ARL 670276
ANALYSIS AND DESIGN OF A HIGH PRESSURE
A.C. ARC HEATER
D. E. GEISTER
GAS DYNAMICS LABORATORIES
DEPARTMENT OF AEROSPACE ENGINEERING
THE UNIVERSITY OF MICHIGAN
ANN ARBOR, MICHIGAN
DECEMBER, 1967
Contract No. AF 33(615)1326
Project No. 7065
This document has been approved for public
release and sale; its distribution is unlimited.
AEROSPACE RESEARCH LABORATORIES
OFFICE OF AEROSPACE RESEARCH
UNITED STATES AIR FORCE
WRIGHTPATTERSON AIR FORCE BASE, OHIO
FOREWORD
This is one of two reports constituting the final technical report
of research performed by personnel of the Gas Dynamics Laboratories,
Department of Aerospace Engineering, the University of Michigan,
Ann Arbor, Michigan for the Aerospace Research Laboratories, Office
of Aerospace Research, WrightPatterson AFB, Ohio. The research
was supervised by Professor J. A. Nicholls, Head of the Gas Dynamics
Laboratories. The work reported herein was accomplished under
contract AF33(615)1326, on Project 7065, "Aerospace Simulation
Techniques Research, " under the technical cognizance of Major Ralph
Prete of the Fluid Dynamics Facilities Research Laboratory. This
work was performed January 1964 to July 1966 as a continuation of work
performed on Contract AF33(657)8630 and reported in ARL 6429.
This report describes the design background for a high pressure
A. C. arc heater.
ii
ABSTRACT
This work reports on the analysis and design of an A. C. arc heater capable
of steady state operation at 2500 psia.
A generalization based on the arc column gas flow interaction is postulated
whereby all arc heaters are divided into two types. In the parallel flow arc
heater the gas flow is parallel to tne arc column whereas in the normal flow
case tne gas flow is perpendicular to the column. In the latter case an applied
D. C. magnetic field is essential for successful operation. The problem of
scaling each type to a different operational level is discussed. In the parallel
flow case a simple analytical model of the gasarc column interaction is available thus providing a good basis for any scaling process. The lack of such a
model for the normal flow arc heater, which must include the effects of the
applied D. Co field, makes the scaling process very complicated. It was found
that tne normal flow arc heater is best suited for application to a 3phase A. CO
power sourceo The problem of scaling each type is discussed. Scaling trends
were found for each type and are presented herein.
Using the results of the scaling studies and previous experimental data,
detailed studies concerning the material selection, expected heat transfer rates,
stress levels, and the required cooling system are presented. These studies
indicated that the structural material needed to withstand the high pressure
and thermal stresses would have to be an alloy of copper, the final choice being
copperzirconium. The heat transfer studies indicated that the dominant heat
iii
loss mechanism in the arc chamber would be radiation, while for the nozzle
convective heat losses predominated. The stress analysis showed that the
wall thickness determinations could not be based on the assumption of only pressure stresses acting, but had to include the thermal stress terms. Finally,
the high thermal loads imposed on these components coupled with the limited
laboratory pump equipment indicated the need for an efficient cooling system.
A cooling system which incorporated fins on the surfaces next to the coolant was
usedo Analysis would indicate this system to be two to three times more effective tnan the conventional water jacket.
iv
TABLE OF CONTENTS
Page
I. INTRODUCTION 1
II. GENERAL DESIGN CONSIDERATIONS 4
A. Parallel Flow Arc Heaters 5
B. Normal Flow Arc Heater 10
1. Normal Flow Scaling Characteristics 12
2. Power Considerations 19
3. Application to 2500 psia A. C. Arc Heater 20
III. HEAT TRANSFER ANALYSIS 22
A. Arc Heater Operating Condition 22
B. Arc Chamber Heat Transfer 23
1. Wall Heat Transfer 31
2. Application to Arc Heater Operational Regime 33
C. Nozzle Heat Flux 43
1. Radiative Heat Flux 45
2. Convective Heat Flux 47
IV. MATERIAL SELECTION 49
V. STRESS ANALYSIS 58
A. Arc Chamber 62
1. Point of Maximum Stress 63
2. Optimization of Wall Thickness 67
B. Nozzle 73
VI. ARC CHAMBER COOLING SYSTEM 78
A. Effect of a Finned Surface 81
B. Cooling Coil Mass Flow Characteristics 85
C. Cooling Coil Heat Transfer Characteristics 88
D. Arc Chamber Cooling System Performance 95
VII. SUMMARY AND CONCLUSIONS 101
REFERENCES 105
v
LIST OF ILLUSTRATIONS
Page
Fig. 1. Parallel Flow Arc Heater. 6
Fig. 2. Normal Flow Arc Heater. 7
Fig. 3. Effects Magnetic Field and Blowing on Arc Column. 15
Fig. 4. Heat Transfer Model. 25
Fig. 5. Thermal Conductivity of Equilibrium Air. 36
Fig. 6. Planck Mean Absorption Coefficient of Air. 38
Fig. 7. Effect of Wall Temperature on Arc Chamber Temperature
Distributions. 40
Fig. 8. Effect of Optical Thickness on Arc Chamber Temperature
Distributions. 42
Fig. 9. Arc Chamber Wall Heat Flux. 44
Fig. 10. Nozzle Wall Heat Flux. 48
Fig. 11. Arc Heater Material Guide vs Stress. 53
Fig. 12. Arc Heater Material Guide vs Temperature Difference. 54
Fig. 13. Effect of Temperature on Yield Strength of CuZr and CuBe. 56
Fig. 14. Model for Arc Chamber and NozzleThroat Stress Analysis. 59
Fig. 15. Effect of Temperature on the Properties of CuZr. 64
Fig. 16. Safety Factor vs Arc Chamber Wall Thickness. 68
Fig. 17. Safety Factor vs Arc Chamber Wall Thickness. 69
Fig. 18. Variation of Safety Factor with Arc Chamber Heat Flux. 71
Fig. 19. Variation of Safety Factor through the Arc Chamber Wallo 72
Fig. 20. Schematic of Arc Heater Nozzle. 74
Fig. 21. Safety Factor vs Nozzle Throat Wall Thickness. 76
Fig. 22. Variation of Safety Factor with Nozzle Throat Heat Flux. 77
Fig. 23~ Arc Chamber Cooling Configuration. 80
Fig. 24. Optimum Fin Cross Section vs Nusselt Number 83
Fig. 25. Variation of the Properties of Water with Temperature 87
Fig. 26o Effect of Tube Size on Pumping Requirements. 89
Fig. 27. Variation of Flow Mean Velocity with Tube Size. 90
vi
Page
Fig. 28. Pressure Requirements vs Flow Rate for the Arc Chamber
Cooling System. 98
Fig. 29. Effect of Pump Operating Pressure on Arc Chamber Wall
Temperature. 99
Fig. 30. Effect of Water Flow Rate on Arc Chamber Wall
Temperature. 100
vii
NOMENCLATURE
A surface area
B magnetic field strength
Bth thermal stress coefficient
B Planck function
V
C specific heat at constant pressure
P
D diameter
d dimension defined in Eq. (92)
E modulus of elasticity
E (t) exponential integral as defined in Eq. (22)
F force
f friction factor
H enthalpy
h heat transfer coefficient
I current
I modified Bessel function
I modified Bessel function
o
I monochromatic intensity of radiation
thermal conductivitygas
k thermal conductivitygast
k thermal conductivitywater
w
k thermal conductivitycopper
L length
QSB ~ dimension defined in Eq. (92)
rm mass flow
P pressure
Q power
q radiative heat flux
R(T) surface radiant flux
r radius
viii
*.
Vlll
S fin height
T temperature
T mean temperature as defined in Eq. (26)
T bulk temperature
0
u velocity
x coordinate along length of the arc chamber
y coordinate perpendicular to the arc chamber
a linear coefficient of thermal expansion
1,P 3constant as defined in Eq. (64)
y ratio of specific heats
6 fin thickness
E emissivity
K absorption coefficient
K Planck mean absorption coefficient
Aj Poisson's ratio
I/ cos 0 as defined in Eq. (22)
v frequency
v kinematic viscosity as used in Eq. (116)
P density
a stress as used in Section V
a StefanBoltzman constant as used in Section III
T optical depth
W solid angle
subscript
c chamber
e material 0. 2% offset yield strength
o flow stagnation conditions
m mean value
t tube in Section VI
ix
w wall
1 inside dimension
2 outer dimension
~~* ~conditions at M = 1. 0
x
I. INTRODUCTION
All of the experimental facilities that are capable of true temperature and pressure simulation at the very high Mach numbers (hot shot tunnels, shock tunnels, or
shock tubes) are limited by short run times. Pebble bed and resistance heaters
have been used for much longer run times but these devices cannot produce the stagnation temperatures characteristic of hypersonic flight at Mach numbers above 7 or
8. For example, at Mach 10 and an altitude of 155, 000 ft, the required stagnation
conditions are 2500 psia and 41500K. These conditions (and even higher temperatures)
can, potentially, be effectively produced on a steady state basis by an arc heater.
Thus the arc heater has a definite complementary place in the arsenal of high temperature gas dynamic facilities.
The task of developing arc heaters for these purposes has been vigorously undertaken by numerous industrial and research organizations (1, 2, 3, 4). The result of
these endeavors has been the development of numerous low pressure D. C. arc
heaters. This developmental work has encountered two major difficulties; the extrapolation of the design of low pressure arc heaters to the high pressure regime
and the realization that arc technology is still in the research stage.
For a number of years personnel of the Department of Aerospace Engineering,
Gas Dynamics Laboratories, have been engaged in the development of a high pressure 3phase A. C. arc heater for the Fluid Dynamic Facilities Research Laboratory,
Aerospace Research Laboratories. Due to the pucity of work on A. C. arc heaters,
the lack of understanding of arcs under the conditions of interest, and the new problems
associated with A. C. as compared to D. C., it was necessary to conduct substantial
Manuscript released by the authors October 1967
for publication as an ARL technical report.
1
research along with the development. It was found necessary to consider the entire
arc heater system rather than the arc heater alone.
In effecting this research and development program, the arc heater system was
divided into the following general areas, each found to strongly affect the performance of the arc heater as pressure levels increased; 1) the A. C. power supply and
stabilizing elements, 2) the gas flowarc interaction scheme, 3) the electrode system, 4) the D. C. magnetic field, and 5) the basic arc heater structural components.
Studies were conducted in each of these areas with the aim of developing an arc
heater operable over a given pressure range. It was found that optimization in each
of the above individual subsystems would not produce an optimized arc heater. Consequently, considerable trade off studies and subsystem developmental work had to
be done before and/or concurrent with the actual arc heater design and development.
The program to date has resulted in the design, development and operation of
two A. C. arc heaters; a low pressure unit and a high pressure unit. The former arc
heater, capable of operating in the 500 psi pressure range, provided some operational and experimental data for an extrapolation to the higher pressure unit. These
data served to show the effects of pressure level on power requirements, the component thermal loads, and the new requirements that must be met in a subsequent
heater. A detailed report on this low pressure unit is given in Ref. (5) and (6).
The aim of the followon studies was to develop an arc heater capable of operating in the 2500 psi range with a power input of 1 Megawatt. There were two distinct
phases to its development; 1) a detailed design investigation of those arc heater
2
structural components most effected by the higher pressure levels, 2) the development and testing of the arc heater and its numerous auxiliary components at their
new design conditions. To adequately summarize this effort, it was felt that two
reports need be presented, each covering the salient features of the above phases.
This report summarizes the investigations into the problems of designing an arc
heater capable of operating at the pressure and power levels stated. The trends
observed in operating the low pressure arc heater and how this information affected
the design considerations on the high pressure unit are discussed. A generalization
of all heaters, classifying them either as parallel or "normal" flow, is presented.
This distinction is of consequence in scaling an arc heater. Detailed studies are
presented on the design of the arc chamber and nozzle.
Part two of this final report, which appears as a separate report (7), gives the
final design and experimental performance of the high pressure A. C. unit.
3
II. GENERAL DESIGN CONSIDERATIONS
With the design, development and successful operation of a low pressure arc
heater (up to 550 psi) completed, it was tempting to merely scale the existing configuration for the structural loads that would be imposed by a chamber designed for
operation up to 2500 psia. However, the scaling of an arc heater is extremely complicated in that it is a complete system involving a number of distinct scientific disciplines (gas dynamics, arc physics, electrical engineering, heat transfer and
structural mechanics). Therefore the scaling process requires either an intimate
knowledge of each of these fields as they relate to arc heaters or the development
and testing of a number of model arc heaters with appropriate scaling similarities.
An extensive literature search was conducted in hope s of determining the influence
of power level, arc voltage, arc rotational speed, radiative heat transfer, electrode
characteristics, and other variables on arc chamber performance. It was determined that the fundamental information was simply not available nor was sufficient
information available on experimental tests of various scale models. This was
especially true in the case of A. C. arc heaters. It was further determined that a
five fold increase in pressure, from 500 psi to 2500 psi, would not be accomplished
by a small perturbation of the existing low pressure arc heater system.
Of the many sizes and shapes of arc heaters built and tested there appears to
be one "type" most generally developed. This is the "parallel flow" or tube arc
(an outgrowth of the Gerdien arc) which takes the form of a water cooled tube in
which the arc is contained and the gas to be heated passed through and parallel to
4
the arc column. This unit usually runs on D. C. power with the tube or arc chamber
serving as one electrode as shown in Fig. 1. Some success has been achieved in
determining scaling laws for this type. The "type" we have been investigating has
the arc attached to two or more electrodes; so oriented in the arc chamber that the
gas flow to be heated is passed perpendicularly through the arc column as shown in
Fig. 2. In the following the characteristics and scaling of these two types of arc
heaters are discussed.
