THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Mechanical Engineering Technical Report ENGINE PERFORMANCE WITH DIRECTLY DRIVEN SUPERCHARGERS Part I: Performance of Compression Ignition Engines When Fitted With a Supercharger Driven Off the Engine Shaft E. T. Vincent N. Tokuda ORA Project 05847 under contract with: U. S. ARMY DETROIT PROCUREMENT DISTRICT CONTRACT NO. DA-20-018-AMC-0729-T DETROIT, MICHIGAN administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1963

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii ABSTRACT ix OBJECT 1 MECHANICALLY DRIVEN SUPERCHARGERS 1 Type 1 1 Type 2 2 Type 3 2 COMPRESSOR CALCULATIONS 6 Overall Cycle 11 Typical Calculation 14 Displacement Supercharger 16 Displacement Charger With Compression 16 Engine Driven Centrifugal Supercharger 22 Turbo-Charged Engine 25 PART LOAD PERFORMANCES 25 Displacement Supercharger 25 Centrifugal Supercharger 34 Turbo-Charger 34 ENGINE OVERALL VOLUME 39 Displacement Supercharger 39 Centrifugal Supercharger 43 Turbo-Charger 45 BATTLEFIELD DAY REQUIREMENTS 45 COMMENTS 46 ENGINE TORQUE CHARACTERISTICS 47 CONCLUSIONS 50 FUTURE WORK 51 REFERENCES 52 iii

LIST OF TABLES Table Page I. Engine Performance With Directly Driven Root's Supercharger 17 II. Engine Performance With Directly Driven Displacement Compressor With Compression 23 III. Performance With Directly Driven Centrifugal Supercharger 24 IV. Performance With a Turbo-Charger 26 V. Part Load Performance of an Engine With a Displacement Compressor 28 VI. Performance of a 500 BHP (Net) Engine With Displacement Supercharger Delivering 1.452 lb of Air Per Sec at 2.2:1 and 3000 rpm 29 VII. Part Load Performance With Centrifugal Compressor 35 VIII. Part Load Performance With Turbo-Charger 36 IX. Fuel Requirements for Battlefield Day 46 X. Summary of Data for 500 BHP Engines at 3000 rpm 48 v

LIST OF FIGURES Figure Page 1. Comparison of Lysholms and Roots supercharger. 3 2. Typical Lysholm performance map. 4 3. Typical Bicera performance map. 5 4. Typical centrifugal performance map. 7 5. Theoretical Root supercharger indicator diagram. 8 6. Ideal engine indicator diagram. 11 7. Full load performance curves with various types of compressors. 18 8. High-ratio Bicera compressor. 19 9. Friction and cooling losses (estimated). 20 10. Friction and cooling losses (total). 21 11. Part load performance with displacement compressor at 3000 rpm. 30 12. Part load performance with displacement compressor at 2400 rpm. 31 13. Part load performance with displacement compressor at 1700 rpm. 32 14. Part load performance with displacement compressor at 1000 rpm. 33 15. Part load performance with centrifugal compressor. 37 16. Part load performance with turbo-charger. 40 17. Overall dimensions of displacement supercharger. 44 18. Torque curves. 49 vii

ABSTRACT The object of this report is a comparison of engines fitted with various direct drive supercharges with the engine presently employing a turbo-charger. The report covers the usual types of directly driven superchargers: Displacement type, Displacement with Compression, and Centrifugal machines. Full load and part load performances are calculated for each of the types, as well as for a turbo-charged unit for a similar set of conditions. The engine bulk and weight as well as the battlefield day fuel requirements are estimated for various cylinder arrangements for a 500 BHP engine at 3000 rpm in each case. The degree of responsiveness, or more accurately the lack of it, was also examined for each case investigated. ix

OBJECT The object of this analysis is to establish the expected engine performance when employing an engine driven supercharger and to compare this performance with that of the current Turbo-charged engine version at approximately the same pressure ratios. MECHANICALLY DRIVEN SUPERCHARGERS There are quite a number of different designs of compressors suitable for supplying compressed air to an engine with the object of superhcarging. Those suitable for attachment to a high speed compression ignition engine can be divided into three groups as follows: 1. Simple displacement blower without compression. 2. Displacement blower with compression, 3. Centrifugal compressor. The characteristics of these types are considered to be as follows: TYPE 1 In this group the most common is the Root's type compressor and its derivatives such as the helical impeller used by the General Motors Diesel Engine. It is characterized by simplicity of construction, lack of highly complicated machining operations, low internal friction, and simple reliable bearings, drive, etc. It is not too efficient but, due to low losses, is competitive when employed at low pressure ratios. The displacement feature is a distinct advantage for engine supercharging since the air delivered to the engine manifold by piston action remains almost constant per engine revolution, the result being an almost constant manifold pressure at a constant speed as the engine load varies. In addition, the above feature also tends to maintain manifold pressure at varying speed. There will be some reduction at low speed associated with the additional time for leakage through the clearances as the revolutions fall. This reduction is relatively small so that this supercharger is capable of maintaining high torque at low speeds-a desirable feature in many applications. 1

While at the high speed end of the range, the efficiency tends to fall off due to poor filling with new air plus increasing losses. The bulk of this machine tends to be somewhat great, due to the fact that mechanical and aerodynamic limitations place an upper limit on its speed of rotation, if long life and high efficiency are to be secured simultaneously. Speeds of the order of 6-7000 rpm are common; in special cases up to 10,000 rpm can be considered. A typical plot of efficiency against pressure ratio is given in Fig. 1 from Ref. 2. The dotted efficiency line covering high pressure ratios is to be expected at such high ratios plus higher operating speeds for compactness. TYPE 2 In this group can be included the Lysholm, Bicera, and Ricardo superchargers. The action is similar to that in Type 1 except that there is a compression phase following the completion of the inlet stroke, before delivery begins. This feature does not seem to be of much advantage at low pressure ratios, due to additional losses usually associated with the compression phase. If, however, ratios of compression of 1.5 and above are employed, then the compression machine definitely enters the picture. As regards bulk, weight, etc., there is little to choose between the two types; similarly, the limiting revolutions remain in about the same magnitude. The advantage resides in the improved efficiency. There are some additional complications in manufacture, resulting from the compression process, probably accompanied by increased costs, relative to the Root machine. The torque-sustaining character of the Root supercharger is also well retained with the compression type. Figures l(b) and 2 record typical performance characteristics, and Fig. 3 records those of a Bicera supercharger.2,3 TYPE 3 The centrifugal supercharger driven directly from the engine, or exhaust-turbine driven, has been in use for about 50 years, and has given excellent performance under certain limiting conditions. This machine has the advantage of an equivalent compression process, low losses, small bulk and weight, and very high speed of rotation. Efficiencies of the order of 80-85% can be obtained today in small, well designed units. 2

90 Lysholm Supercharger 8o 7000 I 000 S Extrapolated Efficiency 70 Al I / \ For High Speed )00 2000 2 3000 ~a), ~ ~ ~' | 1000 rpm 60 Xwr;^~~~~~ | ^i^i ^^ ~Root Supercharger i yf7o ~, ^F>// m^^~~~ ^^^~ ^Extrapolated Efficiency 50 For High Speed %oo 2000 4000 1000 rpm 3000 301.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Pressure Ratio Fig. 1. Comparison of Lysholms and Roots supercharger.

2.4 9000 2.2 8000 100 200 3 0~ 400 500 600 700 ~Fig. 2. Typical 0ysholm performance map. 04 1.8 0 O 1.6 1.4 1.2 1.0 100 200 300 400 00 6oo00 700 Air Volume Flow Rate (ft3/min) Fig. 2. Typical Lysholm performance map. 4

2. 2000 2500 00 0 0 1.8 0H 1|5 r500 m Ct, o 1.6 Efficiency % 73 0.4 7 Ai Volume Fl^ ate 500 Fig. 3. Tyical Bicer Perfo ne~e map. 56 65~ 1.2 B 1.0 loo 200 0 4oo 5000 Air Volume Fl~wRt o 700 Fig. 3. ~w at (f t9/rin) Ty~calBicra erformance map

