diameter perpendicular to the flow, were computed~ These also are tabulated, On
the same basis, Reynold's number values for the standard temperature
and pressure air machines were computed and listed.
To estimate the actual efficiency of an axial flow compressor
for given conditions with a given working fluid, the efficiency for a
machine of the same volumetric capacity pumping air at standard temperature and pressure suction conditions is first noted from the curve of
Figure 12. It is then necessary to consider those changes in condition
between the air fluid and that under consideration, and to apply suitable
correction factors,
It is usually considered that the efficiency of an axial flow
compressor will be affected by mechanical losses, leakage losses (both
shaft seals and blade tip leakage), and by fluid dynamic losses associated with the blading. The mechanical losses are usually quite small
compared to the overall power. These are assumed as a constant proportion for the investigation. Leakage losses are mainly a matter of
dimensional control (ioe. a certain portion of the prescribed flow path
area through the blading is available for leakage flow around the tips;
shaft sealing losses are also a function of the clearances) and so, for
84

AIR - 14 STAGES
PRESSURE RATIO PER STAGE =, 082
4 450
~ X ~o
ACu= 196.5 -- 94.3
u=385
HELIUM - 16 STAGES
PRESSURE RATIO PER STAGE = 1.071
u=962.5
FIG 13 VELOCITY VECTOR DIAGRAMS FOR AIR AND HELIUM.
85
85

AIR - 9 STAGES
PRESSURE RATIO PER STAGE = I. 121
=934. 0 cC*,34.2O
u 481 o 107
ACu- 69
HELIUM - 21 STAGES
PRESSURE RATIO PER STAGE = 1.050'-I
u 962. - 538
A Cu —1070
FIG. 13 VELOCITY VECTOR DIAGRAMS FOR AIR AND HELIUM.
b. TURBINE DIAGRAMS
86

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (I 1) (I2) (13) (14) (15) (16) (I
T, F)
Pa G T bT d hbd Dhyd.'U'c REc STP
hl h'T % 1 HP
nh'T GFM tip CFM
BTL A f=11~F Corr. Flnol. H
BT PSIA' *1/sec -I Sq. InS. i.ice nhs*h.x11 60SPCMFn
Y I XIO i nc i Sq, lIn inchexl nghel Xl13i
/500/a z~-9 53, o /78 i. 75- 3'7,~ 2,. U~4 zo,(o 6 70 13:~01.~3~-7 1,oo 1,977 71,-3, too 70 5S9 47.6 z Z,1O jq. 6 579,9 z7,q.66 E3.,10,7 4,0,',,E36 /,~~/
~/oo 9'~~.6 4q Z?,C o9:9'o39 6,16 ~::/p_,z/ (:0,4 6,877,1l4 /,51 i,/q
70 i..... _........,=.............3,q 5;e, 5.6 ( q 59 67 0/6
l.,g,' oa4o 6'00.9O -70,8 /CO /zeoo 7,6e.4:1~1,2 72, S_
900 JQ,3O 5- 7_3 3q 4 S-9, 169, 5- q4 6,16 Z:0, 436.J96 7 0,6 /, 9 7 / 4/,9.:
700 -q )] 9,2 i 70, 6 199, 1 09 e? 7 6............. 3..... 1
63,65 q 00 3 010a)0 9S,~o~~~7 ~ ~ ~ ~ ~ d6 ~'~ 97~z O I~ZI
TABLE 4 -CALCULATIONS FOR GAS TURBINE POWERPLANT
Working Fluid —Ait- Te 900 F Out put = 0(fA /Y
PIR.T= 2.799 P Re3.00, Dh / D,.75, 11W 93 NOTE:h:g