A. PARALLEL FLOW ARC HEATERS
The "parallel flow" or tube type arc heater has a number of characteristics
which can make scaling much simpler. Commonly, one electrode is the arc chamber wall and hence the arc column scales with the arc chamber dimensions (thus
eliminating one degree of freedom). A most important feature is that the gas flowarc interaction can be solved analytically by using an asymptotic column solution (8).
In general, the theory of the cylindrically symmetric arc is firmly established and
compares well with experiment; the most accurate investigation being made by Stine
and Watson (9). Therefore, an important set of design guide lines is already available.
Even though vast amounts of experimental data exist on the "parallel flow" arc
heater there was only one study found that was directed toward establishing the arc
heater scaling parameters. This was done by the Speedway Research Laboratories
of the Linde Company and was directed toward the development of a 50 Megawatt D. C.
arc heater (10). For the sake of completeness, this study is summarized here.
5
Gas
Arc Chamber Cathode
Arc Column
FIG. 1. PARALLEL FLOW ARC HEATER.
6
/ v\ \, x
/x /\ \/
Yx X /X\ // X>
Gas Flow
—,,
D I
AnodeC
Cathode
Arc Column
Nozz le
FIG. 2. NORMAL FLOW ARC HEATER.
7
If a reference or standard arc heater is designated by subscript (1) and S is the
ratio of linear dimension of the new unit to the standard, the following scaling is
indicated.
If
I= SI1 (1)
m/A = (r/A)l (2)
Then,
V = SV (3)
Q = S2Q (4)
P = P (5)
H = H (6)
This scaling produces an arc heater operating at the same pressure level and
effluent enthalpy as the standard unit but with higher mass flow.
Equation (2) can be written,
m = S2 (m)l (7)
Defining the effluent enthalpy as Q/mh and holding it constant:
Q/r = (Q/mr)1 (8)
or
Q= s2 (Q) (9)
Therefore a proportionate increase in power with mass flow is needed.
8
The above scaling gives no information relative to different pressure and/or
enthalpy levels. These effects can be estimated by following an analysis first proposed by Suits (11); the arc column being treated as if it were a hot cylindrical body.
This analysis, however, neglected the effect of radiation losses and forced convection on the arc column. These effects are important and have been included in
Ref. (12) which then leads to a fairly accurate representation of the "parallel" flow
arc heater.
Using the latter analysis, the following general trends can be expected. An
increase in arc chamber pressure level increases the arc column voltage gradient,
power loss due to radiation, and gross power input, and decreases the arc column
diameter. An increase in chamber mass flow increases the arc column voltage
gradient, arc column length, and the gross power input, and decreases the gas
enthalpy. An increase in arc current increases the arc column diameter and power
loss due to radiation, and decrease s the arc column length, arc column voltage
gradient and generally the gas enthalpy level.
If one now considers the coupling that exists for the parallel flow arc heater
between the arc chamber and the arc column, a fairly general set of scaling trends
can be established. Assuming one has an arc heater operating at a given pressure,
enthalpy and mass flow level and a new unit is to be developed to operate with an
increase in one of these variables; the direction the arc heater scaling parameters
must go can be obtained from the above trends. Considering the following cases;
I) increased pressure while holding mass flow and enthalpy constant, II) increased
9
mass flow while holding pressure and enthalpy constant, III) increased enthalpy while
holding pressure and mass flow constant, the following table summarizes the necessary change in scaling parameter.
TABLE I*
Case
Scaling Parameter
I II III
Arc voltage increase increase decrease
Power increase increase increase
Thermal losses increase increase increase
Arc heater length increase increase decrease
Arc heater diameter decrease increase increase
*Thermal losses are shown here in lieu of a scaling parameter that would reflect
the arc heater thermal "efficiency. "
These relatively simple observations stem from the fact that the arc chamber
is one of the arc heater electrodes and hence the arc column assumes its dimensions.
Therefore the arc heater scales to meet the requirements of the arc column.
B. NORMAL FLOW ARC HEATER
As previously described, the arc column in the "normal" flow arc heater will
be oriented 90~ with respect to that of the parallel flow arc heater. A stationary arc
column so oriented will fill only a small fraction of the arc chamber cross sectional
10
area and thus lead to inefficient heating of the working fluid. Further, the thermal
loads imposed by the concentration of the arc roots on a small area of the electrodes
would cause frequent burn throughs. To overcome these problems a D. C. magnetic
field, in the form of a solenoid wrapped around the arc heater, is applied to the arc
column with its field vector so arranged (along the axis of the chamber) that the resulting Lorentz force causes the arc column to rotate in the annular region between the
electrodes. Thus an applied D. C. magnetic field becomes an important feature of
the "normal" flow arc heater and is of consequence to the scaling procedures.
Since a high arc column rotational rate is desirable, the driving Lorentz forces
should be a maximum for a given field strength. The Lorentz force is given by:
F = B xI (10)
and the magnitude by
F = BI sin 0 (11)
Applying this to the geometry of the arc heater, Fig. 2, the force will be a maximum
when the magnetic field is oriented parallel to, and the arc column normal to, the
arc chamber axis. This indicates the wisdom of locating the second active electrode
at the same axial position as the first. Further it indicates the disadvantage of using the arc chamber wall as an electrode for then the higher mass flow rates would
tend to blow the arc root at the wall downstream; thereby reducing 0 and F. Finally,
when electrodes fail (as they eventually will), it is far easier to replace a simple
electrode than the chamber wall. A possible disadvantage is that the separate electrode essentially divorces the arc column from the arc chamber and thus complicates
scaling procedures.
11
It should be pointed out that the application of a D. C. magnetic field to the arc
column is not unique to the "normal" flow type arc heater. The "parallel" flow arc
heater previously discussed must also have some means of spreading the imposed
heat load of the arc root over the electrode surface area. Here too, the arc root is
rotated with two methods available to accomplish this; magnetic or aerodynamic.
If we consider the region of the arc column in the vicinity of its root, Fig. 1,
we see it must turn 900 in order to attach to the cathode (arc chamber wall). In so
doing the current vector is locally so oriented that a D. C. magnetic field, applied as
previously mentioned, will create a Lorentz force which tends to rotate the arc root
over the surface of the arc chamber wall. The same effect can be also obtained by
introducing the gas flow tangentially thereby creating a strong vortex in the arc
chamber which in turn will drive the arc root. The latter method, however, is limited
to low pressure operation and is found primarily in the parallel flow arc heater.
Nevertheless, being concerned with the effects of a D. C. magnetic field on the
"parallel" flow arc heater we find; 1) any applied field is done so locally at the arc
roots, 2) looking at the orientation of the field vector with the major portion of the
arc column, the resultant Lorentz force will be small. Therefore, the effects of a
magnetic field on the arc heater scaling are considered negligible. Just the opposite
effects are felt and indeed, required in the "normal" flow arc heater.
1. Normal Flow Scaling Characteristics
A plausible assumption might be that the same scaling that existed between the
length of the "parallel" flow arc heater and the arc column would still exist here but
12
applied now to the diameter of the "normal" flow arc heater, i. e., if a longer arc
column is required the electrode spacing has to increase, and consequently, the arc
chamber diameter has to increase. Therefore, just as the parallel flow arc heaters
can be described as being small in diameter and rather lengthy, the normal flow arc
heater would manifest itself as being short and rather large in diameter (a distinct
disadvantage for high pressure operation). This general description, however, is
accurate only to the extent that the normal flow arc heater will be larger in diameter
than the parallel flow type and that its diameter will be governed by the largest electrode.
The normal flow arc heater has available two mechanisms which will allow a
change in arc column length without physically changing the electrode spacing; a
necessity if stable operation is required over a range of arc heater power, mass
flow, and pressure levels. The "effective" electrode spacing can be changed by
either blowing (magnitude of gas velocity vector through the electrode region) on the
arc column or by applying a D. C. magnetic field to the arc column. Each mechanism will cause the column to lengthen in one of two different planes, the resultant
arc column becoming a rather complicated threedimensional shape. Figure 3 illustrates these effects. These features were used to advantage in designing the 2500
psi arc heater to be smaller than the low pressure unit.
As shown in Fig. 3(a), the effect of increasing the velocity vector into the arc
column causes the column to bow thereby lengthening the arc column in the axial
plane and moving the arc root forward, axially, around the electrode. The effect of
13
the D. C. magnetic field, Fig. 3(b) is to rotate the arc column at constant angular
velocity. Therefore, that part of the arc column farthest from the axis of rotation
will tend to have the highest velocity.
Defining for the moment, the head of the arc column as that part moving at
the highest velocity and the base the slowest part, our investigations with the low
pressure arc heater showed that the head of the arc column could lead its base
by as much as 90~, this lead being a function of D. C. field strength and arc chamber pressure. The angular lead was limited by the maximum field strength available (3000 gauss). The investigations of Jedlicka (13) also show the same trend.
It was shown theoretically and verified experimentally that the shape of the arc
column in the radial plane would be that of a cycloid of a circle. Therefore, the
length of the arc, so driven, can be significantly greater than the physical electrode spacing, approaching what may be considered a mean circumference of
the electrode spacing.
An interesting limit is evident for by creating a large enough Lorentz force,
the head of the arc column can lead its base by 3600. The resultant discharge
would no longer take the form of a column, but rather that of a current sheet
completely filling the annular electrode gap. This phenomenon, referred to as
a diffuse arc, would spread the concentrated heat load of the arc column roots
over the entire electrode surfaces, significantly reducing their rate of erosion.
This type of arc discharge would be very desirable from the standpoint of arc
heater operation, particularly the normal flow type which requires an applied
14
Cathode
Anode
Magnetic Field
Magnetic
Applied
Field
/ //////// /// Z// ///
AirFw I
Flow IL
 Strong Magnetic
>Y ~Field Applied
Cathode
With Air Flow
No Air Flow
Anode
Air
Flow
FIG. 3. EFFECTSMAGNETIC FIELD AND
BLOWING ON ARC COLUMN.
15
D. C. magnetic field. Although frequently mentioned in the literature (14), no one
as yet has developed an arc heater system that can produce a diffuse arc at even
moderate pressure levels. The primary difficulty in high pressure arc heater
operation (> 1 atm) is the large field strengths required (> 20, 000 gauss) due to
the large aerodynamic drag forces experienced at high pressure levels.
We find, then, for the normal flow arc heater, that the length of the arc column can be significantly larger than the physical spacing of the electrodes and that
its shape will be more than a simple cylinder normal to the electrode surface.
Both now become a strong function of arc chamber mass flux and D. C. magnetic
field strength. These features not only serve to complicate any scaling between
the arc column and some characteristic length (e. g. electrode spacing) but also
require that any meaningful theoretical model of the arc column must assume it
to be three dimensional. As yet, no theoretical model for an arc under the influence of blowing (normal to its axis) is available. It is felt that this lack of a theoretical model is the major difficulty found in either initially designing the normal
flow arc heater for a given operational regime or scaling a given design to a new
operational condition. For this reason most of the theoretical and empirical data
found is for the "parallel" flow arc heaters.
The following scaling trends were arrived at by using the conclusions derived
from Ref. (12) and qualitatively allowing for the previously discussed arccolumn
interactions found in the "normal" flow arc heater. Due to the lack of experimental
as well as theoretical information on these arc interactions most of the trends or
16
conclusions were establisned by the information obtained in developing and operating our low pressure arc heater. An increase in arc chamber pressure level increases the arc column voltage gradient, power loss due to radiation, and gross
power input, and decreases the arc column diameter and arc column rotational
rate (the latter decreasing arc column length). An increase in chamber mass
flow increases the arc column voltage gradient, arc column length, and the gross
power input and decreases the gas enthalpy and arc column rotational rate. An
increase in arc current increases the arc column diameter, power loss due to
radiation, and arc column rotational rate, and decreases the arc column voltage
gradient and the gas enthalpy level. It can either increase or decrease the arc
column length.
Assuming one has a "normal" flow arc heater operating at a given pressure,
enthalpy, and mass flow level and a new unit is to be developed to operate with an
increase in one of these variables, the direction of change for the scaling parameters can be obtained from the above trends. Table II summarizes this for three
particular cases; I) increased pressure while holding mass flow and enthalpy constant, II) increased mass flow while holding pressure and enthalpy constant; III)
increased enthalpy while holding pressure and mass flow constant.
In keeping with the generalization on arc heater scaling, changes in scaling
parameters, length and diameter, were included in Table II. The indicated changes
were based on the assumption that if one were scaling co a new performance regime,
the resulting unit would be slanted toward improving and/or at best maintaining
17
TABLE II*
Scaling Parameter
I
Arc voltage
Power
Applied D. C. magnetic
field
Thermal losses
Arc heater length
Arc heater diameter
increase
increase
increase
increase
(decrease)
decrease
Case
II
increase
increase
increase
increase
(decrease)
increase
III
decrease
increase
increase
increase
(decrease)
increase
*Thermal losses are shown here in lieu of a
reflect the arc heater thermal "efficiency. "
scaling parameter that would
thermal and structural efficiency. However, due to the weak coupling between the
arc chamber and the arc column, the scaling of the arc heater dimensions can become quite arbitrary. This is particularly true with respect to the arc heater
length (so designated by bracketing the suggested changes). In fact, quite often
these dimensions can be completely dictated by other arc heater components, e. g.,
optimum size of the solenoid needed to produce the required D. C. magnetic field
strength. This type of interaction turned out to have a significant effect on the
eventually scaling of our 2500 psi arc chamber. This point will be elaborated
upon in the following section.
