A model of a hypersonic two-dimensional oblique detonation wave ramjet

July

1985

A MODEL OF A HYPERSONIC TWO-DIMENSIONAL

OBLIQUE DETONATION WAVE RAMJET

TEC

HNISCHE

OGE,

HOOl DELFT by LUCHTVAAAT- E ~ U· T .. , ARTTECHNIE(

BI LI T éEK Kluyverweg 1 - DELFT

Y. Sheng and J. P. Sislian

r

9

OKT. 1985

UTIAS Technical Note No. 257

CN ISSN 0082-5263

A MODEL OF A HYPERSONIC TWO-DIMENSIONAL OBLIQUE DETONATION WAVE RAMJET

by

Y. Sheng and J. P. Sislian

Subrnitted January 1985

,

Acknow1edgements

We wi sh to thank Professor 1. I. G1 ass and Professor Peng Chengyi of the Nanjing Aeronautica1 Institute, Peop1e's Repub1ic of China, for their encouragement and continued interest throughout this work. The financia1 support from the Natura1 Sciences and Engineering Research Counci1 of Canada is acknowledged with thanks.

Abstract

The possibility of using an oblique detonation wave ramjet as a power plant for a hypersonic vehicle is examined. The performance of a model of a two dimensional oblique detonation wave ramjet is analyzed in terms of thrust, lift and fuel consumption.

TABLE OF CONTENTS

Acknowledgements Abstract

Notation

1.

INTRODUCTION

2.

FLOW FIELD ANALYSIS

3. DETERMINATION OF THE HALF-OPEN NOZZLE CONTOUR

4.

EFFECTS OF DESIGN VARIABLES UPON THE PERFORMANCE OF THE OBLIQUE

i i i i i v 1 2 6

DETONATION WAVE RAMJET

• • • • •

8

5. CONCLUDING REMARKS

REFERENCES

TABLES

FIGURES

8 9

a P Pij

=

Pi/Pj qij Qij = qij/C pj Tj Qi = qijlC P1 T 1 r T u v y 6 p

e

Subscripts i j Notation speed of sound

specific heat at constant pressure Mach number

pressure

pressure ratio

heat release in gasdynamic discontinuity

dimensionless heat release in gasdynamic discontinuity dimensionless heat release parameter in gasdynamic discontinuity (j = i-I)

radius vector temperature

velocity normal to discontinuity surface velocity tangential to discontinuity surface ratio of specific heats

flow turning angle across a wave density

wave angle; polar angle

downstream of the wave upstream of the wave

1. INTRODUCTION

Hypersonic ramjets using a standing detonation wave were first considered by M. Roy in 1946 (Ref. 1). This concept differs marked1y from the diffusive burning supersonic combustion ramjet (scramjet). In the diffusive burning scramjet the compression process in the inlet shou1d be carried out to high pressures and tempertures required of the flow cycle, whereas in detonation wave ramjets the compression process in the in1et is moderate and carried out to re1ative1y low pressures and temperatures. The shock wave produced in the detonative process generates additiona1 large compression and temperature increases required for rapid combustion.

Initia1 concepts for the use of detonative combustion for propulsion purposes considered: (1) normal (to the flow) detonations at f1ight Mach number; (2) ob1ique detonations at f1ight Mach number; (3) normal detonations at be10w flight Mach number; and (4) oblique detonation waves at bel ow f1 i ght Mach number (Fi g. 1). These concepts have recei ved 1 itt 1 e attention in the past, but recent1y there has been renewed interest in this mode of propulsion (see, for examp1e, Refs. 2 and 3). Analyses performed in these references show that ob 1 i que detonat i ons at bel ow f1 i ght t~ach number offer great potentia1 as an air-breathing propulsion device for the hypersonic f1ight Mach number range.

