~ 

b 

NASA Contractor Report 179557 

I 

I 

1) * Detonation Wave Compression 

in Gas Turbines 

(NASA-CR-179557) DETCNBTION LiAVE N87-13443 CCHPRESSION IN GA: IUEBINES Final 

Ccntractor Report [ISTAR, Inc,) 77 p 

CSCL 81D Unclas 

G3/07 43932 

A. Wortman 

ISTAR Inc. 

Santa Monica, California 

December 1986 

Prepared for 

Lewis Research Center 

Under Contract NAS3-24854 

1 

t' 

~b 

National Aeronaurics ana 

Space Administration 
TABLE OF CONTENTS 

INTRODUCTION ............................................ 1 

THEORETICAL CONSIDERATIONS ............................. 4 

Detonation Wave Engines ........................... 4 

Augmented Gas Turbine ............................. 7 

BASIC CALCULATIONS ...................................... 11 

Baseline Gas Turbine .............................. 11 

Compressor ........................................ 12 

Detonation Duct ................................... 12 

Combustor ......................................... 12 

Parametric Studies ................................ 19 

Mixing and Wave Compression ....................... 13 

ENGINE PERFORMANCE ..................................... 23 

Performance of a Pure Jet Engine .................. 23 

Performance of a Turbofan ......................... 24 

.Performance of a Bypass Jet Engine ................ 25 

Performance of a Shaft Output Engine .............. 27 

CONCLUSIONS ............................................ 28 

LIST OF SYMBOLS ........................................ 30 

REFERENCES ............................................. 32 

APPENDIX A ............................................. A-1 

APPENDIX B . .... ...... ....... ..... 

i 

..... ...... ..... . B.1 
INTRODUCTION 

Aircraft propulsion currently is almost completely 

dominated by gas turbines with essentially isobaric combustion so that the thermodynamic cycle approximates the 

classical Brayton cycle with isentropic compression and 

expansion, and isobaric heat exchange. 

It has been known virtually since the beginning of gas 

turbine development that significant gains in efficiency 

could be achieved if energy release could be accomplished 

at constant volume, rather than at constant pressure. The 

constant volume or Humphrey cycle is compared with the 

constant pressure Brayton cycle in Figure 1 in pressurevolume and temperature-entropy thermodynamic diagrams 

P 

V 

- - - - Brayton 

Cycle 

T 

3 

3' 

4 

A 

Figure 1. Comparison of the Brayton and Humphrey Cycles 

The ideal gas thermodynamic efficiency of the closed 

Humphrey cycle is given by: 

1 
and that of the Brayton cycle by 

Here p, v, and T, following convention, denote the pressure, volume, and temperature respectively and 

R - pressure ratio = p2/p1 

Y - isentropic exponent 

Numerical subscripts denote the thermodynamic states in the 

cycle. Comparisons of the performance of the two cycles 

are shown in Figure 2. The displayed results indicate the 

significant superiority of the Humphrey cycle to the 

Brayton cycle even at modest temperature ratios. 

Numerous attempts have been made to achieve constant 

volume combustion, but the complications of valves, such as 

those used by Holzwarth, did not result in a practical 

engine. Recent improvements in gas turbine performance 

have diminished somewhat the interest in the development of 

alternative engine cycles. However, improvements in 

performance have been gained at the expense of the cost and 

complications of multistage axial compressors. Such 

compressors are economically unacceptable for smaller gas 

turbine engines which might find applications in light 

aircraft or cruise missile. 

Presented here is the summary of the second phase of a 

study aimed at demonstrating the feasibility of employing 

transient transverse detonation waves to augment the 

performance of gas turbines using low pressure ratio compressors. The ultimate objective is to replace multistage 

axial compressors in smaller gas turbines with single stage 

centrifugal units augmented by an array of detonation 

ducts. Alternately, specific fuel consumption and thrust 

coefficients of low-to-medium pressure ratio gas turbines 

could be enhanced through the use of detonation ducts. In 

the initial study (Reference 1) performance of pure jet 

engines with low pressure ratio compressors augmented by 

detonation ducts was studied parametrically,and it was 

shown that significant reductions in specific fuel consumption could be achieved concurrently with greatly 

2 
. 

. 

enhanced thrust coefficients. The main objective of the 

present study is to analyze the gas dynamics of the detonation duct-combustor interactions with the aim of determining the realistic bounds of performance in actual engines. 

In the interest of clarity of presentation of the main 

objective of the program, details of the detonation duct 

gas dynamics have been placed in Appendix A, the supporting 

experimental work is in Appendix B, and the listings of 

computer codes developed specifically for this study are in 

Appendix C. 

.7 

.6 

GI 

* 

0 

z 

- w 

0 -5 U 

LL 

LL 

w 

.4 

.3 

Figure 

Y = 1.4 

Bray t on ) 

0 10 20 30 

PRESSURE RATIO -II 

2. Comparison of Humphrey and Brayton 

Gas Turbine Cycles 

3 
THEORETICAL CONSIDERATIONS 

The theoretical upper limit on performance could be 

achieved if the whole compressor output was processed by 

detonation waves. Lower limit corresponds to 100% of the 

compressor flow going through the combustor, which is the 

case with conventional gas turbines. It is of some 

interest to establish the upper limit as a measure of the 

potential performance improvements. 

Detonation Wave Ensines 

In this case, the heat addition is by means of detonation waves. It is known (e.g., Stanyukovich2) that a 

Chapman-Jouguet detonation is essentially equivalent to a 

constant volume heat release. In the strong wave limit, 

the speed of the detonation wave, D, is given by: 

with Q being the energy release 

detonated mixture. The pressure 

relations are: 

per unit mass of the 

temperature and density 

with the subscript D denoting conditions downstream of the 

detonation wave. Because of the assumption of the ChapmanJouguet state, the gas behind the detonation wave is at 

Mach 1. Assumption of isentropic compression to stagnation 

conditions and- ideal compressor and 

results in the relation for engine 

given by: 

turbine performance 

efficiency which is 

4 
with 

Maximum efficiency is then achieved at: 

with I’D being the isentropic process exponent of the 

detonation products. Variations of efficiency with pressure ratios for a range of values of H is presented in 

Figure 3. For hydrocarbon fuels, H ranges from 5 to 10. 

It should be noted that the efficiency of about 53%, which 

is reached by the proposed cycle at a compressor pressure 

ratio of 5, is matched by a standard Brayton cycle at a 

pressure ratio of about 14. Alternatively, augmentation of 

a R = 5 Brayton cycle with detonation wave heat release 

increases the efficiency from 37% to 53%. 

5 
.7 

.6 

.5 

W 

e( 

.4 LL 

LL 

W 

.3 

.2 

0 

H=5 

/ 

/ 

/ 

/ 

/ 

/ 

/- 

Brayton 0 

0 

0 

5 10 15 

COMPRESSOR RATIO -n 

7 

12 

Y = 1.4 

YD = 1.2 

20 

Figure 3. Performance of Augmented and 

Brayton Gas Turbines 

6 
Aumented Gas Turbine 

A theoretical detonation wave engine considered above 

cannot be realized because of practical considerations such 

as complete detonation of the whole flow, starting problems, unacceptably high temperatures and maintenance of 

flow through the engine. An engine which could be made to 

work is shown in Figure 4 in pure jet engine form. 

DIFFUSER , COMPRESSOR @TI-u- TURBINE NOZZLE 8 

DETONATION @ EXPANSION 

CHAMBERS 

ODENOTE STATION NUMBERS 

Figure 4. Schematic Representation of a Detonation 

Wave Augmented Jet Engine 

The station numbers are given for easy reference. The 

detonation duct could be a rectangular channel such as is 

shown in Figure 5. An array of injectors sends pulses of 

gaseous, or liquid, fuel into the duct where the mixture of 

air and fuel is detonated by an array of igniters fired in 

sequence with the injectors, or operated continuously. 

Maximum rate of energy release is obtained when the flow in 

the channel is at Mach 1. The rapid area increase at the 

upstream channel is necessary for the attenuation of shock 

waves. Area increase at the downstream end may not be 

necessary with ejector mixing-wave compression mode of 

operation. Preliminary experimental studies using a 

detonation duct with spark plug igniters are described in 

Appendix B. 

