AlAA 94-3221

Mixing and Combustion Enhancement from Unsteady Shock - Fuel Layer interactions

J.-L. Cambier, H.G. Adelman Thermosciences Institute, NASA-Ames

G.P. Menees NASA-Ames, Moffett-Field, CA

30th AIANASMEISAUASEE Joint Propulsion Conference

June 27-29, 1994 / Indianapolis, IN For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 370 L'Enfant Promenade, S.W., Washington, D.C. 20024

MIXING AND COMBUSTION ENHANCEMENT FROM UNSTEADY SHOCK - FUEL LAYER INTERACTIONS

Jean-Luc Cambier', Henry G. Adelman' Thermosciences Institutet

& Gene P. Meneest NASA Ames Research Center

Abstract

We present here the calculations of some config- urations of the Pulsed Detonation Wave Augmentor (PDWA), described by the authors in a previous pub- lication. The PDWA is a concept of a hybrid engine for Single-Stage-To-Orbit (SSTO) air-breathing hy- personic vehicle. This concept relies on the use of pulsed detonation waves, both for thrust generation and mixing/combustion augmentation. Two config- urations not previously studied are considered here. The results indicate that the mixing enhancement is very small in these cases, compared to the previ- ous ones. The simulations shed light on the nature of the interactions necessary to effectively stimulate the mixing in a supersonic combustor. /

I. Introduction

The problem of mixing enhancement in scramjet combustor flows is a critical element for the sucess- ful operation of this type of engine a t high Mach numbers. Several methods for mixing enhancement have been suggested and studied. One technique is to rely on the massive production of longitudinal vor- tices by a careful design of injectors [l-31. Since lon- gitudinal vortices are less damped than transverse vortices in a high convective Mach number flow, one could say that this technique is mostly concerned with the survival of vortices. Other techniques rely on their production, which can he accomplished, for compressible flows, with the appropriate combina- tion of pressure waves and density gradients. This can be accomplisbd primarily by using the baro- clinic effect (& Y Vp x ? P / p 2 ) as the main source of vorticity [4]. Steady oblique shock waves are a tool of choice for this approach 15-71; expansion waves can also he considered~[S], although the smaller gradients

*Senior Research Scientist, member AIAA. fMailing address: MS 23&2. NASA Ames Research Cen-

1 Research Scientist, Associate member AIAA. -i ter, Moffett-Field, CA 94035.

This paper is declared a work Of the U.S. Gov- rrnmenk and ia not subject to copyright PIOLBC- tion protection in the United States.

should make them less effective. An examination of the expression of the source term immediately shows that the production is maximized for strong presure gradients, and nearly perpendicular to the density gradients of the mixing layer.Unfortunately, this is undesirable, since strong shocks would increase the losses in stagnation pressure.

Unsteady shocks may he an alternative method of generating the mixing vortices while minimizing these losses. Oscillating shocks have been consid- ered for example by Kumar et al 191. That work showed that periodic curvature and strength fluc- tuations in an oblique shock can generate Reynold stresses. Although these results may be applied to mixingenhancement, i t is doubtful that the enhance- ment will he sufficient. In addition, the influence of fluctuations in gas composition in the free stream was not considered, although it could be more im- potant: it was shown for example in [lo] that very strong fluctuations in shock curvature, and therefore strong vorticity production, can he realized by the passage of an oblique shock through the fuel layer. Strong mixing enhancement could result from these interactions. Techniques relying on the perturbation of a free mixing layer may he effective at low Mach numbers only, and still require considerable length. Generally speaking, a t high flight Mach numbers, we need rapid and violent processes to generate the mix- ing vortices, while still trying t o minimize the losses. In an attempt to simultaneously satisfy these crite- ria, we must turn to combustion-driven, high pres- sure oscillatory flow dynamics.

In a previous paper [ll], we studied the concept of a Pulsed Detonation Wave Augmentor (PDWA), where a tube generating a sequence of pulsed detona- tion waves was imbedded into a conventional scram- jet engine. The concept aims a t providing supple- mental thrust, while enhancing the performance of the scramjet engine. It was shown that a t least for one type of engine configuration, the unsteady blast