( )II<2) (3~) (4)'(5) (6) (7') (8) (9) (10) (11) ('12)'(13) (14) 015)I 16)I (i)(8 (9
T,(OF) v Rc a 7HP
a pi T AT bd ~~ c AC hbdG D hyd.'U'CRoST c 9
h' ~~~~ ~~~~~Ttip ~/T
hT CFM CFM 1~1 Cr.H
BTLk PSlA *1/#ee -a, rLinhsice
IO =l/hr.ft x 16)* X 16 lrSP CMFina
/s~ 0/~~1 6 6, o J/,o5 ~/,~ 9,3 / 1/.4 2._ e./ 4. ~$;-~z~._/3,-0 F1,~"',, 6- /3 86
41.. 7001 253 lb,?S'Y94.,b 1.25-..T 7 /3,.3 /S94,qZ, 68 /.?q,4_~,:1o o6,~' / 41,D/q.,86.~, l,
/~7/~~,to2~- 5T,- /65- 1,60 34d / 232,3o s:.-5 563 2.3.77,46,.~/7,3Y:o, 09-3, 4 ~~37,:-I,/oo RS2 Il 6,I-~~ ///O z/~' ~.7 7,13 /~-5 7o),,98.3 00o6,869~,,
_ 15. 46 s3 14' /7o 4.80 Io)/,8~6 6;Z47?- /4,6,7.0~,0~{ /046 17,O"-,f0',,G., 70a 1361 t9,0 o./4 i,?J 30,3 /9croP~ 3,z.z202./.s,c_6 ~'oo &Z.o,,qoz,6,,,'
/ lo~O 361/l.3.Zoo~1 t,0 40s93,? Z 4CO 4,z~6.2:.0 ~_'-Z 79 4.o,6-,~761,o0 $7 0,7
~~~~~~~~~~~/oo 6 /339~ 3,z~ Si,.~~C3 4~ 190 l~'gzI
475"-36/ ee6 112s'q90 /12,9?94 3Y3o/Z, 7 -'.4.7,oq$6 /Z?4z,qe 7-,o~,7 ~,
9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-1~/m('6',_~. /9,/ //j,6" /,1(,) 0 34:,2 2-2~,K,6 2. 73.'7c]',0,'qq,00,7~o 4,~.7or 6Y 2.72/-,. 9o o, 4Z$, qo~6 2.64,Od-~6 664 -4uL.1:,o5 ~q 8, Z
~64oo632 479 27 /, 75"- Y- 4 3, 798,-Iq AZ 4.6.;-7oo -,,o,?z,o/73 4,~ &:.....~~- 0~6~ zF'o2 /61 9'/~ 6J8o/6. /i2 0436 169!6,' 4,9 -5-, qo9.329
TABLE ~ CALCULATIONS FOR GAS TURBINE POWERPLANT
Workn Flui, e9O Output = 000/j/O,
PR.T= 2:79 P. Re-3.00, Dh/Dt =.75S,1 =R.93 NT'Ac

( ~) I. (2).(3)' (4) (5)I (6) (7) (8) (9) I 0) ( 11) I (12) (13) i(14) (15) (16) (17) I (18 (19)I
T,(~F) RI HPT
T P ( GT AT h D Gc Ac h D Re S % a /c I -
a pi bd tp b hyd. Lc STP P17
A hT PSIA CFMti CFM c h Cr no
e ~CMT/ti ~/ecSq I.
X1 lO inches inches x I1 S, tin- inches inchesl x i6ll 16 STP
toooo? F,9 1330 ~-~1 //5 Z, 7~.~'.~, /.Z: ~2o ~l>4' 75 /,.8/Z 0o3;3 90. F
700.75:9 q, 76 9 6I,7 /. 4g I_/,; l7,6o /.s7G -- i' 7, /9.oLo.,-0 o9.s: — 9
I ~..........~~~~~~ I........i.............~~i/~~~7o~~~~~[~3 8 ~o793 7, 4::'o 7 59,6. 9, 6 87- /,9, 7 6.9 1_3, / 9,9 /30 o::6 / 73:5 19.,~3,01, /7.:647' /90,F<
/oo /'s33." ", 1/ 7S" z_,34 7, / 9.5 13:.7, 3'4,9 -.6 0,s136,,5S /9, 572,863Z,
qS- i 7.5-, 724 4q 6 601's 5 /,9 74, q 0-77,36~?4 701.7 - 89 4 ~J3
iC~OC? CO I..D... 1 6 ) 9 1774 I/f S87 3 E l/5sS0.87.. &2 33 S' —C 2'''''J''.4 70,5" E6!.97,5
70I/ /Al,!-.1'7,.3 4 S- J16.9.169,. 6,4 6/6;,_6 /7 13,,~' 7, 7,o,126 1 1.47 O/R3'2
I'I 1 o 0Q, 4 I Zo1o /i4 0, 1je6 23, 8361 0 67 ZO 1/3~..,7
_I I o W o 0 1 /..., 4,,, l, 0 870 74 l S0
coi I 4s~ l~11o 1,o 13.07 6,.6 1.5 1? 16.94.,3 i.4 168,0......,zi./3. 19
9.010 /,.................9~
TABLE ~ rl-CALCULATIONS FOr GAS TURBINE POWERPLANT
Working Fluid —/4/., T~ 90 F, Out put= 46000)/-//I
I~ t 9 I I-I. I I I. I _ I I f
P m~O 2.79 P., 1,R3:00, Dh/6 =.56 1?R 19359 NOTE h= 5~
| |700 199 - S1, /7 1q<7 / 175- jz?2g 3 19.94I //9 1232 -5f 043 36j 4 36 | 020. 8561/ IM
53,6- 14~~ 1#99m1r/Y 3 1b 195-0 29,S- I7,45 eVD 13,0 2 7 74'50'56 94 7 1.5 86a I931
I /00 146-S- 7, 3 lD4Y 1&8$- IS7/'6 9,1 R3416 /6, 6, 1 <6] 137 1 07 7 1SO188I/ 1
A? I #, 1270 763 4 1ZZ 1 76! <A i-4.1519 /E t'32. 911 9/ 0D6 892 1 91. 097 ~/
TABLE -CALCULATIONS FOR GAS TURBINE POWERPLANT
WOrkino Fluid-Aie, Te,9O~F,output= -/ 60007//9
PR. T =2.79, P Re=300, Dh/Dt =.75, 17 =.93 NOTE:^h=C

(I) (2) (3)' ~4) (5) ~(6) (7) (8) (9) (lO) (l I)' (12) (13) (14) 05) (16)[ {l?) (18) (19)
PI W GT AT
DTtip
CFM hbdT CFM
% Dhyd- $TP ~G A~c ~c T ~ITH
BTt~41~ PSIA
dl~#c Sq. IrL
IC~I inche. inche. X IC? St~ in. inches inches 4P/hr. ft X 164 X 164 STP Corr. Finol HP
Xll)I.....,........ ~......
I
~:oo~/o~zo.~l;r/586o.62s~,oo /// /3,3 ~ ~.~:s. 6 z. 66 798 -- 796 4z6 359
~,,,, -J _ J.
7co~~/~~6oCz~-~.oo/59 19. o ~.~,o4s~/qq, sq. II,~o~ --,8o~ 4,..30,364
mi.8 4~d.... Za~ 5.,~Z/~',6,fS I/T 2. 78_5s.4 /.zz.~)4 ~3q.~/o9.SIZ,/o,g'/ff,o/8,Sz/ 4.zz,:~-..... ~,..
/coZo2/z,/~' 7~'.g /,/o Z3.8 //, I /-~:~ 2.46 /.6~..~s6 s',~,~24, Z,83~.oo7,$48 4.4o,4oz..... q~3o. 2 29.2 / 75' / 7~ ~~ ~4. 8 296.3:.5-6~~2.39:, o436 ~ ~, g 36, ~.A~74, -7., Sen ~.4~, 41 /
moSlOOO41.oI~/3-lq, 4,GZs~oo/,~> I~, I ~ ~,.oqsd2.oz _~,q3,8o/ --,Go/ 4,91.299'
~
7~oq/0 ~, 16 26,0,E~8- I0,5 21~ ~.~ Lo 9 ~.7z7.o4~618a,~Io, 6, ~o~, ozz,E~$ o4.9~,$o
/o2.8,:/00 4/.0 3,?/~ ~'E2,~3- /5..7' $,?b-,~,0t.~5'..?.5'41,L~I$6 /Z? lq, O,~/9, o~8,837 4,99,320
/~o 410 /~:/c9~9 /,/o ~z?/~~ //~/.Z__~ES /.e~~36 ~,9'IZ~..~,8'~.,0~.6,e~-o ~,o7,~g
0,.o 45" 410 ~$,7,2.02 1, 8o 41,.s' 53,4 ~oz ~50 2.E~7,ps3_6 42.8 4Z~,86/ -- ~61'6"/~t. ~45.....,......,,1. _,.......,..... I ~.,',,.
I............. _ ii........
70064.4~?~24.4',Sz(/~,/ ~.3E~40,6/,~6,,~o7,o~6~,lZ /z4,8/7,oz~,~e~,4o,zo7
~,.......!,,.,.....,
8z.6~ 40o ~q.44.~635,.8,6z~!z9 3794 7/.z. 186 /.4~,,o4s6/6o. /z~,8Z~,o/7,8qs-6,4~-,z!.6.
loo ~4~19.'~/./6~ //Q 34. 62. ~.6 2,5'4 if, Go _z / o.~, ~ 6 8 o 36',~,8~'4, oo6, ~ o E5'5, z..q /....q~E~.44~.5?E~ /7o ~'445'2.5'e;3o ~:~- 3.~{,o~6s,~.6o~,o.n7! -:,eT/ 6.~6,zd!,................,.....,.....,............ i.... I........ ~..,...........
TABLE ~ -CALCULATIONS FOR 6AS TURBINE POWERPLANT
Working Fluid —Air', T~ 90~F, Output:2/000/-/'/~Z~
PR. = 2.79 P. Re=5.00 Dh/Dt =.75 ~R= 93,=.,~.~
T'''' NOTE' Ahc
-~ C EN TR IF U OAL COM PR E,&50R

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ( 1) (12) (13) 1 (1'4) (15) 1(16) (17) (18) (19)
G h D G A ReCSTP 7 H
Tbd T (AC b D hd. I
P,,A#/ CFM,T tipGFM / H
_Ba,#x PSIA fhT CF x c i-./h4 XiI t STPX Corr Flnol X 01
z<-~'~ /0 L 5A~730 8,60,625 6,00 283 /4.60! * 3 - 22r) -7 79 1Jo7 ol03,5Y6 &418.60,625 Kooo Z, 6,-o I + __ I _-s. ___ -193? 0 6 A24jo 625 j 3,1?4/0 1/,37?/#0 30,s-l /3'5 8/? 907 8' 1/?2 376
9 I I I I L..0... /l --
/ J/64,6os,6Ok67,0?. 9",61/ 7/,?? |. * 3,. _,,7 &4 -,784 93 26 t
700c 1 /57 5i ~60j I, 6256 Soo,8|5 3990. I3,9| - _-2790 19/ 7861 0
_I _ 15 0 16_6_18 O C) 7 5. I/0. c Z 16 _i43G 8 lII|;19 L2 228
_ _ /)1c /3.6 5C o? 30?,e 62~5 o 9I9 I7526/ ___C
9Q0o0 1o K~2P0 9 1.t 4 I60 | 6jZ | 1. /5 6 * 4 36 |7 796 - 796 |3./f6
jj~e'92i/?6 1801626815, 00_l_-/? I 0 - Roz /86 /
3 _4O927 77? 0o92/ f7 16$ 2 | / 3 / 15 5 30.6 1/5 157 4|3 6 t // Z u8/2 |o8 83/ 93 j
___ 40 j2. 6 41 <4 i' 6 1.690 1/' 3 1 9,1O 0/ 12? -? /148 Af_ 0t;, s7 6 84 1,45 i?/ 3I
9L'293. S6 194i 4? -1,41 5 9 / 3/1 / 271 36. 851 z7.2
TABLE 2:-CALCULATIONS FOR GAS TURBINE POWERPLANT
Working Fluid —Air, T 900 F, Output = 600/-P
PR. =2.79, P R-=3.00, Dh/Dt =.75, T*.93 NOTE: Ah' 4f
* CENTRIFUGAL COVIPREFSOR

a given physical size of machine they are approximately a constant
proportion of the through flowo Such an assumption is utilized for
the study,
The fluid dynamic losses through the blading are a function
of the blading geometry as well as Mach number and Reynold's number,
The influe.nce of the geometry is evident through such factors as aspect
ratio loss, friction loss*, and blading form, involving the concepts of
angle of attack, lift, and drag. The blading form is intimately concerned with the required pressure ratio per stageo
For the purposes of this investigation it is assumed that the
blade width to height ratio, the pressure ratio per stage, and the blade
forms are always optimized. In this connection a pressure ratio per
stage of 1.082 is assumed, Such a value is believed to be reasonably
typical of high efficiency designs. Therefore the only factors which
cause a variation in efficiency from the standard air machine are Reynold's number and Mach number. If closed-cycle air gas turbine plants
are considered, there is no substantial variation of sonic velocity at
compressor inlet from that obtained in the conventional open-cycle,
since the sonic velocity is not a function of pressure. If the same
velocity triangles are assumed, there is no Mach number effect, It will
be noted that the maximum Mach number, based on relative velocity, is
about.308. If closed cycle helium plants are considered, and the same
velocity magnitudes are used, the Mach number at compressor inlet will
be reduced. from the air case by a factor of about 2.9 and compressibility
effects will be negligible if the air velocities are used. Thus, it
appears that a high efficiency helium compressor can be safely designed
for considerably greater gas velocities than an air compressor. The
limit would then be one of wheel stresses. The ratio of the number of
helium stages required to obtain a given pressure ratio to the number
of air stages, if identical fluid velocities are assumed, is about 7.
(See Appendix Section 8.5. ) However, if the Mach number were held constant between the machines, the number of stages would be roughly the
same(except for variation in k). See Appendix, Section 8.3 for derivation. The air compressor wheel speed assumed for the study is about
385 fps (see the velocity diagram of Figure 13). In view of the low
temperature of the fluid in the compressor, it seems reasonable to
assume a wheel speed for helium of about 2-1/2 times the value for air
or 962 fpso From this viewpoint, the number of stages for the helium
compressor for a given pressure ratio does not greatly exceed that for
air and the diameter for a given volumetric flow is considerably less.
* Controlled by blade width. There is an optimum between increasing blade
width to reduce sharpness of turning and decreasing it to reduce friction
losso
92

REYNOLD NUMBER FOR AIR COMPRESSORS AT STANDAIRD TEMP. Si PRES.
~~~P C ~ ~~o;.I a 4 - 00 4 tr M -4 W W w 4 h3 m a O to 0
O~~~~~~~~~~~~~~AA
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4H H
~O r I -I r~? 1 rrr rrrnT II-inI rrl ~n II lr-1 ~~ I-I I!C1117 ~1 1 T1I_71I~-IT7 __1_LLLLLU I I I I I-II I 1 I'''''-''''-'~-4 i
co
<
0
1,0~~~~~~~~a
rl ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~I_ H
a~~~~~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(O~~~~~~~~~~~~ —
I)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~K
lo ~ ~~~~~~~~~ L
C)~~~~~~~~~~~~1
\O~~~~~~~~~~~~~~~~~~~~ I
~~~~~~~~~~1 ~ ~ ~ ~ _ -I
Crl~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ll
~~~~~~~JI~~~~ ~~~ ~~~=

p901 dH —- 3Nlt n Ol0
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0~,C,.I~~~~~......~~a1Eli~~~ 111!1I f I 111 0I i11 ilil Iof I I 1| III I 11 1 SL.l -Il
I9 II
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J~~~~o)~~~ 00o N CO@~~~~~~ 0e~~~~ w~ 00 N C~r 10 ~, NL

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6
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4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' al' 4 —
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BilHll _AII40I I I 313IV i
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s z~~~~~~~~~~~~~~~~~~~~~~
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-95- S3H3NI —dll JO t~~~~~~~~~~~~~~~~313W~11il

co
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V
5
I
B~~~~~~~
I I~~0 0TI0
9
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-T- Iood06
II
I B-~~~~~~~~~~~~~~~~~~~
I II III I II I T1
9~~~~~~~~~~~~~~~~
r ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~1rI
8
7
5
4
3
2
I I
1LkkIHI[MT4L~bI~+If~fl+HIIbI4IIIH i~IfI~iIf~~IiilIf~ltI~III 0
rC) CUJ - o) I', -n Q n
-96- S3H3NI —dll JO -4343-1IO