Figure 1 represents a model of a two-dimensional ob1ique detonation wave (at be10w f1ight Mach number) ramjet. The inlet consists of a ramp AB on which supersonic compression of air occurs, through the attached ob1ique shock wave AO, from the f1 i ght Mach number to the detonat i on Mach number. Fue1 (hydrogen) is injected a10ng the wall AB of the in1et into the supersonic stream, and is assumed to be thorough1y mixed with the f10wing air at some distance downstream of the injection ports. A detonation wave operating at the Chapman-Jouguet point, assumed to be stabi1ized across BO, interacts with the ob1ique shock wave AO. For the range of oncoming flow Mach numbers and strengths of shock and detonati on waves consi dered in the present investigation, the resu1ting wave configuration consists of a Prandt1-Meyer rarefaction wave Rand a transmitted shock wave T, separated by a slip-1ine OC (see Ref. 4). Although the magnitudes of the heat released in the detonation wave and the specific heat ratio of the combustion products behind the detonation wave significant1y affect the interaction pattern and hence the strengths of the rarefaction and transmitted shock waves (Ref. 4), for the sake of simplicity, these quantities have been given prescribed p1ausib1e va1ues for the hydrogen-air reactions considered in the present investigation. The upper contour AK of the two-dimensiona1 ramjet is a1igned with the oncoming flow direction. The lower contour consists of three sections: the in1et wall AB, the primary half-open nozzle wa11 BLJ, which coincides with the streamline in the Prandt1-Meyer expansi on f1 ow, and the ha lf-open nozz1 e wa 11 extensi on JMK. The forms of these contours are determined in function of the f1 ight Mach number Mt and the dimension1ess heat release parameter in the detonation wave. he performance of this model ramjet is eva1uated by numerical calcu1ations. The results show that this type of detonation wave ramjets cou1d be a promising air-breathing propu1sor for hypersonic cruise f1ight conditions.

2. FLOW FIELD ANALYSIS In order to design

detonat i on wave ramjet

assumptions are made:

a simple model of a two-dimensional oblique

and ana lyze its performance, the fo 11 owi ng

(1) The fuel is injected along the inlet wall AB, assumed to be a wedge and long enough to allow the fuel to be thoroughly mixed with the airstream, so that a uniform combustible mixture is formed before the

detonation wave. The injection of fuel does not change the gasdynamic

state of the flow in region 2 (see Fig. 1).

(2) A Chapman-Jouguet detonation wave is formed in the combustible mixture

and is assumed to be stabil i zed at poi nt B. Heat i s rel eased duri ng

the detonation process. Although the amount of heat released and the

magnitude of the specific heat ratio of the combustion produets behind the detonat i on wave si gnifi cantly affect the flow pattern resulti ng from the interaction of the detonation wave with the shock wave (see Ref. 4), for the sake of simplicity, in the present investigation, these quantities are not determined from a detailed thermodynamic calculation of the detonation wave, but are rather given plausible prescribed values for the flow conditions considered.

(3) The expansion flow behind the detonation wave is assumed to be frozen.

For given fl i ght Mach number Mp the wedge angl e Öw, the amount of

heat released in the detonation wave, and the ratio of specific heats of the combustion produets behind the detonation wave, the flow variables in different regions (Fig. 1), resulting from the interaction of the shock wave S with the Chapman-Jouguet detonation wave 0, can be determined from the laws of conservation of mass, momentum and energy applied to the plane oblique shock wave or exothermic discontinuity (see Fig. 2):

Continuity: p·u· J J Momentum: p. + p·u· 2 and J J J v· J Energy: u·2 + v·2 a·2 J J ₊ J ₊ 2 y.

-

1 J = _Piui

=

_Pi + _{Pi ui}2

=

vi u·2 + v·2 qij = 1 1 2 a· 2 + 1 Yi

-

1 (1 ) (2) (3 ) (4 )

When Yi = Yj and qi·

=

0, the above equations reduce to the usual

oblique shock-wave relaiions.

The premi xed gaseous mi xture of reaetants , and the gaseous react i on produets are assumed to be perfect gases with equations of state of the form

(5) Manipulation of the above equations yields the following relationships for the determination of the flow variables behind the detonation wave in functions of the pressure ratio Pij = Pi/Pj:

Normal velocity ratio (or density ratio):

-p. u· P· · +b·+Q J = , = ' J J .

-

-

,

Pl' u· _J b_{, , J} ·P·· + 1 Temperature ratio:

Mach number ratio:

Mi

-

-M· J

-T· R· PiJ·+bj+QiJ· - , =

J

Pi ' ----'''--::--'''---::-'''''':<'' T· _{J '} R· J b·P_{, 'J} ··+1 p . .

_-

₁ 1

_-

'J 2

-2 Yj 1 y·M· _{J J} Yi p .. _'J p ..

-

1 1

-

'J (6 ) (7) p ..