8 

7 
MIXING CHAMBER 

I 

-- 

INJECTORS 

Figure 5. Schematic Representation of 

the Detonation Duct 

The range of operating conditions for the engine is 

bounded by no detonation duct flow and the maximum frequency cycling of the ducts. In the previous study, it was 

assumed that the combustor and detonation duct flows were 

mixed in an ejector. Since the cycling frequency of the 

duct was not determined at that time, the fraction of flow 

through the combustor Xb was used as a free parameter. The 

studies were confined to a pure jet engine and representative performance parameters for a pressure ratio of 4 are 

shown in Figure 6. The limit of Xb = 1 represents no 

augmentation by detonation ducts. Even though the concept 

is aimed primarily at the use of very low pressure ratio 

compressors, it is interesting to note in Figure 7 that 

significant gains are possible with moderate pressure 

ratios. 

In the present study, the pure ejector mixing model 

was rejected in favor of a mixed ejector-wave compression 

mixing of combustor and detonation duct flows. The more 

efficient mixing offset the lower than expected detonation 

wave compression which was measured in a preliminary 

experimental program. 
20 

15 

10 

5 

0 

-. 

-MD=7 

MD = 6 0- 

I 

0 .2 .4 .6 .8 1 

COMBUSTOR FLOW - Xb 

1.4 

ul 

rc 

I 

c 

v, 

z 

0 

1.3 

1.2 

I 

Figure 6. Engine Performance Variation with 

Combustor Flow Fraction 

9 
a 

r, 

1.5 

1.4 

1.3 

1.2 

1.1 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

Io 

I 

c 

z 

w 

n 

V 

n 

LL 

LL 

w 

0 

0 

24 

22 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

0 2 4 6 a 10 0 2 4 6 8 10 

PRESSURE RATIO PRESSURE RATIO 

Figure 7. Influence of Gas Dynamic Models 

on Engine Performance 

10 
BASIC CALCULATIONS 

All of the physical quantities in the detonation wave 

augmentated gas turbines are scaled on the detonation duct 

parameters evaluated prior to the detonations and denoted 

by the subscript 0. The natural scaling quantities are the 

detonation volume acoustic velocity, ao, detonation volume 

cross-sectional area, and length, A. and Lo detonation 

volume mass PoAOLO, and internal energy cvTo. In the 

following analyses, these quantities appear: 

Time 

8 = tao/Lo 

Area and length 

A = A/Ao and x/Lo 

Mass 

m = m/PoLoAo 

Energy 

All thermodynamic quantities and velocities scale on 

corresponding detonation volume parameters. 

Baseline Gas Turbine 

Performance of detonation wave augmented gas turbines 

is compared with a corresponding conventional turbine with 

pressure ratio R, compressor and turbine efficiencies ec 

and eT respectively, and a maximum to ambient temperature 

ratio 4 = TmayJTa. The efficiency of such a turbine is 

given by : 

11 
ComDre s sor 

The total temperature of a compressor with a pressure 

ratio R and an isentropic efficiency ec is: 

The ambient temperature Ta is related to To through the 

total temperature and isentropic relations. Compressor 

work, nondimensionalized by the detonated volume energy, is 

given by: 

Detonation Duct 

The dimensionless heat released in the detonation 

volume is: 

with the subscripts d, D denoting the conditions prior to 

and subsequent to detonation. In the calculations, the 

acoustic velocity ratio is taken as 2.5 and therefore the 

energy release in the three sequenced firings is: 

Q1 = 5.25 Q2 = 6.40 43 = 8.24 

Detailed calculations of the gas dynamics of the duct and 

its output for various modes of operation are given in 

Appendix A. 

Combus tor 

Heat is assumed to be added isobarically during the 

period he. The dimensionless mass is: 

12 
. 

Initial combustor and detonation duct quantities are 

related through isentropic flow assumptions and Mach 

numbers Mb and Mo. The temperature at the completion of 

combustion is: 

with Q* being the heat release parameter. The total 

dimensionless heat added is: 

with 

.I = (3Y - 1)/2(Y - 1) 

Taking 

ec = 0.85 Mb = 0.25 Q* = 2 R=5 

Y = 1.32 

the maximum combustor temperature is calculated to be 

Tbf/Ta = 4.82 which corresponds to a turbine inlet temperature of about 2000OF. In order to maintain a constant Mach 

number in the combustor under the condition of the above 

parameters, the combustor flow area must increase by a 

factor of 3112 between the entry and exit. 

Mixins and Wave Compression 

The output of the combustor is steady while that of 

the detonation duct alternates volumes of fairly steady 

flow with sharp pulses of high pressure and temperature 

gas. When the detonation duct output is almost steady, the 

streams are mixed as if pressure changes. At exit from the detonation duct, the 

pressure pulses expand suddenly and because of their much 

higher velocity and pressure, immediately compress the 

preceding volumes of mixed gases. In the initial phase of 

this process, the overall volume remains virtually 

unchanged while the flow equilibrates to an essentially 

uniform pressure and velocity. In the proposed system, the 

flows of 2 detonation ducts are mixed with the outflow from 

1 csmbustor. The arrangement is something like that shown 

in Figure 8. Further equilibration of the flow could be 

achieved in the optional spiral collector. Without the 

spiral collector, the turbine would be operated in purely 

blowcl,ow?? zde. 

in an ejector with moderate 

13 
TURBINE NOZZLES 

ALTERNATIVE BURNER AND 

DETONATION DUCT PORTS 

GAS 

INLET SIDE AUGMENTATION PASSAGES 

TURBINE SIDE 

I 

I 

I 

I 

I 

I 

I 

I 

I I I1 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I y 

Figure 8. Collector and Gas Dynamic Augmentor 

14 
The mixing-wave compression section mixes the combustor and detonation duct flows and compresses them by the 

detonation wave moving downstream. The mixing is accomplished by momentum transfer as in ejectors. The high 

pressure detonation wave expands into the collector section 

and transfers energy to the mixed gases by doing expansion 

work on them. Curvature of the collector is considered 

necessary because in a real engine, this would add some 

length to ensure good mixing and would increase pressure by 

reflections of the detonation waves. A schematic representation of the collector section is shown in Figure 9. 

// "DETONATION WAVE 

DE1 

Figure 9. Mixing-Wave Compression Section 

15 
The conditions at the end of mixing of the detonation 

duct and combustor streams are determined from the solution 

of the continuity, momentum, and energy equations. With 

all quantities normalized by the initial detonation duct 

values, the governing equations are: 

continuity 

Momentum 

Energy 

with the definitions 

and 

Subscripts i denote the individual volumes of gases entering the mixing section. The solution for the mixed velocity is: 

The remaining quantities are then evaluated by simple 

substitution. 

When the high pressure volume of the shock wave compressed flow exits the detonation duct, it undergoes a 

sudden expansion into an area Am. Accompanying this sudden 

expansion is an entrepy increase or the so called "shock 

loss" which is accounted for here using the relations given 

by Rudinger. Immediately after expansion, the gas 

exchanges energy with the mixed gases by decelerating and 

expanding 

16 
to some common pressure Pe in a flow area Ae. In the first 

approximation, the equilibration process may be considered 

to be isentropic. 

The continuity equation is written as: 

The statement of constant total energy is: 

When the wave compression exit area Ae is specified, 2 

equations are solved by iteration for Pe and Ue. This 

determines the thermodynamic state points of the wave 

compressed gas. The parameters of the mixing wave compression process are: 

the 

&/Ad - combustor flow area 

Ae/Ad - wave compression exit area 

AdAd - mixing region area 

Other parameters which bear directly on the problem are the 

combustor conditions and single or multiple firings of the 

detonation duct. A representative example of the output of 

the mixing-compression section is shown in Figure 10. 