The limiting conditions are mainly associated with the fact that the pressure capable of being supplied by the compressor is a function of the square of the speed of rotation. A more or less constant manifold pressure with varying engine speed is an impossibility when directly geared to the engine; thus the high torque maintainance of Types 1 and 2 is lost. The greatest use of this machine was as supercharger for aircraft engines where almost constant speed operation is common. The centrifugal compressor can be employed for the purpose being investigated as a result of its efficiency and small bulk; and, if coupled to an engine and transmission which tend to employ a limited engine speed range, can give excellent results. The main disadvantage is the high speed of rotation required (25-50,000 rpm), and the higher dependency upon the impeller diameter employed. This results in very high inertia of the impeller mass, and speed fluctuations of the engine, resulting from the firing frequency, must be isolated from the supercharger drive by means of slipping torque responsive clutches, fluid couplings, etc. A very high degree of accuracy must be maintained in the manufacture of the gear train. The transmission from the crankshaft to the centrifugal impeller, though relatively small and light, can be expensive. A typical compressor map is given in Fig. 4 taken from Ref. 5; an engine operating line has been added. Some improvement in efficiency can be expected in a modern design. Details of these various types can be checked in Refs. 2-5. COMPRESSOR CALCULATIONS Compressors of Type 1 are best represented by the various designs of the Root blower. The design is characterized by veing a displacement machine, with much air being taken in at the inlet and displaced into the outlet; there is no compression of the air as it flows through the machine. The delivery pressure depends on the outlet restriction, in this case the engine; each charge delivered by the blower is compressed by back flow of air compressed by previous cycles, and not by change of volume of the trapped air. As a result the theoretical indicator diagram of the process is as shown in Fig. 5. by abcd, a simple rectangle, with air inlet at Po, the ambient pressure, and delivery at Pm, the manifold pressure. The work done in the process is given by Eq. (1): 6

Engine Operating Line'3. 800/ 2. 0 / 1%9~ 240rooo EQ/ 22 22000 20000 1.6 18ooo 16ooo 14000 200 280 360 440 520 580 Air Volume Flow Rate (ftS/min) 1200 2000 2800 36oo00 4400 5200 6ooo 68oo00 Q/ %-, ft3/min Fig. 4. Typical centrifugal performance map.

d Pm e c a ) Po I P0 Volume V Fig. 5. Theoretical Root supercharger indicator diagram. Ideal Work of Compression = 144 (Pm-Po) 7 1728 for suction volume / 1 (Pm-Po) ft lb 12 where Pm and Po are in lb/sq in. abs / is in cu in. There will of course be some mechanical losses due to bearings, friction, etc., of the mechanical parts as well as some due to air friction of passages, turbulence, etc. The total work of the machine can be defined by the sum total of these losses as follows: Input Work = (Pm-Po) ft lb (2) 12xr where = ratio of the ideal work to that actually required. 8

In order to relate the input work to some ideal process which involves no losses, and thus represents the 100% efficiency work, Eq. (2) can be related to the isentropic work of compression from Po to Pm, a process involving no losses of any kind-friction, heat, etc. The isentropic efficiency is defined as Isentropic Efficiency Isentropic Work of Compression c Input Work The isentropic work is represented in Fig. 5 by the area abed in place of the area abcd of the compressor, the curve be being represented by PVk - constant. This isentropic work is given by Work of Isentropic Compression = wCp(Tli-To) Btu's where Tlt = temperature of isentropic compression from Po to Pm = To (Pm/Po)k-1/k To = ambient temperature w = air flow rate lb/engine cycle = v P(V1-Vo) 12RTm V1-Vo = engine displacement in cu in. Tm = manifold temperature for pressure Pm rv = volumetric efficiency of cylinder. Employing an isentropic efficiency of compression Tc covering the cycle losses, plus mechanical efficiencies Tm for frictional losses, Work Input of Compressor = WCP(T1-To) Btu's ~cnm which becomes Input Work = nv778 Pm(V-Vo)CpTo(rk-l/k-) ft b () 12R.Tmncfm 9

where Pm/Po = r = pressure ratio of charger Pm = manifold pressure, psi To = ambient air temperature, ~F R,Cp,k = gas constants. It is to be understood that the isentropic efficiency nc is to be based upon all aerodynamic losses of the blower; suction will not be exactly at Po, delivery will not be exactly Pm, etc. Thus Tc is the efficiency based on a pressure difference of Pm-Po between a practical compressor and an isentropic compressor for the same pressure difference. Equivalent Engine Cylinder Mean Effective Work = dV Pressure of Blower n778 PmCp T(rk-1/k-) - -ps (4) RTmiclm The mean effective pressure represented by Eq. (4) is based upon the charge of air trapped in the engine cylinder and makes no allowance for the air flow through the combustion chamber during the valve overlap period. This scavenge air usually amounts to about 5% of the air charge with normal valve overlap and can increase beyond this where large overlap is employed. Now the average volumetric efficiency of a highly supercharged engine can be as high as 95% or better; as a first approximation it will be assumed that the 5% excess air required will balance the 5% loss due to volumetric efficiency. It can now be stated that Equivalent Mean Effective 778 P pT(rk-l/k ) 778 PmpTo(rk- /k) (-) Pressure of Charger RTmlm Similarly, the input work of Eq. (3) can be modified by dropping the term nv to include the excess air flow of scavenge air when necessary. Equations (5)-(5) are in terms of ambient air, manifold pressure, and pressure ratio of charger; the equivalent effective pressure of the charger 10

has been referred to piston displacement (V1-Vo) and thus can be subtracted directly from the gross IMEP of the indicator diagram shown in Fig. 6. OVERALL CYCLE The overall engine cylinder cycle of a supercharged engine with a mechanical driven Root's type charger is represented by an indicator diagram of the type shown in Fig. 6 where the area 1278 represents the work done during the suction stroke (1-2) and exhaust stroke (7-8) of the piston; 234562 represents the work on the piston by the gas trapped in the cylinder during compression, combustion, and expansion. 4 5 psi P pm i i2 10 --- e 9 8 7 Volume in cu in. Fig. 6. Ideal engine indicator diagram. Gross Total Work on Piston = (Area 23456+Area 1278) ft lb (6) Wrof Compressr 778 Pm(V1-V) CpTO(rkl /k-1) (at nvo=100) 12RTmTcNm Net effective indicated output of engine = (6) - (3). 11

In terms of IM4EP this is given by: Gross IMEP of Cycle = 12(gross indicated work in ft lb) displacement (V1-Vo)cu in. Gross IMEP of Blower = 778 PmpT( r -k) RTmcm (IMEPnet) of Engine Plus Blower = 12(23456+1278)in ft lb Vi-Vo 778 PmCpTo( rkl/k l) - ---- -psi (7) Net Effective IHP of Engine = IMEPnet( ~) hp (8) 2k12x33000 Net IHP/lb of Air/Sec = net IHPx2x6O (for 4 cycle) (lb of air/cycle)N RTmXIMEPnet 550 Pm 4.36( IMEPnet)........r~~~ (9) r where N = rpm of engine Tm = 200~F (intercooled temperature) Po = 14.7 psi (ambient pressure). If this IHP/lb of air/sec is obtained with a fuel-to-air ratio of F/A then Fuel Flow/Hr = F x 3600 lb/hr. 12

Thus F 3600 x A Specific Fuel Consumption = IPlb of airse (10) In this analysis the displacement charger has been assumed; however, the same expressions apply to all superchargers if the actual isentropic efficiency is employed for each type, since the isentropic work is the same for all machines operating between pressures Po and Pmo It is seen from the above that the answer to the problem of the performance of a blower charged engine depends upon a knowledge of the area 23456, since the rest of the values can be easily calculated. All other superchargers are handled in the same way since the area 23456 remains constant irrespective of the type of charger employed (with intercooling to Tm = constant). Adjustment need be made for the manner in which the area 1278 may charge and for the compressor work onlyo In The University of Michigan Report No. 04612-3-F, Contract No. DA-20018-ORD-23664,1 are given methods for obtaining the output of turbo-charged engines. If the cycle in such cases is compared with that of Fig. 6 it is seen to consist of the areas 23456 and 12910 determined by an engine back pressure of Pe which is the exhaust manifold or turbo inlet pressure. In the above report the relation Pe = 0.85 Pm (11) was maintained at all times; it follows that the gross work of the cycle presently under consideration is given by Ideal Gross IMEP = IMEP of Ref. 1 + IMEP Equivalent of Area (87910) = IMEP of Ref. 1 + (Pe-Po) IMEP of Ref. 1 + (0.85 Pm-Po) = IMEP of Ref. 1 + 0.85 PO(r-l.18) (12) The full effect of the change of pressure from Po to Pe can be employed here, since an allowance for the absence of square corners, wavey lines, etc., has already been made in Ref. 1. 13

It follows that the net output of a supercharged compression ignition engine in terms of Ref. 1 is given by Net IMEP = IMEP (Ref. 1)+0.85 Po(r-l.18) 7- 78 PCpTo(rk/k1) (13) RTmlcjlm If this value of the net IMEP is used in evaluating Eqs. (8), (9), and (10), the required performance figures can be calculated. The methods of Ref. 1 can be applied to various F/A ratios and the corrections as given above can be applied for part load operation also. TYPICAL SAMPLE CALCULATION We shall determine the output of a compression ignition engine when fitted with a Root's blower giving a pressure ratio of 2.4:1, the fuel-air ratio being 0.0473. An aftercooler maintaining an inlet manifold temperature of 200~F is employed. Under the above conditions a turbo-charged engine would give an ideal IMEP of 285 psi for a SFC of about 0.27 lb/IHP/hr. See Fig. 2 of Ref. 1. r = 2.4, Pm = 35.3 psi, Po = 14.7, and To = 520~F. Expected Gross IMEP With Root's Blower = 285+0.85 PO(r-1.18) Eq. (12) = 285 + 0o85 x 14.7(2.4-1.18) = 300.0 psi approx. Net IMEP of Engine (Eqo (11)) = 3000 - 778 PmCpo( k 1) RTmlc am = 300o0 - 48.2 = 251.8 psi. This calculation assumes that 0m = 0~97 and that 1c = 0.60, an optimistic value for a charger of this type. Then if the rpm = 3000, 14