This i': crease of velocl.ty results in. a very substantial reduction in
tu.rbomachinery size for a given application. However, in substituting
a smaller machine there is a consequent efficiency reduction (Figure 19).
Thus the efficiency "?ceiling" is not approached as closely for helium
as for ai.r, However, it seems a reasonable assumption that the large
saving in cost and size should more than overbalance the loss in efficiencyo The diameters are tabulated in Tables X through XIV and plotted
in Figure 1.6 The number of compressor and turbine stages (turbine assumptions are consid.e:red later) for various pressure ratios are tabulated
in. Tabl e Gio
Fo-~ cabon dioxi.de, the Mach number effects (as compared with
air) are in the opposite direction from helium. If the air velocity
d.i.agram we e assumed for a carbon-dioxide compressor, the Mach number
would be.ncreased over the value with air by a factor of about 1.248.
Thus for acabon0dioxide the velocities should be reduced by this factor
if the efficiencies are to'be compared. For a given volumetric flow
rate and pressure ratio, the diameters and blade heights for the carbondioxide compressor will be somewhat greater than for the air unit. The
ca culations for this fluid are not presently complete and will be reported at a later date.
It is assumed in these estimations, that the Mach numbers must
be limited *to those of prese:nt day conventional practice if the high
efficiencies, reported in the literature, are to be obtainedo It is'believed that the as'sumption of a drop of efficiency with increase of
Mach numb.e:r is well substantiated by present experience, but may well
be a function of the state of the art and not an inherent limitation.
For exampl.e, it is known that a certain degree of success has been obtained with t;ransonic and supersonic compressors, although the operating
characteri.stics and efficiencies for the preliminary attempts have not
been as favorable as was hoped.
To summarize the estimating procedure to this point, the
compressor flowpath designs are assumed to be arranged in such a way
that the Mach numbers, blading desiguns, leakage areas and vector diagrams are the same as those for a'"typical" series of air designs for
which the efficiencies as a function of flow rate are known. The only
remaining variable parameter is the Reynold's number. This has been
computed as explained previously for the "'typical" air designs and is
plotted in Figure 14 as a function of inlet volumetric flow rate (which
of course determines the physical size of the machine under the stated
assumptions). JN'ow, to estimate the efficiency of an axial flow compressor with given flow, temperature, pressure, and fluid, it is
necessary to rough out tShe cesign of9 the machine under the assumptions
97

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (II) (12) (13) (14) (15) (16) (17) (18) (19)
T, (OF IH r
G h D A, h DT DhydM.C Re c aS1 HP T
a pi W T AT bd T A h D C RdSTP 1
hl T IX SFp Comr Fln -
BT PSA# X ia Sq. nftichs inches xi? Sqln- inchls inches I X Xi6 STP C Fn
zoo IXO ~ J4 22~-,'/,~ 339/60 14j /8a zc4sz/99z1 I266 $75o jg/~iI,5 J1441
4k 700 /2 26,4 33 ~2 5?~;7 4?7, 6 52j 3 t, K~ 32$ 18g" Ii 4 9
19 0go /2 96 $ ~92 6.9.L.1 399 4, 4 s /S2 41L j860 o05 1g46s 6,4c7
/0Iw00o Ix 16 4 9 26.6 4.9.3 - z5 Q O ~ /23 i%
41 700 Yj 344 a 3,9Z 4e.61 -C 15,09; 1lae 3. 7 CvQ~ 9 j A,i~94 A00 __6 /2gQ 6.9 4/5 /2 390 3i/l 6 L 5~ 5 /6OO
OD
9000 ~~000 7 730o 4 6 6' 8 L 56 3,0 3 0539 33 65, ___
L 00 67L0 5LZ ~ /36 / $54"360 S -4, 7L 2Y3z z
6-69 4oo Z /9~0 110 242 26 237 /140 7, 7 o / 71.1 4 884 0 2L s
TABLE I-CALCULATIONS FOR GAS TURBINE POWERPLANT
Working Fluid-HeIIluT, T9OOF, Output&O 000 /-P
PR.T= 2.79, P Re3.009 Dh,/Df =75, "WR93 NOTE: Ah'= 336

(1) (2) (3) (4) (5) (6) (7) (8) (9) ( 0) ( 1) (1 2) (13) (14) (15) (6) (17)(8 (9)
T, (OF) R (18)P(19
a pi vv AT bd 0T C AC hbq G Dhyd D Gc RAc STP 1c D
MhT CFM t ST tiH
BT~PSIA 1 CFM H
BTA xC ~o sq. In inches inches s C~ Sr. In. i s h /hr. t X I. X I4 SrP Corr. Final
X10 x 0 linches inchenes'
Isc~f'~ ~ 14, /~~ 127...9 S 3 l.e4'i/ z/ ~0 _ 6 4~2 /...-..
7oo / 7 /g, 3,o z,,9 7/'77,I 16 /04,59?.6//3.J 33,09 7,/'3r 0.37)
6( 9400 41,o7 L. 8 1/Q7,0;,0o /9. 7 I7, 6 33 2,46 /6, 04 6, 72, Z,2,39, 40 d/,
too 4/, 7 /I/ 7) 6,39,4 /// 5'3 4,9, 3,29,c)4 1 &6490,7-o 7, / 00_, _03
__'q 41. 7 2Z /7S-o 7ZO -5%'Z416 //0o 72.8R,q.s9241 7,2 5,L,-2 ),............________ __ __]__________________________
(z~/6& /9)0 1 /6,5 99, o.'49 /~,Z /6.4 79? /, 9o I2 7,//9 / t5. 4,'_
-700 61-P 3.6 M/4z eg96 ZS S 11 /3?2 7 /,6_/ 0q9 71~-~kl.'ISZ~i~St
694 400/ 41,Z/ _24'.92 a4.0 4,/ 0 /97 30) 2009,~ P, -/ 1,2 3a
/0 0. 7oL 9. o 70 140 /4 792,00 4, 0;,4 q, q4,o o-9,0,7 o. 7-7,1/,33
3 j.?6s5- /20!8 7/3 S~3~ /75o,9Z: w,os-96 8 ___ sD,"?7
9"lloc~o i 19 1_Z6.0 16 4,2: Isti263 1,76 - OS160lt Si ~~l. 7o00 19 37?.23 325a2/ 5/?/35 3,70.7 / 71oo //4ji 26'9
js69' qo0 19 ~5-,0390 Z —33.3 _79, 380o,1/6 7, /73 41,0 060,2834,
oo // 20 1o.60 6 s- 66,~s3/8 5 /sZo 5,32 5 4,"j_9 6_4,-O/ 9,,..q5, 46-0 (700 6~r99,3 700 370 45,4 B45'0469,q to12g 960Ir 2 s~d
TABLE "XI-CALCULATIONS FOR GAS TURBINE POWERPLANT
Working Fluid-IH'(, T90F, Out put.2 O, HP
Porkig 2, -He P R=0O, Dh/Dt 9 output NO=A0,000hJ3
PRT 2.799, P Re3.00, Dh / Ot = 75, 17W. 93 NOTE: bhc=

( I) ('~2) (3) II 4) (5) (6 ) (7~) (8):(9) Il 1i.. (I ) (12)i (i3) (14) (15) (16) (17)I1)(9
E~o pi W GT AT hbDT Gc A h DRc?,
a ho ~~~~~~~Tt AC Tpb, Dhyd. jur, Rec C$TP IV Alc.,/!T
aTl T41 PSiA C1/i F1/r CFM ~' X 1(~4 ST*P C~wr. Finellp
~~~~~~~~~~~~~~~~i s x I() inchlm inche Xli
/50/oo /z:34.26 25.-, b Z=/g~ 7.B D8. 60 17. 55.,-' 5'9/.4 6,-96~4 9.0 ~]:01 t Ole,Elq.5,4
t.7~~.) /_~.y' 6',ID 36;,6 ifZ 8,.47 5,15 ~-4. 7 1/06,77.0.:9.:'4.9 to,4 IqO,D7 f -o ]S',~-.~/,?/ 0 l,:o /s.. -/,?o 0.~.25 //.2o 9,00 43,/ q J Olqo 4,Becm/4 /zq,3/9, o Ioz/./,57
22 /00IZ,:5'4. 2._9'6 4.. 6 2.4 370 /75 3 1 8 o'c: f,og. q9,,4 -";- S002,(4!; Z?2,7....."5 93,!5.-q 56 9 6d.E33-.4 60,0 3B: d, I 7 e, 79 oqs4-9 /5,9 4 /,,.,,E6:0 01o 9S'
ZO, 7:~~~...6f33,.15-0-5 Z50?0~~~ ~ ~~~~~ - /7..4 1,,.z3
7~o~ 000 790 474,7,5 786 r /4S1 Is, 7;-. //09 6 7..5.. 9. /0,-F,: f3~ -, O/3,,Z~ 6 ~,?
700 7.7..9 47f214!,G9 7.3.,E 1, 3 85,c~b, /,!.. r7o,~Z C459,8~
~9'q qoo,20.7..3327,15.F4~,46Z,3D'qS-'2617 3 7365 6.7 d],4 /?2.5'6,:./7.ifd,5,c),S' /Z_,~ le/,6G:.G d9:7.~Z.,.................G-~.i9~~~~ 1200 799.6/l l' /Xjo 2[ 9o~B/Ozd 7_ /ll~ 7L0,4 ~'i~~hg'E'i -~'Z'
~~~~1,:0.9,Zo/o...9 3.8/.49,70 7I,o4,s-9 4.7o 4,1 136b.00,oo,9 7, ~
L~~~~~~~~~~~~~~~~~~ I I4
TABLE LY._L!.-CALCULATIONS FOR GAS TURBINE POWERPLANT
Working Fluid —He~urri, Te90*F, Out put = (5)00 0///D
P.T= 2.799 P. Ric:.00, Dh / Dt =.75, 7.9 OE

(I) (2~) ('3') (4) (5) (6)' (7)'(8) (9) (i0)I (1'1) (12) (13) (14) (15) (6
T'F pi hbdGT A h D Gc Ac h,uD Rec Rec aHPT
TAhFr CFM~
BT PSlA 4P/mec as.S6i-ice#h X 16IO 1, SqPCr. Ir
X10 Irlinches inches X I(: 6 I.inchesinhsl/h.fX OXI(4SPCr.FalIH..................~S7,3 0,~,o i 9
_.700 ~ 3 2,5 4~/4, 7 /os- e.06 zo9.90.? 71 ~,.$5,6o79o olb,5o6,~,,o 6 016
9 a,T-q. 5 4Z__ oS'Z7 /~I 5 7..!o,6/. / 7.3.887,5cJ,osq. 46.2, ES,-o 36~-)
I)o -T,43171! /02,,$j'~,91 /4,]s- /141 tl 6, e I, 7 7 /, /8,b%5-9 / z,l:124ae 0,02To
I ~/5" ~37.W3 SE8,/;?28 q, 32 21, I4 1,o 5-q oe. 6q /. 76.0959 9,Tb6.,,~40.o/!,r~/~Z,6
200;A,P9 3:/6 /9. 0 /, 166.z/-/-, /,E_6,s —e,b/S 42, 7 IP j, 798 ~ov,/,~,4
b94 400.R,,954"-?,,2],q6 8,2?$'Z6,d4 [.o9,17?6-',_oq-9'~.0 /o,9,_b_9 0,/o,c I. 6,Z/o-R9o,,q -2.;J-' 4?.9 /25-'c~n?-,o0 /o 6 19 lq7 0,o~. 16, W. e-/,6 ii5- —;oo,q 1 6, 2
906)'/m~~rlt~,3 og.7.43,C) /,'06 5_,j4 4(,8, 4F,.0, L'0.,686,Odt0..7., 8 /0 0 "806 f, 01 7. 43/~,/4
_~ 700_ 1B.2 8', 69 3,/ /,,2d_.q<L' 6,90,53, z /, z:3. a9, o'96Z. 3 _,4,8/ 40,.,8?z,/,
569 / —18-/O l,e 9, 9-',6 /.6d /Z0"Z / 8,Ol6Z.! 08,0459 4.7, 6,Z,~3~o9 BZ/./ /5
_ /0o 184. Z 9.7 7P9 J3,4. 257*9'46.?Zo 3 01;, / 6.~459 24, O 2, /,3gC)g- bob,- /,4,/
45' 18,B.93.0 l'9 Ye73.tb' 7I/V 7 ~"/4,85 1,~ p?-,10459 /6,/1 WE9,/,8G7':,857/255,,
PR., 2, 9, Pe..O DhD =7, 7.93NT
TAL Z-/-ALUTION FORA L CTURBIE P5OWRPL