_-

₁ 'J 2 yjM jn (8 )

where the norma 1 component of the Mach number of the flow before the detonation wave, Mjn' is given by

2 (P,'J' - 1){b,'_PiJ, + 1) M j n =

--~~----=-~----::--y. ( 2 p . . _ 2 - Qij) J Yi - 1 'J Yj - 1

(9 )

Normal Mach number ratio:

-p .. _{, J} + b· _J + Q .. _{, J} b·P·· _{, , J} + 1 Yj 1 Y,' ~ 'J (10 )

Tota1 pressure ratio: y. - 1 M· 2 Yi jy;-1 p~ [1 + 1 2 Mj2(M~)] _1

= p .. _ _ _ _ _ _

~J _ _ _ _ o

p.

1J _{(1 + Yj;} 1 _M/) y·jy·-l _{J J} J

Tota1 temperature ratio: o T· y. (y. 1 = J 1 T~ Yi(Yj J (11 ) (12 )

The pressure ratio at the Chapman-Jouguet condition PgjtiCJ = I/P ijCJ can be determined from Eqs. (9) and (10) with Min = 1. We e

[Yi+1 (1 + Yr1

Q ..

)]2 _ b.(b. +

Q .. )

y.-l 2 1J . 1 J 1J

J (13)

bi The flow def1ection angle is given by

y.M.2[(b.-l)P .. - (b·-l) -_{J J 1 1J J}

Q

_1J

.. ]

₁

1

(p .. - l)(b·P.· + 1)

-1J 11J (1 ·)

where the upper sign corresponds to a c10ckwise deflection.

In terms of the pressure ratio Pij and the flow deflection angle öi· across the wave separating regi on 1 af ter the wave from regi on j

betore it, we can write the fo110wing conditions:

or

log PS1 = log P43 + log P32 + log P21 (15 )

(16 )

valid across the contact discontinuity OC. The deflection angles in Eq.

(16) are given by Eq. (14) with the appropriate values of Yj, Qij, Mj and Pij on the corresponding discontinuity (in the case of a shock dlscontinulty, the relevant value of Y is assumed conserved across the shock wave and Qij = 0). In the case of a reflected rarefaction wave, the

corresponding deflection angle is given by

(17)

where

(18 )

Elimination of P43 from Eqs. (15) and (16) yields the following equations for the single unknown PSl :

(19 )

For given Mp P21' P37 , Yl' Y3 and Q32.. (given fuel/air mixture), we can determine PSI from Eq. l19). Equations (6)-(14) and Eqs. (17) and (18) wi1l then yield the values of all the flow variables of interest in the considered interaction problem. For the range of oncoming flow Mach number MI' streng~hs of the shock and detonation waves and the heat release parameter Q32' considered in the present investigation, the resulting wave configuration consists of a Prandtl-Meyer rarefaction wave Rand of a transmitted shock wave T separated by a slip line OC. Results of computations for a typical example: M~ =, 7.0, PI = 0.056 kg/cm 2, Tl = 216.5°K, Q3 = 10.0, Y3 = 1.30,

ÖW

= 4.0 are given in Table 1.

It is obvious that the lower limit of the interval of variation of Öw i s Ö_w J.. = O. Th e up per 1 i mi t o f th i s i n ter val, ö_{wm a x '} i s determined by the condition that for given MI' Y2' Y3 and Qn ttiere is a minimum Mach number M_{2 in region} 2 for which the detonatlon wave is operating at the single Chapman-Jouguet condition [see Fig. 9(d), Ref.

4J.

Letting Mn3 = M3 = 1 in Eqs. (8)-(10) _{and eliminating Mn2 and P32 from}

these equations, we get the following equation to determine M2:

1 _{(20 )}

With this Mach number M2m in' the maximum wedge angle ö_Wmax can be determined from shock-wave relations.