Engine Suction Volume (V1-Vo) = wTm Per lb of Air lvPm RTm /lb of air 1vPm 53.34x660 0. 95x355.144 = 7.29 cu ft/lb of air =12600 cu in./lb. Displacement/Sec/Lb of Air = V-VO x N 1728 2x60 12600 cu in./lb/sec. If there were "n" cylinders of the four-cycle type having a diameter of D" and stroke L" Vi-Vo = Dn x L x n cu in./rev 4 and suction volume is irD2 N 4 x L x n x 12600 cu ino/lb/sec 4 2x60 Net IHP = 251.8x144 12600 Net IH = - x 550 1728 = 481o0 IHP/lb of air/sec 3600 x F Specific Fuel Consumption = IHP/lb air/sec 3600x0. 0473 481.0 = 0 354 lb/IHP/hr. 15

By repetition of this calculation over any range of pressure ratios, efficiencies, etc., a plot of the engine performance is possible for the assumed conditions. DISPLACEMENT SUPERCHARGER The results of such calculations are shown in Fig. 7 and Table I for a Root's type charger; in all cases the results presented are calculated for the maximum that can be expected from the engine on the assumption that 90% of the expected performance at a F/A ratio of 0.0473 can be achieved. The same assumption is true for the other results given in this report, and thus the curves are relatively comparable. It should be noted that an air-cooled engine is assumed and that the net BHP and SFC with cooling fan is given; this fan will be capable of cooling the engine plus normal engine and transmission oil. This should be allowed for if comparison is being made with water cooling, for exampleo See Figs. 9 and 10 for the fan performance. DISPLACEMENT CHARGER WITH COMPRESSION A displacement blower with compression is represented by the Lysholm or Bicera superchargers.2,3 In each of these types there is compression of the charge along such a curve as be of Fig. 5. These machines have a certain built-in compression ratio that is fixed in the case of the former but is variable for the latter typeo It follows that, other things being equal, the Bicera should have the higher efficiency over a variable load and speed curve; therefore it was chosen for the engine estimates. In addition, it is the easier type to calculate since the delivery pressure will correspond to any ratio desired within limitso The following calculations employ Eq. (5) for the equivalent mean effective pressure of the charger —also employing, of course, the appropriate values for the various efficiencies applicable to the type of compressor being investigated. Examination of Ref. 3 has resulted in consideration of the diagram of Fig. 8 as the closest representative of what might be obtained for the performance of a Bicera compressor. Figure 8 has been estimated for a built-in compression ratio of 2.0:1, which should give an actual delivery ratio up to about the desired maximum of 2.6:1, which is employed in these calculations. The values used are thus hypothetical to some extent but do seem to be possible of achievement. It is believed that the results presented will also be applicable to a machine of the Lysholm type with but slight variations; thus only the one set of data are presented for the displacement supercharger with compression. 16

TABLE I ENGINE PERFORMANCE WITH DIRECTLY DRIVEN ROOT'S SUPERCHARGER (Full Load) Manifold ^^^^^^ Manifold atm 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Pressure, Pm Basic imep Rsef 1e psi 117 141 162 189 211 254 259 279 506 Ref. 1 x 0.90 0.85 P0 (r-1.l8) psi 0 2.4 4.5 5.5 7.8 10.5 12.8 15.5 17.8 Isentropic work Btu/lb O 7.2 15.4 18.8 22.8 28.8 33.4 47.. of compressor Efficiency ^^^ ^^^^^^^ ^ ^^ Efficiency - 0.55 0.56 o.56 0.56 0.55 0.50.4 0.40 Ic x Tm Tm R 545 6oo 660 660 660 660 660 660 60 Compressor work psi 0 6.o 11.5 20.0 25.5 56.5 51.0 70.0 95.0 Net imep psi 117 157.4 155.0 174.5 195.5 207.8 219.8 224.5 250.8 Ihp Ib-air sec 511 500 484 476 470 455 457 407 588 Isfc Ib/ihp/hr 0.33554 0.541 0.552 0.558 0.565 0.578 0.591 0.420 0.440 Fmep psi p2.5 25.5 24.0 25.0 26.0 26.7 27.5 28.5 50.0 Bmep psi 94.5 114.1 1.0 149.5 167.5 181.1 192.5 195.8 200.8 Bhp Ib-air sec 44.o 416.0 40o9.0 408.0 407.0 596.0 585.0 555.0 558.0 Bsfc Ib/bph/hr 0.412 0.41o 0.417 0.418 0.419 0.451 0.445 0.480 0.504 Net bp with lIb-air sec 522.0 33558.0 544.0 550.0 556.0 549.0 541.0 517.0 505.0 cooling fan Net sfc with lb/bhp/hr 0.529 0.504 0.495 0.487 0.478 0.488 0.500 0.558 0.562 cooling fan