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waves resulting from the pulsed detonation device were interacting strongly with a supersonic mixing layer in a way which promotes the mixing between fuel and air. In the sequence of Figure 9 of that ref- erence, i t was shown that the fuel layer was rolled-up by the blast wave. This process increases the overall area of the interface between the fuel and air, thereby increasing the mixing rate. Additionally, consider- able amounts of vorticity are generated, which can then decay into turbulent eddies. Again, this en- hances the mixing at the micro-scale level. The pas- sage of the shock through the mixing layer generates vorticity through two mechanisms: 1) the conven- tional baroclinic effect, when the gradients of density and pressure are misaligned. This will be most effec- tive for a shock perpendicular to the mixing inter- face. 2) the Richtmyer-Meshkov [12,13] instability, which is effective for unsteady shocks only, parallel to the interface. The second effect has not been consid- ered previously, and can be put to good use in engine design. It operates directly on the interface, and can be further accelerated by multiple passages of the shocks. Notably, one can aim at realizing a series of unsteady shocks bouncing between the combustor walls, and propagating in a direction nearly normal to the stream direction. At each passage through the fuel-oxidizer interface, mixing vortices will he gen- erated; yet, these shocks would lead to very small losses in stagnation pressure. By contrast, a steady near-normal shock would maximize the production of vorticity by the baroclinic effect, but would result in severe performance losses. The PDWA concept min- imizes these losses by using unsteady shocks, such that the normal component of the blast wave propa- gates in t h e same direction as the supersonic stream.

The shock heating of the mixing layer by the blast wave produced another benefit, by reducing the ig- nition delay. The preliminary calculations shown in [I11 demonstrated that very rapid combustion can be obtained at some locations, during the time of in- teraction hetween a single pulse of the PDWA and the scramjet flow. This also can have a profound ef- fect on engine design, since it may lead to smaller combustors. I t was shown for example in 1141 that the combustor length is an important parameter in determining the engine performance: as the combus- tor length increases, so does its weight and its cooling requirements. Excess hydrogen is required for active cooling and the specific impulse is dramatically low- ered. I t is clear therefore that by enhancing the mix- ing and combustion in the scramjet combustor, one can minimize its length and considerably improve on engine performance.

: i There are several methods to incorporate the

pulsed detonation device within the scramjet com- bustor. In [ll], we reduced the possibilities to four different mechanisms. The first design uses blast waves propagating transversely to the direction of the main flow in the combustor. As the detona- tion wave propagates down the detonation tube, it reaches small orifices on the tube wall (see Figure l), which allow communication with the scramjet combustor. The high pressure behind the detona- tion wave in the tube will create the transverse blast waves, which will then interact with the mixing lay- ers, and stimulate the mixing process. The remain- der of the detonation wave exits the detonation tube and provides additional thrust. Since the interaction with the mixing layer occurs through blast waves that propagate transverse to the main combustor flow, this configuration is called transverse coupling.

The second option does not use transverse b l a t waves, hut directly exhausts the detonation wave, axially, a t the end of the tube into the scramjet flow. There are no blast waves from the holes on the sides. The tube is shorter, and the interactions are between the expanding blast wave a t the end of the tube and the surrounding flow. The shorter tube may also al- low for faster cycling. Additionally, if the mixing layer surrounds the tube, we may rely on the baro- clinic effect. In this configuration, the density gradi- ent (mixing layer) and pressure gradient (blast wave) are misaligned, thereby creating transverse vortices. This configuration is called azia[ coupling. The dis- tinction between transverse and axial couplings is somewhat fuzzy, since transverse blast waves are gen- erated by diffraction of the detonation wave in the axial coupling case. An important difference is that the source of transverse waves is not fixed, but is he- ing convected in the direction of the main stream.

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The fuel for the scramjet engine can be injected through struts or wall injectors. Struts will provide a fuel layer within the combustor flow, a t a certain distance from the walls: the fuel layer therefore is not bound by the walls, and we will call this case an open mode. By contrast, wall injection results in a fuel la2 'I. close to the wall: this the bound mode. Sketches of the bound mode configurations are also shown in Figure 1. Two of these cases were stud- ied in [ll]. In the present paper, we study the Bound-Mode/Axial Coupling configuration. We did not consider i t worthwhile to simulate the Transverse Coupling version, a t least for the present; all config- urations will be discussed, however, in section IV.

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In addition to these four fundamantal modes of interaction, we recently considered another case, where the fuel injector and detonation tubes are com- bined into a single device. It has been suggested, for example in [15], that pulsed fnel injection may help increase the rate of mixing in the combustor; the eii- ergy source behind these forced pulsations could then very well be the detonation tube itself. This can he easily accomplished by varying the mixture in the injector, either gradually or suddenly, from pure fuel to a detonable mixture. This configuration will also be briefly studied.

