AI AA-92-5022 An Aerospace Plane as a Detonation Wave RamjeVAirframe Integrated Wave rider T. Atamanchuk, J. Sislian & R. Dudebout, University of Toronto, Downsview Ontario, Canada

AlAA FOURTH INTERNATIONAL AEROSPACE PLANES CONFERENCE 1 - 4 DECEMBER 1992/0RLANDO, FL

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" AN AEROSPACE PLANE AS A DETONATION WAVE RAMJET/AIRFRAME INTEGRATED WAVERIDER

Taras M. Atamanchuk Jean ?. Sislian Rudolph Dudebout

University of Toronto Institute for Aerospace Studies 4925 Dufferin St., Downsview Ont. Canada, M3H 5T6

Abstract subscripts denotes free-stream condition Shocked-Comhustion ramjets (SHcramjets) are inves-

tigated as a means of hypersonic propulsion for lifting- propulsive waveriders. An explicit Godunov scheme, em-

mixture of hydrogen and air, is used to determine the in- viscid flowfield generated by an misymmetric body. The A revival of interest has occured lately in S H ~ ~ ~ ~ ~ ~ ~ shock and discontinuity tracking capability of this com- (hocked sombustion ramjet) propu~sion for hypersonic putational m t h o d is used to construct a series of wall flight vehicles ( ~ ~ f ~ . 1-17).~ this type ofengine, a pre- contours, at shock wave and wall intersection points, to mixed combustible mixture, such as hydrogen and air, at form a body geometry operating at design conditions. below its ignition temperature, passes through a shock The misymmetric flowfield is then used to generate a wave generated by a wedge placed in the stream) three-dimensional waverider containing this flowfield and which raises the temperature and pressure of the gas operating at two Values of flight dynamic Pressure. The mixture. If the temperature is sufficiently high, the mix-

waverider are calculated and used to determine various that the ensuing combustion process does not influence the preceeding shock wave then the combustion is said vehicle performance parameters.

to influence the preceeding shock wave, the combustion process couples with the shock wave and generates a det- n,

P onation wave. The principle advantages of the SHcram- H" total enthalpy jet over the Scramjet are short combustor length and less L net lift force inlet diffusion. Le. leading edge It is by now well established that there is a strong in- m mass flow rate teraction between the propulsion aspects and airframe M Mach number aerodynamics of a hypersonic air-breathing vehicle. To M i yield high thrust margins and high lift force, the engine r ordinate and the airframe must be highly integrated in a vehi-

cle with high volume efficiency. One attractive means R universal gas constant u z component of velocity for studying the aerodynamic, propulsive and geomet- u r component of velocity ric characteristics of such highly integrated vehicles is V total velocity to utilize the waverider concept. At their design condi- w, tions, the shape of waverider vehicles can be generated z abscissa from known, accurately determined planar or axisym- 8, anhedral angle (Fig. 3) metric Rowfields. p In the present paper, an axisymmetric SHcramjet flow- p density field is used to generate a class of three-dimensional en-

.Graduate Research Assistant, now deceased. gine/airframe integrated waveriders. Similar attempts 1 Professor. Associate Fellow AIAA. at integrating Scramjets on waveriders are presented in IGraduate Research Assistant, Student Member AIAA. references 18 and 19. The finite-rate shocked combus-

body denotes three-dimensional body cowl refers to cowl

ploying finite reaction rate combustion of astoichiometric Introduction

" Pressure, and hence forces, acting on the surfaces o f the ture ignites; if the ignition occurs farenough downstream

Nom enclature to he shock-induced. If the ignition occurs close enough

= p i / p , m a s fraction of species i force produced by a solid surface

molecular weight of species i

production rate of species i

molecular wcight of mixture (Eq. 2)

u

Copyright @ 1992 American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1

tion process of the hydrogenfair mixture is described by 33 reactions between 13 species. A first order Godunov computational scheme with discontinuity tracking capa- bility is used to determine the whole SHcramjet flowfield. For a given vehicle air capture area, and hence leading edge of the waverider, calculated coordinates of the ax- isynimetric flowfield streamlines and the pressures acting along them are used to determine forces actingon the wa- verider by replacing the streamlines with solid surfaces. Net thrust, fuel specific impulse, thrust to lift ratio and volumetric efficiency are determined for an accelerator waverider, for two constant freestream dynamic pressure trajectories, in function of the flight Mach number and the geometry of the air capture area of the vehicle. No attempt has been made to optimize the vehicle perfor- mance characteristics.

Although the investigated waverider configurations represent a restricted class of vehicles, their study prc- vides reliable baseline results for a wide range of flight conditions and geometric parameters.