IHP Turbo 500 Centrigual o o BBiera 400 0 ^sd 94 Roots P+ 00 300 - ~~~~~~300 ~~~~- h~~Turbo Centr ugal b0 IMEP 150 - 100.50- + CH 0 Roots.40 _ ~ Bicera I.S.F.C. Centrifugal Turbo.30 I I I I, I I 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Manifold Pressure, Pm(atm) Fig. 7. Full load performance curves with various types of compressors. 18

~~~2.600 - 2 13000 Bicera Speed 1519oo 2.4 2.2' ciency ~ 2.0 a'67 1.8 -1000 rpm 62 1.6 100 200 300 400 500 6oo00 70 Volume Flow Rate (ft3/min) Fig. 8. High-ratio Bicera compressor. 19

6o 40 -- U) _(D Pm/Po = 0 y^ 20-20 10 0 1000 3000 R.P.M. Fig. 9. Friction and cooling losses (estimated). 20

Engine Speed = 3000 rpmE 50 4o 2400 U) 10 cd 20 Manifold Pressure (atm) Fig. 10. Friction and cooling losses (total).

The results obtained by the methods already outlined are given in Table II and Fig. 7. These data are obtained on the BHP basis from the estimated friction and fan power curves of Figs. 9 and 10, as was done in the case of Table I. ENGINE DRIVEN CENTRIFUGAL SUPERCHARGER The third type of engine driven supercharger to be investigated is the conventional single stage centrifugal machine. The advantage of this is of course its great air handling ability, resulting in low size and weight. The principal of this supercharger is the employment of changes of kinetic energy to produce the pressure rise, but in the final analysis the process still involves the same equations used previously for the work required, viz. Eq. (3). The performance of an engine fitted with this type of machine can be calculated exactly as the two previous ones, provided the correct efficiencies for this type are employedo It follows that the results calculated for the centrifugal machine can also represent the result to be achieved by any improved efficiency compression blower, irrespective of type, for the same pressure ratios. The centrifugal supercharger has been operated at speeds up to 100,000 rpm in some instances, mainly as turbo-compressors. In order to operate at such speeds when driven from a compression ignition engine of conventional design a high ratio gear train is required plus, in general, some form of flexible or slipping drive to eliminate as far as possible the cyclic speed variations which result from the engine firing sequence and in turn from being transmitted to these highly loaded, high speed gearso These problems have been solved for such engine applications; they are only mentioned here to indicate that the centrifugal compressor application may involve a higher class of gearing and transmission apparatus than the previous type of machines. Assuming the same conditions regarding pressure and temperature as were assumed previously, and employing a centrifugal compressor of quite modern design-aimed at exploiting the higher isentropic efficiencies proved possible in small gas turbine applications-it is estimated that a compressor map similar to that shown in Fig. 4 could be achieved in a small machine with the efficiencies given in Table III. The appropriate curve of Fig. 7 records the expected performance of an engine so equipped. The gas volume flow at the engine cylinder inlet for a given constant engine rpm will vary directly as the manifold pressure Pm, provided aftercooling maintains a constant Tmo It follows that the engine performance line will be approximately straight as shown in Fig. 4, Employing such a compressor map for a modern design of centrifugal compressor with an efficiency schedule as shown in Table III, the performance data calculated are shown in 22

TABLE II ENGINE PERFORMANCE WITH DIRECTLY DRIVEN DISPLACEMENT COMPRESSOR WITH COMPRESSION (Bicera) Manifold atm 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 pressure, Pm Basic imep psi 117 141 162 189 211 254 259 279 506 Ref. 1 x 0.80 0.85 P0 (r-1.18) psi 0 2.4 4.5 5.5 7.8 10.5 12.8 15.5 17.8 Isentropic work Btu/b 0 7.2 1.4 18.8 22.8 28.8 33.4 57. of compressor Efficiency ^ ^ ^ ^ Eff~iciency - 0.55 0.65 0.70 0.75 0.74 0.70 0.68 0.62 Tc x im Tm OR 545 600 650 657 660 660 660 660 Compressor work psi 0 5.9 9.5 14.9 19.4 26.9 56.2 45. 6o.o LM Net imep psi 117.0 157.5 157.2 179.4 199.4 217.4 255.6 248.8 265.8 Ihp lb-air sec 511 500 490 488 482 474 466 452442 Isfc Ib/ihp/hr 0.555 0.540 0.348 0.549 0.3-55 0.560 0.565 0.577 0.85 Fmep psi 22.5 25.5 24.0 25.0 26.0 26.7 27.5 28.5 50.0 Bmep psi 94.5 114.2 13355.2 154.4 175.4 190.7 208.1 220.5 255.8 Bhp Ib-air sec 414.0 415.0 4l6.0 420.0 420.0 415.0 4135.0 400.0 592.0 Bsfc Ib/bhp/hr 0.412 0.411 0.41 0.406 0.406 0.411 o.41.46 0.4 55 Ne-t bhp with coolin fnt lb-air sec 522.0 33558.0 550.0 565.0 568.0 570.0 571.0 562.0 556.0 cooling fan Net sfc with lb/bhp/hr 0.529 0.504 0.487 0.470 0.463 0.461 o.46o 0.470 0.478 cooling fan

TABLE III PERFORMANCE WITH DIRECTLY DRIVEN CENTRIFUGAL SUPERCHARGER ManifolId Manifold atm 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 pressure, PM Basic ieppsi 117 141 162 189 211 254 259 279 306 Ref. 1 x 0.90 0.85 Po (r-l.l8) psi 0 2.4 4.5 5.5 7.8 10.5 12.8 15.5 17.8 Isentropic work Btu/lb 0 7.2 1.4 18.8 22.8 28.8 5.4 7. 41.1 of compressor Efficiency ^^ ^^ ^^ ^^ Efficiency o 0.78 0.80 0.82 0.82 0.81 0.81 0.80 0.79 71c X 1Tm Tm OR 545 584 607 641 660 660 660 660 66 Compressor work psi - 5.8 8.2 12.8 17.5 25.7 51.7 59.2 47.0 R) Imep psi 117 159.6 158.5 181.5 201.5 220,6 240.1 255.1 276.8 Ihp Ib-air sec 511 507 494 495 488 480 479 464 463 Isfc Ib/ihp/hr 0.33554 0.33556 0.546 0.544 0.549 0.55 0.356 0.567 0.566 Fmep psi 22.5 25.5 24.0 25.0 26.0 26.7 27.5 28.5 50.0 Bmep psi 94.5 116.5 154.5 156.5 175.5 193.9 212.6 226.6 246.8 Bhp gross Ib-air sec 4l4.0 425.0 418.0 427.0 425.0 425.0 422.0 412.0 415.0 Bsfc Ib/bhp/hr 0.412 0.402 0.417 0.599 0.40 0.405 0.404 0.414 0.411 Net bhp with lb-air sec 522 546 354 570 574 576 582 574 578 cooling fan Net sfc with lb/bhp/hr 0.529 0.492 o.481 0.46 0.455 0.453 0.446 0.455 o.4s cooling fan

that table and Fig. 7. As mentioned previously, the data at the low MEP is somewhat adversely affected by the use of the same direct drive cooling fan for both the high and low ratings; a slip drive would improve the results. It should be understood that the compressor map proposed is associated with an existing conpressor, one that has not been specially designed for this particular problem. It follows that the results obtained are typical for such a mechanism and do not represent a specific combination to yield the best overall results. TURBO-CHARGED ENGINE In order to complete these comparisons, typical data for a straight turbo-charged engine are given in Table IV. These data are as calculated in Ref. 1, and the main difference between this and the previous machines is seen to be in the fact that turbo and compressor efficiencies, and their work factors, do not enter into the problem since it is assumed (and well established in practice) that the energy of the exhaust gas is sufficient to carry the work of the compressor without the aid of any engine power. The only change necessary is the employment of sufficient back pressure on the engine to secure this requirement. The back pressure employed in these calculations was constant at 0.85 Pm, i.e., at a 15% drop below the inlet pressure. It must be recognized that the back pressure will probably exceed the manifold pressure at low engine speed and power. As is normally the case, this does not affect the data of Table IV since in all cases the compressor has been assumed to be designed for the particular case being investigated, with the necessary margin of pressure across the manifolds for satisfactory scavenging of the cylinder. PART LOAD PERFORMANCES The material presented above records the full load and speed data expected for the different types of superhcargers covered. Of equal importance is the part load fuel requirements, etc. This side of the problem was examined in the manner outlined in Ref. 1 with the following results. DISPLACEMENT SUPERCHARGER Employing a displacement machine without compression, directly driven at some desirable ratio from the engine, and assuming a constant manifold pres25