17 
5 

4 

3 

2 

1 

0 

TE'MPERATURE 

---- PRESSURE 

--- MACH NO. I -..+---- 

I 

r-- 

- 

I 

I 

I------ 

___ 

F-' 

2 3 4 

DIMENSIONLESS TIME 

-- -1- 

5 6 

Figure 10. Gas States at Collector Exit 

18 
Parametric Studies 

Extensive parametric studies were performed to determine the efficiency of detonation wave enhancement of the 

performance of low pressure ratio gas turbines. The basic 

engine parameters were: 

R = pressure ratio =5 

ec = compressor efficiency = 0.85 

eT = turbine efficiency = 0.9 

Q* = energy parameter =2 

With these parameters, the basic isobaric combustion conventional gas turbine has an efficiency of 0. 256. The 

parameters of the augmented gas turbines are: 

Ab - combustor area 

Am - mixing area 

Ae - wave compression area 

There are two modes of firing of the detonation ducts which 

are discussed in Appendix A. In the single firing mode, 

the duct is operated at its nominal conditions, fuel is 

injected and the mixture is detonated. The flow in the 

duct is then allowed to return to its nominal conditions 

before it is detonated again. With 2 detonation ducts 

associated with each combustor, the maximum frequency is 

known to be controlled by the time for the detonation gases 

and associated wave systems to exit the duct ( H = 3) and 

for flow to be re-established, which is also H = 3. Thus 

in 8 = 6, which is the shortest theoretical period of the 

system, the detonation ducts will fire twice. The other 

limit is obtained when the detonation ducts have no flow 

going through them. Calculated efficiencies for the single 

firing mode of operation are shown in Table 1. 

The detonation ducts can also be fired after the 

upstream contact surface exits the duct and the detonation 

duct volume is occupied by compressed gas. In principle, 

the duct could be fired the third time, but the pressure 

waves retard the flow significantly and the firing frequency diminishes with each firing quite rapidly. With 

double firing and two detonation ducts for each combustor, 

the minimum period is 19 = 10.2. Calculated values of 

efficiencies are shown in Table 2. 

19 
It is clear that augmented gas turbines offer the 

potential for significant improvements over the conventional gas turbine efficiency of 0.256. Efficiency is 

higher for single firing mode of operation because greater 

fractions of the duct flow are processed by the detonation 

and shock waves. Efficiency also increases with decreasing 

mixer area, but the results for the lowest values of Am are 

probably not realizable because stable ejector operation 

may not be achievable. For Ab = 1 the combined detonation 

ducts and combustor exit area is 3.73 and a mixing area of 

4 is probably realistic. The effect of the wave compression area on efficiency is minor so that it does not merit 

much consideration at this stage of the analysis. For Ab = 

2 the combined areas are 5.4 and a mixing area of 6 is 

probably quite reasonable. Representative results for a 

single firing mode are therefore: 

Ab = 1 77 = 0.45 

=2 = 0.37 

Similarly , for a double firing mode 

Ab = 1 77 = 0.31 

=2 = 0.29 

Clearly the single firing mode is superior and significant 

improvements over the conventional gas turbine efficiency 

of 0.26 are indicated. Even if the losses in the mixing 

and compression are greater than are currently estimated, 

the potential for enhancing the performance of low pressure 

ratio gas turbines has been demonstrated. 

20 
Table 1. 

Ab 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

Efficiencies of Augmented Gas Turbines 

Single Firing 

3 

3 

3 

3 

4 

4 

4 

5 

5 

5 

6 

Ae 

3 

4 

5 

6 

4 

5 

6 

5 

6 

6 

7 

xb 

.350 

.350 

.350 

.350 

.350 

.350 

.350 

.537 

.537 

.537 

.537 

rl 

.256 

.534 

.537 

.539 

.452 

.459 

.461 

.418 

.422 

.373 . 

-376- 

I 

Note - All areas are normalized by Ad 

21 
Table 2. Efficiencies of Augmented Gas Turbines 

Double Firing 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2.5 

2.5 

2.5 

3.0 

3.0 

4.0 

4.0 

3.0 

3.0 

3.0 

4.0 

4.0 

4.0 

5.0 

5.0 

Ae 

3.0 

4.0 

5.0 

3.0 

4.0 

4.0 

4.0 

4.0 

5.0 

6.0 

4.0 

5.0 

6.0 

5.0 

6.0 

Note - All areas normalized by Ad 

xb 

.285 

.285 

.285 

.285 

.285 

.285 

.285 

.461 

.461 

.461 

.461 

.461 

.461 

.461 

.461 

77 

.406 

.411 

.412 

.368 

.375 

.313 

.318 

.385 

.387 

.388 

.332 - 

.336 

.338 

.293 

.296 
ENGINE PERFORMANCE 

The basic calculations presented in the previous 

section indicated the potential of the detonation wave 

augmentation in terms of thermodynamic cycle efficiency. 

Here, the discussion will be in conventional terms of 

performance of various types of gas turbines. In the 

following, the representative optimum augmented gas turbine 

will be a single firing mode, Ab = 1, Xb = 0.35, = 0.45 

system. The off-design condition will be a conventional 

gas turbine with R = 5 and 1 = 0.26. With the conditions 

stated previously and propane as fuel, the combustor air 

fuel ratio is about 30. At design conditions, the detonation duct air/fuel ratio is about 45. The overall fuel/air 

ratio is therefore: 

Performance of a Pure Jet Ensine 

The case considered is shown schematically in Figure 99 

II . 

1 - INLET 5 - MIXING CHAMBER 

2 - COMPRESSOR 6 - TURBINE 

3 - COMBUSTOR 7 - NOZZLE 

4 - DETONATiON CHAMEERS 

Figure 11. Schematic Representation of a 

Detonation Wave Augmented Jet Engine 

23 
In this case, the net work is simply the increase in the 

kinetic energy of the gases, or: 

With thrust F equal to the time rate of change of momentum, 

the fuel flow rate per unit of force is: 

In conventional terms, the performance of the optimum 

(maximum augmentation) and off-design engines is: 

Optimum wf = 0.83 lb/lb hr 

Off-Design = 1.23 lb/lb hr 

Here, qf for propane was taken as 22,000 Btu/lb. 

Performance of a Turbofan 

In this case, the net work is used to power the fan, 

as shown in Figure 12. When the net work is equated to the 

change in kinetic energy of the total flow through the 

engine and the thrust is taken as the rate of change of 

momentum then: 

with 

p - bypass ratio 

x - velocity ratio = VEB/VE 

With eg = .85, x = 1/2, VE = ,200 ft/s, qf = 22,000 

Btu/lb, and p = 8, the performance parameters are: 

Optimum Operation wf/F = 0.345 lb/lb hr 

Off-Design = 0.596 

24 
U 

Figure 12. 

Performance of a Bypass Jet Ensine 

Schematic Representation of the Turbofan Engine 

In this configuration, the flow from the detonation 

ducts is used directly for propulsion as shown in Figure 

13. In this case, the turbine must deliver sufficient 

power to compress all the flow while only a fraction of it 

is going through the turbine itself. 

Compressor work 

Turbine work 

Mt cp Tbf(1 - R'r)et 

Equality of the above results in 

Mc/Mt = ec et (Tbf/Ta) R'r 

25 
The fuel 

With the 

expanded 

is: 

here 

c1 

Xi 

input is 

assumption that the detonation duct flow is 

to ambient pressure, the specific fuel consumption 

= Mc/Mt 

= mass function of total flow 

In conventional units, the performance is calculated to be 

Optimum design wf/F = 2.4 lb/lb hr 

Off -Design = 3.36 

The reason for the poor performance of this idea is -that 

over 60% of the flow from the detonation ducts is at a low 

temperature and pressure. The high pressure pulses, which 

in this case do not compress the rest of the flow, give 

sharp thrust pulses but of very short duration. 

Figure 13. Bypass Jet Engine 

26 
Performance of a Shaft Output Ensine 

In this case, the whole output of the gas turbine is 

taken as shaft power. The arrangement is shown in Figure 

14. The specific fuel consumption is given in terms of the 

efficiency by the relation: 

In conventional units of specific fuel consumption, the 

performance of the shaft engine is calculated to be: 

Optimum engine 

Off-Design 

wf/W = 0.257 lb/hp hr 

= 0.445 

Figure 14. Schematic Representation of a 

Shaft Output Engine 

With the exception of the bypass jet engine, all the 

configurations indicate significant improvements in performance. Even if the full potential cannot be realized in 

a working engine, it appears very likely that detonation 

wave augmented engines could represent a major advance in 

technology. 