The SHcramjet Model The system of equations describing the steady axisym-

metric flow of an inviscid, non-heat conducting and re- acting gas are used to generate the SHcramjet geometry and determine its flowfield variables :

aa ab' - - - + - = f aZ ar where

with u =O for planar and 1 for axisymmetric flows. The variables u , v , P , p , H" , a, and ti, are the velocity com- ponents in (.he 2 and r directions, pressure, density, tot,al enthalpy, species mass fraction and production, respec- tively. This system of equations is closed by the equation of state:

P = p'RT/p(G) ('4

p(G) = aiM; 13

i

where 'R is the universal gas constant, Mi the molecu- lar weight of species i and p ( 6 ) is the molecular weight

~~ ~

of the gas mixture. The finite-rate shocked-combustion process of the hydrogenlair mixture is described by 33 reactions between 13 species (Hz, 0 2 , H, 0, OH, H20,

20. The rate coefficients used for the forward reactions are those given in the above reference. The rate coeffi- cients for the reverse reactions were calculated from the forward rate coefficients and the appropriate equilibrium constants. All thermochemical data for the hydrogen, oxygen and nitrogen species were taken from the J A N A F (1971) tables.

A first-order Godunov computational scheme (Ref. 21) employing the above combustion model and cap& ble of discontinuity tracking was used to solve in a cou- pled manner the chemical kinetics and gasdynamic equa- tions. Details of the numerical solution procedure are given in Ref. 15. This method was chosen because it allows, if desired, the tracking of discontinuities (Le. shock waves, slipstreams, ...) in the flow with resulting sharp,discontinuous profiles in the Aow variables across them. Thus, in the shock-induced combustion process, the shock and post-shock combustion processes are well delineated. This capability is essential for the design of the SHcramjet in the present paper as it allows the de- terminat.ion of the point of intersection of shock waves with walls or other shock waves as well as the position of the slipstream separating the nozzle from the outer flow, and any shocks which are created or destroyed in the flow field. 4'

The SHcramjet model considered is shown in Fig. 1. It requires that the fuel injected somewhere in the in- let flow be homogeneously mixed with the airflow before reaching the region in th vicinity of the cowl lip. To cir- cumvent this formidable task, the present study assumes the portion of the oncoming flow captured by the inlet to be a homogeneous hydrogenlair mixture at a prescribed equivalence ratio. The inlet, which consists of a biconic, compresses the oncoming mixture through two shocks ac and bc (Fig. l), thus raising its pressure and tempera- ture. The flow is then deflected back towards the cen- terbody by the upper surface of the cowl placed at the point of intersection c of the shocks ac and bc (on-design conditions) which generates a third shock ce. The tem- perature behind this third shock cd is prescribed, effec- tively controlling the amount of compression in the inlet. This prescribed temperature (for example, 1500 O K in Fig. 1) should not exceed a value for which the tempera- ture of the fuellair mixture before the third shock would be greater than the ignition temperature. yet should be sufficiently high to ignite the mixture after shock cd. The two angles of the biconic and the cowl deflection angle are determined from the condition that these three shocks be of equal strength at their points of inception ( a , b and c in Fig. 1). The cowl h a s a flat lower surface and fornrs a

HO?, H 2 0 2 , N, N O , HNO, Nz, N 0 2 ) taken from reference W

- 2

v inlet a-b-e nozzle e-f-g X Y c

9

Body

Figure 1: Axisymmetric Shocked-Comhustion Ramjet Model; Mo = 14, Stoichiometric hydrogen/air.

5" (arbitrarily chosen minimum value) leading edge an- gle. The upper surface of the cowl consists of an initial straight portion followed hy a contoured section which corresponds to a streamline in a centered Prandtl-Meyer expansion flow until it intersects the lower surface of the cowl. The transition point is determined by the condi- tion that the head (first characteristic) of the Prandtl- Meyer expansion does not intercept the detonation wave de (typically, the head intercepts 0.01 rn downstream of the detonation wave interception point e ) . This ensures that the cowl upper surface does not weaken or quench the combustion process before it reaches the centerbody. The cowl length is varied by controlling the position of the focal point along the head of the centered Prandtl- - Meyer expansion.

The combustion products are expanded in a half-open nozzle which consists of a surface corresponding to a streamline in a centered Prandtl-Meyer expansion (con- gruent with the upper cowl curved surface) to point f (Fig, 1) where the slope is zero. From this point to the exit point g the nozzle wall is of the form cosq(x). The cowl and nozzle design is by no means optimum but has been used in the current study as a convenient design alternative.