(I~)(2) (3) (4) "(5) (6)' (7) (8) (9) 0ll.... 0 1 ) (I12) (13) (14) 015) (16)I i)(l)(9..
1(0 G h D G ~~~~~~~~~~~~~Rec
a pi Gv T AT hd T c Ac hb'hy Roe~ 1c a?/C, "P
a~ he tprT
TPSIA *scCF or
BT*x 6aSqlt nhs nhe e/ n ice ice #/hrft C t x16.T
15060 ~ ~ ~ ~ b" X0 /9~46 —86625-6.n 1
(f~ ~~~~ ~Dii 700 Dh.R68378 2-50/76Z5 2
(519 400 AR/ / 43 ~ S, 6 6?y S70o /1,61:~o ~ST9 Y9c
0~~~~~ F HP36,,-3,76_ 8, — 2 67&6.89896-0
B,T~ CF64 T I.-6,,3/ 692 6
12cd~~~~ I(0 8~.6 Inihe inie XI8 I.ieel.b$ 6 2r ie
~__19 4vo/29/., 9~ S,6.6z5 6<00 / 9 o ~ ~ ~3,04s9 6. 6.-, 79 74 /,6 I..... 4 75' 1,91 //.5- 6,90 3,]/ 9.70 48.046,9 4S,415'9. lqS-.?9 -r/ 87 /,f 7,S
}2o9I00 3,7- 9/,~.-.80 65,7 6p3' 1.6 3, IP'.l~,'2 -,9Zq9,0
094~~~e0 2op~19~ 6P5~ 66 /,9: 4>51 ~....5,M~,1_~ 6~6-, 034Z~9,p pd1
/T0BLE -,CALCU.LATqIONS FO/R GAS TUR2.BIN,C POW,2 ERPLANT0.,,PO2,4,
~ro...R. T= 2.79 e-0 h/.75.. 9I 0
9oo~/oTo8.48/.4.OMRE S: o.. Ro. o

01 S01 dH-3NIS8t lN t01
01
0I
m
096
OO
01
OZfoe I
IM IQ~~ 00
0160lrtNlr00Xs Lw)lllC'l~~~~~~ A 1 I Il 111110111|1~ a 61- _li1 i T1t111 t 1 1111 11 1II
Mfl2 m MA11 1 11 | I II I II I I II I II I I II I II I I II j I1 - 1 11 1 l itt0 1 Li _ = T TF TFF _ T F II f I I X II I + I I I+ I I 141 1 1 11 1 11 1 T I It I1
LLALLM1I4III 1
lilI llllliilslrllirmirIrIIIr tr IIrrll~l = lT~ ll rT11111 rr111ll11 t1-
II I "lilmW i i 1:$IIXTIIIIIIIII mlnX rFTlII tt11111111111lll1111111111111111111F
_ llllllLL111ILLMI#Fll IIII1111111111111113 111111-11 m w r_ s i>EE E ZX0111 ~liiilxIll|4|6
1t Ililililill~rililililiilililltull4Tril4LIIIIIIIIILIIIIIILIII~lililililr~LIITIIIIIIIIIIIIIIIIII [1L I I I 1111111111111111111111111111111111111111111111111 1 1 f I [ 1~~if
1All JJTLllFllllllllllT" I IIlllllllilllllll lllll t Irllr 1111|1111111111111111111111111
AA I III I I I I I~lIIT114tiiiilllllliiiil1l iiiilllFI IIIItL 1!1111111111111111111111111111111
itl- IIIIIItIlmlmllll1 I lIL11 111111111111111 }-Illl L L X T - 61 1 1111111-l114III _
I lAlllllltliiiiiiiiii 11111111Iiil_ Ill LIH~illlllllllll IIIII1 lllliiiiiiitllllllllllllllllIIIIIII111
111Ilullilrrr 11111 111i11|Xl 1lllll I I x 1llllllll 11Ti ilN
1 —-- --- II~ iiiiiiiiiitIllll IIIW Iiil lll l4ll l lllllllILIk TI111111111111111111111111111 ---

N ~4 ~~~~~~ CMI 00 % 0( M11~Ci i~ 00 (Dco
N (4 co 0~*0(
140
130
120
I10
1~oo
I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~II
9O'100
H
0
90
Cl)
w
I
50
80
30
70
w60I
H
LUJ
c~50
40
30
20
I0
10 104 TURBINE —-HP 1O5 I0P
loS 104 TURBIME —HP~~~~~~~~~~~~~~~~~~~~~I -O A 1.05 l -

140C - ei1t lX-, 4i[A
H 4C
140 Ace - ili11
10
i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i
90
5 -.-I —
0 i
40 —10
i.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IllI
9&J0 I I I0 1 1' 4
Hn- -------------- ~ ---;;
450
30
Alo3 104 TURBINE-HP 105 1&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_' —720 +i+ +i17 444j~'
LL~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.
10 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1031,04 TURBNE —HNP,05,dw

TABIE XV
REQUIRED NUMVER OF COMPRESSOR AND TURBINE STAGES
FOR INCREASED PRESSURE RATIOS
(Pressure Ratio/Stage per Figure 13)
Plant
Fluid Component Pressure Ratio No. Stages
Air Compressor 2 9
3 14
4 18
6 23
8 26
1.0 29
Air Turbine 2 6
3 9
4 12
6 16
8 18
10 20
Helium Compressor 2 10
3 16
4 20
6 26
8 30
10 33
Helium Turbine 2 13
3 21
4 29
6 37
8 43
10 47

pre~viously described., compare its blading Reynold's number with that
of the "typical" air machine, and make the proper efficiency adjustment.*
For the closed-cycle air machines, this involves first the calculation of the inlet volumetric flow rate, blading passage dimensions,
and Reynold's number~. Then comparison is made with the Reynold's number
for the same inl'et volumetric flow rate (and hence same size machine)
which is plotted. for the "typical" air machines in Figure 14. For the
helium or carbondlioxidde units an additional step is necessary in that
the calculated inlet volumetric flow must be corrected for the change
in velocit~y diagram (due to the requirement of constant Mach number)
to determine an adjusted flow for comparison with the same size "typical"
air desigir, The results of these calculations are tabulated in Tables
V to XIV and sample calculations for typical cases are shown in the
Appendix, Section 8.40
It is generally true in fluid flow work that the loss coefficient for any given condition decreases with increasing Reynold's number. A very common case in point is pipe flow. This same trend applies to turbomachinery flow passages; thus blading loss coefficients,
which are a function of Reynold's number, are applied to estimate the
e:fficiency of a given machine. Blade loss coefficient data, showing
the loss as a function of Reynold's number and turning angle are plotted
in Figure 17, This is based on test work conducted by one of the wellknown manufacturers of this type of equipment (results not published in
the open literature) and is believed to'be fairly typical. Certainly
the trend illustrated. is correct. Somewhat similar results are no doubt
available through NA.CA work in this fiel.d, and also through recently
reported work at MIT (:reference 7).
The compressor d.esigns considered for the study utilize symmetrical blading. Thus the loss coefficient is to be applied both to
stator and rotor, and affects each equally. For the purposes of this
study, it is simply necessary to note the loss coefficient for the
"typical"s machine at the given flow rate, and that of the closed cycle
machine, and. then adjust the "typical"4 efficiency accordingly. The
resulting efficiencies and the major steps in the calculation are
shown in Tables V -to XIV.
* The machine efficiency is assumed to vary in proportion with the blading
efficiency because the rotor and stator kinetic heads (to which the loss
coefficient is applied) are equal and are always about 1/2 the enthalpy drop
per stage:for the assumed velocity diagrams. Thus the loss coefficient
is effectively applied to 1/2 the stage enthalpy drop for both rotor and
stator, or to the whole enthalpy drop for each stage, as is necessary if
the assumed type of variation is to exist,
107

BLADE LOSS COEFFICIENT -0O -
Il 1 I I I I I I I II 1h I HIM I HillI 11H MA 1I 11I 111111!111 H S XI VA HIM IIII
t
I ~tttttttt~ Jill I I HtL Hill I IIII I' I I I i I A I HIM 111 I T (IZiTG
0l I i i i i I i I I I m 1 I I n i I I Ii I I ITI II I - - I I I I I I i 1 1
ou C A~t A ME S~g g I Y II 9 I i T
o'IiLS~mtEX~tZI]:11 lulalil!1l~mmHl
z t II1 1 IIII II! 41 IIII III III I II II I 1 1 1 I II 1 11 I 1 n 1 11|II! III TIIII|, i -
C11 1!II11 1II,,1! 11III1TIII I.1IIIrr r I 1 1 I 1.!I irrig
K~~~~~~~~~~~~~~~~_ U
w~~~~~~~~~~~~~~~~~~~~~~~~~~fl