Based on the preceding analysi s a model of a two-dimensi onal obl ique detonation wave ramjet can be designed. The upper contour AK is aligned with the oncoming flow direction. The lower contour is formed by the streamline AB behind the oblique shock wave S and, because the transformation of chemical energy into heat takes place in a very narrow region (detonation wave), represents the inlet and the mixing and combustion chamber simultaneously. Behind point B, the gas is under high pressure and temperature. In order to produce thrust (and lift), the gas must expand along a wall and turn back to the flight direction. The streamline BLJ in the Prandtl-Meyer expansion flow, issuing from point B, represents the wall of this primary section of the half-open nozzle. At point J, where the flow is parallel to the flight direction, the gas is still under high pressure, and in order to make full use of the energy of the hot gas, the flow must be further expanded along the half-open nozzle wall MK, which is assumed to be a straight line. In order to avoid sudden changes of the flow variables, the transition wall contour between the primary nozzle wall BLJ and the extension nozzle wall MK is assumed to be a circle. It is clear that the grade of the nozzl e wa 11 MK will affect the mgnitudes of thrust and 1 ift generated by the oblique detonation wave ramjet. lts value can be determined from the required lift to th rust ratio.

3. DETERMINATION OF THE HALF-OPEN NOZZLE CONTOUR

In the polar coordinate system with its origin at the point of intersection of the shock and detonation waves (see Fig. 1), the equation of the stramline issuing from point B, in the Prandtl-Meyer expansion, can be obtained from the expression for the velocity (see, for example, Ref.

5).

Y + 1 M

de

= -

_2 _ _ _ _ _ _ _ _ dM _{(21 )}

(1 + Y - 1

M

2

)/M

2 - 1

and the equation for mass continuity

d 9 = _ _ _ d_r __ _{(22 )}

Substituting (22) into (21) and integrating we get the equation for the primary section of the half-open nozzle,

r =

h

+ [tan(tan-1

The pressure along this contour is given by

L

= (I-) P3 r 3 2Y3 Y3+l (23 ) (24 )

where r 3

=

OB, 93, M3 and P3 are determi ned from the sol ut i on of the interaction problem of the oblique shock and detonation waves.

The pressure distribution on the extension nozzle wall JMK for given transition circle radius and slope can be determined by the method of characteristics. The curve JEH (Fig. 1) - the extension of the curve BLJ - on which all gasdynamics parameters are determined from Eqs. (23) and (24), is chosen as the initial value line for these calculations. Numerical resul ts for pressure di stri but i ons and coordi nates of the half-open nozzl e are shown in Tables 2 and 3 for a typical case when M₁

=

7.0, Pl

=

0.056 kg/cm2 , Tl

=

216.5°K, Q3

=

10.0, Y3

=

1. 30, Öw

=

4.0°.

Ot

=

15° and AB = 100 mmo

The net thrust and 1 ift generated by thi s model of ob l i que detonat i on wave ramjet can be obta i ned by i ntegrati ng the pressure along the whol e lower wall contour. If the heat release is assumed to be proportional to the fuel/air ratio for a given fuel, then the fuel consumption can be evaluated from the flow field calculations.

4. EFFECTS OF DESIGN VARIABLES UPON THE PERFORMANCE OF THE OBLIQUE DETONATION WAVE RAMJET

Results of computations are shown in Figs. 3-7. Figure 3 shows the dependence of the net th rust and 1 ift upon the dimensi on1 ess heat rel ease parameter in the detonation. The net thrust decreases with the heat release and is equa1 to zero when the dimension1ess heat release parameter Q3 approaches 3.0; the corresponding lift is equa1 to 12 kg/cm, i.e., this model ramjet wi 11 produce zero net thrust and enough 1 ift when the dimensi on1 ess heat rel ease parameter Q3 is somewhat above 3. Consequent1y, even for given constant design variables, this model ramjet can serve as a powerplant for a hypersonic cruise vehic1e by adjusting the fue1 supp1y. If the fue1 mixture is too 1ean to ignite, it is necessary to change other design variables to get this condition. Figures 5(a)-(d) show that the dimensi on1 ess heat rel ease parameter Q3 correspondi ng to zero net thrust increases with f1ight Mach number MI and in1et wedge ang1e Ów- Therefore, such measures as se1ecting lower heat release fue1 species, higher f1ight Mach number and 1arger in1et wedge ang1e will be effective in getting net zero thrust with richer fue1 mixture.

Figures 5(a)-(d) a1so show that for high dimension1ess heat release parameter Q3' for examp1e, 10.0 when the f1ight Mach number MI is 1ess than 9, there is an optimum wedge ang1e Ó_w RI 4° corresponding to a maximum net

thrust. This optimum wedge ang1e exists for any va1ue of the dimension1ess heat release parameter; however for 10w va1ues of Q~, the optimum in1et wedge ang1e is too small to be adopted in practical deslgn • .