27 
CONCLUSIONS 

The study employed highly simplified, but realistic 

models of the gas dynamics of transient transverse detonation waves in transonic duct flows to estimate the maximum 

frequency at which such ducts could be operated. Concurrently, a preliminary experimental effort not only proved 

the correctness of the hypothesis of the possibility of 

generating such waves, but also demonstrated that the 

induction distance for the formation of detonation waves 

was only about 1-2" and indicated that the pressure ratios 

across the wave were approximately 10. The combined 

theoretical and experimental results suggest that the 

salient features of the complex gas dynamic phenomena 

involved are modelled correctly. Therefore, the performance of detonation ducts operating as gas generators is 

predicted well enough for estimates of system performance. Losses due to mixing and sudden expansion into the mixing 

duct are accounted for using standard techniques, but it is 

possible that significant errors could result from the 

usual assumptions of quasi-one dimensional flows. Since 

the mixing process involves turbulent diffusion among 

streams at different pressures, calculated results of 

temperatures and velocities must be viewed with some 

caution. The pulse compression model for the transient 

flows of dissimilar volumes of gas contains the necessary 

conditions on energy and continuity equations but Some 

uncertainty remains with regard to the ultimate state of 

the flow. The above considerations lead to the conclusion 

that even with highly reasonable models for the flow 

phenomena involved, considerable uncertainty remains as to 

the actual turbine entry conditions. 

Calculations of performance of the gas turbines 

operations in various configurations demonstrate significant enhancement of performance. At pressure ratios of 5 

the augmented gas turbines showed efficiencies of about 45% 

versus 26% for conventional engines. Even if the losses in 

the mixing and wave compression processes were doubled, a 

50% increase in efficiency still appears to be realizable. 

In view of the high cost of additional compressor stages 

which would be required to achieve such an improvement in 

performance, the probability of using very inexpensive duct 

remains should merit further attention. 

28 
The theoretical work in this field has gone as far as 

is practical. Far more elaborate flow models could be 

invented but the same uncertainties would still remain. It 

is concluded that the concept has been shown theoretically 

to have a high probability of success and must now be 

validated in a simple engineering laboratory experiment. 

29 
A 

Af 

cP 

CV 

C 

D 

e 

E 

F 

H 

LO 

m 

M 

P 

9f 

Q 

Q* 

R 

t 

T 

Tmax 

V 

LIST OF SYMBOLS 

area 

air/fuel ratio 

specific heat at constant pressure 

specific heat at constant volume 

acoustic speed 

detonation wave speed 

efficiency 

energy 

thrust 

gravitational constant 

heat release parameter 

length of the detonated volume 

mass 

Mach number 

pressure 

heating value of fuel 

heat 

heat release parameter 

compressor pressure ratio 

time 

temperature 

maximum temperature in the engine 

specific volume 

30 
VE 

Wf 

W 

X 

xb 

Y 

r 

t7 

.A 

Q 

P 

e 

Subscripts 

a 

air 

b 

B 

bf 

C 

d 

D 

e 

f 

m 

0 

exit velocity 

fuel flow rate 

thermodynamic work 

axial distance 

fraction of flow through the combustor 

isentropic exponent 

1 - 1/Y 

engine efficiency 

(3 - 1)/2( Y - 1) 

TmadTa 

density 

dimensionless time 

ambient 

air 

burner or combustor 

bypass 

combustor exit conditions 

compressor 

detonated gas 

detonation wave 

wave compressor exit 

fuel 

mixing region 

detonated volume initial conditions 

31 
I 

REFERENCES 

1. Wortman, A., "Detonation Wave Augmentation of Gas 

Turbines," Report No. IST-NAS-07-84-01, ISTAR Inc., 

Santa Monica, CA, June 1984. 

2. Stanyukovich, K. P. Unsteadv Motion of Continuous 

Media, Translated from the Russian, Pergamon Press, 

New York, 1960. 

32 
APPENDIX A 

GAS DYNAMICS OF THE 

DETONATION DUCT 
GAS DYNAMICS OF DETONATION DUCTS 

Presented here is an outline of the modelling and gas 

dynamics calculations which were performed as part of the 

feasibility study of detonation wave compression augmentation of gas turbines. Surveys of open literature showed no 

comparable theoretical or experimental work so that this 

represents a new approach in the field of detonation waves. 

An independent laboratory experiment was performed to prove 

the existence of transverse detonation waves and to estimate some of the critical parameters. This work is described in Appendix B. Existing published work on detonation waves may be divided into three major categories: 

a. Studies of propagating steady waves 

b. Studies of stabilized waves in very high speed 

flows 

c. Studies of transitions from deflagrations to 

detonations 

The basic theory of steady detonation waves of the ChapmanJouguet type has been known for about a century (e.g., 

Stanyukovichl) but numerous questions still remain. A 

detonation wave represents an essentially constant volume 

heat release with an associated increase in temperature and 

pressure. Extensive experimental studies of various 

explosive mixtures indicate that the fundamental ChapmanJouguet hypothesis of sonic outflow from the detonation 

wave front is essentially correct. Calculations (e.g., 

Eisen, et a12) are generally in good agreement with experimental data. However, the nature of the detonation wave is 

itself in some question. While the Chapman-Jouguet detonation with sonic relative velocity of the exploded gas 

occurs most frequently, non-Chapman-Jouguet waves have also 

been observed (Gross and Oppenheim3, Schott4). The latter 

cites instances of detonation products Mach numbers of 

1.1. Pressure ratios across detonation waves are also 

somewhat uncertain, with Eisen, et a12, calculating 

stoichiometric H2-Air pressure ratios to be 15.6, while 

Jost5 shows values of 15.2 and Sokolik6 shows a value of 

13. Similar uncertainties exist in the values for pressures and temperatures after the detonation wave is 

reflected from the wall as a shock wave. 

. 
When a detonation wave is stabilized in high speed 

flow, total pressure is diminished, but this is deemed 

acceptable in ramjets because intake losses are reduced. 

Such a loss could not be tolerated in gas turbines. 

Because of the continuing interest in high speed ramjets, 

the problem of stabilizing detonation waves in undiffused 

hypersonic flow has received considerable attention. Among 

the published studies are those of Waltrup, et a17-9. The 

latter is an extensive survey of the field which updates 

that of Duggerlo. Numerous other experimental studies of 

standing detonation waves demonstrated the feasibility of 

stabilization of oblique detonation waves (e.g., Nicholls 

and Daborall and Dunlap, et a112) and advantages of supersonic combustion for certain ramjet applications were 

demonstrated by Duggerl3. While the field has been 

thoroughly explored, it is not clear that engineering 

applications for standing detonation waves do, in fact, 

exist. 

The problem of transition from deflagration to detonation in ducts filled with quiescent explosive mixtures has 

also received considerable attention. These studies have 

concentrated on the determination of the effects of size, 

surface roughness, residual turbulence, ignition mechanism, 

and the thermodynamic state of the explosive mixture. It 

is well known that wall roughness or obstacles which 

generate turbulence in the flow can reduce the transition 

distance by an order of magnitude (e.g., Sokolik6 and 

Brinkley and Lewisl4). The configuration and the energy 

output of the igniter are also known to play an important 

role in the initial acceleration of the- flame (Laderman, et 

alq. Reference 14 describes experiments in which placement of obstructions near the igniter reduced the transition or induction distance from 60 to 5 tube diameters, for 

a wide range of tube diameters. Reference 2 gives a 

transition distance for a quiescent ethylene-oxygen mixture 

of only 6 cm. Jost5 shows that detonations tend to form in 

about 3-4 tube diameters for tube diameters greater than 

about 15 mm. Jost also shows that the transition distance 

decreases by 15-40% when the initial temperature is 

increased form 15% to 180OC. The speed of the detonation 

wave appears to be very weakly dependent on the mixture 

pressure and temperature. When the detonation is formed in 

short tubes or vessels then the precursor pressure waves 

can compress the unexploded mixture to a pressure ratio as 

high as 5 (Brinkley and Lewis14). A comprehensive 

parametric experimental study of Lee, et a116 showed the 

effects of mixture composition and obstacles in the tube on 

induction distances in hydrogen-air mixtures. 

A-3 
All of the above studies are for detonation waves in 

stationary fluids and thus the results have very little 

direct bearing on the transverse waves in high speed flows 

which are of interest here. A comprehensive literature 

search using the extensive facilities of the UCLA Engineering Library revealed no published data on transient transverse detonations in ducts. The only studies of the 

applications of travelling detonation waves in gas turbines 

appear to be those of Edwards17 who demonstrated that 

stable Chapman-Jouguet waves could be produced in an 

annulus. These results are interesting but they do not 

contribute to the gas dynamics problem considered here. 

The large number of uncertainties in the fundamental 

processes and details of the gas dynamics of the flow 

situation renders exact calculations essentially meaningless and it is necessary to model the physics of the 

problem using reasonable approximations to the actual 

phenomena. Physical reasoning based on the experimental 

work performed in support of this program has led to the 

following mathematical models of the gas dynamics of 

transient, transverse detonation wave ducts. 