18
2. Power Considerations
Considering now the question of using A. C. applied directly to the arc heater
electrodes instead of D. C., it is felt that the "normal" flow arc heater is best
suited for A. C. operation. This statement is based on the assumption that if one
uses A. C. it would take the form of multiphase A. C. The minimum number of
electrodes needed would then be three which, looking at possible electrode configurations, will lend itself best to the normal flow arc heater. These statements
are not meant to exclude single phase A. C. for it can readily be used in either
type of arc heater. However, it is concluded, as a result of our research and
others (Ref. 15 and 16), that there are few, if any, advantages of using single
phase A. C. instead of D. C. power. Some reservations must be made, however,
as this conclusion is based on single phase A. C. operation of an arc heater designed for D. C.
In keeping with the generalization on two types of arc heaters, we have purposely neglected the possibility of electrically paralleling a number of parallel
flow units and exhausting them into a common plenum chamber. Such arc heaters
usually take the form of a multiarc chambered unit and have been proposed and
developed (Ref. 17) for both A. C. and D. C. operation. In view of the limitations
of the understanding of arc heater fundamentals, it was felt that this sophistication was not warranted.
The low pressure arc heater previously developed was of the "normal" flow
type using a three phase A. C. power source. One of the considerations that had
to be made before designing another unit for higher pressure operation was what
19
type of arc heater was best suited for our particular application. Investigations into both types of arc heaters indicates the "parallel" flow arc heater will
result in the smallest diameter unit, hence structurally lends itself better to high
pressure operation. The use of multiphase A. C. power (a major point of research interest in this program) requires a multielectrode configuration which
can, in general, only be obtained in the "normal" flow arc heater. Therefore
only a design of the latter type was considered feasible in the allotted research
period.
3. Application to 2500 psi A. C. Arc Heater
The objective of the extension of the A. C. arc heater program was to develop
a heater for higher pressures (up to 2500 psia). Therefore, the scaling trends
indicated in Table II, along with structural and thermal analyses, indicated the
changes necessary for a new unit. These considerations showed that the high
pressure arc heater must be capable of handling higher arc voltages, power levels,
and thermal heat loads; the applied D. C. magnetic field strength would have to be
increased and the arc chamber volume decreased. These trends were supported
by the experimental data from our low pressure unit. These data showed that for
a given open circuit voltage, power input, and D. C. magnetic field strength, an
increase in arc chamber pressure produced a decrease in arc heater stability
(arc column extinction), increased electrode erosion (decrease in arc column
rotational rate), and an increase in thermal losses to the arc chamber walls
(increased radiative heat losses). It was felt that these three trends would best
establish the guide lines leading to the development of the 2500 psi arc heater.
20
The above guides were used in concentrating on the design of the arc chamber
and nozzle, those components being considered the most sensitive to scaling. The
design was further restricted by magnetic field considerations. Experimental
data from the low pressure arc heater indicated that a D. C. magnetic field strength
increase on the order of six would be optimum for high pressure operation, the low
pressure unit having a field strength of 3000 Gauss with a power input of 120 KW.
With our power supply limited to 120 KW, it was found impossible to achieve the
desired six fold increase in magnetic field strength and still have a chamber capable of withstanding the new performance levels. Accordingly, a compromise
was required and the final solenoid design resulted in a field strength of 11, 000
Gauss.
21
III. HEAT TRANSFER ANALYSIS
The results of the scaling studies and the experimental data from the low
pressure arc heater indicated that the new arc heater would be subjected to
higher thermal losses as the operational pressure level was increased. Therefore an analytic heat transfer model was sought that could predict the heat loads
impressed on the major arc heater components in the new operational regime.
The major difficulty expected was the prediction of radiation losses at increased
pressure levels.
A model was chosen that included all three modes of heat transfer (convection, conduction, and radiation). It was anticipated that experimental data obtained from the new arc heater could be used to better establish radiative heat
losses as a function of pressure level. Since the radiative heat losses will limit
the ultimate pressure levels an arc heat can produce, this type of information
would prove useful for any future arc heater development. This type of data is
also required since the assumptions made which allow for solutions of the energy
equation with the radiative term (i. e. gray gas, optically thin or thick, etc. ) do
not hold as the pressure level is increased.
A. ARC HEATER OPERATING CONDITION
Preliminary to the heat transfer estimates, it is necessary to establish the
state of the gas in the arc chamber. It is assumed that the new arc heater will
produce a gaseous effluent with stagnation conditions of; temperature 1000 K to
5000 K and pressure to 170 atmospheres. These conditions would be produced with
22
a nominal power input greater than 1 megawatt with a maximum mass flow capability of 0. 5 lb/sec at any given pressure level.
Assuming the arc heated gas to obey the perfect gas law and that slug flow
prevails in the arc chamber, conservation of mass indicates that the flow velocity
will be very low (less than 3 ft/sec for a 6 in. diameter chamber). This is conducive to good arc column stability.
A calculation of the Reynolds number, based on the arc chamber diameter
indicates that the chamber flow could be either laminar or turbulent, dependent
on the operating conditions. For either case, data from Schlicting (18) indicates
that the flow will be far from fully developed as the L/D of the chamber is less
than 5. Therefore, it is concluded that the flow through the arc chamber can be
treated as slug flow. Also, with a heat source (arc column) located approximately
in the middle of the arc chamber, the temperature profile should develop very
2 2
quickly in the axial flow direction so that a T/ax is small.
Postulating that the above conditions represent the gaseous flow in the arc
chamber, the following analytic model is assumed to describe the heat transfer
process.
B. ARC CHAMBER HEAT TRANSFER
The heat transfer characteristics of the flow through the arc heater is estimated by assuming it to be analogous to slug flow of a radiating gas in a constant
height duct formed by two parallel plates. This simplification is used to avoid the
complexities of the dependence of the radiant heat flow on the flow configuration.
23
The configuration considered is shown schematically in Fig. 4. A hot,
nonscattering, absorbing and emitting gas with uniform velocity across the
channel flows in the x direction between two infinite parallel plates separated
by a distance L. The two plates (chamber walls) extend to infinity normal to the
y axis and parallel to the x axis. The walls (y = 0, y = L) are at constant temperature T and both have the same emissivities. Steady state conditions are also
w
assumed.
Since the velocity is assumed constant in the x and y directions, the conservation equations of mass and momentum are both satisfied. Therefore only the conservation of energy equation need be considered. The twodimensional steadystate energy equation including conduction, convection and radiation terms but
neglecting work, heat generation and viscous heat dissipation, is expressed as
aT (aT a2T f, (12)rq
pC u —=k  + dv. (12)
P ax a x ay a
0 0
where qr (x) and q (y) are the monochromatic radiant flux, in the x and y directions.
Applying the previous assumption of small axially gradients, we neglect the
axial (x) gradient of temperature and radiant heat flux with respect to the y direction, therefore
a2T a2T aqr(Y) aqr (x)
7; A' W__ _ r (13)
a y ax T
24
////////// d/ // / /T
dy
u L.  _ y. _ I Y L
x
Radiating Gas Layer Arc Chamber Wall
FIG. 4. HEAT TRANSFER MODEL
25
The energy equation (Eq. 12) simplifies to:
aT T)2T r aqrv(y)
p C u  =+ d (14)
a y 0
The radiant energy flux q (y) across any plane in the fluid is found by integrating
the intensity of radiation, I (0,y) over all solid angles, w.
0
qrv(y)= f I (0,y) cos 0 dc (15)
47T
Iv (0, y) is obtained from the radiative heat transfer equation
dI (0,y)
 cos 0 K dy = I (0,y)  Sv (0,y) (16)
where S (0, y) is a source function.
Assuming the gas to be gray, isotropic, in local thermodynamic equilibrium
with an index of refraction of 1, the intensity of radiation and absorption coefficient
will be independent of wavelength. The source function will also be expressed as
4
(a/r )T (y). Equations (15) and (16) can now be written as
q(y)= f I(0,y) cos 0 dw (17)
co=47
with
cos 0 d 0 I(0,y)  (y) (18)'K dy' y
26
The formal solution of the radiative transfer equation has been given by
Chandrasekhar (19), for a plane parallel gray gas and can be shown to be
qr() =qr + (T)  qr ()
T
2R(T ) E3T  r) + a J T4(t) E2(t T) dt
T
(19)
 R(o) E3) J T4t) ( t) d
 R(o) E3(r)  af T(t) E2(r  t) dt
0
where T, the optical depth, defined as
y
= K dy
0
is the new independent variable. The optical thickness T is defined as
L
=f K dy
0
and the functions E (t) are the exponential integrals defined as
(20)
(21)
1
fn2
E (t)= 2
0
exp ( T/pM) d/J
(22)
27
where t = cos 0. The radiant flux leaving the surfaces of the duct wall is due to
both radiation emitted from the wall and the fraction of incident radiation which is
diffusely reflected from the surface.
w=27T l
4 4
ET (o)+ 2(1  E) R(T E (To+ a o T () E2() d (23)
E 3 1 2
0
and
2rT
T= T
R(T) = I(T cos 0 dw for ~
0 0 1~<0
or
=ET (T) + 2(1  E) R(o) E3(T) + a f T4(T) E2(T  T) dT (24)
0
Using the previous assumption of a fully developed temperature profile, the
axialtemperature gradient can be expressed as (Ref. 20)
aT T T (25)
wahex the= ma tmeaue orsgflwi deid (25)
where the mean temperature, T, for slug flow is defined as:
where the mean temperature, T, for slug flow is defined as:
28
L
T= Tdy/L (26)
0
Taking an energy balance for an element dx of the duct
p C uLdT = 2q dx (27)
p w
where the total heat flux at the wall, q, is represented by
a T= T=O T=T T=T
0 0
O O
4
Introducing the dimensionless quantities 0 = T/T, R = R/aT and
Q = q /aTo4 and combining Eq. (19) through (28) with the gradient of q (T)
gives the following form of the energy equation.
d20 2Q ( ) 4 1
N 2 = 2Q +( 2 ) E2(') + R(RO) E2(T+  T)
2 T 0 2 1
0 T
where the dimensionless parameter N is defined as
k K
N =  (30)
4aT
which expresses the relative role of energy transport by conduction to that by
radiation.
29
The boundary conditions for Eq. (29) are:
7=0, e= e
E) w
T = T, e = O
0 W
Since the temperature profiles will be symmetrical, i. e. T(o) = T(T ) = T, the
0 W.
fluxes R(o) and R(r ) will also be equal. Therefore
T
O4 + 2(1  e) J T) E2(T)d
R(o) R(_ _ LW 0 (31)
R(O)= R  O 1  2(1  E) E3(r ) (
3 0
The energy equation in its final form is:
d20 2Q (O  O) 4 1
N  2 [R(() E + E2(T  )]
dT o W m
T (32)
T 0o
+ f 04(t)E(r t) dt+ fJ 4(t) E(t T) dt
0 T
which is a nonlinear integrodifferential equation satisfied by a temperature
distribution T(y)* yet to be determined.
Unfortunately, there is no closed solution to the above equation, and one
must use numerical means and a computer to obtain solutions. However, this
equation or a similar form, has been solved numerically by Goulard (21),
*Once the distribution 8(T) = T( )/T is established, T(y) is obtained through
the relation dT= kdy.
30
Viskanta and Grosh (22), and Usiskin and Sparrow (23), using an iteration
procedure. Viskanta (24) and Yoshikawa and Chapman (25) also solved a
similar equation based on a truncated series expansion of T4(y). The former's
results must be relied upon for this analysis.
1. Wall Heat Transfer
The solution of Eq. (32) gives the temperature distribution between the two
walls. Its solution is by no means trivial but all heat transfer results can be
calculated once the temperature distribution has been established. Dismissing
this for now, the local radiant energy flux can be written as:
qr (T)
Qr(T) 4
4aT
0
T
0
R(T ) E(T  T) + f e4(t) E2(t  T) dt  R(o) E3(T) (33)
rT T
 J e4(t) E2(T t) dt
0
Again using the property of a temperature profile symmetric about the duct
centerline
Qr(o)=  Qr(T ) (34)
which allows Eq. (33) to be rewritten as:
31
1 f0
Q(~) = R(T ) E3() + 0J e4() E2(r) dT  R(o)/2 (35)
0
The total heat flux at the wall will be
q w dO
Q  Nd  Q (o) (36)
w rT 4 dT T=~ r
0
Viewing Eq. (35) and (36) in light of the equations for R(o) and R(r ), we find
4
a solution is possible if the functional form of e (T) is known. This single dependence on 0 (r) suggests the following simple approximation to the radiative heat
flux equation. It is assumed that the gas confined by the walls radiates at a mean
temperature. This mean, as previously defined in Eq. (26) is
o
em _ I eQ4()dr (37)
m T
00
The integrals in Eq. (33) for the local radiative flux Qr(T) can now be evaluated,
giving
Q (T) R(o) E3(r r)  E (T) + 8 4 [E T) + E3(T (38)
The radiate flux at the wall (T = 0) with R(o) evaluated at the mean temperature
will be
32
((4 eW m4) [E3(T0o) (1/2)]
1 2(1E)E3(T0) (39)
Qr(~) = 1  2 (1  e) E3(r )
One assumes the flow between the walls to be isothermal. Its absolute value
is T which, for application in the arc chamber, would be the stagnation temperature of the arc heater effluent. This assumption should be fairly accurate, if the
temperature distribution across the duct were flat and/or the contribution to the
radiant energy flux from the gas small (optically thin approximation). As will be
shown this approximation will not be valid for estimating the radiative wall flux
to the arc chamber walls, but does find application for the arc heater nozzle.