Combustion of the fuellair mixture is either shock- induced or by a detonation wave. For flight conditions shown in Fig. 1, the third shock wave from the upper surface of the cowl (ce) raises the temperature of the hydrogen-air mixture so that combustion begins, but far enough downstream that it does not initially effect the

3

I

I 1

(a) Delayed Detonation Wave

r I

(b) Shock-Induced Combustion

Figure 2: Various Shocked-Combustion Processes

immediately behind the detonation wave ( d e ) , where the Mach number in the z direction was subsonic. At this point the computational method failed hence, all results presented here are for flight Mach numbers of 11 to 16.

For a given flight Mach number, the net thrust pr- duced by SHcramjets subject to the above-described design methodology is controlled by varying the cowl length. As this length increases, the net thrust increases to a maximum value and then decreases. In the following sections, maximum net thrust SHcramjet axisymmetric flowfields are used to generate SHcramjet/airframe inte- grated waveriders. All geometric dimensions are referred to the distance of the cowl lip to the axis of symmetry (i.e. the cowl inlet radius is fixed at unity).

L,

The SHcramjet/Airframe Integrated Waverider

The three-dimensional waverider configuration con- sists of four surfaces; the upper surface, the lower sur- face, the base area, and the cowl surface. The leading edge is defined by specifying the vehicle capture area in the z=O plane, and projecting it onto the axisymmetric shock surface of the SHcramjet. The trailing edge con- tour may take any form desired provided tha t i t begins and ends on the streamlines from the leading edge, and that the Mach number normal to the trailing edge con- tour is greater than or equal t o 1. For simplicity, this con- tour is chosen in the plane z = L, where L is the length of the waverider. Since the shock wave is attached to the leading edge at the design condition, the upper and lower surfaces of the configuration have independent flowfields and can thus be designed separately. With the leading and trailing edge contours specified, the lower surface of the waverider is generated by replacing the stream sur- faces with solid surfaces. The upper surface is aligned with the free-stream flow, starting at the leading edge

-

- - . oblique shock wave. As the combustion begins on the and ending a t the z = L plane. The area between the surface of the cowl it generates a series of compression upper and lower surfaces of the configuration at z = L is waves which coalesce and impinge on the cowl leading the vehicle base area. The cowl, located at point e (Fig. edge shock wave (ce) creating a kink at point d 2s shown 1) on the leading edge, is embedded in the axisymmet- in Fig. 1. From this point to point e the wave which be- ric flowfield and spans from one side of the body to the gan as an oblique shock wave now behaves as a detana- other. tion wave. For other flight conditions, the shock-induced ln the present study, the vehicle capture area in the combustion occurs far enough downstream of the shock y-r plane, a t = 0, is defined by a circular arc of radius cd that it is unaffected, but eventually forms a detonation R, tangent to a line drawn at an angle 8, (anhedral angle) wave (Fig. 2a, dk portio]]). I n Fig. 2b, theshock-induced from the z-axis at the origin (Fig. 3). The purpose of combustion process is sluggish and, therefore, takes a designating the capture area curve OA concave upwards sizeable distance to completion. I n all cases, because is to obtain a wing at a positive angle of att,ack (Ref. 22). of the discontinuity tracking capability of the ComPuta- A typical example of a waverider with such an air capture tional method, the shock and combustion components area generated from a Mach 14 axisymmetric SHcramjet are well delineated. flowfield is shown in Fig. 4.

Results presented here are for a stoichiometric air/fuel The pressure acting on the base area, and hence the ratio. For M, _< 10 this ratio gave rise to a small zone, thrust contribution of this surface, was assumed to be v

4

upper surface of cowl’

Figure 4: Views of a M, = 14 three-dimensional body; R = 5 rn, anhedral angle E. = 30°.

5

Figure 3: Vehicle Air Capture Area or Projection of Leading Edge Contour on z = 0 plane, 8, - anhedral angle (negative for y > 0).

zero (i.e p E 0) since the flowfield behind the body is no longer twc+dimensional. This assumption results in a conservative estimate of the propulsive z-force of the body since the pressure acting on this surface is probably of the same, or slightly smaller, order of magnitude as the free-stream pressure. In any case it is small compared to pressures acting on the lower surface.

The lower surface of the body of the waverider con- sists of the main body of revolution and wings (formed from stream surfaces). The flow over the main body is axisymmetric, thus the 2- and y- components of the force acting on it, and the surface area of the body can be expressed as :

where P b ( E ) is the radial coordinate of the main body surface. Similar expressions are used to calculate the forces on the upper and lower surfaces of the cowl by replacing#. by 8, in Fig. 3, n ( X ) by r : ( x ) and r:(z) - the cowl upper and lower surface coordinates, respectively, and L by 1 - the cowl length.