Figure 4 shows the variation of thrust and lift with the slope of the extension nozzle section. As the slope decreases, the lift is proportionately increased; however, th rust first increases then levels off.

Figures 7(a)-(d) show the rate of fue1 consumption as a function of the inlet wedge angle for different values of the heat release parameter. Figure 7(a) represents the special case for hydrogen/air mixtures with the dimensionless heat release parameter Q3 assumed to be equal to 10.0 for stoichiometric composition. The general trend of the curves is similar for any fue1 system.

5. CONCLUDING REMARKS

The shock component of the detonat i on process supp 1 i es an addit i ona 1 large compression and alleviates demands upon the diffuser. The externa1 heat addition by a detonation wave also simplifies the engine design. Numerical results for a model of a two-dimensional oblique detonation wave ramjet show that there are adequate margins for obtaining zero net th rust with sufficient 1 ift. Therefore, such a ramjet can serve as a plant for a hypersonic cruise lifting propulsive vehic1e. To put this kind of ramjet model to use, it is necessary to perform additional investigations on stabilizing the detonation wave at the right place, so that the inherent simplicity of the model wil1 not be offset by complex stabilization means.

REFERENCES

1. Roy, M. Comptes Rendues de 1 'Academie des Sciences, Feb. 1, 1946. 2. Morrison, R. B. Evaluation of the Oblique Detonation Wave Ramjet.

NASA CR NASI-14771, 1978.

3. Morrison, R. B. Oblique Detonation Wave Ramjet. NASA CR NASI-15344, 1980.

4. Sheng, V., Sislian, J. P. Interaction of Oblique Shock and Detonation Waves. UTIAS Technical Note No. 235.

Table 1

Computational Results for a Flow Model MI

=

7.0, PI

=

0.056 kg/cm2 , Tl

=

216.5°K

Q3

=

10.0, Y3

=

1.30,

Ow =

4°, AB

=

100 cm

~

Ra refact i on Rarefaci on

Shock Detonation Wave Wave

Wave Wave (initial) (final)

Deflection (degrees) 4 -14.97 0 27.52 Wave Angle (degrees) -11.02 55.7 55.7 9.2

:~

Region Flow 1 2 3 4 Parameters M 7.0 6.3 1.4 2.3 P [kg/cm2] 0.056 0.107 1. 966 0.491 T [OK] 216.5 263. 2504 1818 Transmitted Shock Wave 16.55 -66.68 5 4.2 0.491 523.8

Table 2

The Coordinates and Pressure Oistributions of the Primary Nozzle Contour for a Typical Model

MI = 7.0, PI = 0.056 kg/cm2, Tl = 216.5°K, Q3 = 10.0 Y3 = 1.30,

Ow

= 4°, AB = 100 cm X [cm] Y [cm] P [kg/cm] 7.70619 11.02824 1.94061 7.94020 11.07173 1. 91314 8.17674 11.11435 1.88597 8.41591 11.15806 1. 85909 8.65773 11.19689 1.83250 8.90233 11.23678 1. 80620 9.14975 11.27575 1. 78018 9.40005 11. 31372 1. 75446 9.65325 11.35070 1.72902 9.90947 11.38663 1. 70388 10.16881 11.42156 1.67902 10.43125 11. 45541 1. 65444 10.69687 11.48812 1. 63016 10.96579 11.51973 1. 60615 11.23803 11.55017 1.58243 11. 51367 11. 57944 1. 55899 11.79274 11.60749 1. 53583 12.07534 11. 63425 1. 51296 12.36152 11.65975 1. 49036 12.65136 11.68393 1.46803 12.94487 11.70672 1.44599 13.24216 11.72813 1.42422 13.54329 11.74811 1.40272 13.84835 11.76665 1. 38149 14.15734 11. 78362 1. 36053 14.47033 11.79908 1. 33984 14.78745 11.81294 1. 31941 15.10873 11.82516 1. 29925 15.43417 11.83568 1.27935 15.76393 11.84452 1. 25971 16.09802 11.85157 1.24033 16.43658 11.85680 1. 22121 16.77960 11. 86020 1. 20234 17.12712 11.86166 1.18372 17.21594 11.86175 1.17904

Tab 1 e 3

.