TABLE IV PERFORMANCE WITH A TURBO-CHARGER Manifold atm 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 pressure, Pm Basic imep psi 130 156 180 210 255 260 288 310 340 Ref. 1 0.9 basic imep psi 117 140.3 162.0 189 211.2 234.0 259.0 279.0 306 Ihp lb-air sec 511 510 505 515 512 510 514 507 513 Isfc lb/ihp/hr 0.334 0.334 0.337 0.330 0.332 0.334 0.331 0.336 0.332 Fmep psi 22.5 23.3 24.0 25.0 26.0 26.7 27.5 28.5 30.0 Bmep gross psi 94.5 117.0 138 164 185.2 207.3 231.5 250.5 276 Bhp gross lb-air sec 414 425 430 446 449 452 459 455 463 R0 Fan mean pres. psi 21.0 21 0 21.0 21.0 21.0 21.0 21.0 21.0 21.0 Net bmep psi 73.5 96.0 117 143 164.2 186.3 210.5 229.5 255.0 Net bhp with lb-air see 322 549 365 390 398 406 417 418 427 cooling fan Net sfc with lb/bhp/hr 0.529 0.488 o0.466 0.437 0. 428 0.419 0.408 0.407 0. 99 cooling fan

sure as the F/A ratio varies, a condition closely followed for a constant engine speed. The calculated performance was then obtained as follows. The engine is assumed to have a maximum speed of 3000 rpm and F/Amax = 0.05 approx.; the data are calculated for 3000, 2400, 1700, and 1000 rpm. With the above engine revolutions, typical compressor maps indicate that, if the design is set for a pressure ratio of 2.6:1 at 3000 rpm, ratios of 2.2:1, 1.8:1 and 1.4:1 can be expected at 2400, 1700, and 1000 rpm at the air flow requirements for these speeds. Under these conditions the data of Table V are calculated. The frictional and cooling fan losses are considered constant at constant speed and pressure ratio, while the compressor input is also considered constant, since little if any change in air flow will occur under such conditions. If the engine is designed for 500 BHP net at the 2.2:1 ratio and 3000 rpm, then the air flow at that condition becomes Required Air Flow for 500 hp = 1 x 500.0 344.0 = 1.452 lb/sec. Since the manifold temperature (at least at the high ratios) has been maintained at 660~ abs., the air flow varies directly as the engine speed and pressure, as below: Air Flow Lb/Sec Manifold Pressure Atms. 3000 rpm 2400 rpm 1700 rpm 1000 rpm 2.6 1o72 --- 2,2 1.452 1.17 --- -- 1.8 1.19 0.951 0.675 --- 1.4 0.925 0.74 0.524 0.308 It follows that the engine performance data for a 500 BHP engine fitted with a 2.2:1 displacement blower becomes as given in Table VI and Figs. 11-14. The 2.2:1 ratio was chosen for full load in this case since there was a distinct drop in performance of the system when the ratio was increased to 206, as can be seen from Table VI. This indicates the limitations arising from low efficiencies at the high pressure ratios that are associated with this type of chargero Ratios in the lo4 to 1.6 range give the best performance from a SFC point of view. 27

TABLE V PART LOAD PERFORMANCE OF AN ENGINE WITH A DISPLACEMENT COMPRESSOR Rpm, Specific Fuel Rap F/A Air For = 1 lb/sec Consumption, F/A Air Flow = 1 lb/secConsumpti and F/A Consumption, and F/A Consumption, Ratio ___Consumption,_ Pres. Ratio Ratio lb/hp/hr Pres. Ratio Raio Ib/hp/hr Imep Bmep Ihp Bhp ihp Net bhp Imep Bmep Ihp BhpNt Net bh 0.015 102.8 --- 172.0 --- 0.313 0.015 67.8 8.2 164.0 19.8 0.328 2.72 0.020 139.8 --- 234.0 --- 0.308 -- 0.020 91.8 32.2 222.0 78.0 0.324 0.924 0.025 192.8 48.8 323.0 81.9 0.278 1.01 0.025 132.8 73.2 321.0 177.0 0.281 0.509 3000 0.030 237.8 93.8 398.0 157.0 0.272 0.689 2400 0.030 157.8 98.2 382.0 238.0 0.283 0.454 r = 2.6:1 0.035 267.8 123.8 449.0 207.5 0.281 0.6o6 r = 1.8:1 0.035 177.8 118.2 430.0 286.0 0.293 0.441 0.040 292.8 148.8 491.0 249.0 0.293 0.579 0.040 195.8 136.2 474.0 330.0 0.04 436 0.045 307.8 163.8 516.0 274.0 0.314 0.592 0.045 207.8 148.2 503.0 359.0 0.322 0.451 0.050 317.8 173.8 533.0 291.0 0.338 0.619 0.050 215.8 156.2 522.0 379.0 0.345 0.476 0.015 92.8 --- 184.0 --- 0.293 --- 0.015 54.5 ll.o 169.5 34.2 0.318 1.58 0.020 117.8 18.3 233.0 36.2 0.309 1.99 0.020 69.5 26.0 216.0 81 0 0.333 0.889 0.025 162.8 63.3 322.0 125.3 0.280 0.717 0.025 108.5 65.0 334.0 202.5 0.270 0.444 3000 0.030 206.8 107.3 409.0 213.0 0.264 0.507 2400 0.030 134.5 91.0 418.5 283.0 0.258 0.382 r = 2.2:1 0.035 227.8 128.3 451.0 254.0 0.279 0.496 r = 1.4:1 0.035 149.5 106.0 465.5 330.0 0.271 0.382 0.040 247.8 148.3 491.0 294.0 0.293 o.490o 0.040 158.5 115.0 494.0 358.0 0.292 0.402 0.045 257.8 158.3 511.0 314.0 0.317 0.516 0.045 174.5 131.0 544.0 408.0 0.298 0.399 0.050 272.8 173.3 540.0 344.0 0.334 0.524 0.050 179.5 136.0 559.0 424.0 0.322 0.429 c0 0.015 67.8 163.0 0.330 --- 0.015 67.8 20.3 164.0 49.2 0.328 1.096 0.020 91.8 18.6 222.0 45.0 0.324 1.60 0.020 91.8 34.3 222.0 83.0 0.324 0.867 0.025 132.8 59.6 321.0 144.0 0.280 0.625 0.025 132.8 85.3 321.0 206.0 0.280 0.436 3000 0.030 157.8 84.6 382.0 205.0 0.283 0.528 1700 0.030 157.8 110.5 382.0 267.0 0.283 0.404 r = 1.8:1 0.035 177.8 104.6 430.0 253.0 0.293 0.498 r = 1.8:1 0.035 177.8 130.5 430.0 316.0 0.293 0.399 0.040 195.8 122.6 474.0 297.0 0.304 0.485 0.040 195.8 148.5 474.0 360.0 0.504 0.400 0.045 207.8 134.6 503.0 326.0 0.322 0.497 0.045 207.8 160.5 503.0 389.0 0.322 0.416 0.050 215.8 142.6 522.0 346.0 0.345 0.520 0.050 215.8 168.5 522.0 408.o 0.345 0.44 0.015 54.5 --- 169.5 --- 0.318 --- 0.015 54.5 21.5 169.5 67.0 0.318 0.805 0.020 69.5 13.0 216.0 40.5 0.333 1.78 0.020 69.5 36.5 216.0 114.0 0.333 0.632 0.025 108.5 52.0 334.0 162.0 0.269 0.555 0.025 108.5 75.5 334.0 235.0 0.270 0.383 3000 0.030 134.5 78.0 418.5 243.0 0.258 0.445 1700 0.030 134.5 101.5 418.5 316.0 0.258 0.342 r = 1.4:1 0.035 149.5 93.0 465.5 289.5 0.271 0.436 r = 1.4:1 0.035 149.5 116.5 465.5 363.0 0.271 0.347 0.040 158.5 102.0 494.0 318.0 0.292 0.453 0.040 158 5 125.5 494.0 391.0 0.293 0.368 0.045 174.5 118.0 544.0 367.5 0.298 0.442 0.045 174.5 141.5 544.0 441.0 0.298 0.368 0.050 179.5 123.0 559.0 383.0 0.322 0.470 0.050 179.5 146.5 559.0 456.0 0.522 0.395 0.015 92.8 6.3 184.0 12.5 0.293 4.31 0.015 54.5 32.0 169.5 99.6 0.318 0.54 0.020 117.8 31.3 233.0 62.0 0.309 1.16 0.020 69.5 47.0 216.0 146.5 0.333 0.491 0.025 162.8 76.3 321.0 151.0 0.281 0.596 0.025 108.5 86.0 334.0 268.0 0.270 0.336 2400 0.030 206.8 120.3 410.0 238.0 0.261 0.454 1000 0.030 134.5 112.0 418.5 349.0 0.258 0.310 r = 2.2:1 0.035 227.8 141.3 450.0 280.0 0.280 0.450 r = 1.4:1 0.035 149.5 127.0 465.5 396.0 0.271 0.318 0.040 247.8 161.3 490.0 319.0 0.294 0.451 0.040 158.5 136.0 4 4.0 422.0 0.293 0.41 0.045 257.8 171.3 510.0 339.0 0.318 0.478 0.045 174.5 152.0 544.0 472.0 0.298 0.343 0.050 272.8 180.3 540.0 358.0 0.333 0.503 0.050 179.5 157.0 559.0 489.0 0.322 0.368

TABLE VI PERFORMANCE OF A 500 BHP (NET) ENGINE WITH DISPLACEMENT SUPERCHARGER DELIVERING 1.452 LB OF AIR PER SEC AT 2.2:1 AND 3000 RPM RPM Manifold R Pressured F/A 5000 2400 1700 1000 Bsfc Bsfc Bsfc Bsfc Pratmess, Bhp lb/hp/hr Bhp lb/hp/hr Bhp lb/hp/hr Bhp lb/hp/hr 0.015 0.020 0.025 141 1.01 2.6 0.030 270 0.689 0.035 356 o.606 0.040 429 0.579 0.045 469 0.592 0.050 500 0.619 0.015 -- -- 14.6 4.31 0.020 52.6 2.00 72.5 1.16 0.025 182 0.72 177.0 0.60 0.030 310 0.51 279.0 0.45 0.035 369 0.50 328.0 0.45 0.040 427 0.49 574.0 0.45 ~4^ 0 o.o45 456 0.52 397.0 0.48 0.050 500 0.52 419.0 0.50 0.015 --- - 18.8 2.72 33.2 1.1 0.020 53.6 1.60 74.2 0.92 55.8 0.87 0.025 172 0.63 168.0 0.51 139.0 0.44 0.030 244 0.53 226.0 0.45 180.0 0.40 0.035 301 0.50 272.0 0.44 213.0 0.39 0.040 354 0.49 314.0 0.44 243.0 0.40 0.045 388 0.50 342.0 0.45 262.0 0.42 0.050 412 0.52 360.0 0.48 275.0 0.44 0.015 -- - 25.5 1.58 35.0 0.81 30.7 0.54 0.020 37.4 1.78 60.0 0.89 59.7 0.63 45.1 0.49 0.025 150 0.56 150.0 0.44 123.0 0.38 82.6 0.34 0.030 225 0.45 209.0 0.38 165.0.4 108.o 0.31 0.035 267 0.44 244.0 0.38 190.0 0.35 122.0 0.32 0.040 294 0.45 265.0 0.40 205.0 0.37 130.0 0.34 0.045 339 0.44 302.0 0.40 231.0 0.37 1-45.0 0.34 0.050 354 0.47 314.0 0.43 239.0 0.40 151.0 0.37

A ^ = * ~ 2^^ - 00SI C 4 - F/A - - - 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Manifold Pressure (atm) Fig. 11. Part load performance with displacement compressor at 5000 rpm. 50 4/ 200 / F/A

5300.o4o 200 F/A =.050Z o, 100 4S.0 wo l _ 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Manifold Pressure (atm) Fig. 12. Part load performance with displacement compressor at 2400 rpm. 31