2. Application to Arc Heater Operational Regime
To effect a solution of the energy equation, values for the independent parameters, eO, ew, E, T, and N, must be established. These parameters are functions of the arc heater structural material, gas properties, and arc heater power
input. The effects of pressure level are reflected in the conductive heat transfer
parameter, N, and the optical thickness, T. Once established, there still exists
the mathematical difficulties of finding the temperature distribution that satisfies
the energy equation.
Considering the effect of increasing temperatures on the yield strength of
copper alloys leads to the conclusion that the wall temperature, Tw, should be
kept below 600~F (_ 590~K) if reasonable safety factors are to e maintained.
Therefore, we find
0 <0.3
w
33
for the stagnation temperature range considered. The stagnation temperature is
assumed to be the average temperature of a given temperature distribution. This
relationship then determines the values of %0, for a given stagnation temperature
and temperature distribution.
The value for the wall emissivity, E, is somewhat arbitrary, being dependent
on both the material and surface condition (the assumption is made that emissivity
as used in this gray gas approximation is also independent of wavelength). The
material used in the arc heater is a copper alloy which, if highly polished, has
an emissivity of the order
E .15
It would be highly optimistic to expect this surface condition, if obtained, to last
for any period of time. It was found from the experimental data on the low pressure arc heater that after a relatively short period of time the interior surfaces
of the arc heater became covered with a dark layer of material. Analysis indicated that it had to be a combination of a number of the oxides of copper. These
oxides are either formed due to erosion of the copper electrodes or by chemical
reaction of the surfaces with the high temperature air. Now the emissivity of
copper oxide ranges from
e =. 60 . 80
for a smooth surface. The formation of the compound on the arc heater surface
was in the form of a rough powder, which would yield higher values for the emissivity. Hence, it is felt that a surface emissivity of the order of one would be
more accurate for the heat transfer analyses.
34
Using the values for the thermal conductivity of air given in Ref. 26 and 27,
and snown here in Fig. 5, and the mean linear absorption coefficient as shown in
Fig. 6, we find that
N< 1
for the stagnation pressure and temperature range of the arc heater flow. Again
these properties were evaluated assuming the stagnation temperature to be a
mean temperature. The highest value for N occurs at the maximum in temperature and pressure (T = 5000~K, P = 2500 psia). As such these values are very
m
low and indicate that the role of conduction as a heat loss mechanism, either in
establishing the wall heat load or the temperature distribution across the flow,
would be small compared to that of radiation. This statement must be qualified,
however, if large temperature gradients are present or if the temperature distribution across the flow is fairly flat and a cold wall exists. The latter case is
approached as the absorptivity of the gas is increased, i. e. optical thickness is
large.
The effects of thermal radiation on the temperature distribution and heat transfer to the wall can be characterized by the role that the optical thickness, T, plays
in the energy transport mechanisms. To couple this parameter to some physical
dimension of the arc heater, we will define T as the ratio of the diameter of the
0
arc chamber, D, to the mean free path of radiation, 1/K,
T =KD
0o
35
10
0
o
E

*O
CE..C
Ir,
8
6
Pressure
10
30
Atmospheres
1
100
4
2
0
I
I
0
1
2
3
4
5
Temperature, KOx 103
FIG. 5. THERMAL CONDUCTIVITY OF EQUILIBRIUM AIR
36
This is a measure of the diameter of the arc chamber in radiation mean free
paths which can serve to show the effect of a change in either physical size or
arc heater operational level on the heat transfer mechanism.
It should be noted here that for a gray gas approximation, the linear absorption coefficient K is constant, but K for air varies considerably as indicated in
Ref. 28 and 29. Hence a mean value snould be used. The mean value, which
was presented in Fig. 6 as a function of temperature and pressure, will be the
Planck mean absorption coefficient
oc
K B d
V V V
0
K= oC. ——. (41)
B d
0
The values for K are computed from the above references.
The optical thickness is then defined as
T = KD (42)
Evaluating the optical thickness for the arc heater stagnation temperature
and pressure levels for an arc chamber diameter of 6 in., we find
4
10 < T <.6
 o
indicating that the radiative heat transfer cannot be accurately assessed by an
optically thin approximation. Equation (39), which gives a simple approximation
for the radiative heat transfer to the arc chamber wall, is valid only over part of
37
2.0
1.0
0
1.0
2.0
3.0
4.0
5.0
*O
I
E
0
0
CO
00
2 4 6 8 10 12 14 16 18 x 103
Temperature, ~K x 103
FIG. 6. PLANCK MEAN ABSORPTION COEFFICIENT OF AIR.
the arc heater operational regime. Therefore the estimate for the maximum wall
heat flux must be made. This is particularly true considering the role that the
heat flux plays in any structural analyses coupled with high pressures.
Since the design of the arc heater system is directed toward a unit capable of
encompassing its operational range with as much latitude as its materials and
design schemes allow, the main interest lies in the maximum heat loads that will
be encountered. To ascertain these levels, the magnitude of these independent
parameters will be chosen such that the maximum heat transfer is indicated for
the given operating conditions. Hence, it is assumed that these operational levels
are characterized by a conductivity parameter, N = 0. 001, optical thickness,
T < 1. 0, wall temperature T of 500 K, and wall emissivity, e = 1. 0.
The temperature distributions used, which are solutions of the energy equation, are those resulting from the analysis of Viskanta and Grosh (24). These
distributions are presented in Fig. 7, for two values of O. As shown, the effects
on the temperature distribution for w varying from 0. 1 to 0. 5 are very small.
Therefore over the range of 9 previously indicated, it will be assumed that the
w
heat transfer estimates will not vary strongly with the wall temperature and can
be adequately established by assuming T to be constant.
It must be noted here that for the temperature distribution shown a value of
N = 0. 01 was used instead of the required value of 0. 001. The information of
Ref. 30 and 31 indicates a small affect of N on the flow temperature distribution.
The chamber wall transfer estimates, however, are made assuming N = 0. 001.
39
1.0
a 6 c t.6
QC o
Cb.5.4.3.2.1
0
0.1.2.3.4.5
Radial Distance, rT/o
FIG. 7. EFFECT OF WALL TEMPERATURE ON ARC CHAMBER
TEMPERATURE DISTRIBUTIONS.
40
Values for O were obtained by integrating the various temperature distributions, e  ew/eO  0w, and finding a mean value, T. The stagnation temperatures investigated were equated to this mean value and the corresponding values
for T established. These values were used in nondimensionalizing the various
0
heat transfer parameters.
The resulting arc chamber temperature distributions for various values of
optical thickness are presented in Fig. 8. These curves show the effect that
changes in either stagnation temperature or stagnation pressure have on the
temperature profile. An increase in either quantity is reflected by an increase
in K and hence r. This tends to drive the gas layer between the arc chamber
O
4
walls toward blackbody radiation, i. e. q  a T.
0
A simple illustration of this is to look at the radiation from a constant temperature slab of gas between two black walls. Equations (33) through (36) for this
case reduce to
q=2 aT 4E2() dr (43)
0
where q is the radiative heat flux at the wall
~~w~~~~~
qw T4 [1  2E3(T)] (44)
and since
E3(T)  O
3 ~ (45)
T  O0
0
41
1.0 o = U. \
to= 0.2.9
to= 0.1.8.7.6.4.3.2.1
0.1.2.3.4.5
Radial Distance, rITo
FIG. 8. EFFECT OF OPTICAL THICKNESS ON ARC CHAMBER
TEMPERATURE DISTRIBUTIONS.
I
I
42
as
q  oT4 (46)
These observations, coupled with the low values of the conductivity parameter,
N, point to radiation as the dominant source of wall heat flux.
The resultant heat flux to the arc chamber wall as a function of stagnation
temperature and pressure is presented in Fig. 9. These values are obtained by
using the temperature distribution of Fig. 8.
This range of wall heat flux is used in the analyses on the arc chamber structural and cooling requirements. These studies in turn, help map the arc heater's
operational levels of stagnation temperature and pressure.
C. NOZZLE HEAT FLUX
The arc chamber is considered to be terminated by a sonic nozzle. Thus, the
highest velocity, and probably highest heat transfer, in the nozzle will occur at
the throat. Assuming an isentropic compression from the arc chamber stagnation
conditions the local temperature and pressure in the nozzle throat can be expressed
as
T* = To(1~ + Y2) (47)
o 2
=P*~~~ P0 2 ~~~~~(48)
P=P [(1 \1) yo (48)
where the subscript * indicates conditions at M = 1. 0. Values of y will be functions of both temperature and pressure, with a nominal value of 1. 2 felt to be
43
Heat Flux Limit
For Water Cooled Coppej
Po = 2500
Po =1500 psia
Po = 500 psia
Arc Chamber Material
Structural Limitation,
N
4=. 5
C13
LLa)
r
N = 0.001
Tw = 500 K
= 1.0
102
10 L
0
1
2
3 4 5
Stagnation Temperature, ~K x 103
6
FIG. 9. ARC CHAMBER WALL HEAT FLUX.
44
representative of the arc heater flow conditions. The decrease in temperature
and pressure from stagnation conditions causes a decrease in the ability of the
gas flow to absorb thermal radiation. This effect becomes more pronounced if
we consider its optical thinness. Defining the optical thickness in terms of the
nozzle throat diameter,
=K Dt (49)
The maximum value of T occurs at the highest values of stagnation temperature
and pressure with the throat diameter sized to the arc heater mass flow.
For the range of operating conditions previously discussed we find
< 2x104
owhich is considered to be indicative of an optically thin gas. The radiative heat
flux at the wall is small compared to the convective heat flux and therefore the
approximation previously discussed for the thermal radiation from an optically
thin gas should be valid at the nozzle throat. This also uncouples the radiative
terms from the energy equation allowing the contribution of each mode of heat
transfer to be calculated separately and summed. The wall heat flux is then:
+ (50)
qw = qconv qrad (50)
wall wall
1. Radiative Heat Flux
Rewriting Eq. (33) for the local radiative heat flux after letting
(51)
qr
Qr (T) = .. (51)
4a T
m
45
T
O
1i~4
Qr (T) R(T) E3(  T) + f 4(t) E2(t  T) dt  R(o) E3(T)
 4(t) E2(  t) dt (52)
2
0
Assuming a symmetric temperature profile the radiative heat flux at the wall
becomes
T
Q 2 Ro) E3(T ) + J (T) E 2() dT  R(o) (53)
r wall L2 (3 2 2
Applying the assumption of an optically thin gas, radiating at the mean temperature defined in Eq. (26),
4'1
4 =  e0 () dT (54)
00
Reevaluating Q (T) at the wall (T = 0) and assuming a wall emissivity of 1. 0.
r ll = (m4  e4 ) [1  2 E3(To) (55)
wall
For T <~ 1, E3(rT) can be approximated by
E3(T )   T (56)
3o 2
46
Hence
Qr = (o 4 2 1
wall m
(57)
=2 (0  0 4) (T)
m w 0
Substituting in Eq. (57) and assuming T = 500~K and T = T*, we find
qr l 5 kw/ft2
wall
2. Convective Heat Flux
The convective heat flux, qc, is estimated using the empirical equation of
Lobb (32). The heat flux at the throat is expressed as
(P 75.23
q = 1.19 x 103( (T  Tw) (58)
wall (D 8 w
The resulting convective heat load is shown in Fig. 10 as a function of stagnation
pressure and temperature. A material limitation will again be felt and maximum
allowable stagnation temperatures of the order of 3500 K to 4500 K at the higher
pressure levels are indicated.
Comparison of the range of convective heat flux values to the maximum value
for the radiative heat flux indicates the small role radiation plays in the nozzle.
The values used in the analysis on structural and cooling requirements are those
of Fig. 10.
47
105 
Po, psia
Heat Flux Limit For 2500
Water Cooled Copper 1500
xs ~~ "t~~ / /.^^.^^^~~ =50~1500
L I l II
x 102
Stagnation Temperature, ~Kx 103
FIG. 10. NOZZLE WALL HEAT FLUX.
a): 103
103
1 2 3 4 5 6
Stagnation Temperature, "Kx 103
FIG. 10. NOZZLE WALL HEAT FLUX.
48
IV. MATERIAL SELECTION
Since the temperature of the gas confined by the arc heater is above the
melting point of available metals and refractory materials, a conductive material
in conjunction with a cooling scheme is required. This scheme, however, introduces temperature gradients in the material which can cause high thermal stress.
Coupled with this are the stresses due to the high pressure levels so that the requirement of high strength at elevated temperatures is also necessary.
If one is to survey available materials for the purposes of arc heater construction a meaningful guide to material selection must be made. One such comparison
will be made by looking at a simple analytic study of the stress in the arc chamber
wall. The total stress is assumed to be the sum of the stress due to chamber
pressure differential and the thermal stress from the temperature difference
across the wall.
If we idealize the chamber as a thin walled, semiinfinite cylinder the stress
can be expressed as follows:
total= thermal+ pressure
E aAT APD ()
2(1 ~)+ 2t
We can get Eq. (59) in terms of material properties by using the Fourier heat
conduction equation. Substituting for the wall thickness, t, its equivalent kAT/q:
EaAT APqD (60)
"total 2(1  ) + 2kAT
49
so
dtotal Ea APqD (6
(61)
d(AT) = 2(1 ~ 2kAT2
Minimizing atotal allows a solution for the minimum stress at a given AT
qDAP(  1/2
AT [. J (62).