The Coordinates and Pressure Distributions of the Extension Nozzle Contour for a T~~ical Model

MI

=

7.0, PI

=

0.056 kg/cm2, Tl

=

216.5°K, Q3

=

10.0 Y3

=

1.30, 6w

=

4°, AB

=

100 cm, 6t

=

15° X [cm] Y [cm] P [kg/cm] 17.37567 11.86384 1.08026 17.53529 11.87011 0.98875 17.69470 11.88056 0.90400 17.85376 11.89517 0.82564 18.01241 11.91395 0.75317 18.17050 11.92687 0.68618 18.32794 11.96393 0.62434 18.48462 11.99509 0.56738 18.64043 12.03035 0.51487 18.79527 12.06967 0.46654 21. 07257 12.67988 0.39721 23.34988 13.29088 0.34287 25.62720 13.90029 0.29945 27.90453 14.51049 0.26423 30.18184 15.12070 0.23524 32.45917 15.73090 0.21108 34.73648 16.34109 0.19071 37.01381 16.95131 0.17335 39.29112 17.56151 0.15849 41. 56845 17.96381 0.14292

A

Air

y

M

~::::...-,. \ ' - 1

iUel"'"

I -I

S~

•

iDL--~

..

J " " '

-•

( I )

(4)

(5)

FIG. 1 THE FLOW MODEL IN A TWO-DIMENSIONAL OBLIQUE DETONATION WAVE RAMJET.

K

-.

·

---L'V~J~~~~~---

__________

~

Uniform

Flow of

S

Goseo~s

PI'

lj.Jlj.

j Pi>

7j.,o,.

S

Pre-mixed

0"(0

M

_ _

-!..

i

Reoctonts

Pi'

j ' j

Pi~

1ï~M;-(i>

{j>

FIG. 2 PLANE OBLIQUE DETONATION FLOW MODEL.

Uniform

Flow of

Goseous

Reoction

Products

F

Y

(kg/cm)~

(kg/cm)

-3.0+ 25

2.0+20

/

/

1.0

+

15

0+10

-1.0

2

4

6

FIG. 3 THRUST F AND LIFT Y AS A FUNCTION OF

F

Y

(kg/cm), (kg/cm)

y

F

10

Q3

35

2.J

--L;

2.4

30

2.3

2.2

2.1~25

2.01

•

21

19

17

15

13

FIG.4THRUST F AND LIFT Y AS A FUNCTION OF

11

F

(kg/cm)

2.2

MI

2.0

₇₀

1.8

75

1.6

8.0

1.4

8.5

1.2

9.0

1.0

I ~

3

4

5

6

FIG. 5(a) THRUST F AS A FUNCTION OF INLET

WEDGE ANGLE FOR DIFFERENT FLIGHT MACH NUMBERS.

7

Bw

Q 3 = 1 O. 0, r 3 = 1. 3 cm, P 1 = O. 056

F

(kg lcm)

2.0

1.5

1.0

0.5

MI

70

7.5

8.0

8.5

9.0

Ol

~

3

4

5

6

FIG. 5(b) THRUST F AS A FUNCTION OF INLET WEDGE ANGLE FOR DIFFERENT FLIGHT MACH NUMBERS.

F

(kg/cm)

1.0

J-

_--~

_...

0.5~

" "

"'" "

"

₁₀

MI

15

O~

" "

"-

8.0

8.5

-0.5

~

_\9.0

3

4

5

I ..

-1.0

I

₆

7

Bw

FIG. 5(c) THRUST F AS A FUNCTION OF INLET

WEDGE ANGLE FOR DIFFERENT FLIGHT

F

(kg lcm)

0.5

0

~

_{"" ""}

-0.5~

MI

" "

" "

" "

- -

" "

-

' " 10

-7.5

I

" "

~

8.0

-1.0

I

\. ' 8

.

5

9.0

-1.5

-~Ol

•

3

4

5

6

FIG. 5(d) THRUST F AS A FUNCTION OF INLET

(kg Jcmli

MI

9.0

40~

/h

8"5

8:0

7.5

35l

J$'

7.0

30

25

20.

•

3

4

5

6

78

FIG. 6(a) LIFT Y AS A FUNCTION OF INLET WEDGE

~

ANGLE FOR DIFFERENT FLIGHT MACH

NUMBERS.

(kg~cm,j

MI

9.0

/

8.5

/AH

30

25

20

15

10.