3.4.2 Centrifugal and Positive Displacement Compressors
As previously explained, and illustrated in Figure 12, it is
assumed that positive displacement or centrifugal compressors should
replace the axial flow machines below a flow rate of about 2,000 CFM.
It seems a reasonable assumption that size of machine alone influences
the efficiency in the case of the positive displacement device, particularly if rotary units are considered. Typical efficiencies for Lysholm type rotary positive displacement blowers for standard temperature,
pressure air are to be found in reference 6. It is felt that this type
of machine, due to its broad operating range, relatively high efficiency,
and reasonable size and weight has a good possibility for application
in fairly small gas turbine plants. In fact, it has been previously
used successfully in such an application by the Elliot Company (reference
8). Hence it is on this type of machine that the efficiencies are based.
It is realized that there are other possibilities and that these would
give somewhat differing efficiencies. However, the results are more or
less typical.
The lower end of the curve of Figure 12 is determined by the
positive displacement machine efficiencies and the upper end by the
axial flow. While the axial flow efficiencies are affected by Mach
number and Reynold's number considerations, the positive displacement
efficiencies are not. Between the axial flow and the lower positive
displacement ranges, largely overlapping the positive displacement
range, is the area of application of the centrifugal compressors. These
are affected by Mach number and Reynold's number in the same way as the
axial flow machines. Since the range of application is approximately
the same as that of the positive displacement machine, and since adequate data relating these effects are not available to the authors, it
has been assumed that below about 2,000 CFM there is no Mach or Reynold's number effect. Therefore, to determine the efficiency of a
closed cycle compressor, with an inlet CFM below this value the efficiency corresponding to the applicable CFM is simply noted from the
curve of "typical" machine efficiencies of Figure 12.
564.3 Turbines
As previously stated, it is assumed that axial flow, full
admission, impulse turbines are suitable over the entire range of the
study. Although centripedal, centrifugal, or positive displacement
expanders might be selected for given applications, it is believed that
the assumed axial flow machine will give at least comparable efficiency.
Thus, it is chosen as the basis for the efficiency estimation.
For the larger flow rates, where both turbine and compressor
are of the axial flow type, it is assumed that turbine efficiency and
109

compre-ssor. efficiency are equal. It is realized sthat in general, for
any given set of conditions, it is possible to design a turbine of higher efficiency than the corresponding compressor because of the favorable
diecstion of the boun=dary layer pressure gradient. However, due to the
more difficult mechaani.al conditions applying to the turbine (i.e. higher temperature), it is usually desirable to increase the work per stage,
and thus the Mach numbers in the turbine, over those existing in the
compressor. Thus the inherently obtainable efficiency advantage of the
tu:rine tends to be offset to some extent in actual practice. To reduce somewhat the length of the required calculations, it was decided to
assume for the purposes of this study, that these opposing factors balanced for the axia.l'lo-w1 r jazge faaid rhat hI.e turbine and compressor efficiencis are the sasme.
]in the case of air, it is usually assumed that the limitation
of the allowa ble work per stage is one of thermalcentrifugal wheel
stresses. From this viewpoint a reasonably conservative value, for the
pitch-line velocity, consistent with all but perhaps aircraft practice,
is 1000 ft/sec. - However,, since the turbine and compressor generally
run at the same RPMN a somewhat lower value may be desirable, both to
avoid excessive diameters a:nd to allow higher efficiencieso A typical
veloci-ty diagram, whi-ch. is considered applicable throughout the range
of the st:udy, is showr iLn Figure 13. The rela-tive Mach number with air
is only ~394 even for the case of 900 F inlet. Therefore no possibility of a t;ranso.nic or supersonic, turbine exists and usual data is
substat+tially applicable.
For this reason, in the general case, turbine and compressor
rotating speeds will be equal. This assumption is made in the determinatlon of the turbin.e w-heel diameters which are plotted against turbine output for variouss fluid and operating conditions in Figure 15.
To avoid excess.ive diameters'the turbine wheel dimensions are based on
the assumption of a peripheral velocity 1.25 times (in the case of air)
that for the (-ompressorTs. n 2some cases, it may be desirable to reduce
the d.iamnetel. and number of stages by allowing an RPM greater than that
of the compressor. Numbers of stages, for different pressure ratios
based on the initial. assumptionr, are tabulated in Table XV.
Ia many installations, there is the likelihood that the compressor may be divided into a two shaft, high and low pressure machine.
* The use of a 1.000 ft/sec turbine with a 385 ft/sec compressor would of course
lead to a corsiderable mismatching of diameters if direct coupling is assumed.
Considering the very large power'transmitted between compressor and turbine
(several times the output power) any interposed speed reduction mechanism
seems a serious hardicap~
110

In this case, the shaft speed for the higher pressure unit will probably
exceed that for the low pressure, since volume flow is less, and a higher speed high pressure turbine could be conveniently coupled to the high
pressure compressor. For this type of design, the low pressure portion
of the turbine would be coupled directly to the low pressure compressor.
Thus it is not necessary in all cases that the rotating speed (RPM) of
the high pressure turbine match the low pressure portion of the compressor.
For helium, there has been no increase from the compressor
design in the assumed turbine peripheral velocities (as there was for
air) since the tip speed limitation due to stress is applicable even
though the Mach numbers are quite low (Figure 13). The axial turbine
velocity was reduced from 500 ft/sec to 400 ft/sec to allow more reasonable blade heights, since in most cases the first stage turbine volume flow is less than the first stage compressor flowo For fluids with
a sonic velocity less than air, as carbon-dioxide, it is felt that a
reduction in peripheral velocity is necessary to maintain the assumed
efficiency (i.e. maintain Mach numbers equal to the air machines) considering the present state of the art, The assumption of equal turbine
and compressor efficiencies in the axial flow range is made for helium
as well as for air.
An arbitrary ceiling of turbine and compressor efficiency of
0.90 is assumed as the flow rates become increasingly largeo This is
based on the consideration that it is impractical to build a single
machine above a certain physical size and that compromises with optimum velocities, or even the dividing of the flowpath into two parallel
machines, becomes advisable. It is for this reason that there is the
leveling-off of the efficiency curves shown in Figures 18 and 19 where
turbine efficiency is plotted against turbine horsepower output for
various pressure and temperature levelso The logarithmic nature of
the plot distorts the curve from the intuitive expectation especially
at the high flow end. This type of plot is necessitated, however, by
the wide range of outputs considered.
As previously mentioned, it is arbitrarily assumed that full
admission axial flow turbines are suitable down to a minimum size of 5
inches tip diameter and 5/8 inch blade height. The power levels corresprding to this size, at the different pressure and temperature levels
investigated, is used as the lower cut-off point for the assumed velocity diagram (Figure 13 )o For power outputs below these points, it
is assumed that the peripheral speed is reduced, increasing the required number of stages. Efficiencies for each of these designs is
estimated on the basis of the blade loss coefficient data previously
discussed and plotted in Figures 18 and 19 (these calculations determine the lower portion of these curves), Leakage loss estimation was
111

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based on the assumption of a blade tip clearance of 0.010 inches, which
seems reasonable for a 5 inch wheel~ Mechanical efficiency of 0.97 was
assumed. Sample calculations are shown in the Appendix (Section 8.4),
3.5 Results and Tabulations
The final turbine and compressor efficiencies are tabulated in
Tables V through XIV for air and helium plants (carbon-dioxide results will be
reported at a later date) ranging in output from 60,000 to 600 horsepower, from
45 to 1000 psia in compressor discharge pressure, and from 1500 to 900 in turn
bine inlet temperature~ In all cases, a compressor pressure ratio of 3.0 is
assumed. As previously mentioned, this is fairly near to the optimum for the
type of cycle studied, for all. the cases. The remainder of the cycle assumptions
were given previously in Section 3.1 and include notably a regenerator effectiveness of 0.93 and a ratio of compressor pressure ratio to turbine expansion
ratio of 1.07. These latter assumptions appear generally on the optimistic side.
However, they appear feasible for an economically optimum closed-cycle plant.
In this type plant the heat transfer coefficients are considerably improved
over those common to a conventional open cycle installation. For plants varying in the different parameters and arrangement from those assumed for these
studies, it is possible to estimate the attainable efficiency on the basis of
the curves of Figures 6 through 9. These show the change in efficiency due to
a change in any one of the operating parameters with all others constant, as
explained in Section 1.
Considering the listed turbine and compressor efficiencies, together with the other cycle assumptions, it is possible to compute the overall
cycle efficiency. This has been done for all cases, using the sources for gas
data given in Section 3.2. The resulting plant thermal efficiency values are
tabulated in Tables V through XIV and plotted in Figures 20 and 21. These
efficiencies do not include reduction gear or generator losses, or any shielding or transmission heat losses which may be associated with a given nuclear
reactor plant. A 3% radiation loss from the gas tur'bine ducting was assumed.
3.5.1 Discussion of Results
There are several interesting points which may be mentioned
in connection with these tabulated and plotted resultso As might be
anticipated, the attainable plant efficiency drops considerably with.
power output, for any given temperature limit and for any pressure
level. This, of course, is the result of decreasing turbo-machinery
efficiency with decreasing flow rate. Also, except at very high outputs, where the arbitrary physical machine size cut-off is imposed,
the efficiency is less for higher operating pressure (not, in general,
pressure ratio)o This results from two opposing trends As pressure
level is increased, density increases directly in proportion, whereas
hydraulic diameter (for a given mass flow under given temperature and
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velocity conditions) decreases only as the square root of the pressure.
Since viscosity does not change substantially with pressure, (not at all
for a perfect gas), the Reynold's number increases with pressure. However, the physical size of the machine decreases. The effect of this
change on the component efficiency as abstracted from the data of
reference 6 and plotted in Figure 12 is more pronounced than the effect
of the increasing Reynold's number (see Tables V through XIV), Therefore, the component efficiency decreases. In practice of course, the
use of high pressure will result, up to a point, in the reduction of
equipment cost and weight. This factor will, in many cases, overcome
in an economic analysis the corresponding efficiency loss. Stated
another way, for a given capital outlay, it may be possible to achieve
higher efficiency at higher pressure because a more highly effective
regenerator, more adequate ducting, and a more nearly optimum (in
number of stages) turbomachine design can be obtained. The balance of
these various factors is of extreme importance and will be the subject
of additional analytical effort.
There is, of course, a large decrease of efficiency with
source temperature level. This is of extreme importance in many cases.
A further disadvantage of low source temperature is that the flow rate
and hence machinery size (see Tables V to XIV and Figures 15 and 16)
becomes excessive. This factor may be as important in an economic balance for a given application as the reduced efficiency, since it results
in a greatly increased machinery capital cost. Additional investigation
of these factors will be conducted.
It will be noted (Figure 21) that the cycle efficiencies
shown for helium under given power, temperature, and pressure conditions
are considerably less than for air under the same conditions. Partially,
this is the result of an inherently lower monatomic gas efficiency (Figure 6a for example) with the same component efficiencies. It is also
the result of the fact that the pressure ratio assumed for this study
gives theoretical efficiencies further reduced from the optimum for helium than for air (monatomic gas efficiency is considerably more sensitive to pressure ratio than diatomic which is a real disadvantage of
the monatomic gases). An additional factor is the use of higher velocities (almost equal Mach numbers) for helium than for air. This results in smaller machinery than would otherwise be the case and hence
reduced efficiency (Figure 12), However, it appears likely that the
additional efficiency obtainable from a reduced velocity design could
not balance economically the increased machinery cost. These factors
will be further evaluated in the continuation of these studies.
A very high regenerator effectiveness has been assumed for
these studies. Even though this may be feasible, it may not be desirable where there is a requirement for low temperature heat, as
125

perhaps for area heating, low pressure steam, etc. In these cases, a
low regenerator effectiveness is advantageous from the viewpoint of
capital cost reduction, without prejudice to overall thermal efficienoy,
since, as with steam extractions in a steam plant, extraction of low
level heat at this point is thermodynamically more advantageous than
the supplying of the heat requirement directly from the high levesl heat
source.
126