Substituting into Eq. (60) gives
[E~ODaP]'1/2
[E.paqDAP"1 /2 (63)
min k(l l)J
Therefore any material used must have an allowable stress equal to or greater
than a
min
If for the moment we let the allowable stress be equal to amn and assume
m in
Aj to be constant (Poisson's ratio is generally Q 25 to 0. 33 and does not vary
appreciably for most materials), a figure of merit can be established for any
material.
2 EaqDAP
allowable k(l  i)
or, (64)
2 k
allowable qDAP
Ea (1 M)
We now have a relationship between the physical properties of a material and the
parameters pertinent to the design of the arc heater. Therefore, allowable stress
and thermal conductivity of the material should be high while the modulus of
50
elasticity and thermal expansion coefficient should be small. The higher this
ratio the more effectively the material can withstand high pressures and high
heat loads.
Letting (a2 l bl k/Ea) = 3, we can now survey available materials.
Since the material is subjected to high heat load, the properties will be taken
at a temperature on the order of 600 F. The following table shows the pertinent
properties of a number of commercially available metals.
Material
CuBe (alloy 25)
C.W. and H.T.
CuBe (alloy 50)
C.W. andH. T.
CuZr (. 15% Zr)
C.W. and H. T.
Tungsten
Molybdenum
Rene 41 (Nickel alloy)
Aluminum
Stair ess Steel
Silver
V36 ( cobalt base alloy)
OFHC copper
Columbium
Monel
oallow
psi
x 10
140
90
58
47
35
140
20
100
8
50
8
10
22
TABLE HI
k
BTUft
hr ft2 ~F
80
135
200
72
75
6. 3
116
9. 3
240
11
225
31
17
a
1 x 106
F0
10
10
10
2. 5
2. 5
7
13
10
11
9
10
3. 5
10
E
psi
x 10
19
17
17
40
40
30
10
29
8
30
17
14
24
x 8
x 10
82. 7
64. 3
39. 5
15. 9
9. 2
5.9
3. 58
3. 2
1. 75
1. 05.85.63.343
51
Table III indicates that the materials having the highest j are the copper
alloys. However, this can only serve as a guide to material selection. It is
yet to be determined if these materials can withstand the stress levels imposed
by the arc heater.
If AP and D are held constant and q made a parameter, curves of a i can
be shown versus (Ea/(1  1i), Fig. 11. Typical values for the arc heater will be
AP = 2500 psia, D = 6 in., and with q's of 100 to 500 KW/ft. Superimposed on
Fig. 11 are the properties of the materials given in Table III. Here again the
copper base alloys are the only materials with the proper physical characteristics
which allow them to withstand the design temperatures and pressure loads. It
remains, then, to determine which one of the two alloys is best suited to our
particular design; copperberyllium or copperzirconium.
In view of the data presented in Table III and Fig. 11, it is interesting to note
how poorly the standard OFHCCopper compares to the other material. It appears
to be of little use as an arc heater structural material. However, the effect of
one very important variable is not snown in these data. Since the comparison is
based on minimizing the stress levels in the material, for a given AT, it does
not reflect the magnitude of the temperature differential necessary to transfer
a given heat flux. A more complete comparison is made if the results of Eq. (62)
are included. Using the same range of parameters as in Fig. 11, curves of AT
versus akE are shown in Fig. 12. Here the reason for using copper or copper
alloys is evident. For a number of the materials showing favorable characteristics, by the previous comparison, we find here an increasing operating
52
106
105
VI
L"
c(1)
C,,,=,=
L
Alloy (25)
CuBe f
Alloy (10)
T..1
qw= kw/ft2
500
250
100
t Stainless
CuZr
t
V36
t
Cu  Be
Aluminum
Monel
Columbium
1Q4
OFHC
in3
I
I l I I I I I I I
I I I I I I II
I I I I I I I
1U 103
104
Material Index,
105
106
EOC
k(1FL)
FIG. 11. ARC HEATER MATERIAL GUIDE vs STRESS
53
103,
Rene
Stainless
V36
Moly and Monel
Tungsten
ns nCuRe (25) and Aluminum', I i Silver
o^ ~~~~ ~ ~~~~~~  ^^ ^ Cu  Be(1
102Q),,~
i10
103 104
EoCk
FIG. 12. ARC HEATER MATERIAL GUIDE vs TEMPERATURE
DIFFERENCE.
0),u Zr
OFHC
q, kw/ft2
54
temperature level. By this comparison OFHCcopper, and copperzirconium would
produce the lowest wall temperatures and hence have a simple cooling scheme.
Regardless, while the standard copper was adequate for the low pressure arc
heater, the two copper alloys still appear to be best suited for high pressure
application.
If we look at the strength of both alloys at elevated temperatures, Fig. 13,
we find that copperzirconium has a slow falloff of strength with temperature,
while copperberyllium exhibits a rather sharp falloff. Although copperberyllium has a 3 to 1 strength advantage over copperzirconium, the falloff in
strength with temperature is considered to be characteristic of a brittle material.
Further evidence of the hot brittleness of copperberyllium is indicated by the
data shown in Table IV, (33).
TABLE IV
Reduction of Area %o
Test Temperature
Test Temperature CuBeAlloy 50 CuZ R 57
R b
Room 28 67
200 30 70
300 33
400 25 70
500 10
600 6 70
800  67. 5
1000  78.0
55
180 r
o CuBe Alloy 25
o CuZr (0.15 %Zr)
160
140
120
c \
) \
*, 80
60
40
400 500 600 700 800
Temperature, ~F
FIG. 13. EFFECT OF TEMPERATURE ON YIELD STRENGTH
OF CuZr AND CuBe.
56
Also, copperberyllium alloys are notch sensitive beginning at 500 F. The
reduction of area data in Table IV indicates that CuZr is more ductile throughout the temperature range and that increasing the temperature of CuBe above
400~F causes increasing brittleness in the material.
Although CuBe has a room temperature yield strength advantage over CuZr,
it is the notch sensitivity and brittle character of CuBe which makes it undesirable for the arc heater material. The arc chamber design will incorporate threads
as a means of mounting both the end closures and electrode glands so that a material with notch sensitivity is not desirable. It is concluded that a copperzirconium alloy is the best material for this particular application.
57
V. STRESS ANALYSIS
The physical model of the arc heater's chamber, nozzle, and cooling system
upon which the stress calculations are based is shown in Fig. 14. The principal
features are that the wall is unrestrained axially with no external loads imposed
on either the arc chamber or nozzle. Therefore all wall loading arises from
pressure and thermal differentials. The effective wall thickness is also assumed
to end just below the spiral groove in the chamber or nozzle outside surface. All
material properties used are those derived from tests subjecting material samples
to "short term" heating. Properties of interest for copperzirconium are shown
in Fig. 15 and Table V, (34).
TABLE V
Property CuZr
KThermal Conductivity.66
BTUin.66
ft2sec  F
a linear coefficients of 1 6
thermal expansion 1/F0
E modulus of2 1. 6 x 10
elasticitylb/in.
gL Poisson's Ratio 0. 33
The octahedral shearing stress theory is the basis for determining the loads
required to cause material failure by yielding. The maximum octahedral stress
58
/////////////////I
Tb, Pw  Coolant Flow
ycp /WVO^
t
cR
Stagnation
Conditions Jo o
~ ,Coolant Flow
O`3
O'
FIG. 14. MODEL FOR ARC CHAMBER AND
NOZZLE THROAT STRESS ANALYSIS.
59
at a point in the material must not exceed the allowable stress. Values of heat
flux, wall thickness, and gas side wall temperature are chosen as the independent
variables and varied over limited ranges. Optimum wall thickness and wall temperature are determined by plotting various combinations of the independent
parameters.
Consider the free body in Fig. 14, which shows a section of the particular
wall subjected to pressure and temperature differentials. For a thick walled
cylinder, the various normal stresses are expressed as:
Longitudinal Stress:
r2
Plrl. = 2 2 (65)
r2  r1
Circumferential Stress:
2 2
2 2 rl r2
Plrl  P22 + 2 (P1 P2)
r
at.. —. —— 2 (66)
r2 r1
Radial Stress:
2 2
2 2 r1 r2
P2r2  Plrl + (P1  P2)
r
= =.. r(67)
r 2 2
rl r
Thermal Stress for thin wall cylinder:
0th = Br (T1  T2) (68)
60
For steady state heat transfer the thermal stress coefficient is expressed as:
Ea rr  (r2 + rl)
Br:2<[ (r^2 1 J
(69)
The three principal stresses at a point, P, in the material for any wall location
in the cylinder are as follows:
1 = aQ +th
a2 = R
(70)
(o3 =at + th
The preceding may be substituted into the octahedral shearing stress relation
which is written
c = (1  2
+ (2  3 + (3
2 r3) (3
1)211/2
orIJ
(71)
Allowable octahedral shear stress:
A 3e'A 3
(72)
Resulting in a safety factor,
N=A
C
c
(73)
Taking a heat balance on an element Ak of the arc chamber wall
t 2 rm A (T T2)
w
or,
61
Q tw
TT T
1 2 2 2r Ar k
m
(74)
q tw
k
There are two criteria that can be used to establish an optimum wall thickness for the chamber or nozzle. One criterion is to assume that the material is
most efficiently loaded when the total combined stress is equally divided between
the inside and outside wall elements, i. e.
1 2 2 3 3 1 12 2 2 232
(a ) + (a2 a3) + ( ) = (a  a + (a  l2 a3) + (oa3  )al
r r2
(75)
The other criterionis to find the point in the wall where the stress is the maximum
and independent of wall thickness. The latter criterionis usedin the ensuing
stress analyses on the arc chamber and nozzle.
A. ARC CHAMBER
From this general analysis it is apparent that numerous solutions are possible,
each dependent on the particular assumptions made at various stages of the calculations. These assumptions are quite arbitrary, provided they tend toward the
functional purpose of the design and meet the requirements of practicability in
manufacturing and assembly. In the following sections, a number of assumptions
will be made and values used without argument or presentation of studies establishing a standard of "best possible" value. In these instances, it will be the basic
62
design ground rules and/or arc heater support equipment which will dictate
that particular assumption.
Listed below are the design parameters for the arc chamber:
Chamber pressure, psia 2500
Chamber inside radius  in. 3
Cooling water pressure, psia 250
Mechanical and physical properties of the chamber materials are snown in
Fig. 15 and Table V. It should be noted that the values used result from "shortterm" tests at elevated temperatures on small specimens, with optimum cold
working and heat treatment. These data show high tensile properties but represent the only information that could be obtained on the alloy. Final values of
tensile properties will depend, of course, on the material fabricator's heat treating and cold working facilities.
In applying the stress equations to the arc chamber wall, it is assumed that
the pressure stress is created by the difference between the cooling water pressure and the arc heater stagnation pressure. Since the radial stress contributes
very little to the total combined stress, the stress system is also assumed to be
biaxial. This allows, 2', to be dropped from Eq. (71). A significant reduction
in the number of calculations can also be realized if the dependence on the variable, r, can be eliminated.
1. Point of Maximum Stress
Equations (65) through (69) indicate that the point of maximum pressure or
thermal stress occurs on the inside of the wall surface. However, considering
63
(I
a:),.n. w
4#)
a)
w,.7.n
80
60
40
CuZrCold Work and Aged
(Short term heating)
0.2% Yield,, o~ ——,
0
E
I
rr
I
300 m
0 "'f
200 2
t0
100 E
L.
a)
I
Thermal Conductivity
20
0 L
0
 I i I II I I
200
400
600
800
1000
1200
Material Temperature,~F
FIG. 15. EFFECT OF TEMPERATURE ON THE PROPERTIES
OF CuZr
64
the total stress at a point, the thermal stress is subtractive on the inside and
additive on the outside of the wall. The difference between the stress at the inner
and outer surface is
a 1= a (Br  B (T2  T1) (76)
r r r2 r1 2 1
a1 > aT (77)
r2 r1
and
a3i  a (  + (B B (T2 T) (78)
33 w r2 r r1 2 1
or
3 >03 a (79)
r r
r2 I1
if
(B  B ) (T  TT1 > (P P ) (80)
2 1
Therefore the effect of thermal stress is to shift the maximum stress point
to the outer surface of the wall. Thus the maximum stress point will be at the
outer surface and invariant if Eq. (80) is satisfied.
For the purposes of the analysis on the arc chamber and nozzle it is necessary
to establish whether the magnitude of the thermal stresses anticipated will shift
the point of maximum stress. To estimate these levels the following analysis is
65
made assuming, for the moment, that the various stresses can be found using
the "thin wall" stress equations. Rewriting Eq. (80), we have the requirement.
2B (T2 T2) > (P P) (81)
2
or
(P  P )
ath > o (82)
Letting
EaAT
0th = 2(1i () (83)
and including the Fourier heat conduction equation gives,
Eoaqt (84)
th = 2(1  k
The minimum wall thickness, t, is established by pressure stress requirements:
t APDm (85)
2a
e
Therefore
EaqAPDm (86)'th = 4(1  j) ka 86
This must be greater than AP/2 or
EaqDm > (7)
(87)
4(1'2 )kcre 2
For a given material and size, a minimum heat flux can now be established.
66
For our particular material this would correspond to heat fluxes into the
2 2
arc chamber wall greater than 35 KW/ft, and greater than 200 KW/ft into the
nozzle wall. Therefore, for the heat loads considered (Fig. 9 and 10), the point
of maximum stress will be on the outer surface and invariant with wall thickness.