•

3

4

5

6

7

8~

FIG. 6(b) LIFT Y AS A FUNCTION OF INLET WEDGE ANGLE FOR DIFFERENT FLIGHT MACH NUMBERS.

y

(kg

lcm)

I

MI

9.0

8.5

301-

//~

8.0

7.5

7.0

251-

~/// 20~ ~

15

10,

..

FIG.

3 4 5 6 7

6(c) LIFT Y AS A FUNCTION OF INLET WEDGE

~VV

y

(kg

lcm)

30

MI

9.0

25~

h

8.5

8.0

7.5

7.0

I

/~//

20

15

10,

~ FIG.

3

4

5

6

7~

0.10

0.09

0.08,

..

3

4

5

6

7

8

w

FIG. 7(a) FUEL CONSUMPTION AS A FUNCTION OF

INLET WEDGE ANGLE FOR OIFFERENT FLIGHT MACH NUMBERS.

0

3

=

10.0, r3

=

1.3 cm, PI

=

0.056 kg j cm 2, T I = 216. 5 oK, Öt: = 15 ° ,

0.08

0~07

3

FIG. 7(b)

4

5

6

7

8

w

FUEL CONSUMPTION AS A FUNCTION OF

INLET WEDGE ANGLE FOR DIFFERENT FLIGHT MACH NUMBERS.

0

3

=

8.0, r3

=

1.3 cm, PI

=

0.056

G

G

(kg/m sec)

MI

t

_{(kg/m sec)}

9.0

MI

8.5

_~

_9.0

0.070 :

8.0

0.045

1

/

~

8.5

7.5

%~.~

0.065

r

_{/ / / / / 7 . 0}

7.0

0.060

0.040

0.055

0.035

0.050

0.045

1 I I I ~

0.030

I I I I I I ~

3

4

5 6 7 3 4 5

-

-8

w

FIG. 7(c) FUEL CONSUMPTION AS A FUNCTION OF

UTiAS Technlcal Hote Ho. 257

Unfverslty of Toronto, Instltute for krospace Studies (UTlAS)

4925 Dufferin Street. Downsview, Dntario, Canada, M3H 5T6

A MODEL OF A HYPERSOHIC TlIO-DIMENSIONAL OBLlQUE DETONATION WAVE RAHJET Sheng, Y. and Slsllan, J. P.

1. Detonatlon wave 2. Ramjet 3. Propulsion

l. UTiAS Technlcal Hote Ho. 257 Il. Sheng, Y. Sisllan, J. P.

~

The possibflity of using an oblfque detonation wave ramjet as a power plant for a hypersonic

vehicle is examined. The performance of a model of a two dimensional obI ique detonation wave ramjet Is analyzed In terms of thrust, lift and fuel consumption.

UTiAS Technlcal Note Ho. 257

University of Toronto, Institute for krospace Studies (UTlAS) 4925 Dufferin Street, Downsview, Dntario, Canada, M3H 5T6

A MODEL OF A HYPERSONIC TlIO-DIMENSIONAL OBLlQUE DETONATIOH WAVE RAHJET

Sheng, Y. and Slsllan, J. P.

1. Detonat I on wave 2. Ramjet 3. Propul sion

I. UTIAS Technlcal Hote No. 257 Il. Sheng, Y. Sfslfan, J. P.

~

The possibfl1ty of using an oblfque detonation wave ramjet as a power plant for a hypersonic

vehicle is examined. The performance of a model of a two dimensional oblfque detonation wave ramjet Is analyzed In terms of thrust, 11ft and fuel consumption.

Available co pies of this report: are limited. Return this card to UTIAS, if you require a copy. Available copies of this report are limited. Return this card to UTIAS, if you require a copy.

UTiAS Techni cal Hote Ho. 257

Unfversfty of Toronto, Instltute for krospace Studies (UTlAS) 4925 Dufferin Street, Downsview, Ontarlo, Canada, M3H 5T6

A MODEL OF A HYPERSONIC TlIO-DIMENSIONAL 08LlQUE DETONATION WAVE RAHJET Sheng, Y. and Slsllan, J. P.