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11. Bound Mode / Axial Coupl ing

In this configuration, the fuel is injected near the bottom wall of the combustor, while the detonation tube is above the fuel injector. This configuration is similar to base flow injection, with conditions ap- proximately matched to prevent deep penetration of the fuel into the air, and associated bow shock losses. The region behind the step is filled with hydrogen, and there is a shear and mixing layer created at the fuel-air interface, almost parallel to the air stream. The growth of this mixing layer in these conditions is minimal, which is certainly worsened by the fact that we are limiting our model to two-dimensional lami- nar flow. Again, we emphasize that the conditions and the characteristics of the simulations are such that mixing and combustion are minimized, in order to better identify any observed improvements with the presence of the pulsed waves. The conditions for the fuel injection are the following: U = 1700 m/s, P = 1.22 atm, and T = 500“K. The super- sonic air stream is at U = 4000 m/s, P = 0.54 atm, T = 1120°K. These rather severe (M=7) conditions are typical of the entrance to scramjet combustors a t high Mach number flight.

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The detonation tube is filled with a stoichiomet- ric mixture of H Z - 0 2 , at P = 0.5 atm, T = 500°K, which is at rest. Ignition is enforced at the left hand side of the detonation tube (closed end), by raising a few cells to high temperature and pressure, and a detonation wave is generated and propagates to the right. The solution sequence starts when the wave reaches the end of the tube.

In Figure 2 we show the density contours at var- ious times. Early in the sequence, the blast wave is seen to diffract a t the tube end. The wave then propagates into two very different fluids. At the bot- tom, there is a low velocity, low density gas which

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offers little resistance to the blast wave. On the up- per half, the wave propagates into the supersonic air flow, which has a high total pressure, of the order of 29 atm. A strong oblique shock is formed in that region, sustained by the high pressure of the deto- nation products escaping from the detonation tube. The high pressure “bubble” rapidly dissipates, and by 200 psec, even the primary oblique shock is de- caying. The flow is left in a near - quiescent state, with a train of weak oblique shocks emanatingfrom a slowly oscillating fuel-air interface. The lower branch of the blast wave propagating into the fuel layer is difficult to observe in that figure. A better way to visualize the flow in that region is to show the tem- perature contours, in Figure 3. The penetration of the hot detonation products can he clearly seen in that figure. A pocket of burned gases propagates into the fuel layer, and is slowly stretched and convected away. Several periodic, shear-driven oscillations are formed at the bottom lip of the detonation tube. The most important result is probably the axial extent of the burned gases; as can he seen in the frame at 200 psec, the burned gases form a buffer layer between the wall-hounded fuel layer and the supersonic air stream. Thus, there can he no mixing of fuel and air in that configuration; in fact, this configuration impedes the mixing and combustion, and is clearly not desirable. This is purely a two-dimensional re- sult; the situation could he considerably improved if, for example, strong longitudinal vortices can be set up, such that all three flow components, fuel, air and burned gases can be mixed together. This remains, however, to he proven with three-dimensional com- putations. The problem is not necessarily restricted to the PDWA concept. In a conventional scramjet, one can very well have designs that call for staged fuel injection: thus a similar configuration could he created, where a layer of burned gases covers a layer of fresh fuel, and prevents or a t least slows its mix- ing. It is doubtful that longitudinal vortices can ef- fectively remediate the situation, unless they are pro- duced by special features of the combustor design.

111. Combined Injector/Detonation Tube

In this configuration, the same tube is used to inject the fuel, and to generate a detonation wave. This method intends to realize a pulsed fuel injection, where the detonation wave provides the source of en- ergy for the pulsations. The mixture in the injector can be continuously varied from pure fuel, to very rich conditions while still within the limits of detona- tion. However, it also takes more energy to directly initiate a detonation which is not at stoichiometric

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conditions. We will idealize the system by assuming that, a t a certain time, the fuel being injected in the tube is replaced by a stoichiometric hydrogen-oxygen mixture a t the same conditions. The mixture is then ignited at the closed end of the tube, once it has filled the complete volume of the tube. The detoua- tion wave thus created propagates to the right aud decays into a blast wave that propagates into the fuel in front of i t , which has already left the tube..