2. Optimization of Wall Thickness
The arc chamber is the component most affected by the increase in heat flux
at increasing pressure level. However, the main emphasis is placed on operation at the high pressures and, therefore, its design is slanted toward a structure
capable of withstanding the design pressure at the highest possible thermal load.
To help establish the pertinent arc chamber dimensions, a computer program
using Eq. (65) through (74) was utilized. The chamber stress was calculated for
various combinations of wall thickness, heat load, and stagnation pressures.
Figures 16 through 19 show the results of this analysis.
Examination of the generated data revealed that a heat flux of 500 KW/ft at
a stagnation pressure of 2500 psia could be handled using copperzirconium as the
arc chamber material. Safety factors at various heat fluxes and two stagnation
pressures are shown in Fig. 16 and 17. The safety factor is as defined in Eq. (73).
Superimposed on these figures are lines of constant gas side wall temperature,
T. These values are obtained assuming a cooling system which allows no localized boiling. As shown, the wall temperature would not exceed 500 F. Therefore
the previous assumption, used in the section on material selection, of an average
material temperature below 600 F will be realized.
67
2.2h
Material: CuZr
Po = 2500 psia
2.0
~ Tw = 300~F
>< Tw = 400~F
1.8k
o,)
L)
s3 HooOa
CO
1.6
1.4F
 Tw= 500~F
1.2
200 O
 500
qw, kwlft2
Tw= 600~F
1.0
I
I
0.2.4.6.8
1.0
inches
1.2
1.4
Wall Thickness,
FIG. 16. SAFETY FACTOR vs ARC CHAMBER WALL THICKNESS
2.8
Tw= 300~F
2.6k
2.4H
Material: Cu  Zr
P = 1500 psia
Tw = 400~F
2.2
200
2.0
0
t)
LL
a)
u>)
1.8 
1.6_
 Tw =500~F
1.4.=..
500
_q, kw/ft2
1.2
1.0 
I
I.8
0.2.4.6.8
1.0
1.2
1.4
Wall Thickness,
inches
FIG. 17. SAFETY FACTOR vs ARC CHAMBER WALL THICKNESS.
These plots would indicate an optimum wall thickness of 0. 25 in. for the case
of highest pressures and heat fluxes. This wall thickness is impractical, however,
when one considers the overall design of the arc chamber. Since the arc heater
end closures are attached by threads in the chamber wall, the effective wall thickness would be reduced to a value smaller than required to counteract pressure
stresses alone. This design feature coupled with the emphasis on high pressure
levels, led to a final wall thickness of 0. 6 in. In doing so, the resulting heat flux
2
that can be carried by the chamber wall at the 2500 psia level will be 400 KW/ft
A plot of safety factor versus wall heat flux for this wall thickness at two stagnation pressure levels is shown in Fig. 18. The relatively small effect that the
pressure stress, in comparison to the thermal stress, has on the safety factor is
apparent
The calculated stresses used to determine the safety factor are those at the
outer surface of the arc chamber wall since maximum stress occurs at this point.
Figure 19 presents the variation of safety factor through the arc chamber wall.
Further, the results of the stress calculation, if reflected back to the chamber
heat transfer analyses, would tend to lower the allowable stagnation temperature
levels at 2500 psia. This effect is shown on Fig. 9.
70
3.0
Material: CuZr
Wall Thickness =0.04 inches
2.0
LS.
0
CU
ca
CO
a)
00
Po, psia
1.0
1500
2500
I _ II
3000
4000
Wall Heat Flux,
5000
kw/ft2
6000
FIG. 18. VARIATION OF SAFETY FACTOR WITH
ARC CHAMBER HEAT FLUX.
71
5.0
Material: Cu  Zr
Wall Thickness 0.6 inches
qw= 400 kw/ft
PO = 2500 psia
4.0
0
(])
VlL
3.01
/
/ "
Cooling Water
I nterface
2.01
_  Air Interface
1.0 
I I I I I I
0

0.1.2.3.4.5.6.7.8.9 1.0
Fraction of Wall Thickness
FIG. 19. VARIATION OF SAFETY FACTOR THROUGH
THE ARC CHAMBER WALL.
72
B. NOZZLE
As in the heat transfer study, the nozzle throat was selected as the point for
the stresses calculations. It is assumed that the throat structure can also be
modeled by the free body shown in Fig. 14. Again it is assumed that all wall
stress is a result of pressure and temperature differentials. CopperZirconium
will also be used for the nozzle, therefore the material properties will be those
of Fig. 15 and Table V. Since the nozzle is used only to constrict the arc chamber flow it takes the form of an orifice.
The axial pressure stress at the throat is now due to the difference between
the gas flow pressure distribution on the converging portion of the nozzle and the
cooling water pressure acting on the cooling system geometry. The cooling water
pressure for this analysis is assumed to be 250 psig. The radial pressure stress
term P1, is assumed to be functionally determined from the well known isentropic
relationship given in Eq. (48). As in the case of the arc chamber, the isentropic
exponent, y, is assumed to be constant through the nozzle and a value of 1. 2 to
be representative for our enthalpy range. The resultant equation for radial pressure being
P =. 563 P
1 o
For the range of throat wall heat flux shown in Fig. 9 and the nozzle geometry given in Fig. 20, the equations and computer program used to calculate the
arc chamber stress levels was modified to give the stress levels at the nozzle
throat. The throat wall stress was calculated for various combinations of wall
73
Water
Nozzle Insert
1.25
t
FIG. 20. SCHEMATIC OF ARC HEATER NOZZLE.
thickness, heat flux, and stagnation pressure. Figures 21 and 22 reflect the
primary results of these calculations. The calculated stresses used to determine the safety factor are those at the outer surface of the nozzle throat wall.
These data would indicate an optimum wall thickness on the order of 0. 01 in.
for the nozzle throat. However, the machining of the nozzle throat to this dimension is quite impractical. The fabrication of the nozzle being the prime consideration, a wall thickness of 0. 04 in. was the final choice. In doing so, the resulting
heat flux that can be carried by the chamber wall at the 2500 psia level will be
5000 KW/ft. A plot of safety factor versus wall heat flux for this wall thickness
at two stagnation pressure levels is shown in Fig. 22. The relatively small effect
that the pressure stress has on the safety factor is again apparent.
75
4.0 F
qw, kwlft2
Tw = 300
3000
J
3.0 
4..
0
CD >L.
Q)
1 
4000
5000.,
6000 A
Tw = 400
2.0 F
Tw = 500
1.0 F
I
I
I
I
I
L .01.02.03.04.05
Wall Thickness,
inches
FIG. 21. SAFETY FACTOR vs NOZZLE THROAT WALL THICKNESS.
2.6
2.4
2.2
Material: Cu  Zr
Wall Thickness  0.6 inches
0
Uao
LICD
V1.
2.0
1.8
1.6
1.4
1.2
1.0.8
P, psia' 1500' 2500
200
Chamber
300
Wall
400
Heat Flux,
500
kw ft2
FIG. 22. VARIATION OF SAFETY FACTOR WITH
NOZZLE THROAT HEAT FLUX.
77
VI. ARC CHAMBER COOLING SYSTEM
The general requirements on a cooling scheme for any component are:
1. The selected water flow rate and water passage configuration must
ensure that the inside wall temperatures and thermal gradients through
the wall are compatible with results of the stress analyses.
2. The water flow rate and pressures must be compatible with the available
water supply system.
3. The flow rate must be appropriate to the demands on the pumping system by all components.
4. The cooling scheme will allow no localized boiling to occur.
If condition (1) is satisfied, tne required wall to water heat transfer coefficient
may be determined. However, this will be a function of both flow rate and cooling
passage geometry, with no optimum combination apparent. Limits will exist when
one considers conditions (2), (3), and the requirement of fabrication practicability.
Therefore, a cooling scheme that is commensurate to the existing pumping capabilities will be the strongest governing factor.
Just as in the case of the other aspects of the arc heater design, the unknown
magnitude of radiation losses at elevated pressure tends to slant the design of
this component towards a system capable of handling high thermal loads. Therefore, an arc chamber cooling scheme is needed which allows for the possible
monitoring of temperature distribution along the chamber wall and easy introduction of additional cooling water if hot spots are detected.
78
The cooling scheme used is shown in Fig. 23. It consists of a continuous
copper tube soldered to the outer wall of the arc chamber. A spiral groove
(thread), is machined in the outer wall of the arc chamber and the copper tube
placed in the groove. This arrangement gives a flexible, accessible cooling
system and in addition the machining and installation effort for it is not overly
complicated. This system requires the tube to be imbedded into the surface
which can, by proper mating to the chamber, produce an effective cooling surface
area greater than the surface of the arc chamber. Some simple expressions
establish the depth the tube must be imbedded.
The required cooling surface per unit length of arc chamber is
A = rD (89)
C C
The surface area of the tube in contact with the chamber will be:
ATbe = Sr D N (90)
Tube c
S= rt (91)
Equating the two surface areas we get the angle subtended by the tube surface to
be:
e = 2 radians
Some pertinent dimensions of the coilsurface interface are found from the
geometric construction in Fig. 23.
d = rt (  cos (92)
and
79
Cooling Coil
(Thin Wall Copper Tubing), Effective Arc Wall
tw Thickness
Inside Surface of Arc Chamber Wall
rt
FIG. 23. ARC CHAMBER COOLING CONFIGURATION.
80
=rt sino (92)
t 2
The range of cooling coiltube sizes considered are from 0. 25 to 1. 0 in.
By imbedding a given cooling tube greater than d, an effective cooling surface
greater than the cylindrical surface of the arc chamber can be realized. A "fin
effect" can then be obtained, resulting in a cooling scheme more efficient than
enclosing the arc chamber with a water jacket.
A. EFFECT OF A FINNED SURFACE
Although this effect is not as pronounced when using coolants with high heattransfer coefficients it can be advantageous when using high conductivity materials. This is shown by equating the filmtransfer resistance and the thermalconduction resistance of a plane wall of thickness equal to onehalf the fin thickness.
The fin will result in high heat transfer rates if,
2k
> 1 (93)
Typical values for copper and water would indicate:
k = 0(6 1) (94)
For the geometry shown we will assume 6 to be equal to 0. 32 rt. Since the largest
cooling coiltube considered was 1 in. O. D.,
2k
> 6. 25 (95)
Therefore, this cooling scheme can result in high cooling capabilities.
To better establish the effectiveness of this cooling scheme and/or an optimum
height, a simple finsurface geometry is needed. Considering the coolingcoil
81
geometry and assuming the fin height, S, to be no greater than the tube diameter
S < 1.54 rt (96)
Taking the ratio of chamber diameter to fin heignt and assuming the cooling coiltube to be 1 in. O. D. or smaller
S/D < 0. 1 (97)
Therefore, to establish the fin characteristics, the arc chamber surface is
assumed to be a plane finned surface.
If we now analyze it as a fin of rectangular profile, we can establish an optimum cross section for a given Nusselt number range. Aviame and Little (35)
gave a general derivation of this problem with optimum values as shown in Fig.
24. For our range of interest, the following values for fin height are indicated.
S =.21 rt . 54 rt
Thus the imbedment depth into the chamber wall will vary from 0. 75 rt to 1. 07 rt.
Considering the fact that there will be some thermal contact resistance between
the cooling coil and the arc chamber (conductivity of bonding material), one would
like this contact surface to be as large as possible, within this optimum range.
It was therefore concluded that the cooling coil would be imbedded one tube radius,
resulting in both a low thermal contact resistance while still producing an optimum finned surface on the arc chamber.
The increase in heat rejection for this system is found by looking at a
"surface effectiveness." This is the ratio of the heat rejected from a finned
surface to the same heating surface with no fins. Letting this ratio be r7 and
82
1.0
to.10 
I.:.1 1.0 10
2S /6
FIG. 24. OPTIMUM FIN CROSS SECTION vs. NUSSELT NUMBER
83
~1.01
V)~ ~ ~ ~~~~2/
FI.4 PIUtInRS SCINv.NSETNME
27 1 ~~~~~~~8,rest
looking at a fin more representative of our specific design, i. e., fin of triangular
profile,
1/2 I (21VT)
q = L(2hk6)/2 1AT (98)
I (2VBS)
where, q, is the heat loss from the fin. Defining the heat loss from the surface
without fin as
q = L6hAT (99)
then
R =q/q0
2k1/2 I1 (2 (100)
= (^h]  = (100)
I (2/BiS)
O
Substituting into Eq. (99) for the range of values previously used
2. 0 7r < 3.0
The finned surface is, therefore, able to transfer 2 to 3 times that of a plane
surface.
Equation (99) also shows that r7 varies inversely with tube size. Therefore,
if the cooling system were optimized by this criterion, it would tend toward
small tube sizes. This trend unfortunately increases the pumping requirements
of the cooling system. Since the existing pumping system has moderate pressure
capability it is expected it will strongly influence the final choice of tube size.
The above analysis, however, does enter strongly, when one considers the heat
transfer characteristics of the cooling coil.
84
B. COOLING COIL MASS FLOW CHARACTERISTICS
The flow through the cooling coil will be calculated by taking an energy balance
across a typical section of the coil. The functional form and complexity of the
equation will depend strongly on whether the flow can be considered laminar or
turbulent. The laminar or turbulent nature of the flow will be felt not only in the
equation describing the wall shear stress, but also help establish whether the
curvature effects of the coil or nonisothermal character of the flow need be considered. Therefore,the Reynolds number regime for the flow through the coil must
be established.