1. Detonat i on wave 2. Ramjet 3. Propul sion

I. UTiAS Technlcal Hote Ho. 257 Il. Sheng, Y. Slsllan, J. P.

~

The posslbfllty of uslng an obllque detonatlon wave ramjet as a power plant for a hypersonlc vehlcle Is examlned. The performance of a model of a two dlmenslonal obllque detonatlon wave ramjet Is analyzed In terms of thrust, 11ft and fuel consumptlon •

UllAS Technical Note No. 257

Universlty of Toronto, Instftute for krospace Studies (UTlAS) 4925 Dufferin Street, Downsview, Ontarlo, Canada, H3H 5T6

A MODEL OF A HYPERSOHIC TlIO-DIMEHSIONAL OBLlQUE DETONATION WAVE RAHJET

Sheng, Y. and SlsHan, J. P.

1. Detonation wave 2. Ramjet 3. Propul sion

l. UTIAS Technlcal Hete Ho. 257 Il. Sheng, Y. Sisllan, J. P.

~

The pass i bil fty of usl ng an obllque detonati on wave ramjet as a power pI ant for a hypersonic vehlcle Is examined. The performance of a model of a two dimensional oblfque detonation wave

UTIAS Technfcal Note No. 257

University of Toronto, Institute for Aerospace Studies (UTIAS) 4925 Dufferfn Street, Downsview, Ootarfo, Canada, M3H 5T6

A MODEL OF A HYPERSONIC TWO-DIMENSIONAl OBLIQUE DETONATION WAVE RAMJET Sheng, Y. and Sisllan, J. P.

1. Detonatfon wave 2. Ramjet 3. Propulsfon

I. UTIAS Technical Note No. 257 II. Sheng, Y. Sislian, J. P.

~

The possibflity of uslng an oblique detonation wave ramjet as a power plant for a hypersonic

vehicle fs examined. The performance of a model of a two dimensional obl ique detonation wave ramjet is analyzed in terms of thrust, 11ft and fuel consumption.

UTIAS Technfcal Note No. 257

University of Toronto, Institute for Aerospace Studies (UTIAS) 4925 Dufferin Street, Downsview, Ootario, Canada, M3H 5T6

A MODEL OF A HYPERSONIC TWO-DIMENSIONAL OBLIQUE DETONATION WAVE RAMJET Sheng, Y. and Sislian, J. P.

1. Detonat i on wave 2. Ramjet 3. Propul sion

I. UTIAS Technical Note No. 257 11. Sheng, Y. Sislian, J. P.

~

The possi bil ity of us i ng an oblique detonat i on wave ramjet as a power pl ant for a hypersoni c

vehicle is examined. The performance of a model of a two dimensional oblfque detonation wave ramjet is analyzed in terms of thrust, 11ft and fuel consumption.

Available copies of this report are limited. Return this card to UTIAS, if you require a copy. Available copies of this report are limited. Return this card to UTIAS, if you require a copy.

UTIAS Techni ca 1 Note No. 257

University of Toronto, Institute for Aerospace Studies (UTIAS) 4925 Dufferfn Street, Downsvfew, Ontario, Canada, M3H 5T6

A MODEL OF A HYPERSONIC TWO-DIMENSIONAl OBLIQUE DETONATION WAVE RAMJET Sheng, Y. and S15lfan, J. P.

1. Detonation wave 2. Ramjet 3. Propul sion

I. UTIAS Techni cal Note No. 257 11. Sheng, Y. Sislian, J. P.

~

The possfbflfty of usfng an oblfque detonation wave ramjet as a power plant for a hypersonfc

vehicle fs examfned; The performance of a model of a two dimensfonal oblfque detonation wave ramjet f sana lyzed fn terms of thrust, lf ft and fue 1 consumpti on.

UllAS Technical Note No. 257

University of Toronto, Institute for Aerospace Studfes (UTIAS) 4925 Dufferin Street, Downsview, Ontario, Canada, M3H 5T6

A MODEL OF A HYPERSONIC TWO-DIMENSIONAL OBLIQUE DETONATION WAVE RAMJET Shen9, Y. and Sislfan, J. P.

1. Detonation wave 2. Ramjet 3. Propul sion

I. UTJAS Technical Note No. 257 11. Sheng, Y. Sislian, J. P.

~

The possibility of using an oblique detonation wave ramjet as a power plant for a hypersonic vehicle is examined. The performance of a model of a two dimensional oblfque detonation wave ramjet is analyzed in terms of thrust, 11ft and fuel consumption.