Initial Detonation 

Standing detonation waves were rejected for - gas 

turbine applications because of the very high total pressure losses associated with the Mach 4-6 shock waves. 

Initially, transient waves propagating longitudinally in 

ducts were given some consideration, but the idea was 

rejected because of the difficulties of uniform ignition 

across the duct which would be necessary for the establishment of a planar wave. Evaluation of numerous other ideas 

led to the conclusion that transient transverse waves were 

most likely to be successful. This was confirmed by the 

experiments described in Appendix B. The basic idea is to 

ignite a volume of detonable mixture from one or more sides 

of a rectangular duct or from the centerline of a circular 

duct. A line of symmetry or a solid surface are necessary 

to support the pressure which accelerates the combustion 

front and leads to the transition from deflagration to 

detonation. Schematic representations of the ignition 

models are shown in Figure A.l The model assumes that at 

the entrance to the detonation duct is a grid of fuel 

injectors which deliver fuel intermittently. Synchronized 

with the fuel injectors is the firing of the igniters at 

the sides or on the centerline of the duct. The latter is 

A-4 
not considered in depth at this time because of possible 

problems with unacceptably large induction distances for 

the formation of the detonation wave. After ignition the 

flame accelerates away from the wall while it is being swept 

downstream by the approximately Mach 1 channel flow. At 

some point a detonation wave is formed and is reflected 

from the far wall as a shock wave. The gas ahead of the 

detonation wave will be compressed by the precursor pressure waves generated by the accelerating flame. Some 

spreading of the flame in the longitudinal direction is 

inevitable as is turbulent diffusion so that the flame line 

will be quite irregular. It is also known (e.g., Jost5) 

that detonation waves tend to exhibit transverse instabilities which in tubes manifest themselves as spin. It almost 

certain that in the highly turbulent transonic duct flow 

some transverse instabilities will appear and a simple 

trajectory of the detonation wave is unlikely. The sudden 

increase of pressure in a volume of gas will generate shock 

waves in the longitudinal direction and the gas dynamic 

situation will be somewhat like that shown in Figure A.2. 

It is known from the limited test data obtained from a 

simple detonation duct that the detonation wave forms 

within a short distance from the igniters (approximately 

1-2"). With duct width/length ratio in the ignition region 

of about 3-4 and a detonation wave Mach number of 4-6, the 

traverse time in the transverse direction is an order of 

magnitude lower than the longitudinal traverse time for an 

acoustic pulse. A reasonable engineering approximation to 

this very complex situation is therefore a concept of a 

sudden appearance of a volume of high pressure and temperature gas. This leads to a sudden expansion which generates 

shock waves which propagate away from the detonated gas. 

In the limit this model is that of a shock tube in which 

diaphragms are burst on both sides of the chamber of high 

pressure gas. 

A-5 
COMBUSTIBLE MIXTURE - 

DETONATION WAVE 

----e 

- FLOW 

------- -t \/ \/ \/ \I 

/\ /\ /\ I' /' '\ 

IGNITERS 

A. Rectangular duct - single side ignition 

-----a 

- 

IGNITERS - xxxxx -c 

B. Circular duct - central ignition 

Figure A.l. Formation and Propagation of Detonation 

Waves Moving Transversely to the Flow 

DETONATION WAVES 

SHOCK WAVE FLOW BURNT GAS 

IGNITERS 

Figure A.2. Expansion of the Detonation Products 

A-6 
The Shock Tube Problem 

When regions 1 and 2, initially at different temperatures and pressures, begin to interact with each other, a 

shock wave is propagated into the low pressure region and a 

train of rarefaction waves moves into the high pressure 

region. The two gases are separated by an interface at 

which pressure and velocities are equal. The situation is 

depicted in Figure A.3 which also shows a shock wave 

entering an expanding duct. 

I I 

DETONATION I I 

PRODUCTS I I 1 I 

I 

I 

I 

I 

I 

I 

I 

I 

I \- 

I INTERFACE REFLECTED i SHOCK WAVE / RAREFACTION I 

I I I I SHOCK I /INTERFACE 

WAVE 

Figure A.3. The Shock Tube Problem and Shock 

Wave in a Variable Area Duct 

A-7 
Analyses of the formation of the initial shock wave and the 

strength of the rarefaction waves follows the very clear 

exposition of Rudingerl8. The velocity of the gas in 

region 3 is given by the usual normal shock wave relation: 

with a being the acoustic velocity, Ms the shock wave Mach 

number, P pressure, U velocity, Y the isentropic exponent 

and subscripts denoting the corresponding regions. The 

Riemann invariant for region 4 is expressed as: 

2a2 

Y2 - 1 

u4 = 

with P3 = P4 and U3 = U4 

r Y2- 

The relation between pressure ratio and shock Mach number 

is shown in Reference 19 to be: 

P 

- Y-1 +Y+1 3 Ms2 - - 

2Y 2Y P1 

Solution of Equations A.3 and A.4 leads to the calculations 

of conditions across the shock and in the rarefaction fan. 

A-8 
and 

Conditions in region 4 are evaluated by means of isentropic 

relations. These solutions constitute the initial conditions for the interaction phenomena which are studied using 

the method of characteristics. 

The representative calculations exhibited in the 

following are based on the following initial conditions: 

Y1 = 1.4 Y2 = 1.25 

a2/al = 2.5 P2/P1 = 8.5 

These values are based on theoretical considerations- and 

preliminary test data. The initial values corresponding to 

these parameters are: 

In all of the following calculations, it was assumed that 

in every flow region the gas was perfect and that the 

isentropic exponents were different but constant. 

A-9 
Initial Interactions 

The initial expansion of the detonated mixture creates 

rarefaction wave fans, which intersect within the detonated 

volume, as shown in Figure A.4. The numbers on the characteristics are the Riemann invariants which in this case 

are defined as: 

I = 500[1 + a/ao + Y - 1 u/ao] 

2 

(A.7a) 

I1 = 500[1 + a/ao - y- 1 U/ao] 

2 (A.7b) 

This identification of the invariants is purely arbitrary 

and is used here simply for convenience. The fundamental 

statement is that the quantities [a + (7- 1)U/2] remain 

constant on trajectories defined by U-+ - a. 

The changes in state variables indicated in the above 

Figures are due to the interactions of the initial and 

reflected rarefaction wave trains and the passage of 

interfaces and shock waves. 

The dimensionless time for the problem is: 

e = tao/Lo 

and the dimensionless coordinate is X/Lo with X measured 

from the downstream boundary of the detonated volume. 

Variation of pressure with time throughout the detonated 

volume is shown in Figure A.5. The same variations at 

later times are shown in Figure A.6. All of the above 

quantities are shown in a coordinate system which moves at 

Mach 1 with the flow in the duct. 

A-10 
1.0 

.8 

.6 

.4 

.2 

0 

0 ,2 .4 .6 

AXIAL LOCATION - X/L, 

.8 1.0 

Figure A.4. Characteristics Net far the Initial 

Interaction in a Moving Coordinate System 

A-11 
10 

e= o 

I 

0 

/ \ \ 

.2 .4 .6 .a 

AXIAL tOCATION - x/L, 

1.0 

Figure A.5. Distribution of Pressure in the Detonation 

Volume in a Moving Coordinate System 

A-12 
0 

CL 

\ 

n 

I 

0 

tQ 

LY 

w 

LY 

3 

v, 

Ln 

W 

cz 

U 

n 

3.0 r I 

2.5 

2.0 I I I 

0.5 ' 1.0 1.5 2.0 

AXIAL DISTANCE - X/L, 

.80 

.75 

.70 

W 

LY 

3 

I- 

< 

LY 

w 

n 

E 

w 

I- 

-. 

Figure A.6. Distributions of Temperature and Pressure 

within the Detonation Gas 

A-13 
Motion of Discontinuities 

After the rarefaction wave trains intersect in the 

detonated volume, the waves intercept the contact surfaces. 

1nterception.of a contact surface by a rarefaction wave 

results in the deceleration of the contact surface, reflection of a rarefaction wave and a transmission of a weak 

rarefaction wave. The situation is shown in Figure A.7. 