For flow through a tube the Reynolds number is expressed as
41i
Re = (101)
The range of mass flows needed is estimated from an energy balance
qc = mr C AT (102)
c p
For q > 50 KW and assuming a maximum allowable temperature rise of
150~F
mi > 19 lb/min
The corresponding Reynolds number range for the range of tube sizes considered
is
Re> 1.4 x 104
The frictional data of Nikuradse (36) on flow through smooth tubes would
indicate the coil flow to be well into the turbulent regime.
85
Since the flow is turbulent, the effects of velocity profile distortion (curvature
of coils) and dependence of fluid properties on temperature are not as pronounced
(37). Therefore, the ensuing analysis will neglect them. It will be shown later
that the nonisothermal value of the flow can be accounted for by evaluating the
fluid properties at a "reference" temperature.
The pressure drop through the tubing is calculated from the well known
relation,
P1  P2 D
1=L 4 (103)
Introducing a resistance coefficient (friction factor)
1 2
x = fpu (104)
Prandtl's equation (36) for f is used since it gives excellent agreement with the
experimental data of Nikuradse over our particular Reynolds number range.
Defining the mean velocity of flow through the tube as
u = —. (105)
pr D2
and combining Eq. (103) through (105) we can plot the pressure required to pass
a given mass flow through a specific tube size and length. These data are presented for a tube length of 50 ft for water at a mean temperature (Tb) of 100~F.
The fluid properties used for this and the following analysis are those shown in
Fig. 25.
86
Cp = 1 BTU/lb F
4
LL
" 63
P 162
461
~~~~t:~~~ 2 60
E
k
40 60 80 100 120 140 160 180 200 220 240 260
Temperature, F
FIG. 25. VARIATION OF THE PROPERTIES OF
WATER WITH TEMPERATURE.
87
Plots of AP and u versus m and tube outside diameter are given in Fig. 26
and 27. Superimposed on them are the maximum pressure capabilities of the
existing laboratory pumps. The pressure data of Fig. 25 coupled with the Eq.
(102) clearly indicate that the cooling coil tube must be larger than 0. 3 in. if any
but minimal arc chamber heat losses are assumed.
C. COOLING COIL HEAT TRANSFER CHARACTERISTICS
The following analyses are aimed at determining the range of tube diameters
capable of handling the required heat loads with respect to their mass flow capability.
For the present we assume; (1) the fluid properties are constant, (2) the
mean temperature at any radius does not vary with angular position or time,
(3) there is no appreciable radial velocity, and (4) the tube flow is turbulent and
fully developed. The latter assumption allows the equations to hold for the
entire length of the coolingcoil. (The intake length for the development of the
temperature field in turbulent tube flow is of the order of 10 diameters which,
for our geometry, will be approximately 2% of the coil length. )
The order of the required heat transfer coefficient is established by equating
the heat flow from the tube wall to the heat removed by the coolant. That is,
q =hA(T  T) hC (T  T in)
"c v w wb p out in
or (106)
m C (T ou T.in )
h A (T  T)
w b
88
103
,Maximum Pressure
Capability of Existing
Pumping System
*.
o,
0
a)
CD
L.
0)
102
10
120 GPM
120 GPM
\ 110 GPM
80 GPM
i 60 GPM
40 GPM
I I I I I I I I 1_.1.2.3.4.5.6.7.8.9 1.0
Tube Diameter, inches
FIG. 26. EFFECT OF TUBE SIZE ON PUMPING REQUIREMENTS.
89
1000
P = Constant
L =50 ft.
Tb = 100 ~F
~\ \ \ \ \\ Maximum Pressure
Capability of Existing
Pumping System
100
k  \'^ \< \ \^^ 100 GPM
>^  \ \ \ \X~ N80 GPM
_i>~~ _P~ \ \ \^~ ~60 GPM,o \ \S 40 GPM
1020 GPM
10 GPM
1.1.2.3.4.5.6.7.8.9 1.0
Tube Diameter, inches
FIG. 27. VARIATION OF FLOW MEAN VELOCITY WITH TUBE SIZE.
90
For the purposes of this analysis, T is allowed to vary such that (T  Tb)
=(Tout  Ti). Equation (106) becomes
m C
h (107)
For our application this is considered to be the necessary heat transfer coefficient,
i. e. the character of the tube flow must be such that it produces these values of h.
Combining this into a Nusselt number
fiC D
P t
N(required) Ak (108)
The presence of a finned surface on the arc chamber is felt through an
"effective" area term in Eq. (108). To establish this area the heat transfer
characteristics of a finned surface are investigated. In the previous sections it
was shown that imbedding the cooling coil into the chamber resulted in a finned
surface. Therefore we have an available heat transfer surface greater than the
outer surface of the arc chamber. It was also shown that an optimum fin height
is obtained if the tubing were imbedded about one tube radius into the arc chamber.
The resultant surface area available for heat transfer, Fig. 22, is
7T2D L
A =  (109)
Equation (106) for the transfer of heat from the tube wall assumes the surface to
be a uniform temperature T. The presence of the fins on the surface, however,
create just the opposite effect. Due to the finite conductivity of the material
91
composing the fins, a temperature gradient exists along the fin. Therefore, the
available surface at temperature, Tw, will be less than shown in the above equation. To accommodate the assumptions of Eq. (108) an "equivalent" fin surface
area at temperature, T, is defined, which when added to the area between the
fins results in what is considered the effective heat transfer surface area.
Equating the heat flow into the fin to the heat loss from this "equivalent" area
dT
q kA b dn hA (T  T) (110)
b dn e w b
or
ql
A (111)
e h (T T) (
w b
In the previous section on the cooling requirements a surface effectiveness, 77,
was defined as the ratio of heat rejected from a finned surface to that of the same
surface with no fins.
ql
h Ab (Tw (12)
Substituting into Eq. (4)
A = 7 Ab (113)
with
>1
The resulting expression for the "effective" heat transfer surface area is
A = A + n Ab (114)
92
Equation (114) shows the effects of fins on the arc chamber wall. They essentially
increase the area available for heat transfer by the amount, 77 Ab. Rewriting
Eq. (114) with respect to the cooling system geometry,
A = iL (D+ 77 2 (r  ) [D + (R  d)]) (115)
\(c t d)]l)
The actual heat transfer coefficient that characterizes the flow through the
cooling coil is obtained from the equation given by Dittus and Boelter (38). That
is,
0 8 0. 4
hD.023
hD 023 )0 ) (116)
k V k
written in terms of Reynolds number, Prandtl number, and Nusselt number.
0.8 0. 4
Nu =.023 (Re) (Pr) (117)
with the Reynolds number and Prandtl number evaluated at the average fluid
temper ature.
Examination of Eq. (107) with respect to the coil mass flow characteristics
indicates that the heat transfer coefficient necessary to remove a given heat
flux from the arc chamber will increase as some power of the cooling coil tube
diameter. The equation describing the actual heat transfer coefficient produced
by the tube flow also shows a power law dependence. Hence, by using these
equations, along with the data shown in Fig. 25, and iterating a tube diameter
can be found beyond which the confined tube flow cannot transport the necessary
heat flow.
93
To circumvent this process, curve fits were made on the data of Fig. 26 and
27. This coupled with the following equations allows for a solution in terms of
tube diameter. Rewriting Eq. (99) for r7 in terms of Nusselt number
1/2
~' /2 Nuk S2 2
1/2 { w
2ku Dt 1/2 [2( k 2) ]
cu 1 t C
^ 5NuTl~   172T ~~(118)
6 Nu k 1/2
 5 Nuk Sk
I [2 c%
t cu
Assuming the following to represent the ratio of I1 to I over our range of interest,
1 (a) 558
a = 0.45 a. (119)
0
and substituting for k and k gives
w cu
71 = 9. 27 Nu 22 (120)
The "effective" heat transfer area is expressed as
A = 2. 09 + 3. 1 Nu (121)
The required Nusselt number can now be written
h C D
Nu = (122)
k (2.1 + 3.1 Nu 22)
w
while the actual Nusselt number is
Nu =.023 (NRe) 8 (Np) 4 (123)
94
Equating Eq. (122) and (123) and substituting in values for (I, Cp, k) the following expression in terms of the tube mass flow and diameter is obtained
8. 62
ihD.=026[] +. 08 ] (124)
t' t
Assuming the tube mass flow appropriate to the existing pumps can be expressed
as
7 2.61
r =5.4 x 10 Dt (125)
the following equation in terms of Dt is obtained
3 2. 61 288
10. 6 x 103 D2. 61 8D 288 1 = 0 (126)
10.6x10 Dt 8D t 1 0 (126)
t t
Solving the above for Dt gives
Dt= 0.6 in.
Therefore the results of the previous analysis indicate an upper limit, on Dt
of 0. 6 in. A specific tube diameter in this range would be established by the total
heat loss to the arc chamber cooling system. Since the cooling system is slanted
toward a design capable of handling the highest possible heat loads, the largest
commercially available tubing appropriate to the upper limit was chosen. The
final choice was 5/8 in., thin wall copper tubing, with an inside diameter of
0. 55 in.
D. COOLING SYSTEM PERFORMANCE
The following summarizes the performance of the arc chamber cooling
scheme. It must be shown that the cooling scheme with the coolingcoil sized as
95
indicated will meet the basic requirements previously outlined. For this purpose
a heat flux of 0. 5 Megawatts into the arc chamber wall is used and the system
investigated to the extent that the maximum design arc chamber wall temperature
is not exceeded.
In the previous analysis the fluid was assumed to be isothermal, i. e., fluid
properties throughout the flow were constant and evaluated at Tb. Figure 25 indicates this to be a good approximation for all properties except the flow viscosity.
This quantity in turn enters into both the equations describing the cooling coil
mass flow and heat transfer characteristics.
Eckert (39) and Deissler (40) have both shown that this effect can be corrected
by using the same equations, but with the fluid properties evaluated at a "reference" temperature. Following the reasoning of Ref. 38, the viscosity variation
of the fluid is represented by a simple power function. Using as a base, the
properties evaluated at the tube wall temperature, a "reference" temperature
as a function of Prandtl number is calculated. Evaluating the flow Reynolds number and Prandtl number at this temperature corrects the tube flow pressure
drop and Nusselt number for variable viscosity. The "reference" temperature,
Tr, is defined as
Tr =R (T Tb T b (127)
where R is a function of Prandtl number. The values for R used were those
given by Deissler (40).
The flow, Nusselt number, Prandtl number and friction factor have been
evaluated at this temperature and the tube flow characteristic established
96
for a tube diameter of. 55 in. It is assumed that the water inlet temperature
remained constant at 50 F. The pressure calculations also reflect the requirements for the velocity head and water saturation pressure, the latter required to
prevent local boiling.
The characteristics of the arc chamber cooling system are summarized in
Fig. 28 through 30.
Figure 28 shows the required pressuremass flow for the arc chamber cooling system and indicates a maximum mass flow capability of 35 GPM with the
existing pumping system. Figure 29 shows the effects of coolant mass flow on
the arc chamber wall temperature. Superimposed on this plot are the maximum
design chamber wall temperature and the maximum flow capability of the cooling
system. These data show that the water flow requirements decrease rapidly with
increases in chamber wall temperature. The required water pressure as a function of wall temperature, Fig. 30, show a minimum pressure point to exist at
420 F. Above this point the pressure required rises sharply due to the increased
pressure needed to prevent local boiling. This latter effect is also reflected in
Fig. 28. These data indicate that the arc chamber wall temperature can be maintained below the maximum design point of 600 F with the existing pumping system,
the optimum occurring at a wall temperature of approximately 420 F. It is felt
that the cooling scheme not only meets the basic requirements for the arc chamber, but has a fairly wide range in which these requirements can be realized.
97
500
Maximum Pressure
Capability of
400 \ Existing Pumps
300
co ~ c~u)
X _ 200\ /
20\ Po = 2500 psia
E < qw = 0.5 Megawatt
L. I^ — ^ OfDt =0.55 inches
100
5 10 15 20 25 30 35 40
Water Flow Rate, GPM
FIG. 28. PRESSURE REQUIREMENTS vs FLOW RATE FOR THE ARC CHAMBER COOLING SYSTEM.
400
CD
D C
CD
Q)
CL
300
I
Maximum Pressure
Capability of Existing
Pumps//
Z f / / /

200
PO = 2500 psia
qw = 0.5 Megawatts
Dt = 0.55 inches
100
0.!.,I!..!...... I I
300
350
400
450
500
550
600
650
Maximum Wall Temperature, ~F
FIGo 29.
EFFECT OF PUMP OPERATING PRESSURE ON ARC CHAMBER WALL TEMPERATURE.
40
Maximum Output
With Existing Pumps
Po = 2500 psia
qw =0.5 Megawatt
Dt =0.55 inches
30Q
0
0
CD
Qc
0
L.
CD
co
20
Maximum Allowable
Design Temperature of
CuZr
10 ,.I
I'350
400
450
500
550
600
Maximum Wall Temperature, ~F
FIG. 30. EFFECT OF WATER FLOW RATE ON ARC CHAMBER WALL TEMPERATURE.
VII. SUMMARY AND CONCLUSIONS
An A. C. arc heater capable of steady state operation at 2500 psia has been
designed. This represents an extension of our earlier investigations into the
heating of gases by an A. C. arc column. The previous unit built was operated
at pressures up to 500 psia. The studies and analysis leading to the design of
the high pressure unit are summarized below.