300 F/A =.050 45.44 ~4o 200. " 100 52 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Manifold Pressure (atm) Fig. 13. Part load performance with displacement compressor at 3.700 rpm. 32

.6 1.0 1.2 1.4 1.6 1.8 2.0 Manifold Pressure (atm) Fig. 14. Part load performance with displacement compressor at 1000 rpm. 33

CENTRIFUGAL SUPERCHARGER. If the centrifugal machine, of modern design, is employed as the example to be investigated for part load performance characteristics it will, due to the high efficiency of this type, give about the best performance of the directly driven superhcargero The Lysholm and Bicera machines would lie between the displacement and centrifugal machines. It is not proposed to calculate part load for each of these machines at this time; the centrifugal is examined as presenting the most efficientO The centrifugal machine has a definite compressor map depending upon the resistance encountered at the discharge; a typical map has already been represented in Fig. 4. The problem then arises as to how the engine requirements are supplied by the compressor. If a complete performance chart was available for the engine, the compressor and engine could be matched accurately. What is to be examined in this investigation is that, at full load and engine speed of 3000 rpm, the compressor will deliver air sufficient to maintain a 2.6:1 pressure ratio at a constant manifold temperature of 660~ abs. The compressor being driven off the engine will also operate at constant speed as the F/A ratio and thus the power is varied at a constant engine speed of 3000; similar conditions will exist at other engine speeds with the manifold pressure ratio varying approximately as the square of the speed as given by Eq. (14). Now at constant engine speed and manifold conditions the air flow of the engine will be considered constant as the F/A ratio varies. This is a reasonable first assumption; without it the solution. becomes quite involved and lengthy. With this assumption, the data of Table VII and Fig. 15 are calculated, for a flow of 1 lb/sec. The data are then corrected to an engine of 500 BHP at 3000 rpm for an air flow of 1.36 lb/sec at 2o6:1 pressure ratio, as for the other chargerso The higher ratio of 2~6 was chosen for full power in this case since the results showed improved performance at this ratio, as a result of the improved compressor performance. (Pm/Po)0.286 - loC rpm2 (14) The effect of the higher pressure ratio, relative to the displacement machine, shows up in a reduced air flow, higher net BMEP, and thus a reduced engine volume and weighto These details will be summarized latero TURBO-CHARGER The part load performance of the turbo-charged engine is calculated from Ref. 1 and presented in Table VIII. In this case it is assumed that the turbine will always drive the compressor and that no power generated by the pistons is lost in compressing the air, This is true except at very low outputs, when the exhaust back pressure may exceed the inlet manifold pressure 54

TABLE VII PART LOAD PERFORMANCE WITH CENTRIFUGAL COMPRESSOR...Hp at i.36 Sfc, Rpm, Hp for 1 lb of air per sec Hp at 1.6 Sfc, p' F/A lb/air/sec lb/hp/hr m ___ Imep Bmep Ihp Bhp at 3000 rmp Ihp Bhp 0.015 102.8 4.8 172.2 8.5 11.5 0.313 6.35 0.020 139.8 41.8 234.0 70.1 95.3 0.308 1.03 0.025 192.8 94.8 323.0 159.0 216.0 0.279 0.566 3000 0.030 237.8 139.8 398.0 234.0 518.0 0.272 0.462 2.6:1 0.035 267.8 169.8 449.0 285.0 387.0 0.281 0.442 0.040 292.8 194.8 491.0 326.0 443.0 0.293 0.442 0.045 307.8 209.8 516.0 352.0 478.0 0.314 0.460 0.050 317.8 219.0 533.0 368.5 500.0 0.338 0.490 0.015 44.0 --- 101.0 --- 0.534 0.020 66.0 3.0 151.5 6.9 5.48 0.475 1.04 0.025 129.0 66.0 296.0 151.0 120.0 0.304 o.596 2400 0.030 169.0 106.0 388.0 244.0 194.0 0.278 0.443 1.9:1 0.035 184.0 121.0 422.0 277.0 220.0 0.299 0.455 0.040 200.0 137.0 459.0 314.0 251.0 0.314 0.459 0.045 219.0 156.0 503.0 358.0 285.0 0.322 0.452 0.050 230.0 167.0 528.0 383.0 304.0 0.341 0.470 0.015 34.5 4.8 107.8 14.9 6.2 0.502 3.62 0.020 74.5 44.8 232.0 139.0 57.7 0.310 0.518 0.025 103.5 73.8 322.0 250.0 95.5 0.280 0.591 1700 0.030 129.5 99.8 403.0 311.0 129.0 0.268 0.347 1.4:1 0.035 149.5 119.8 466.0 373.0 155.0 0.270 0.338 0.040 159.5 129.8 497.0 404.0 167.5 0.290 0.356 0.045 166.5 136.8 519.0 426.0 177.0 0.312 0.380 0.050 174.5 144.8 544.0 450.0 187.0 0.331 0.400 0.015 28.1 14.4 112.2 57.7 10.9 0.480 0.93 0.020 61.1 47.4 244.0 190.0 36.o 0.295 0.378 0.025 86.1 72.4 344.0 289.0 55.0 0.262 0.312 1000 0.030 111.1 97.4 444.0 389.0 74.0 0.243 0.278 1.09:1 0.035 126.1 112.4 505.0 450.0 85.5 0.250 0.280 0.040 135.1 121.4 541.0 486.o 92.4 0.266 0.296 0.045 143.1 129.4 573.0 518.0 98.4 0.283 0.313 0.050 151.1 137.4 605.0 550.0 104.3 0.298 0.328 35

TABLE VIII PART LOAD PERFORMANCE WITH TURBO-CHARGER Pres. Hp per lb of air per sec Air Sfc Rpm Ratio F/A Flow, Bhp lb/hp/hr ___ Imep Bmep Ihp Bhp lb/sec Ihp Bhp 1.07 0.02 60.0 17.0 244 69.3 0.492 34.0 0.295 1.04 1.30 0.025 90.0 46.0 302 154.0 0.598 92.0 0.298 o.584 1.48 0.029 120.0 75.0 353 221.0 0.681 150.5 0.296 0.474 1.77 0.036 165.0 119.0 406 293.0 0.814 238.0 0.319 0.442 3000 2.06 0.041 210.0 162.5 444 344.0 0.947 326.0 0.333 0.430 2.23 0.046 240.0 191.5 469 374.0 1.027 384.0 0.553 0.443 2.4 0.051 270.0 219.5 490 398.0 1.103 439.0 0.375 0.462 2.6 0.052 300.0 249.0 503 418.0 1.197 500.0 0.372 0.448 2.66 0.055 306.0 254.5 502 417.0 1.221 510.0 0.395 0.476 1.04 0.0185 52.3 20.4 218 85.5 0.383 32.7 0.305 0.778 1.33 0.027 105.0 72.5 345 258 0.489 116.0 0.282 0.409 1.48 0.032 131.0 97.9 386 289 0.545 155.0 0.298 0.399 1.61 0.0375 157.0 123.6 425 334 0.592 198.0 0.518 0.404 2400 1.77 0.041 183.0 149.2 450 368 0.651 239.0 0.328 0.401 1.90 0.0445 209.0 175.2 480 402 0.699 281.0 0.334 0.399 2.08 0.049 235.0 200.6 492 420 0.766 322.0 0.3559 0.420 2.21 0.052 248.0 212.3 489 418 0.814 340.0 0.383 0.448 2.29 0.065 275.0 239.8 524 456 0.842 384.0 0.447 0.514 1.0 0.019 52.0 31.3 227 137 0.261 35.8 0.301 0.50 1.0 0.0235 78.0 57.3 340 249 0.261 65.0 0.249 0.34 1.0 0.029 104.0 83.3 453 363 0.261 94.6 0.231 0.288 1700 1.03 0.038 130.0 109.2 502 421 0.268 113.0 0.273 0.325 1.23 0.050 156.0 135.1 554 479 0.322 154.0 0.325 0.376 1.32 0.052 168.0 146.9 556 485 0.544 167.0 0.336 0.386 1.44 o.060 182.0 160.7 551 486 0.376 183.0 0.392 o.444 1.o 0.015 40 25.8 174.5 112.5 0.184 20.7 0.309 0.48 1.0 0.0185 50 35.8 218.0 156.o o.184 28.7 0.306 0.426 1.0 0.02 60 45.8 261.0 199.8 0.184 36.8 0.276 0.360 1200 1.0 0.024 80 65.8 348.0 287.0 0.184 52.9 0.249 0.302 1.0 0.028 100 85.8 436.0 374.0 0.184 68.9 0.232 0.270 1.o 0.0365 122 107.8 532.0 470.0 0.184 86.5 0.247 0.280 1.o 0.059 132 117.8 575.0 514.0 0.184 94.5 0.244 0.273 36

400 o / o oo // o00 200 co 11 0 Manifold Pressure (atm) Fig. 15. Part load performance with centrifugal compressor. 37

by a small amount, which in turn may reduce engine power slightly. The engine performance line is calculated with the use of Fig. 5 of Ref. 1 for the variation of manifold pressure with load and speed. It is seen from this diagram that Pm will vary, at a constant engine speed, as the F/A ratio varies due to the changes in the exhaust gas temperature, etc. The starting point was taken as 2o6:1 at F/A = 0.0473 and 3000 rpm, as before, with ratios of 2.2, 1o77, and 1.0 at 2400, 1700, and 1200 rpm with full load IMEP. This means that the F/A ratio for the lower pressure ratios and speeds would have to change in a manner similar to that shown in Fig. 19 of Ref. 1, to keep the mean pressure constant. These combinations take the F/A up into the smoke regions and thus there will be some limitation to these maximum values. The diagram of Fig. 19 of Ref. 1 constructed for a F/A = 0.043 can be used for the present case by increasing it proportionally to 0.04735, the required ratio at full speed. Then, for example, at 80o speed, viz. 2400 rpm with a smoke limit of 0.052, the maximum IMEP that can be expected would be given at a F/A ratio of F/A at 80o for Max. IMEP = 0.052 x 0.043 0.0475 = 0.0472. In other words, 0.0472 of Fig. 19 of Ref. 1 corresponds to 0.052 on a diagram built up for a F/A of 0.0473. At this value the IHP at 80% speed