4 0 FUTURE WORK
The work to this point has furnished a basis for the estimation of
the attainable cycle efficiencies and the general size of the turbomachinery
for gas turbine cycles operating with either air or helium over a wide range
of power outputs, pressures, and temperatures. However, this basic work suggests the desirability of various avenues of extended effort which would help
to complete the overall picture of the gas turbine plant as applied to nuclear reactor power-plants. Among those additional desirable points of investigation which will be pursued are the following:
1) An extension of the basic study to include economic optimization
of typical nuclear plants. This would then include the effects of
heat exchanger effectiveness, operating pressure level, working
fluid, temperature, etc. vs. capital and fuel costs.
2) Extension of the work to include carbon-dioxide to give a
broader range of molecular weights and the corresponding basic
fluid quantities. Other gases of particular interest from the
viewpoint of nuclear or other special desirability may be included.
3) Study of the effects of radiation on' the various gases and the
degree of machinery contamination involved in their use as direct
reactor coolants. This phase of the study can be broadened to include an estimation of the mechanical and developmental difficulties which may be expected with the various fluids, for cases
where they arejand also where they are notjused as direct reactor
coolants.
4) Problems of control of an integrated,reactor-gas turbine set.
This will involve feedback to the reactor through such parameters
as the reactor temperature coefficient.
5) Preliminary study of the possibility and desirability of the
design and erection of a small-scale gas turbine plant, capable
of operation with a minimum of alteration with various fluids
under various operating conditions~ Eventually, such a plant
could be a portion of a reactor mock-up, and would serve to pinpoint the problems likely to be encountered in a full scale
design.
127

5.0 CONCLUSIONS
A broad investigation of the gas turbine cycle as it applies to
nuclear powerplants has been conducted~ On the assumption that efficiency
is likely to be of more importance than size and weight for this type of
device, the study has emphasized the regenerative cycle with highly effective
heat exchanger components and relatively low pressure ratios. A "basic cycle" was assumed and optimized with respect to pressure ratio for both
diatomic and monatomic perfect gases. Variations of each of the significant
parameters including cycle arrangement and operation were assumed singly,
and the effects on the plant efficiency computed. Thus a basis is provided
for the estimation of any gas turbine cycle efficiency if the component efficiencies and arrangement are known. An interesting result of the study is
the fact that the perfect gas efficiencies do not depend on molecular weight,
but only on pressure ratio and ratio of specific heats. As it turns out,
the attainable cycle efficiency with given component efficiencies is somewhat greater for diatomic than for monatomic gases. However, if a cost balance is included, the balance may in some cases favor the monatomic gas on
the basis of higher component efficiencies for a given capital outlay.
A further detailed study for air and helium plants, utilizing the
"basic cycle" over a wide range of power output, pressure, and temperature
is included. This has resulted in the tabulation of overall cycle efficiency,
turbomachine component efficiencies, turbomachine sizes and types. The
study assumed constant heat exchanger effectiveness at a rather high level,
with the variations due solely to the change in attainable turbomachinery
efficiency with power level, pressure, and temperature. As expected, this
has shown the very serious disadvantage of low inlet temperature, both with
respect to efficiency and machinery size and cost. Under the assumptions of
the study, it has been shown that increasing pressure level results in
reduced component size, but, in general, also in somewhat reduced turbomachine efficiency due to the lower volumetric flow rate. Also, the overall
efficiency for a helium plant, with optimized turbomachinery, but fixed heat
exchanger effectivenesses, is considerably less than that of an air plant
with the same heat exchanger values and optimized turbomachinery. However,
it is a question of optimization between efficiency and capital cost -for
the heat exchangers as well as the turbomachinery. Such an optimization
has been beyond the scope of the investigation to dateo A listing of desirable future endeavors along the lines of this work is included.
128

6.O NOMENCLATURE
T - temperature (noted as F or R)
p - pressure (psia)
PR. - pressure ratio
TR - temperature ratio
A area (sq, in.)
hbd - blade height (in,)
D diameter (in,)
W - mass flow or work (lb/sec or ft-lb)
G - volume flow (cu. ft/min)
Re - Reynold's number
R - gas constant (53o3 for air)
Q - heat input from prime heat source (BTU)
QR - heat input from reheater (BTU)
J 778 ft-lb/BTU
Cp - specific heat at constant pressure
Cv - specific heat at constant volume
k - ratio of specific heats (Cp/Cv)
- viscosity (lb/hr. ft)
h enthalpy (BTU/lb)
- efficiency
HP - horsepower
w - relative velocity (ft/sec)
Cu - absolute velocity (ft/sec)
u - wheel velocity (ft/sec)
v - axial velocity (ft/sec)
129

a - sonic velocity (ft/sec)
I - blade spacing normal to relative velocity (inches)
Subscripts
T turbine
C compressor
th - thermal
hyd - hydraulic
h hub
t tip
R regenerator
p - friction pressure
u - peripheral
Numerical subscripts refer to Figures 1 through 5 of Part II.
Superscripts
Prime refers to the ideal state.
130

700 BIBLIOGRAPHY
1. Keenan and Kaye, Gas Tables, 1948, John Wiley and Sons, New York.
2. McAdams, William Ho, Heat Transmissions, 3rd Edition, 1954, McGraw-Hill,
New York.
3. Kestin, J. and Pilarczyk, Ko, Measurement of the Viscosity of Five Gases
at Elevated Pressure by the Oscillating Disk Method, ASME Paper No. 53A-67o
4o Worthington Research Bulletin P-7637, July, 1949, Compressibility Charts
and Their Application to.... Real Gases, Worthington Corporation,
Harrison, New Jersey.
5. Akin, So W,, The Thermodynamic Properties of Helium, ASME Paper No. 49A-96.
6. Kent's Mechanical Engineers Handbook, 12th Edition, Power Volume,
Section 10, John Wiley and Sons, New York,
7. Nguyen, Van Le, Report on Loss Coefficients in Turbine Blade Passages,
Gas Turbine Laboratory, Massachusetts Institute of Technology,,
Cambridge, Massachusetts.
8. Dolan, W0 Ao Jr., Hafer, A. A,, Gas Turbine Progress Report-Naval Vessels,
Trans. ASME, Volo 75, No. 2, February, 1953.
131

8.0 APPENDIX
8.1 Derivation of Thermal Efficiency Equations
The derivation of the equation of thermal efficiency for the
basic cycle (Figure 1) is based on the following:
WT = Tk T R T1 IPRT- -
WC R T6 k gRC' l ]
T T
"R =T10 9
4 - 9
= PRT.p ___
PRC
PR = PR
k-1 R
Y k CpJ
TR = 1
T6
Q = (Tl - T10) CpJ
T - T= WC
92C J
WT
T1 - T4
CPJ
= output WT - WC
b'th input =from which
-Y 2
-qth = TR 1T [1- (,pPR)-7] - r [ pRY/2 _ 1]
T R 7R + RrT [ 1 - (rlpPR)-]'} + } R I + [pR,-~ 1
132

The derivations for the other cycles are similar. The elimination of the recuperator (Figure 2) can be considered simply by letting
=R = 0 in the previous equation.
For the case of the basic cycle without intercooler (Figure 3)
the work of the compressor becomes
wC = k R T6 [ PRC - 1],
IC k-1 6 k
hence,
TRrlT [ 1 - (rPR)- ] - - [ PRY _ 1]
th C
TR { 1 R + 1RIT [ 1 - (PR) ]} + R- 1 [PRY +C - 1]
Considering a simple cycle of compressor, turbine, heat source
and sink, i.e. without intercooler and recuperator (Figure 4), the thermal
efficiency reduces to:
= TRqT [ 1 - (pPR)-Y] 1 [PRy - 1]
"th T- _C
TR- 1 [ PRY + C - 1]
ICRC
With the basic cycle supplemented by reheat between turbine stages
the thermal efficiency is affected by both the increased work of the turbine and the additional heat input to the system.
Thus, k-1/2k
PRT 1
WT 2 k R T k-/2k
T T k-l PRT
and the heat added by the reheater, QR' equals (T3 - T2) CpJ. The resulting
thermal efficiency is
2rlTTR [ 1 -( PR)y2 2 [ PRYI2
Ilth Yp2 1]
TRt 1-=R + TR]T[ 1-(q PR)- ]} + R [PRy + c]+TR1 /]
133

862 Velocity Vector Diagram Calculations
Velocity vector diagrams of approximate designs for both the turbine and compressor were made considering axial flow symmetrical stage
machines, A pressure ratio per stage within the range of current industrial
practice was used. The diagrams which are shown in Figure 13 for the first
stage only of the turbine and compressor of the air and helium powerplants,
i e. the temperature assumed was for the inlet to the turbine and compressor.
The overall pressure ratio of the compressor is 3~00 and of the
turbine 2,79 due to 7% frictional duct and heat exchanger pressure losses.
The pressure ratio per stage of the compressor is maintained at approximately 1.08. In the case of the helium compressor the peripheral velocity of
the wheel was reduced to keep within a tolerable wheel stress level. Similar
velocity diagrams were considered for both helium and air machines, so that
the helium pressure ratio per stage is reduced to 1.07.
The compressor calculations were based on the following perfect
gas relations.
W = J Cp T6 [ l PRkl/k] (1)
uACu
W u (2)
C g
U
Mu a (5)
k-1
R/J =c( - C =C ( — ))
WT JC T 1 (6)
WT = uACu
g (7)
For the compressor,
-JCpT6 [ 1 (P) ] uk- k Umu acU U2
g -Iug
a2T R k-l
T6 g Jp =I
134

Then,
[- 1 (P t X MU2 (k-l)
or
(PR)stage. = [ 1 + u — (k-) ](8)
2/stage (8)
and,
PR)tot (P2) Tot = [ 1 + Cu (k-) Mu ](9)
u
where Z is the number of stages, and where the subscripts 1 and 2 refer
to the higher and lower pressures respectively.
The derivation for the turbine follows a similar pattern, and gives
k/k-l
PR)stage = / [ 1 Cu (k-l) 2] (10)
As a sample calculation consider the case of the compressor for
air.
Overall P.R. = 3.00
v = 200 fps
k = 1.4
Assume initially:
P.R./stage = 1.08
Cu/u =.368
Overall P.R. = [P.R./stage]Z
where Z is the number of stages
3.00 = (1.o8)
Z = 14.35
135