The conditions for the fuel injection, again are: ci = 1700 m/s, P = 1.22 a tm, and T = 500°K, which corresponds to sonic conditions for hydrogen. The H z - O2 mixture is at the same conditions, The air stream in the combustor is at the same condi- tions as the previous case: U = 4000 m/s, P = 0.54 atm, T = 1120°K. These are supersonic conditions for H 1 - 02. The implementation of this mixture switch, and a more realistic choice of conditions for the detonable mixture should be examined in more detail; we chose these conditions for maximal sim- plification of the problem. Since we are interested mostly in the flow dynamics outside of the tube, the details of the flow inside the tube, prior to the d e b nation can be neglected at first.

The calculations first proceed with the fuel alone, interacting with the supersonic air-stream above un- til a quasi-steady state is achieved. I t should be noted that this solution may exhibit periodic, shear layer - driven, low frequency oscillations. This is ac- ceptable as a starting solution. The left boundary of the injector tube is then changed to reflect the iiijec- tion of the stoichiometric Hz - 0% mixture, and the tube progressively fills with that mixture. Chemical reactions are turned off in that region during this time, to prevent an artificial and premature ignition of the mixture. Once the tube is filled, sufficient en- ergy is deposited at the viciniby of the !& boundary of the tube, to directly initiate a detonation. When the detonation wave reaches the tube end, the time counter is set to zero.

The sequence of Figure 4 shows the pressure con- t,ours obtained by the simulations. The initial so- lution obtained shows a fuel jet expanding through the short nozzle a t the end of the injector, and going through a series of recompressing shocks and their re- flections. in the latter section of the control volume, a relatively high (1. 1 a tm) pressure region is estab- lished after the multiple shock reflections. Neverthe- less. the flow was observed to remain slightly super- sonic. To completely prevent the flow from becoming

subsonict , a small pressure gradient was maintained at the right boundary; this was created by enforcing b’ the pressure on the ghost cell to be 90% that of the cell immediately adjacent, inside the control volume. This constraint was progressively relaxed to 99%, as the calculation progressed. This high pressure re- gion (in red) of Figure 4 is also shown to throw an oblique shock into the supersonic air stream. This is not, however, the fuel-air interface. In fact, it is seen that the interface is only slowly diverging in that re- gion; the denser air, moving at high velocity above the fuel layer creates the effect of a flexible wall; the fuel then makes its own converging-diverging nozzle flow, constrained by the rigid wall a t the bottom, and the shear layer a t the top. The interface can be seen in the top figure (at 10 psec), for example, by noting the position at which the oblique shocks change direction, from the fuel side to the air side.

The high pressure blast wave from the detonation propagates rapidly into both the fuel and air. The amount of penetration in the supersonic air stream is relatively good. As the exhaust of the tube is slowed by the contact with the air flow, a new shock is cre- ated, attached to the lip of the nozzle, and propa- gates back into the expanding detonation products. Eventually, a new pattern of reflecting shocks is es- tablished in that region. On the right, the primary shock decomposes into two branches. As the lower section propagates into hydrogen, it runs ahead of the structure, as expected. The overall flow is rem- iniscent of the one observed previously [ll], in the case of open mode/axial coupling, i.e. when the fuel layer was above the detonation tube. The interac- tion of the two branches of the shock with the mixing layer is of interest, since we could expect that most of the mixing and combustion enhancement, if any, would occur there. In order to better visualize it, we show the contours of a normalized rate of production ofw-ate;, in~Figiiie 5 , ai i = O psec and i=80 psec. in the first case, there is some amount of water being produced, in a very thin region which is exactly cc- incident with the mixing layer. It is interesting to remark that in that figure, one can directly visualize the fuel-air interface, and therefore the shape of the effective upper nozzle “wall”, as discussed in the pre- vious paragraph. The bottom figure, for t 4 0 psec, shows another regiou of chemical activity (in yellow) at the shock leading edge. This region may lead to some mixing enhancement, and therefore merits a more focused study. For this purpose, we generated a sub-scaled grid in that region, with a higher res-

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v‘ tThis would make the problem ill-posed, since we do not

know the conditions at the ex i t .

olution, and which is allowed to slide on top of the background grid, tracking this shock - mixing layer interaction zone. This grid is outlined in Figure 6, which shows the temperature contours for the same time. In the latter, we can clearly see the extent of the fuel layer, which remains cold (blue contours), and is pushed by the detonation products. We can also see the start of a roll-up of the fuel layer, again a feature reminiscent of the previous case stndied in ref. [ll]. The chemical activity, however, is de- ceptive. By examining the flow in that region for the next 20 psec, we see no progress in combustion. This is demonstrated in Figure 7, where the normal- ized water production rate contours are shown next to the temperature contours. The water production is not associated with any significant heat release. The water is actually formed by recombination of free radicals, present in the exhaust of the detona- t,ion tube, and not by the mixing and combustion between the fuel and air. This was confirmed by looking at the (normalized) destruction rate of H z , which showed low values.