I 

t 

1, '/I Contact 

/ Surface 

// 

// 

Transmitted 

Figure 

Conditions for 

A.7. Interaction of a Rarefaction Wave 

with a Contact Surface 

the reflected and transmitted waves are 

obtained from considerations of the Riemann invariants and 

the continuity of pressure and velocity at the contact 

surface. The calculated results for the initial interaction of the rarefaction waves with the contact surface are 

shown in Figure A.8. The transmitted waves propagate at 

sonic velocity and therefore overtake the shock wave. The 

resulting flow situation is somewhat similar to that shown 

in Figure A.7 except that there is no transmitted wave. 

Calculations of interactions of waves and contact surfaces 

in the inertial coordinate system of the duct are shown in 

Figure A.9. During the interactions, the flow is being 

swept downstream (to the left) at Mach 1 so that the upstream extent of the gas dynamic phenomena is rather 

limited. It should be noted that the contact surface which 

A-14 
initially moved upstream is swept back to its initial 

location at 

6 = 2.1. Therefore, in principle, the compressed gas in 

the detonation volume could be of 

fuel and detonated at some time 8 22.1. This is one of 

the alternative modes of operation which is considered 

later. 

8 = 1.1 and clears the detonated volume at 

mixed with a new charge 

The shock wave which has an initial Mach number of 

about 2, in fact initially propagates upstream in the 

inertial coordinate system at a speed corresponding to Mach 

1 since the duct flow is taken to be to the left at Mach 1. 

The first rarefaction waves overtake the shock wave at the 

point X/Lo - 2.1 or about 1 detonated volume length 

upstream of the igniters. Motions of the shock wave and 

the upstream contact surface are shown in Figure A.lO. It 

should be noted that at a distance of 2.4 Lo from the 

igniters, the shock wave Mach number is reduced to about 

1.4. Correspondingly, the pressure ratio has diminished 

from 4.5 to 2.1. This indicates that the rarefaction waves 

from the opposite side of the detonated volume alternate 

the upstream propagating shock wave quite rapidly. The 

phenomena of shock wave and contact surface interactions 

downstream of the detonated volume will be considered in 

the discussion of the duct output. 

A-15 
0 

0 

-J 

\ 

m 

c, 

II 

a 

I 

W 

Im 

v, 

W 

d 

z 

0 

m 

z 

W 

E 

U 

I 

I 

n 

3 

2 

1 

0 

0 

,937, 

1 2 3 

AXIAL DISTANCE - X/L, 

Figure A.8. Interactions with the Detonated Gas and the 

Shock Wave in a Moving Coordinate System 

A-16 
I + 

Figure A.9. Salient Features of the Primary Detonation 

in Inertial Coordinates 

A-17 
12 

10 

a 

6 

4 

2 

0 

0 1 2 3 4 5 

DIMENSIONLESS DISTANCE - X/L, 

Figure A.lO. Motion of Discontinuities in 

Inertial Coordinates 

6 

A-18 
Attenuation of Upstream Shock Waves 

I. 

,- 

The shock waves propagating upstream from the detonated volume must be attenuated to minor acoustic disturbances in order to minimize the pressure fluctuations which 

might affect compressor performance. It is known that 

rapid area increases are very effective in reducing the 

strength of transmitted shock waves. In general, the gas 

dynamic situation is as shown in Figure A.11. 

Waves 

MS / Shock Inc i dent 

4 

P 

HCont ac t 

Surface 

Shock 2 

Area Change 

Figure A.ll. Interactions of Shock Waves 

with Area Changes 

Here, following Rudinger18, the area change is shown to be 

instantaneous. This approximation is discussed by Reference 18 and is shown to give good agreement with experimental results. The more elaborate analysis of Whitham20 

which considers gradual area changes could be adapted to 

the solution of shock waves moving through variable area 

ducts with gas flows, but since only an estimate is needed 

here, the considerable analytical effort involved could not 

be justified at this point. 

The actual flow situation will vary significantly with 

the strength of the incident shock wave and the Mach numbers of the flow in sections 1 and 2. Solutions of the 

problem are obtained by matching the conditions in region 5 

which results from an isentropic expansion through the 

A-19 
reflected waves with isentropic flow between area changes 

from region 5 to region 6 and in turn matching the velocity 

and pressure at the contact surface between regions 6 and 

4. The process is quite straightforward and the required 

large number of interactions is easily performed on a computer. The procedure is as follows: 

a. The velocity of the gas in region 3 is computed 

using: 

b. The temperature ratio T3/T1 is calculated using 

shock wave relations 

c. Mach number in region 3 is calculated using 

U 

a 

1 

d. With a chosen value of P5 the Mach numbers in 

region 3 and 5 are connected using isentropic flow 

relations L 

e. Velocity in region 5 is calculated using isentropic flow relations 

f. Transmitted shock wave Mach number is guessed and 

conditions in region 4 are calculated 

g. Using isentropic relations and conditions in 

region 5, the conditions in region 6 are calculated 

h. Calculated conditions in regions 6 and 4 are compared and the guesses for MT and P5 are adjusted. 

The process is repeated until the contact surface 

conditions are satisfied to an arbitrary degree of precision. Solutions for strong incident shock waves in air 

flowing at Mi = 1 are shown in Figure A.12. 

A-20 
1.4 

1.3 

I 

52 

I 

u 

= 1.2 w 

> 

cc 

3 

Y 

u 

0 

I 

v, 1.1 

1.01 

AREA RATIO 

19 15 12 10 8 7 6 

. / 

.03 .04 .05 .06 .07 .08 .09 .10 

DUCT INLET VACH NO - MI 

Figure A.12. Mach numbers of the Shock Waves Transmitted 

Out of the Detonation Duct - 

In the particular situation considered here, the 

incident shock wave Mach number is 1.4 so that the problem 

is simplified greatly. Since the shock wave is moving into 

a counterflow at M = 1, its net speed in inertial coordinate system is only M = 0.4 are 

swept downstream. The contact surface also moves downstream and the transmitted shock wave is extremely weak. 

In fact, at an area ratio of 1.34 which corresponds to a 

flow Mach number of 0.5, ratio 

is only 1.047. At an area ratio of 2, which corresponds to 

a flow Mach number of 0.3, the transmitted shock wave 

decays to an acoustic pulse. 

and the gases in region 3 

MT = 1.02 and the pressure 

Detailed calculations employing inviscid flow assumptions are not very meaningful when the shock waves are 

weak because of strong dissipation effects. However, the 

results indicate that even if different fuels are used, or 

the distance between the duct inlet and the detonated 

volume is reduced, shock waves with Mach numbers of 1.5 - 

2.0 can be attenr_rated by area ratios of less th2R 5. 

A-21 
Output of the Detonation Duct 

The detonation duct is a gas generator whose outpcc 

varies with time. Here, and in all results exhibited in 

this Appendix, it is assumed that the air in the duct flows 

at sonic velocity, the compressor pressure ratio is 5:1, 

and that a stoichiometric mixture of propane and air is 

detonated. It is shown in Figure A.9 that the upstream 

contact surface clears the detonated volume after 8 = 2.1 

and the flow is fairly uniform at 8 = 3. Similar situation 

exists at 8 = 8. In all of the exhibited results, it will 

be assumed that the duct is fired at 8 = 0, 3, 8. After 

each firing, the flow velocity in the duct is diminished 

and the cyclic frequency is reduced. 

Summary of the thermodynamic states and flow conditions at the duct exit, which is defined as X/Lo = -1 is 

presented in Table A.l for 3 consecutive firings. Obviously, in actual operation the cut could be fired 1, 2, or 

3 times. Variations of the static pressures, temperatures, 

and Mach numbers with dimensionless time are shown in 

Figure A.13. All quantities are normalized by the initial 

duct flow parameters which are denoted by the subscript 0. 

Corresponding total pressures and temperatures are shown in 

Figure A.14. Flow velocities at the duct exit are shown 

in Figure A.15. 

The most important parameter for the gas generator 

aspect of the detonation duct is the power output. Since 

only comparable quantities are of interest at this stage, 

the instantaneous power output is defined as isentropic 

expansion through a turbine to the initial pressure at the 

compressor inlet. This output is normalized by the energy 

flow rate through the detonation duct 

- 

(A. 10) 

The output from such isentropic blowdown turbines supplied 

by the detonation ducts is compared with ideal expansion 

from a combustor with flow at Mc = 0.25 in Figure A.16. 