The new arc heater represents a substantial increase in operational capability
over the lower pressure unit. Accordingly, the problem of scaling an arc heater
to new operational levels was investigated in detail. As a result of these studies
a generalization based on the arc columngas flow interaction is postulated which
divides all arc heaters into two types. The "parallel" flow type is characterized
by the gas flow being parallel to the arc column whereas in the "normal" flow type
the gas flow is perpendicular to the column. A further distinction between the two
is that a strong applied D. C. magnetic field is an essential feature of the latter
type. In the "parallel" flow case a simple analytical model of the gasarc column
interaction is available which provides a basis for the scaling process. The lack
of such a model, complicated by the strong D. C. magnetic field, for the "normal"
flow arc heater makes the scaling process difficult. Scaling trends, however,
were found for each type and are presented. It was concluded from this study that
the "normal" flow arc heater is best suited for our application which uses a 3phase A. C. power source. The importance of the D. C. magnetic field strength as
pressure level increases cannot be over emphasized for the "normal" flow arc
heater.
101
Using the results of the scaling studies and previous experimental data, detailed analysis concerning the material selection, expected heat transfer rates,
stress levels, and the required cooling system were made. This study indicated
that standard OFHCcopper would not withstand the expected pressure and thermal
stresses. Two copper alloys, copperberyllium and copperzirconium, were
found to have the necessary strength characteristics, however, the brittle nature
of copperberyllium at elevated temperatures made it unacceptable as the arc
heater structural material.
At these pressure levels the effects of thermal radiation must be included in
any heat transfer analyses, therefore, a model was chosen that included all three
modes of heat transfer. It was found that the magnitude of the conductive and radiative heat loss to the arc heater walls is established by the parameter, N, and the
gas optical thickness, T. For the arc chamber, N ~ 1 and T < 1, so that radia0 O —tion is the dominant heat loss mechanism. Just the opposite was found for the
nozzle throat where convective heat losses predominate.
The stress analyses clearly indicated that the wall thickness determinations
had to be based on a model which included both pressure and thermal stresses.
The thermal stress was equal to or greater than the pressure stress. The analyses indicated, for both the arc chamber and nozzle throat, optimum wall thicknesses that were smaller than fabrication practicability allowed. The final wall
thicknesses selected were 0. 6 in. for the arc chamber and 0. 04 in. for the nozzle
throat. It is felt that the increase in wall thicknesses, from the indicated optimums, will not reduce the arc heater performance capability.
102
The high thermal loads imposed on these components coupled with the limited
laboratory pumping equipment indicated the need for an effective cooling system.
A cooling system which incorporated fins on the surfaces next to the coolant was
used. Analysis indicated that this system would be two to three times more effective than the conventional water jacket. The method of producing this surface on
the arc chamber is to machine a thread on its outer surface and solder a copper
tube in the thread. The heat transfer capability of this arrangement in conjunction
with the existing pumping equipment indicated an optimum tube size of 0. 6 in. The
resultant cooling system will maintain the wall temperature below the design maximum of 600~F.
From these studies, it is concluded that it will be possible to operate, steady
state, a three phase arc heater at 2500 psia with power inputs greater than 1 Megawatt and mass flows up to 0. 5 lb/sec. It is also concluded that, if higher pressure
levels are desired (to 5000 psia) the next generation arc heaters would have to be
multiwalled, i. e., an inner wall or liner of high conductivity, low strength material supported by an outer wall made of high strength, low conductivity material.
This is based on the assumption that a "normal" flow arc heater would again be
used and that a reduction in diameter appropriate to the increase in pressure levels
would be very difficult to obtain.
As a result of the heat transfer studies, it is felt that the type of heat transfer
surface used on the arc chamber and nozzle (finned copper) will, in future arc
heater development, be one of the most efficient means of handling high heat loads.
This type of surface can also be effectively used in multiwalled arc chamber
103
designs. The only limitations foreseen on its heat flux handling capability would
be produced by the microscopic properties of the materials' thermal conductivity
and the structural design imposed by stress producing loads. Further studies
into both the structural and heat transfer character of this type of surface should
be made; the resultant information applicable to all types of arc heaters. Finally,
if pressure levels of the order attained in hot shot facilities are required (greater
than 10, 000 psia), in conjunction with a threephase A. C. power source, the
"parallel" type arc heater would have to be used. In order to adapt this power
source to the "parallel" flow arc heater a substantial research program is foreseen.
104
REFERENCES
1o Shepard, Co E. and Winovich, W., "ElectricArc Jets for Producing Gas
Streams with Negligible Contamination, " paper presented at the ASME
Plasma Jet Symposium, December 1961.
2. Eschenbach, R. Co and Skinner, G. M., "Development of Stable, High Power,
High Pressure Arc Air Heaters for a Hypersonic Wind Tunnel, " WADD
Technical Report 61100, July 1961.
3. Raezer, S. D. et alo, "Application of D. Co Plasma Arc Heating to Hypersonic Propulsion Testing," J. Spacecraft, MarchApril 1964.
4. "Megawatt ArcHeated Tunnel, " Republic Aviation Corp., RAC 2268, May
1964.
5. Phillips, R. L., "Fundamental Considerations in the Design of an AC Arc
Heater," ARL 649, Aerospace Research Laboratories, WrightPatterson
AFB, Ohio, February 1964.
6. Phillips, R. L. et al., "ThreePhase AC Arc Heater, " ARL 6429, Aerospace
Research Laboraotires, WrightPatterson AFB, Ohio, February 1964o
7o Geister, Do Eo, "Characteristics of a High Pressure A. C. Arc Heater System,"
to be published as an ARL 67 reporto
8. Uhlenbusch, J., "Zur Theorie und Berechnung stationarer und quasistationarer
zylindrischer Lichtbogen, " Dissertation, Rhein. Westf. Technische Hochschule,
Aachen, 1962.
9. Stine, H. Ao and Watson, Vo Ro, "Theoretical Enthalpy Distribution of Air in
Steady Flow Along the Axis of tne DirectCurrent Electric Arc," NASA TN
D1313, 1962.
10. Smith, Ro To and Doyle, J. Po, "A 50Megawatt Arc Heater: Scaling Parameters and Performance Prediction," AF Flight Dynamics Laboratory, WrigntPatterson AFB, Ohio Technical Documentary Report FDL TDR 6491,
August 1964 (AD 607710)o
11o Suits, G. Go and Poritsky, H., Physical Review, 55, 1939.
12. Theoretical and Experimental Investigation of Arc PlasmaGeneration Technology, Part I, "Applied Research on Direct and Alternating Current Electric
Arc Plasma Generators," ASDTDR62729, September 1963.
105
13. Jedlicka, J. Ao, "Shape of a Magnetically Rotated Arc in an Annular Gap, "
NASA TN D2155, October 1964.
14. Mayo, Ro F. and Davis, D. D., Jro, "Magnetically Diffused Radial ElectricArc Air Heater Employing WaterCooled Copper Electrodes, " paper presented
at the ARS Electric Propulsion Conference, Berkeley, California, March 1962.
150 "Development of High Enthalpy, High Power Arc Air Heaters, " RTDTDR634055, February 1964.
16. Browning, J. A. and Poole, J.W., "Arc Gas Heaters Present and Future,"
AGARDograph 84, September 1964o
17. Bond, C. E. et al., "The Development of a TenMegawatt MultiArc and its
Operational use in Hypersonic ReEntry Vehicle Studies, " AVCO Research
Laboratory Technical Memorandum RADTN625, February 1962.
18. Schlichting, H., Boundary Layer Theory, McGrawHill, New York, 1960.
19. Chandrasekhar, S., Radiative Transfer, Dover, New York, 1960.
20. Seban, R. A. and Shimazaki, T. T., "Heat Transfer to a Fluid Flowing Turbulently in a Smooth Pipe with Walls at Constant Temperature, " Trans. ASME,
73, 803809 (1951).
21. Goulard, R. and M., "OneDimensional Energy Transfer in Radiant Media, "
Intern. J. Heat Mass Transfer, Vol. 1, Pergamon Press, 1960.
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Absorbing and Scattering Medium, " Intern. Heat Transfer Conf. Boulder,
Colorado, 1961.
23. Usiskin, C. M. and Sparrow, E. M., Intern. J. Heat Mass Transfer 1, 28,
1960.
24. Viskanta, R., "Interaction of Heat Transfer by Conduction, Convection and
Radiation in a Radiating Fluid," J. Heat Transfer, C85, 1963.
25. Yoshikawa, K. K. and Chapman, D. R., "Radiative Heat Transfer and Absorption behind a Hypersonic Normal Shock Wave, " NASA TN D1424, September
1962.
26. Hansen, C. F., "Approximations for the Thermodynamic and Transport
Properties of HighTemperature Air, NASA TN 4150, March 1958.
106
27. Theoretical and Experimental Investigation of Arc PlasmaGeneration
Technology, Part II, "Applied Research on Electric Arc Phenomena,"
ASDTDR62729, September 1963.
28. Keck, J., Kivel, B., and Wentink, T., Jr., "Emissivity of High Temperature Air," AVCO Research Laboratory Research Report 8, April 1957.
29. Kivel, B. and Bailey, K., "Tables of Radiation from High Temperature Air,"
AVCO Research Laboratory Research Report 21, December 1957.
30. Viskanta, R., "Heat Transfer in a Radiating Fluid with Slug Flow in a ParallelPlate Channel," Appl. Sci. Res., 1964.
31. Einstein, T. H., "Radiant Heat Transfer to Absorbing Gases Enclosed
Between Parallel Flat Plates with Flow and Conduction," NASA TN DR154.
32. Proceedings of the Round Table Conference held in London, 2527 October
1960, on "Low Pressure Aerodynamic Facilities," TCEA TM 12, J. J.
Smoldern (ed.).
33. Horn, D. D. and Lewis, H. F., "Property Investigation of Copper Base Alloys
at Ambient and Elevated Temperatures," AEDCTDR6452.
34. Technical Handbook  CopperZirconium Alloy, American Metal Climax, Inc.
35. Avrami, M. and Little, J. B., J. Appl. Physics 13, 255, 1942.
36. Schlichting, H., Boundary Layer Theory, McGrawHill, New York, 1960.
37. Kreith, F., "The Influence of Curvature on Heat Transfer to Incompressible
Fluids," Trans. ASME, November 1955.
38. McAdams, W. H., Heat Transmission, 3rd ed., McGrawHill Book Co.,
New York, 19 54.
39. Eckert, E. R. G., "Engineering Relations for Heat Transfer and Friction in
HighVelocity Laminar and Turbulent BoundaryLayer Flow over Surfaces
with Constant Pressure and Temperature," Trans. ASME, 78, No. 6,
August, 1956.
40. Deissler, R. G., "Analysis of Turbulent Heat Transfer, Mass Transfer,
and Friction in Smooth Tubes at High Prandtl and Schmidt Numbers,"
NACA TN 3145, May 1954.
107
UNCLASSIFIED..a.~r, r.,.,t ".,fi+;^
beCUnty %AossuicationV n
[
DOCUMENT CONTROL DATA. R & D.~ 5..Wf... _Ut_ _Jjm J 1,J, _. # US RE L..n. ._.4 _^J.4., _.^c.,inA ann Atb MUse he ant fred when the overall r nort is.Imaflfdi
I. ORIGINATING ACTIVITY (Corporate author) I2a. REPORT SECURITY CLASSIFICATION
The University of Michigan Unclassified
Aerospace Engineering Department 2b. GROUP
Gas Dynamics Laboratories
3. REPORT TITLE
ANALYSIS AND DESIGN OF A HIGH PRESSURE A. C. ARC HEATER.
4. DESCRIPTIVE NOTES (Type of report and inclusive dated)
Scientific. Final. Jan 1964 to July 1966
S. AU THOR(S) (First name, middle initial, last name)
Donald E. Geister
6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OP REFS
December 1967 106 40
s. CONTRACT OR GRANT NO. AF33(615)1326 g9. ORIGINATOR'S REPORT NUMBER(S)
b. PROJECT NO. 7065
c. DoD/Element 614450 14 9b. OTHER REPORT NO(S) (Any other numbers that may be ansirned
this report)
d.DoD Subelement 681307 ARL 670276
10. DISTRIBUTION STATEMENT
1. This document has been approved for public release and sale;
its distribution is unlimited.
11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
This is continuation of work reported Aerospace Research Laboratories (ARF)
in ARL 6429. Office of Aerospace Research
TECH OTHER WrightPatterson AFB, Ohio 45433
t i% Amav a e T
I
13. A55TRAC T
This work reports on the analysis and design of an A. C. arc heater capable
of steady state operation of 2500 psia. Included are discussions on the problems
of designing an arc heater for a new operational regime. A generalization on the
arc column gas flow interaction is postulated whereby all arc heaters are
divided into two types. Specifying each group as either a "parallel" or "normal"
flow arc heater the problem of scaling each type is discussed. Scaling trends
were found for each type and presented.
Using the results of the scaling studies and previous experimental data,
detailed studies concerning the material selection, expected heat transfer rates,
stress levels, and the required cooling systems are presented.
mo i k M0%M.  M 
m
DD. NOv651473
TNC SSTA 5,TFTT'T
Security Classification
UNCLASSIFIED
Security Classification
1 4..
~14.~~ TKEYWORDS.LINK A LINK B LINK C
KEY WORDS T t T
ROLE WT ROLE WT ROLE WT
3
Arc Heater
Arc Chamber
High Temperature Research
Steady State Operation
I
L
L
I
U
U
I
  I
Mmj
mmmmmi
MMMM
mm m
mm m
mmlw
TTnnl1o ia~o
Security Classification