is given by Fig. 5 of Refo 1 as 76%; thus the IMEP will be 76/80 x 260 = 248 psi, the 260 being the IMEP at 3000 rpm for 0.0473 F/A. The starting point for the 2400 rpm thus becomes F/A = 0.052, Pm = 67 approx. (see Fig. 3 of Ref. 1), which is 86% of the 2.6:1 ratio at full speed. Checking this with Fig. 5 of Ref. 1, the ratio is there given as 84% approx. Taking the mean of these two values, say 85% manifold pressure resulting in a ratio of 2.21:1 being required from the charger, the balance of the 2400 rpm data can be filled in on Table VIII. At 1700 rpm, maximum IMEP will also be at F/A = 0.0472 on Fig. 19 of Ref. 1; the IHP = 36 5%, giving an IMEP of 36.5/56.6 x 260 = 168 psi. For this value Fig. 3 of Ref. 1 gives that a manifold pressure of 40.5" Hg or 51.5% is required, or ratio = 1.35. Figure 5 of Ref. 1 predicts 49.0% of full speed pressure, or a ratio of lo28. Averaging these two estimates the pressure ratio of 1.32:1 will be employedo Similar calculations were employed for the 1200 rpm, resulting in an IMEP of 122 psi for 0.052 F/A. This can be obtained with no supercharging at a manifold pressure of 22" Hg approx,; Fig. 5 of Ref. 1 predicts 31" Hg. It will be assumed that an unsupercharged condition will meet this case. It is seen that the mean pressure and supercharger ratio varies slightly, depending upon which diagram of Refo 1 is used. The change is quite small, 58

however, in the major operating range of the engine. By taking the average of the results, sufficient accuracy is believed to be secured. This method does result in a slight variance of the final F/A ratio from that originally assumed, but the results are affected only by a small change in the mean pressure. Table VIII and Fig. 16 present the results of these calculations. ENGINE OVERALL VOLUME A casual examination of Tables VI, VII, and VIII shows little difference for engines of 500 BHP output at 3000 rpm. However it must be remembered that the air flow in lb/sec has been varied to obtain this constant output. It follows that the engine bulk is not identical even if the output and fuel flow are constant. Taking these differences in air flow into account, it is possible to determine the engine bulk for each of the cases examined. Let it be assumed that a constant stroke/bore ratio of lo08 is employed for all engines. DISPLACEMENT SUPERCHARGER Air flow = 1.452 lb/sec at 6600 abs and at 2.2:1 pressure ratio and 3000 rpm. If volumetric efficiency is assumed at 96% the engine size is given by TO2 nxN Displacement Volume of Engine = x L x cu in./min 4 2 where D = diameter Of cycle in inches L = stroke of cycle in inches = 1.08D n = number of cylinders N = rpm wRTm Volume of Air = cu ft Pm 60x1.452x55.54x660x1728 = - cu in.//min 144x14.7x2.2 = 12.54 x 105 cu in./min. 39

Pm= 2.2 --- 7 (Manifold Pressure) / 2.0 300 200! 2 1.2 100 1000 2000 3000 Engine Speed (rpm) Fig. 16. Part load performance with turbo-charger.

at 96%L volume efficiency. 12. 54x105 Required Cylinder Volume - -.-9 o.96 = 13.08 x 105 cu in./min = engine displacement therefore D2 x 1.08D x nx3000 13.08 x 105 4 2 nD3 13008xl05x4x2 rxl. 08x3000 1.028 x 103 n 6 8 12 D3 1.711x102 1.282x102 0.855x102 D 5o55 5.04 4.4 L 6.0 5.45 4.75 The possible engine combinations would then be as below: n 6 8 12 D 5-5/8 5 4-1/2 L 6.0 5-1/2 4-3/4 Approx. Vol. cu ft In-line Engine 97 76 Approx. Volo cu ft V- 60~ 63 50 47 Engine 90~ 76 58 54 41

There would be, of course, some difference of weights despite the output being constant at 500 BHP. Assuming 4.5 lb/hp for the V-engines, it is believed that the range would be from about 2300 lb to 3000 lb. This change of weight is quite small and rather negligible when the total vehicle weight is considered. The above calculations are based upon Figs. 10, 12, and 13 of Ref. 1, which are for turbo-charged engines where the superchargers are quite small. The displacement compressor will be of considerable bulk, relatively, and its volume will be estimated on the basis of a Root machine where the average area of the impeller is about 653 of the circle swept out by the tip. In one revolution of the machine, the theoretical displacement of the blower will be, for the two lobes, iTD2 Displacement = 0.37 x 2 x x L su in. where D = diameter of impeller in inches L = length of impeller in inches. A good value of L for low leakage, etc., is given by L = 1.5D:D2 Displacement = 0.37 x 2 x -- x 1.5D = 0.873D3 cu in./rev = 0.873D3N cu in./min N = rpm of blower. If it is assumed that there is a leakage of 7%, then Required Displacement = 0.94D3N cu in./min. This type of blower can be operated at some 7000 to 10,000 rpm. Assume it is geared to the proposed engine at 3:1, giving 9000 rpm of the blower, which a relatively high speed for this type: then the dimensions become 42

Required Displacement = w cu ino/min Po 1.452x60x53.34x545x1728 144x14.7 2.068 x 106 cu in./min. Assuming a 6% air flow during valve overlap, the displacement must be increased to allow for this; thus Displacement = 2.19x106 cu in./min = 0.94D3N 3 2.19x06 0.94x9000 = 259,0 in. D = 6.37 or, say, 6-3/8. With the above impeller dimensions, the overall dimensions would be approximately as shown in Fig. 17 with a length of at least 16 in., giving a total volume of about 16x14x8.5/1728 = 1.1 cu ft. This volume would be added to the engine volume and would be almost constant irrespective of the type of displacement machine employed. CENTRIFUGAL SUPERCHARGER In the case of the centrifugal supercharger driven directly from the engine by gearing, the physical dimensions will be small, comparable with the sizes already allowed for in the turbo-charger in Figs. 10, 12, and 13 of Ref. 1. It follows that the engine bulk can be read directly from these figures when the engine size necessary to handle the air volume has been determined. Employing the same methods and assumptions as for the displacement machine, the following data are determined: 45

9-5/8 in. long 6-5/8'. 8-1/2" Overall _ ^t —- -- — 1-5/8" -- ___________ 14" Overall Fig. 17. Overall dimensions of displacement supercharger. Air Flow at 3000 rpm = 1.36 lb/sec, ratio 2.6:1 No. of Cylinders 6 8 12 Bore 5-1/8 4-3/4 4-1/8 Stroke 5-5/8 5-1/8 4-1/2 Engine Volume cu ft In-Line 66 60 60o 44 42 33 V 900 53 48 38 44

TURBO-CHARGER In the case of the turbo-charged engine, the data calculated are as given below: Air Flow at 3000 rpm = 1o197 lb/sec, ratio 2.6:1 No. of Cylinders 6 8 12 Bore 5 4-1/2 4 Stroke 5-3/8 4-7/8 4-1/4 Engine Volume cu ft In-Line 58 48 60~ 48 34 30 V 90~ 47 38 35 BATTLEFIELD DAY REQUIREMENTS Taking the various engines investigated above and determining their fuel consumption over a 24-hour battlefield day based on the following vehicle data, the relative positions of the various engines are as shown. Vehicle Weight-43 tons Pitch Diameter of Sprocket-22.19 in. Resistance on First Class Roads mph 2 3 4 5 6 7 8 9 10 15 16 17 18 19 20 30 Resistance 67 67.5 68 68 68 68.5 69 70 73.5 72 69 68 67 67 67 70 lb/ton Time Schedule 20% of day 15, 16, 17, 18, Resistance 1.57 times 19, 20 mph that of first class roads 40% of day 2, 3, 4, 5, 6, 7, 2.00 times resistance 8, 9, 10 mph of first class roads 40% Engine Idling 45

The average ground hp for the 20% period becomes 260.0 hp; for the 40% period, the hp averages out at 96 hp. Assuming a 10% ground slip plus an 82% transmission efficiency, the engine power becomes 348 for the 20% and 129 hp for the 40% period. With these powers the fuel requirements for the 24 hours becomes as shown in Table IX. TABLE IX FUEL REQUIREMENTS FOR A BATTLEFIELD DAY Displacement Compressor Centrifugal Charger Turbo-Charger Condition (500 hp) (500 hp) (500 hp) 20% at 348 hp 4.8 hr 845.0 754.0 730.0 40% at 129 hp 9.6 hr 470.0 451.0 435.0 40% Idle 9.6 hr 69.0 57.6 48.0 Total Fuel lb 1384.0 1262.6 1213.0 Of the figures in Table IX those for the idling condition are perhaps subject to the greatest error since both the engine speed and fuel requirements for idling are a function of the injection system in addition to the engine characteristics. The calculations do not permit evaluation of the fine gradations such as the possible difference in the battlefield day consumption of a six and eight cylinder in-line engine. No attempt has been made to evaluate this; it would be small, resulting mainly from change of friction with engine size. COMMENTS No attempt has been made in this report to include any method for achieving responsiveness with these systems of supercharging. It is proposed to examine this phase of engine operation as applied to direct connected chargers in Part II of the report. 46