Comparisons of the total energy generated in a complete 

cycle consisting of 3 firings and recovery of the flow to 

initial conditions is 0.4 shown in Figure A.17. Obviously, 

the highly simplified calculations shown here must be 

viewed as indications of the potential of the detonation 

duct as a gas generator rather than from engineering quantities. 

. 

A-22 
c 

EVENT 

Table A.l. Summary of Duct Output 

P/Po. T/To PT/Po TT/To u/ao M 

0 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

FIRST 

0.00 1.20 1 

0.33 4.47 1 

0.46 4.47 5 

0.49 4.47 5 

0.51 4.20 5 

00 

64 

48 

48 

43 

0.53 3.90 5.35 

0.59 3.20 5.14 

0.73 2.26 4.80 

1.25 2.20 4.77 

1.72 2.11 4.73 

2.82 2.11 4.73 

2.88 1.22 1.12 

FIRING 

1.89 

23.90 

7.26 

7.26 

6.88 

6.08 

4.36 

2.57 

2.49 

2.34 

2.34 

1.97 

1..20 1.00 1.00 

2.65 2.24 1.75 

6.06 2.27 0.97 

6.13 2.24 0.96 

5.99 2.12 0.91 

5.84 2.00 0.86 

5.47 1.62 0.72 

4.92 1.00 0.46 

4.89 0.96 0.44 

4.83 0.89 0.41 

4.83 0.89 0.41 

1.27 0.86 0.81 

SECOND FIRING 

0 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

0.00 1.22 1.12 1.97 1.27 0.86 0.81 

0.35 5.46 1.81 22.10 2.45 2.11 1.57 

0.50 5.46 6.06 8.47 6.62 2.11 0.86 

0.50 5.46 6.06 8.47 6.62 2.11 0.86 

0.53 4.76 5.90 6.74 6.32 1.85 0.76 

0.60 3.91 5.67 4.91 5.93 1.45 0.61 

0.75 2.76 5.29 2.97 5.37 0.80 0.35 

1.27 2.70 5.26 2.81 5..34 0.76 0.33 

1.77 2.57 5.22 2.55 5.25 0.68 0.30 

4.21 2.57 5.22 2.55 5.25 0.68 0.30 

4.22 1.49 1.23 1.91 1.32 0.67 0.61 

0.51 5.13 5.99 7.59 6.47 1.98 - 0.81 

THIRD FIRING 

0 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

0.00 1.49 1.23 

0.32 6.66 2.00 

0.46 6.66 6.70 

0.46 6.66 6.70 

0.47 6.25 6.62 

0.48 5.80 6.52 

0.56 4.77 6 

0.70 3.37 5 

1.20 3.29 5 

1.66 3.14 5 

5.66 3.14 5 

5.80 1.82 1 

27 

a5 

82 

77 

77 

38 

1.57 1.32 0.67 0.61 

20.85 2.77 1.96 1.39 

9.13 7.15 1.87 0.72 

9.13 7.15 1.87 0.72 

8.49 7.04 1.87 0.71 

7.57 6.88 1.69 0.66 

5.59 6.48 1.28 0.51 

3.91 5.03 0.59 0.24 

3.40 5.86 0.56 0.23 

3.22 5.80 0.46 0.19 

3.22 5.80 0.46 0.19 

2.13 1.44 0.56 0.48 

A-23 
KEY TO 

0 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

TABLE A. 1 

Initiation of detonation 

Shock crossing 

Contact surface crossing 

First rarefaction wave 

Second rarefaction wave 

Third rarefaction wave 

Middle rarefaction wave 

Final rarefaction wave 

First wave reflected from the contact surface 

Final wave reflected from the contact surface 

Contact surface crossing 

Reflected wave from the shock 

More realistic power extraction models are used in the 

main report to evaluate potential gas turbine performance 

A-24 
16 

14 

12 

10 

a 

6 

4 

2 

0 

I IIiI I I I I MACH NUMBER 

0 1 2 3 4 5 6 7 

VARIABLES M, T/To, P/Po 

Figure A.13. Variations witn Time of Mach Number, 

Static Temperature and Static Pressure 

at the Duct Exit 

A-25 
16 

14 

12 

10 

8 

6 

4 

2 

0 

0 5 10 15 20 

TOTAL TEMPERATURE AND PRESSURE 

Figure A.14. Gas Dynamic Conditions at 

Duct Exit (X/Lo = -1) 

A-26 

25 
16 

12 

a 

4 

0 

0 .5 1 .o 1.5 2.0 

DIMENSIONLESS VELOCITY - u/ao 

2.5 

Figure A.15. Variation with Time of Gas Velocity 

at Duct Exit 

A-27 
0 

d CD N 0 

M - lndlllO tl3MOd SS3lNOISN3WIa 

A-28 
> 

c3 

z 

W 

z 

w 

a 

W 

c 

Q 

z 

W 

z 

W 

c3 

m 

m 

W 

A 

z 

0 

m 

z 

W 

M 

5 

a 

16 

14 

12 

10 

8 

6 

4 

2 

0 

0 4 

I L 

8 12 

DIMENSIONLESS TIME - 8 = tao/Lo 

Fiq~re A.1?. Energy Generated by the Detonation Duct 

16 

A-29 

11 
List of Svmbols 

a 

cP 

I 

I1 

LO 

M 

P 

Ri j 

t 

T 

U 

w 

X 

Y 

P 

8 

Acoustic velocity 

Specific heat at constant pressure 

Characteristic value 

Characteristic value 

Length of the detonated volume 

Mach number 

Pressure 

Density ratio = pi/Pj 

Time 

Temperature 

Particle velocity 

Thermodynamic work or energy 

Axial distance 

Isentropic exponent of the gas 

gas density 

Dimensionless time 

Subscripts 

0 

1121... 

C 

S 

T 

Initial conditions before detonation 

Regions 

Combustor 

Shock 

Transmitted shock 

A-30 
References 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

Stanyukovich, K.. P., Unsteadv Motion of Continuous 

Media. Translated from Russian, Pergamon Press, New 

York, 1960. 

Eisen, C. L., Gross, R. A., and Rivlin, T. J., "Theoretical Calculations in Gaseous Detonations," Combustion 

and Flame, Vol. 4, No. 2, June 1960, pp. 137-149. 

Gross, R. A., and Oppenheim, A. R., "Recent Advances in 

Gaseous Detonations," ARS Journal, Vol. 29, No. 3, 

March 1959, pp. 173-179. 

Schott, G. L., "Structure, Chemistry and Instability of 

Detonation in Gases," Fourth Symposium (International) 

on Detonation, 12-15 October 1965, White Oak, MD. 

Report ACR-126, NOL, US NAVY, Washington, D.C., pp. 

67-77. 

Jost, W., Explosion and Combustion Processes in Gases, 

First Ed., McGraw-Hill, New York, 1946. 

Sokolik, A. S:, Self-Isnition Flame and Detonation in 

Gases, Akademiya Nauk, USSR, Moskva, 1960. Translation 

from Russian, Israel, 1963. 

Waltrup, P. J., Billing, F. S., and Stockbridge, R. D., 

"A Procedure for Optimizing the Design of Scramjet 

Engines," AIAA Journal of Spacecraft, Vol. 16, No. 3, 

May-June 1979, pp. 163-171. 

- 

Waltrup,P. J., Dugger, G. L., Billing, F. S., and Orth, 

R. C., ttDirect-Connect Tests of Hydrogen-Fueled Supersonic Combustors,'' XVIth International Symposium on 

Combustion. The Combustion Institute, Pittsburgh, PA, 

1977, pp. 1619-1629. 

Waltrup, P. J., Anderson, G. Y., and Stull, F. D., 

ttSupersonic Combustion Ramjet (Scramj et) Engine Development in the United States," 3rd International Symposium 

on Air Breathing Engines, Munich, Germany, 1976, pp. 

835-861. 

Dugger, G. L. , I'Recent Advances in Ramj et Combustion, 'I 

ARS Journal, Val. 29, Nc. 11, Ncvember 1959, pp. 

819-827. 

A-3 1 

I 
11. Nicholls, J. A., and Dabora, E. K., "Recent Results on 

Standing Detonation Waves," Eight Symposium (International) on Combustion, Butterworths Scientific Publications, London, 1960. 

12. Dunlap, R., Brehm, R. L., and Nicholls, J. A., "A 

Preliminary Study of the Application of Steady-State 

Detonative Combustion to a Reaction Engine," ARS Jet 

Propulsion, Vol. 27, No. 7, July 1958, pp. 451-456. 