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Therefore, this configuration does not lead to sig- nificant improvements in mixing and combustion ei- ther; the calculation was not continued beyond 100 psec. The likely explanations for this result are the following: -

1. the detonation product gases act as a piston on the fuel, and push it forward. A small fraction of the gases go over the fuel layer, in the super- sonic air flow. The extent ofpenetration of these products can be seen in Figure 5 , and make up most of the red region. The blue and green nar- row lines, where water is destroyed, correspond to the high temperature shocks within the flow. As in the previous case, the detonation products locate themselves between the fuel and air, and prevent their inter-diffusion.

2. the leading shock in the upper region weakens rapidly, and is not a t a sufficient temperature to rapidly initiate combustion. This is difficult to verify absolutely, since there is not enough mixing t o observe combustion in that region Nevertheless, it is clear that the higher temper- atures are achieved on the opposite side, where the gases meet the incoming air stream, and cre- ate a stronger shock.

IV. Discussion and Conclusions

Combining and comparing our previous results [11] and the present ones, we can draw some tenta- tive conclusions. First, we must point out that we

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have chosen in the present case more severe condi- tions, notably a higher dynamic pressure air stream and a higher velocity. Nevertheless, it is clear that the two presently studied configurations are not as efTective as before. We have already mentioned that the Bound Mode / Axial Coupling is remarkably poor, principally because it creates a buffer layer of detonation products between the air stream and the fuel layer. This result is interesting in itself, because it can also he applied to conventional scramjet com- bustors with staged injection, as explained above. The Combined Injector / Detonation Tube has a het- ter potential, in the sense that it seems to generate some degree of folding of the fuel-air interface, al- though not enough to enhance the mixing for the chosen conditions. I t can be argued that the injector should have been such that the fuel is injected into the air stream at an angle, in order to obtain bet- ter penetration, and t,o increase the efficiency of the pulsations. Obviously, if the fuel is injected not as a continuous jet but as a sequence of dense “clouds”, the effective mixing area is increased, and the mix- ing can be accelerated. This would not be beneficial for the PDWA, since a major fraction of the force generated by the detonation wave would be directed in the upward or downward directions, and a lesser fraction would contribute to thrust. The normal in- jection would also create strong, steady shocks in the air stream and reduce the stagnation pressure and the overall Mach number in the combustor, prior to combustion.

Mixing enhancement will occur if some simple rules are observed:

1. One must aim at achieving the maximum rate of folding and stretching of the fuel-air interface; this was clearly demonstrated for example in thc previous case of Open Mode / Axial Coupling [ll]. The present case of Combined Injector J Detonation Tube showed some degree of folding of the fuel layer, although not enough. The dif- ference is that in the present case, most of the force of the detonation wave is used to push the fuel in the axial direction, and only a small frac- tion can be used in lifting and folding the fuel layer. It is important,therefore, that the high pressure detonation products he injected below the fuel layer.

2. One must he careful to leave a large contact area between the fuel and the air. This implies that the detonation products be injected on either side. Since the fuel is lighter than the air, it is easier to act on the fuel layer. Again, the

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detonation wave must act from below the fuel layer.

Selecting this type of configuration will generate vorticity in the transverse direction. A three- dimensional configuration will also he able to fold the fuel sheets in the other direction, using longitudinal vortices. Since these may he more effective in high Mach number flows, the three dimensional effects may he very important, and should be studied.

As mentioned earlier, we have not considered the Bound Mode Transverse Coupling configuration, although the rules mentioned above seem to indicate that this mode would be efficient in enhancing the mixing. The major flow of the Transverse Coupling, as explained in [ll], is that for the shock waves to affect the free mixing layer a t a certain distance from the boles, a high pressure source must he available. This generates strong oblique shocks, and significant losses in stagnation pressure. This problem may not he present in the Bound Mode, since the fuel layer is close to the wall, and to the high pressure sources of the shock wave. We intend to study this case in the future, to verify this proposition. However, this con- figuration is not optimal from an engineering point of view, since i t uses a longer tube, and therefore re- quires a much longer time for recharging.