Since the number of stages must be an integral number it is taken
as 14 and the P.R./stage is then 1.082.
Then using equation 8:
1 - (P.R./stage)k-I/k
U (u) (k.l)
0 286
M 1 - (1.082) = 94
u (.368) (.4)
u = M a = (.394) (1150) = 453 fps
U
Cu = ACu x u = (.568) 453 = 167 fps
u
The calculations of the triangles (assuming symmetrical blading)
through triganometric identities gives C = W = 246 fps, C2 = W1 = 369 fps,
82 = and1 = 2 = 545~0 The blade turning angle (angle between the two relative velocities, W1 and W2) is then equal to 21.7~.
Since it is desired to have a blade turning angle of approximately
30~, the calculations were repeated with a Cu/u =.510. Mach no. then =.335), u = 385 fps, ACu = 196.5 fps, and the blade turning angle = 30.3~.
The compressor velocity diagram in Figure 13a presents the complete results
of this calculation.
The helium compressor velocity vector diagram was determined
through the same procedure. Table XVI summarizes the results.
8.3 Effects of Gas Turbine Plant Size. Sample Calculations
As typical examples, consider sample calculations for a 1500 F,
100 psia, 20,000 HP helium plant with axial flow compressor and also an
air plant of the same size. In addition a 1200 F, 100 psia, 600 HP helium
and also an air plant are shown. The cycle schematic for all cases is
shown in Figure 1.
8.3.1 Helium Plant, 20,000 HP, 1500 F, 1000 psia
8.3.1.1 Compressor
The compressor inlet conditions arep = 1000/3 = 333 psia
136

TABLE XVI. AXIAL COMPRESSOR AND TURBINE VECTOR DIAGRAM TABULATION
Compressor Turbine
Air Helium Air Helium
Pressure Ratio 3.00 3.00 2.79 2.79
Pressure Ratio Stage 1.082 1.0712 1.121 1.0502
No. of Stages 14 16 9 21
Axial Velocity (v) 200 fps 500 fps 400 fps 400 fps
Wheel Velocity (u) 385 fps 962.5 fps 481 fps 962.5 fps
Mu.335.286.240*.164*
Blade Turning Angle 30.3~ 30.30 76.30 76.20
* Based on the 1200 F case which represents the mean of the inlet temperatures used.
137

t = 90 F = 550 R
P = 333 x 144 0.226 lb/ft5.
1545/4 x 550 I
It was estimated from approximate efficiencies that
required flow rate is
w = 41.7 lb/sec.
Then the volumetric flow rate at compressor inlet is
G = w/P = 41.7/.226 = 184.5 ft /sec = 11,100 ft3/min.
Referring to Figure 13 it is noted that the axial inlet velocity is 500 ft/sec compared to 200 ft/sec for a typical
air machine. Therefore, the physical size of the helium machine
is similar to that of an air unit handling 200/500 x CFM =
200/500 x 11,100 = 4440 CFM.
The efficiency of such an air unit is taken from
Figure 12 and is noted to be.822. The blading Reynold's number
for the air unit is taken from Figure 14 (derivation of these
figures is shown in Section 8.3.2) and is 152,000.
The blading Reynold's number for the helium unit is
computed as below. All calculations are for the first stage of
both compressor and turbine. It is assumed that the efficiency
of subsequent stages will be similarly affected.
The absolute viscosity for helium at 90 F is taken
from reference 2 and is.0459 lb/hr. ft. (viscosity is substantially independent of pressure).
The blade height is computed from continuity utilizing the assumption that Dh/Dt =.75. (1)
Then A =.785 (Dt2 - Dh2) (2)
hbd = Dt - Dh (
=..... (3)
2
Substituting (1) in (3) we get
dhba= Dt (4)
138

Substituting (3) and (1) into (2) we get
2 2 2 2
A =.785 (Dt - 75 D.344 Dt (5)
or
t = /.586 (6)
h~bd ~JAI - - 4A (7)
8 x.586 4.68
A G x 144 184.5 x 144
53 532 sq2 in
hbd = 4 155 in. Dt 8 x 1.55 = 12.4 in.
The blading Reynold's number is
Re = V Dhyd P and it is necessary to evaluate
Dhyd
By definition D 4A
By definition Dhyd = Wetted Perimeter
If it is assumed that the blade height is 2 blade
spacing (2) normal to the relative velocity, then
2
A = hbd. X = hbd
22
Wetted Perimeter = 2(bhd + i) = 3 hb
4 hbd 2'.Dhyd= - h =.667 hba =.667 x 1.55 = 1.04 in.
3 hb
From the velocity diagram of Figure 13 the mean relative velocity is about 300 ft/sec. Then,
750 x 1.04 x.226 x 3600 3
ec =12 x.0459
The efficiency for the helium compressor is assumed
to be equal to that of the "typical" air machine of the same
physical size, operating with STP suction, corrected for the
difference in Re. The air machine efficiency (Figure 12) is.822, and the corresponding Re (Figure 14) is 152,000.
139

Since the machines are compared on the basis of the
same physical size (ie, same leakage, etc.) and same Mach number,
the only efficiency -difference is that clue to Reynold's number.
3lading loss coefficients from typical test data from
one of the manufacturers in this field are plotted in Figure 17
as a function of Reynold's numfber and turning angle. These coefficients are expressed in terms of energy loss. Since symmetrical staging is assumed they apply equally to stator and
rotor and thus directly to the efficiency of the machine.
The blade loss coefficients applying to the air machine (Be = 152,000) is 0.043; that applying to the helium machine
(Re = 1,152,00C) is 0.027. The correction to -the helium machine
is +.016. Since the loss for the helium machine is less than
for the air unit, the efficiency must be corrected upward. Thus
compressor efficiency for this case is 0.8380
8.3.1.2 Turbine
It is assiumed -that turbine efficiency is the same as
compressor efficiency. This reflects a counterbalancing, as
explained in the text, of the more favorable flow conditions
in a turbine against the mechanical desirability of a reduced
number of stages.
Th-tus turbine efficiency is also 0.838.
8,5o33121 1T1urbine Dimensions
It is generally necessary that turbine and compressor RPM be the same, since interposed gearing would
necessarily handle 3 to 4 times the output power. Thus
it is not usually possible to design an optimum turbine
flow path as considered on its own merits.
In a conventional air plant, the turbine diameter
would be somewhat greater than the compressor diameter,
since a greater pressure ratio per stage and peripheral velocity is permissible. However, for the helium compressor,
allowing reasonable Mach numbers, the tip speed. is limited
by stress co-isiderations. nTherefore, since stress is even
more impor-tant for the high temperature turbine, it has
been assumed that the turbine wheel tip diameter is equal
to that of the compressor
Thnlr the blade heights are computed on the basis
14-o

of continuity. Since the volumetric flow for the turbine over
most of the temperature range studied is less than for the compressor, the axial velocity has been reduced to 400 ft/sec (at
least for the first stage) to allow more reasonable blade height
(see the velocity triangle of Figure 13).
w = 41.7 lb/sec.
= p/RT =1000 x 14 1905 lb/ft5
1545/4 x 196o 0
G= w/p = 41.7 219 ft3/sec.
A G x 144 219 x 144 78.9 in.2
400oo 40089
Dt2 Dh2 = A (1).785
(Dt- Dh) = 2 bd (2)
(Dt - Dh) (Dt + Dh) = A (3)
Substituting (2) into (3)
2hbd (Dt + Dt - 2hbd) A (4).785
4hbd (Dt - hbd) = (5).785
2 A
hb2 hbdDt + 4A8 = 0 (6)
hbd - 4 x.785
2
h -h Dt A 0(7)
bd bd t
h Dt- t2'4/t (8)
bd ~ — ~ 2
In this case:
h 12-4.42 -4x78.9/- 2.53 in.
b d 2
Dt = 12.4
8.3.1.3 Thermodynamic Cycle Calculations
The following assumptions have been made:
a) Compressor ratio/turbine ratio = 107
141

b) Regenerator effectiveness = o93
c) Heat sink at 90 F
d) Perfect gas data applicable.
8.3.1.4 Compressor Work
W 2 C T Rk-1/2k _ 1]
c T P 1 c
R 1545 86e.838
p
PR = 5.0
6 = 550 R
Then
W 2 x 1.25 x 550 [ 3.0 1 = 401 Btu/lb
c.838
8.3.1.5 Turbine Work
WT =TCpT1 [ 1 - p ]
rlT=.838
T1 = 1960 R
PRT = 3.0/1.07 2.79
WT.838 x 1.25 x 1960 [ 1 - 2..66/1o66] = 686. 3 Btu/lb
T 2.79
8.3.1.6 Regenerator
Compressor discharge temperature,
+ 401
T9 T6 2+ C 55~ + I 24~1 2= 710 R = 250 F
p e
1- 1225
142