13. Dugger, G. L., "Comparison of Hypersonic Ramjet Engines 

with Subsonic and Supersonic Combustion and Propulsion, 

Fourth AGARD Colloquium, Milan, 1960, pp. 84-119. 

14. Brinkley, S. R., Jr., and Lewis, F., "On the Transition 

from Deflagration to Detonation," Seventh Symposium 

(International) on Combustion, The Combustion Institute, London and Oxford, 1958. 

15. Laderman, A. J., Urtiew, P. A., and Oppenheim, A. K., 

"Effect of Ignition Geometry on Initial Flame Acceleration in Spark Ignited Explosive Gas," Combustion and 

Flame, Vol. VI, No. 4, Dec. 1962, pp.325-335. 

16. Lee, J.H.S., Knystautas, R., and Freiman, A., "High 

Speed Turbulent Deflagrations and Transition to Detonation in H2-Air Mixtures," Combustion and Flame, --Val. 

56, No. 2, May 1983. 

17. Edwards, B., IIMaintained Detonation Waves in an Annular 

Channel: A Hypothesis which Provides the Link Between 

Classical Acoustic Combustion Instability and Detonation Waves," XVIth International Symposium on Combustion. The Combustion Institute, Pittsburgh, PA, 1977, 

pp. 1611-1618. 

18. Rudinger, G., Wave Diaqrams for Nonsteadv Flow in 

Ducts, D Van Nostrand Co., New York, 1952. 

19. Anon., "Equations, Tables, and Charts for Compressible 

Flow," Report 1135, NACA Washington, D.C., 1953. 

20. Whitham, G. B., Linear and Nonlinear Waves, Wiley and 

Sons, New York, 1974. 

A-32 
APPENDIX B 

EXPERIMENTAL STUDIES OF 

DETONATION DUCTS 

! 
EXPERIMENTAL STUDIES OF DETONATION DUCTS 

A simple experimental program was carried out in 

support of, but not as part of, the contract. Due to 

limitations of time and finances, the experimental program 

was aimed at demonstrating that transverse detonation waves 

could be produced, and to indicate the pressure levels 

which could be achieved. 

From the beginning of the program of studies of 

detonation wave augmented gas turbines, serious questions 

were raised regarding the possibility of forming transverse 

detonation waves in transonic flows. With the exception of 

the rotating detonation waves of Edwards, which was noted 

in Appendix A, all previous work in detonation waves had 

been done in quiescent gases or stabilized waves in hypersonic flow. Because of the range of occasionally conflicting experimental data on the initiation and propagation of 

detonation waves, it became obvious that some experimental 

data were needed to support the fundamental assumptions 

underlying the theoretical work. 

A rectangular detonation duct was fabricated out of 

heavy steel plates. Details of the duct and the assembled 

equipment are shown in Figures B.l-B.4. Pressures were 

measured using Kistler 602A high frequency pressure transducers mounted in instrumentation plugs such as may be seen 

in Figure B.5. Air was supplied continuously from a high 

pressure wind tunnel reservoir. Propane was injected 

intermittently from various tanks. Ignition was found to 

be the easiest and most effective when a row of spark plugs 

was fired by a series of high frequency interrupters or an 

automotive distributor. There was no direct control over 

the air/fuel ratio so that various air supply and propane 

reservoir pressures had to be tried until detonations could 

be obtained on every attempt. Occurrence of detonations 

was determined from transducer pressure outputs, and also 

audibly from the very loud sharp cracks, rather than dull 

thuds which followed a misfire or delayed ignition. 

Representative results are shown in Table B.l. The 

relatively reliable velocities which are derived from the 

time increments between the pressure recording at two 

transducers correspond to shock waves whose pressure ratios 

are much higher than those exhibited in the Table. There 

was some uncertainty regarding the pressure level in the 

duct and it is possible that the detected pressures at 

B-2 
different transducers may have been caused by different 

waves. The data does indicate that detonation waves are 

formed in very short distances from the igniters (about 

1-2"). 

In the interest of using conservative basic data in 

the theoretical work, the bulk of the pressure data, which 

indicated pressure ratios of 9.6, was taken as the basis 

and reduced to 8.5 in the calculation. 

. 

B-3 
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B-6 
I 5 I HEX HEAD BOLT I 

LEFT SIDE 

RIGHT SIDE 

2 BOTTOM PLATE kl 

MATERIAL ITEM INO. I DESCRIPTION I 

Figure 4.B. Detonation Duct Assembly 

B-7 
HEX HEAD 

I 

.75 

/ 

_- 

c 

?"'- \ 

.312-24 UNF-28 

THREAD 

-c 

/ 

0-10 UNC-2A THREA J 

Figure 5.B. Details of an Instrumentation Plug 

B-8 
Table B.l. Experimental Results 

- 7 SPARK PLUG 

t Illlllll 

3. 8a 13. 18. 

IO. 

12. 

90 14. 

I. 60 II. 16. 

Irn 17. 

CI 

AIR 2. 70 

40 PROPANE 

TRANSDUCER ARRAY 

RUN NO. 

1 

2 

3 

4 

5 

6 

7 

TRANSDUCER 

LOCATION 

7 

10 

7 

17 

7 

17 

7 

17 

5 

11 

5 

11 

5 

11 

200 

160 

200 

240 

140 

140 

200 

180 

140 

200 

180 

140 

170 

80 

PRESSURE 

RATIO 

13.6 

10.8 

13.6 

16.4 

9.6 

9.6 

13.6 

12.2 

9.6 

13.6 

12.2 

9.6 

11.6 

5.4 

TIME DIFF/ 

VELOCITY 

3880 FT/S 

2917 FT/S 

3646 FT/S 

- 

B-9 
1. Report No. 12. Government Accession No. 

~~ I 3. Recipient's Catalog No. 

NASA CR-779557 I I 

4. Title and Subtitle I 5. Report Date 

Detonation Wave Compression in Gas Turbines I December 1986 

6. Performing Organization Code 

7. Author@) 8. Performing Organization Report No. 

A. Wortman None 

10. Work Unit No 

324-01 -00 

9. Performing Organization Name and Address 

ISTAR Inc. 

406 Alta Avenue 

11. Contract or Grant No. 

NAS3-24854 

Contractor Report 

Final 

Santa Monica, California 90402 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 441 35 I 14. Sponsoring Agency Code 

1 

15. Supplementary Notes 

Project Manager, Wojciech Rostafinski, Advanced Planning and Analysis Office, 

NASA Lewis Research Center. 

16. Abstract 

A detailed theoretical study was made of the concept of augnenting the performance of low pressure 

ratio gas turbines by detonation wave compression of part of the flow. 

stant volune heat release of detonation waves to increase the efficiency of the Brayton cycle. In 

the models studied, a fraction of the compressor output was channeled into detonation ducts where it 

was processed by transient transverse detonation waves. 

cycling frequency of detonation ducts, proved that upstream propagation of pressure pulses represented 

no problems and determined the variations of detonation duct output with time. 

pression were used to reconbine the cabustor and detonation duct flows and a concept for a spiral 

collector to further smooth the pressure and tqrature pulses was presented as an optional caponent. 

the flar could be re-established before the next detonation was initiated. 

of maxim frequency of the detonation ducts, the gas turbine efficiency was found to be 45 percent 

while that of a corresponding pressure ratio 5 conventional gas turbine was only 26 percent. 

rable inprovements in specific fuel conswnption data were found for gas turbines operating as jet 

engines, turbofans, and shaft output machines. Direct use of the detonation duct output for jet propulsion proved to be unsatisfactory. 

to the conclusion that even more elaborate calculations would not diminish the uncertainties in the 

analysis of the system. Feasibility of the concept to work as an engine now requires validation in 

an engineering laboratory experiment. 

The concept exploits the conGas dynamic studies determined the maximun 

Mixing and wave canIt was found that the best performance was obtained with a single firing of the ducts so that 

At the optim conditions 

CarpaCareful analysis of the models of the fluid flow phenomena led 

17. Key Words (Suggested by Author@)) 18. Distribution Statement 

Gas turbine; Detonation waves; 

Compression; Propulsion 

Unclassified - unlimited 

STAR Category 07 

I 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 22. Price' 

Unclas s i f i ed Unc 1 ass i f i ed 75 A04 I I I 

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