We have also restricted ourselves to laminar flows. This is sufficient for preliminary investigations of the flow dynamics, and for determination of the PDWA configurations with the most potential. For more quantitative evaluations of the mixing rate, detailed turbulence models must he included. The appropri- ate tools to perform this analysis need to he devel- oped, and that task has recently been initiated.This is a difficult problem for the following reasons:

The flow is unsteady and has rapid changes of length scale. For example, although the initial state of the free shear layer can be computed with simple algebraic models, the propagation of the blast wave into the flow makes the usefulness of those models doubtful.

I t is not clear if a single-scale, two-equation model is sufficient. The complex interaction he- tween the pressure waves and the density gra- dients occurs a t various length scales, and the time of relaxation of the turbulence spectrum may not be negligible.

The flow is clearly compressible, and these ef- fects should be included in the models.

u Additionally, rapid combustion may occur and af- fect the turbulence. This effect may be neglected at first, if we are principally interested i n the mixing rate. Nevertheless, it is clear that a comprehensive estimation of the turbulent effects will require their estimation by different models, and careful compar- ison of the results.

Although the configurations studied in this pa- per fail to show any mixing enhancement, a more complete picture of the PDWA operation, and of the important characteristics has emerged. We can now focus on the most promising configuration and ana- lyze it in more detail, and gain a more quantitative evaluation of its performance.

Aknowledgment s

Support for J:L. Cambier and H.G. Adelman was provided by a contract from NASA (NAS2-14031) to ELORET. Simulations were performed on the Gray facilities of NAS. The help of V. Hirsch a t the Graph- ics Laboratory of NAS, at Ames Research Center is also gratefully aknowledged.

References McClinton C.R. el a/., “Nonreactive Mixing Study of a Scramjet Swept-Strut Fuel Injector”, NASA TN D-8069, DEc. 1967. Riggins D.W. & Vitt P.H., “Vortex Generation and Mixing in Three-Dimensional Supersonic Combustors”, AIAA paper 93-2144. WaitzI.A., Marble F.E. & Zukoski E.E., “AnIn- vestigation of a Contoured Wall Injector for Hy- pervelocity Mixing Augmentation”, AIAA pa- per 92-2265, June 1991. Picone J.M. & Boris J.P. , “Vorticity Genera- tion by Shock Propagation Through Bubbles in a Gas”, J . Fluid Mech., vol. 189, 23 (1988). Yang J . , Kubota T . & Zukoski E.E., “An Analytical and Computational Investigation of Shock-Induced Vortical Flows”, AIAA paper 92- 0316.

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[6] Menon S., “Shock-Wave-Induced Enhancement in Scramjet Combustors”, AIAA paper 89-0104.

171 Davis D.L.. “Scramjet Fuel Mixing Euhance- . . ment by Cross-Stream Pressure Eradients”, AIAA paper 93-2139.

[8] Li C., Kailasanath K. & Book D.L., “Mixing En- hancement Due to Pressure and Density Gradi- ents Generated by Expansion Waves in Super- sonic Flows”, AIAA paper 91-0374.

191 Kumar A,. Bushnell D.M.. & Hussaini M.Y.. “A . . I ~~ ~~

Mixing Augmentation Technique for Hype& locity Scramjets”, AIAA paper 87-1882, 1987.

[lo] J.-L. Cambier, H.G. Adelman & G.P. Menees, “Numerical Simulations of an Oblique Detona- tion Wave Engine”, A I A A J . Prop. Power, vol. 26, 315 (1990).

ill] J:L. Cambier, I1.G. Adelman 65 G.P. Aleneess: “Numerical Simulations of a Pulsed Detonation Wave Augmentat,ion Device”, 2g th Joint Prop. Conf., AIAA paper 93-1985.

112) Richtmyer R.D., “Taylor Instability in Shock Acceleration of Compressible Fluids”, Comm. in Pure and Applied Math. , vol. 13, 297 (1960).

(131 Meshkov Y.Y., “Instability of aShock Wave Ac- celerated Interface Between Two Gases”, NASA TT F1-13079, June 1970.

(141 G.P. Menees, H.G. Adelman, J.L. Cambier 91 J.V. Bowles, “Wave Combustors for Trans- Atmospheric Vehicles”, A I A A J . Prop. Power, vol. 8, 709 (1992).

1151 D.W. Bogdanoff, “Advanced Injection and Mixing Techniques for Scrarnjet Combnstors” , A I A A J . Prop. Power, vol. 10, 183 (1994).

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