Regenerator Outlet Temperature = (Effectiveness) (T4 - Tg) +'19
TlO = 93 (952 - 250) + 250 -= 903 F
8. 31.7 Heat Input to Cycle
Qin = Cp (T1 - T0) = (1500 - 903) 771
=.97
(a 3% radiation loss is assumed.)
TlO = regenerator outlet temperature
T1 = maximum cycle temperature
Combining of previous relations gives,
Qin = o092 (T1 - 550) -.0561 WC +.959 WT
for the assumptions previously listed.
8.3.1.8 Work from Cycle
Wnet Wr - WT = 686.3 - 401.0 = 285.5 Btu/lb.
8.53.19 Cycle Efficiency
1th = net = 285.3 370
Qin 771
8.35.110 Mass Flow Rate
20,000 x 2545 20,000 x 2545 49.5 lb/sec.
Wnet x 5600 285.3 x 3600oo
This compares with the originally assumed value of 41.7 Ib/sec based
on approximate efficiency assumptions. A recalculation based on the
corrected value would have little effect on the efficiency. It
would affect only the Reynold's number, and the corresponding efficiency effect is small. The diameters and blade heights should
theoretically be corrected. However, the assumption of velocities
is not rigid and may easily be changed by this amount.
8.3.1.11 Air Machine Efficiencies
The data from Table IX given in Section 10 of reference 6
for typical air machines was plotted in Figure 12. It was extrapolated as required. It was arbitrarily assumed (as explained in
143

the text) that an efficiency of over.90 was not feasible for a
standard air machine since the size would become prohibitive and
compromises at the expense of efficiency would be necessary. Thus
the efficiency curve is assumed asymptotic to.90.
It was assumed that the compressor and turbine designs
were similar to those shown in the velocity diagrams of Figure 13.
The Reynold's numbers were computed on the assumption that Dh =
Xhbd.667 as shown in Section 8.3.1 and that the relative velocity
was 300 ft/sec (Figure 13).
The absolute viscosity for air at 90 F, 14. psia is.0436 lb/hr.ft. and p P = p 14.7 x 144 =.0723 lb/ft
RT 535.53 x 550
Assume for example a 10,000 CFM unit
G x 144 10,000 x144 _ in.
A 200 x 60-2in.
as shown in Section 8.3.1
\JA Nf120
=,gA = 4168 = 2.34 in.
and,
Dh =.667 hd =.667 x 2.34 = 1.56
Then
e Dh yd 300 x.0723 x 1.56 x 3600 233.0 x 10
ita 12 x.0436
8.3.2 Air Plant, 20,000 HP, 1500 F, 1000 psia
The air plant differs in several particulars from the helium.
8.3.2.1 Compressor
The compressor calculations follow the same procedure as
for the helium plant with the following exception. No velocity
correction is necessary between the "typical" air machine and the
closed cycle machine under consideration. Thus the volumetric
flow for the closed cycle machine can be applied directly to the
"typical" efficiency curve of Figure 12. The remainder of the
procedure is identical.
The resulting diameter and blade height values are
144

hbdc = 2.23 inches
D = 17.8 inches
tc
It is noted that these are larger than the helium machine
by a factor of about 1.45 (the helium blade height and diameter are
1.55 and 12.4 respectively).
The estimated compressor efficiency is.416 compared to
the helium plant efficiency of.370.
8.3.2.2 Turbine
Again it was assumed that the turbine efficiency was
equal to that of the compressor.
Although an optimum turbine design might utilize peripheral velocities about double that of the compressor, (for the
case of air, this would be allowable with respect to both Mach
number and stress), the factor of constant RPM would then lead to
inconveniently short blading and large wheel diameters. Thus it
has been assumned that the turbine diameter will be 1.25 x compressor
diameter. The air turbine velocity diagram (Figure 13) is identical
to that for helium. The blade heights are computed in the same
manner as shown in Section 8.3.1.2.1 for the helium turbine. The
resulting height and diameter are
hbd 1.05 inches
Dt 21e4 inches
C
It will be noted that this diameter is about 1.7 times that for the
comparable helium case, but the blade height is less than 1/2 that
of the helium turbine.
8.3.2.3 Thermodynamic Calculations
The remainder of the calculations and assumptions are the
same as for the helium case. Thermodynamic data from reference 1
was used instead of perfect gas data.
The resulting cycle efficiency and mass flow rate are
1th =.416
W= 275 lb/sec
Gc 11,900 CFM
145

compared to
rth ~ 370
W= 49.5 lb/sec
G = 13,200 CFM
c
for the helium cycle.
8.3.3 Helium Plant, 600 HP, 1200 F, 100 psia
8.3.3.1 Compressor
The compressor inlet conditions are computed as before
and an approximate flow rate estimated. The volumetric flow rate
is computed to be 7140 CFM.
Referring to Figure 12, it is noted that a machine of
this volumetric capacity falls within the centrifugal or positive
displacement range. Therefore, it is assumed as explained in the
text that the efficiency is not strongly affected by Reynold's
number or Mach number, but is primarily influenced only by volumetric flow rate. Consequently the compressor efficiency is simply read from Figure 12 and is.810.
8.3.3.2 Turbine
The volumetric flow rate for the turbine is computed as
shown in Section 8.3.1.2.1 and is 7190 CFM. If the 400 ft/sec
axial velocity previously considered were used, along with a reasonable Dt/Dh ratio, the turbine would become extremely small. It
was arbitrarily assumed that the minimum turbine of practical interest would be one with a tip diameter of 5.0 inches and a blade
height of.625 inches. It was assumed that this turbine would be
operated at whatever speed (and hence velocity) was required in
view of the available flow (i.e. the possibility of partial admission was excluded on the basis of efficiency).
Typical turbines were computed for 1500, 1200, and 900 F
at 1000 and 45 psia, for air and helium. These were plotted to
show the trend for intermediate machines (Figures 18 and 19;i.e.
pressures )
The efficiency of a typical air machine was estimated,
operating under the following conditions:
Tin = 1200 F PR = 2.79
146

Pin = 45 psia h' = 102.8 Btu/lb
Vaxial = 438 fps C' = 2269 fps
p =.0731 lb/ft3
The impulse velocity diagram sketched below was assumed, since the
simple highly-loaded impulse turbine seems desirable for such small
units.'6'/ v'444
22.
ACu=2181
Figure 22. Small Turbine Velocity Diagram
There is no problem of matching between compressor and turbine in
these cases, since centrifugal compressor design is quite unrestricted compared to axial compressor design in this respect, and,
if a positive displacement unit is employed, gearing will be necessary in any case.
The loss coefficient vs. Reynold's number data of Figure
17 was utilized to estimate the efficiency.
For the stator:
The nozzle angle of turn is about 670~. The nozzle
Reynold's numbers were computed assuming blade spacing (normal to
flow) =.48 blade height (as for the compressor).
On this basis the Re is 154 x 103 and the loss coefficient for 670 angle from Figure 17 is.067. Thus nozzle efficiency for this case is.933 and the velocity coefficient for the
nozzle is.933 =.966.
147

For the rotor:
hbd =.625 inches, Dhyd =.405.
A blade spacing normal to flow of.3 inches for the.625 inch blade
was assumed.
Rebd = WlPDhyd = 1221 x.0731 x.404 x 3600 = 114.9 x 103.0944 x 12
abd =.136 based on 1350 turning angle (See Figure 17 and
vector diagram)
AR.0085 (estimated = aspect ratio loss)
Qbd = 1 - tbd- AR =.856
Cvbd =.9255
w1 = 1221
W2 = 1130
uACu 1008 x 2181 87.8 Btu/lb
Work =87.8 Btu/lb
g 32.2 x 778
C12 2
Input = 1 = 2269 =103.0 Btu/lb
2g 64.4 x 778
Work 87.8.852
TT Input 103 =
Assume mechanical efficiency =.97
Leakage loss =.060 (This assumes.040 for tips and.020 for
seals: based on a tip clearance of.010 giving leakage loss =
Dtt _.010
hDt sin P.625 x sin 22.8
Then stage efficiency =.852 x.97 x.94 =.778 for a standard
air machine of these dimensions.
The ratio of turbine efficiency to stage efficiency for
these conditions is estimated to be 1.02. Then the turbine efficiency is.793.
The turbine horsepowers are computed on the basis of
continuity, utilizing the axial velocity, density, Ah't, and the
computed efficiency.
148

For the case of 1200 F, 45 psia air inlet, the horsepower
is computed as shown below.
Axial area through the first stage of blading is
A 625 (5.0 -.625)t.597 ft2
144
BHP = GAh'TT; G = Avp
bd - P1 (P2)1/kZ
P1 =.0731
P2 1
Z1
PL 2.79
BHP = 597 x 77 x 438 x.0731 x ( 1 )/ x 102.8 x
550 2.79.793 = 106 hp
For other cases of pressure and temperature, the volumetric
flows were computed and the blading Reynold's number for a machine
of these dimensions. The efficiency was then corrected according
to the differences in loss coefficient from Figure 17. The turbine
horsepower output for each of these units was computed and plotted
in the curves of Figures 18 and 19 where the variation of turbine
efficiency with power, pressure and temperature is shown. The computed values are shown below for both air and helium. Slight variations were made in the plotted values to allow smooth curves.
Ratio of Stage to Turbine Efficiency:
For turbine stage work -
Wst stC- [ 1 (P )k-/k]
then for the second stage -
T1 1
12 = sT[T11 i )k_ l' T ] 1
st( Tll - ( 1 -))
149

T13 T12 st (pl/Zk = T [
(pjp( / -2)
etc. If we define
r = [ 1- ( 1 - ( 11/i )]
then
Wturbine qstCpTl1 [ 1 - (pl/p k2 k ](1 + r ~ r2 +,.rZ)
then
WT [ 1 /p )k-l/Zk ] r
z
(Pl/P2)kIf an evaluation is made for the air and helium cases it is found
that
(W ) 1o02 for 2 stages and total pressure ratio of
Wst air 2.79.
andWT
( ) helium 1.03 for 8 stages and total pressure ratio
of 2.79.
The upper portion of the curves of Figures 18 and 19 apply to the
large axial flow compressor units, where it was assumed that turbine
and compressor efficiencies were equal. Some slight alteration of
the points to achieve smooth curves was necessary.
The turbine efficiency for all cases where centrifugal or
positive displacement compressors were used was read from Figures
18 and 19.
Thus for the 600 HP, 1200 F, 100 psi helium unit, turbine
efficiency is.810.
150

TABLE XVII, SMIALL TUI'RINE DESIGNT.AB3JI,,T-u)N
P 4
Fluid psia ~F No Stages u BHP
Air 45 1500 2 771. 7 92 117
1200 1 1008.793 lo6
900 1 931.799 95.5
1000 1500 2 806.837 2820
1200 1 o1048,839 2530
900 1 949.84 8 22 80
Helium 45 1500 10 881.748 159
1200 9 858. 75"7 156
900 7 885 767 159
1000 1500 10 946.822 4000
1200 9 920,826 3890
900 7 946.832 3930
8,533.3 Thermodynamic Calculations
These are identical to the helium calculations previously
discussed as is the remainder of the calculating procedure,
The resulting plant efficiency is;236.
8,3.4 Air Plant, 600 HP, 1200 F, 100 psia
The calculating procedures and methods are ie.anzcal to those
explained in Section 8.3.3 for the 600 HP helium unit.
The air plant resulting efficiency is 4310 as compared to.236 for the helium.
This large difference is the result of the fact that helium
is inherently less efficient at the same component- efficicency, that it
is further from optimum pressure ratio at 30.0, and that the turbine
efficiency under the assumptions of this study is lower,
8,4 Number of Compressor Stages for Air and Helium if Velocities are Equal
W = CT1 [ (P2/p l)k-1/k _ 1]; Assume (P2/Pl air. 0o8 per stage
= constant under the basic assumption.
151

Then
W ir.24 T1 x.0223 =.00535 T1
air
398
Wc = 1L25 T1 [ (P2/Pl) - 1] =.00535 T
5398
(P2/Pl)hel = 1 +.00428 = 1.00428
(P2/Pl1)hel = 1.0108
For p2/P1 = 1.08, seven helium stages are required"
152