The force acting on the lower surface of the wings is de- termined by dividing this surface into longitudinal strip? by adjacent streamlines and subdividing the elernentar))d strip areas into triangles. Knowing the coordinates of the triangle vertices situated on adjacent streamlines and the pressures acting on them, the x - and y- components of the force are determined from :

where S; is the area of the i f h triangle, and n, is the number of elemental triangles.

Vehicle Performance

Waverider designs presented here are derived from maximum net thrust axisymmetric SHcramjets for sto- ichiometric hydrogen/air ratios a t on-design conditions. The vehicle capture area (Fig. 3) depends on two pa- rameters: the anhedral angle 8. and the radius R of the circular arc. Vehicle performance parameters are pre- sented for two values of the free-stream dynamic pres- sure, P d y n = lOOOpsf and 2OOOpsf, and for one inlet compression ratio characterized by T = 1500'K after t h e 4 third shock cd (Fig. 1).

The vehicle fuel specific impulse variation in function of flight Mach number Mo and air capture area parame- ters, Bo and R, is shown in Fig. 5. The specific impulse for R - 03 (flat wings) corresponds to the axisymmetric SHcramjet impulse. The curves show that the specific impulse is not very sensitive to dynamic pressure, nor to 8. and R, but decreases steadily with Mo. For given M o , 8, and P d y n , the specific impulse is larger for R - 00.

The variation of thrust per unit vehicle inlet area (Fig. 6) shows a strong dependence on dynamic pressure and flight Mach number, but otherwise is not very sensitive to 8, and R. Again, for given Mo, 8. and P d y n , maximum thrust per unit iniet a:ea is attained for R - 00. The net lift force shown in Fig. 7 is at a m z i m u m for 8, = 0' and R - 00, other conditions being equal. It strongly depends on P d y n (as expected), and steadily decreases with M o . Its dependence on R is more accentuated for values of 8. # 0. The thrust to lift rat,io is strongly dependent on the anhedral angle and changes drastically when 8. varies between -30' and +30° (Fig. 8) reaching a value of - 0.3 for Mo = 11 and 8, = 60'. The largest T h I L ratio is attained for 9, = -30° , low circular arc radius, low MO and large P d y n . This ratio is not very sensitive to dynamic pressure, hut the influence of R is- quite appreciable in the 8, = -30° case. The variation

6

m. 2riw

--P,-rompst -P*-100OF61 - - - --Pc - wm pi ..... PI.- 2000 pst

16W. - enhedrale.--P- - 1 M O . - Bnhedra18.-60- - W

m.0 ua.0 - -

0.0 0.0 11 12 13 14 15 16 11 12 13 14 15 16

M.

Figure 5: Vehicle Fuel Specific Impulse

25000

-- 5 1x00 - s

- E 4

1mw

5000 m. - v

0.0 0.0 11 12 13 14 15 16 11 12 13 14 15 16

M. M,

Figure 6: Thrust per Unit Inlet Area

ama

m-

t w w -

11 12 13 14 15 16

M.

70000

e m 0

H m O

s c-0 A

30000

2 w 0

10000

0.0 I I 11 12 13 14 15 16

M.

Figure 7: Lift Force. v

7

0.0 I 11 12 13 14 15 16

M.

0.0 I I 11 12 13 14 1s 16

M.

Figure 8: Thrust to Lift Ratio

0.w % f

o.moL 0.02s 11 12 13 14 15 16

M.

of volumetric efficiency is shown in Fig. 9. It steadily increases with Mo, is insensitive to Pdyn, shows a slight dependence on R but an appreciable dependence on 8,. For given Mo, Pdyn and R, it attains the largest value a t 0, = -30' and R = 21n.

sure and anhedral angle are parameters of primary im- portance for vehicle performance analysis; the form of the leading edge contour has a smaller influence on vehicle characteristics. Although the investigated waverider con- figurations represent a restricted class of vehicles, their study provides reliable baseline results for a wide range of flight conditions and geometric parameters. Conclusions

Given the flowfield generated by an axisymmetric, Acknowledgements maximum net bhrust shocked-combustion ramjet, it is possible to generate a corresponding three-dimensional waverider configurat,ion which contains the axisymmetric flowfield a t on-design conditions by choosing appropriate with thanks.

vehicle leading and t.railiiig edge contours. Within the class of flowfield and, lieiice vehicles, considered and the range of flight and geomtric paramet.ers investigated, it is shoum tirat. flight Mar11 number, flight dynamic pres-

This work was supported in part by a grant from Cray Research Inc. Their financial assistance is acknowledged

o.mL O.CQ5 11 12 13 14 1s 16

M.

Figure 9: Volumetric efficiency, = V 2 J 3 / S .

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"

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