This analysis has been made in accordance with the methods of Report No. 04612-3-F, Contract No. DA-20-018-ORD-23664,1 with suitable adjustments to meet the required conditions. The present report is aimed at the highly supercharged cycle with some wider spread of results to be expected at low pressure ratios. The present work includes some predictions at low ratios; these predictions will possibly possess a greater error than most of the work. These low ratios were necessary due to the fact that with some of the types of superchargers examined, high ratios are not possible. In fact, in the case of the displacement superhcarger, the ratios of 2.2 to 2.6:1 are above those generally recommended for this machine. It is believed that, at the engine powers of interest for the purpose in view, the results are sufficiently accurate for a systems analysis. Also, if the results obtained with the various machines are compared with one another, the correct trends will result; any deviation of actual engines, when constructed, will affect each one in about the same proportion. For ease of comparison the various combinations have been summarized in Table X. ENGINE TORQUE CHARACTERISTICS Torque curves have been plotted for the results of each of the assumed combinations in Fig. 18. These curves are plotted on a net output BHP including fan for engine, engine oil, and transmission oil cooling. In Fig. 18 is also included the degree of responsiveness that each system has. It is seen that the displacement supercharger does have a slight degree of responsiveness down to about 75% speed. The centrifugal supercharger falls off in responsiveness most rapidly with the turbo-charger in an intermediate position. In any case the responsiveness is far below that needed for the approximate maintainance of constant horsepower with variable speed. The responsiveness of the displacement compressor is secured at the expense of a considerable increase in fuel consumption. The centrifugal and turbo-charged engines both fall off in torque characteristics, but the gear driven centrifugal due to the positive drive to the compressor wheel appears to hold up fairly well when the responsiveness has fallen to 0.6 approx. The turbo-charger continues on downward due to the fact that with engine speed reduction, the gas flow reduces and the power to drive the compressor falls rapidly. In fact, little or no supercharging occurs at 1200 to 1400 rpm. This feature could be corrected to a considerable extent by the use of a variable area turbine nozzle, increasing the availability of the heat in the exhaust gases at low speed. 47

TABLE X SUMMARY OF DATA FOR 500 BHP ENGINES AT 3000 RPM Compressor Displacement C entrifugal Turbo-Charged No. of cylinders 6 8 12 6 8 12 6 8 12 Bore, in. 5-5/8 5 4-1/2 5-1/8 4-3/4 4-1/8 5 4-1/2 4 Stroke, in. 6 5-1/2.4-3/4 5-5/8 5-1/8 4-1/2 5-3/4 4-7/8 4-1/4 Arrangement In-Line In-Line In-Line Volume, cu ft 98 77 - 66 60 - 58 48 Weight, lb 3000 2800 - 2800 2600 - 2750 2550 Co Arrangement 60~ Vee 60~ Vee 60~ Vee Volume, cu ft 63 50 47 44 42 33 48 34 30 Weight, lb 2600 2450 2300 2500 2350 2200 2450 200 2150 Arrangement 90~ Vee 90~ Vee 90~ Vee Volume, cu ft 76 58 54 53 48 38 47 38 Weight, lb 2800 2600 2450 2600 2450 2300 2550 2400 2250 Fuel used Battlefield Day, lb 1384 1263 1213,~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,

Responsiveness (A Torque at any Speem BMEP in psi ~~~~~~~~~~~Torque at 5000 rpm BMEP in psi 0 R) -- ON Oo 0 i' ON C! I o 0 0 0 0 0 0 0 0 OJ 0)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~P 1 D 0 r OD OD H H o 0! I I~ o —' o 0 0 0 0 OQ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t H- 4::\ 0 0 I —, co ~~~~~~~~~~~ON ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ N 0 0 - D 00 0 0 ~~~~~~~~~~~0 (D ( ~D OO ~~~~~~~~~~~~~~~~~~~~(D ~ ~ ~ ~ ~ ~ 0 (D o U]~~~~~~~~~~~~~~~ 0) 0 0 30 r g~~~~~~~~~~~~~~~~~~~~~~~~~' 4:-~3 CA om4 i) m~~~~~~3 0 0 0 0 _ _ _ _ _ _ _ o o~~~~~~~~~~~~~~

CONCLUSIONS Examination of the data calculated in this report leads to the following conclusions, when a series of engines of similar design fitted with the different types of superchargers are considered. 1. The engine cycle, as represented by the gross IHP at the pistons with no deduction for the compressor, remains constant per lb of air supplied for all types of direct driven superchargers. 2. The engine cycle for a turbo-charged engine with the same manifold pressure as a directly driven engine yields less gross IHP per lb of air due to the higher engine back pressure in the exhaust manifold. 3. Of the compressors examined, the engine performance, on the basis of power output and SFC for the net IHP (engine plus compressor), increases as the isentropic efficiency of the compressor increases. 4. The turbo-charger, involving little if any power loss from the piston unit for compressor drive, provides the best maximum output with the lowest SFC. 5. The various systems arrange themselves in the same order of merit approximately for the part load performance characteristics. 6. Improved efficiency of the units in the case of a turbo-charged engine would only result in very small changes in performance if the inlet manifold pressure remained unchanged (represented by the reduction in back pressure on the engine). 7. Improved efficiency of the turbo units would permit an increase in manifold pressure accompanied by a corresponding increase in the horsepower if operated at the same back pressure as low efficiency units. 8. The direct drive superchargers must use up some of the oxygen tSpplied to the engine cylinder to provide the power for the compressor. 9. The turbo-charger obtains its power from the heat of the exhaust gases by making it available by increase of back pressure. 10. The turbo-charger employs all of the oxygen supplied to the cylinder in the production of work available to the output. The air flow, and thus engine size and weight, is reduced for a given BHP at any speed. 11. The turbo-charged unit maintains a fairly constant SFC as the pressure ratio is varied. 50

12. The positive displacement compressor has the advantage of maintaining torque at its maximum value approximately as the engine speed varies. 13. The turbo-charged engine has the least bulk for a given arrangement in most cases, with the centrifugal supercharger a close second. 140 The bulk of the engine plus fuel for a battlefield day is least for a turbo-charged unit. FUTURE WORK The above report deals only with the direct driven supercharger geared to the engine through a fixed gear ratio. Part II of this work will cover the case of similar superchargers driven off the engine in such a manner as to exploit the possibilities of producing engines with the maximum degree of responsiveness. 51

REFERENCES 1. Flexible Versus Responsive Engines, The Univ. of Mich. 04612-3-F by E. T. Vincent. 2. Sauver Supercharger, The Automobile Engineer, Vol. 46, 1956, p. 539. 3. An Approach to the Problem of Pressure-Charging the CI Engine by D. W. Thayhorn, Proceedings Inst. of Mech. Engrs. (Automotive Division) 1956-57, p. 217. 4. Supercharging the High Speed Diesel Engine by Mechanically Driven Compressors. Proceedings Inst. of Mech. Engrs. (Automobile Division) 195657, p. 229. 5. Centrifugal and Axial Supercharger for Aircraft Engines by K. Catpbell and J. Talbert. Transactions Society of Automotive Engineers, Vol. 53, 1945, p. 607. 6. Various Types of Compressors for Supercharging by R.G.S. Pigott. Transactions Society of Automotive Engineers, Vol. 53, 1945, p. 679. 52

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