[american institute of aeronautics and astronautics 43rd aiaa aerospace sciences meeting and exhibit...

American Institute of Aeronautics and Astronautics

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Parametric and Numerical Investigations of Scramjet with MHD Bypass

E.G. Sheikin* Hypersonic Systems Research Institute of LENINETZ Holding Company,

St. Petersburg, Russia

Parametrical investigations show that MHD bypass allows one to increase the total pressure in the combustion chamber with MHD bypass. Numerical investigations show that MHD bypass allows one to increase significantly the scramjet thrust at off-design conditions. It is shown that MHD bypass allows one to sustain an invariable regime of a flow in the combustor with a fixed geometry at off-design conditions.

I. Introduction Nowadays “AJAX” concept is a very popular concept of hypersonic aircrafts development. It includes some

basic technologies1, one of which is based on using the MHD systems on the vehicle. According to “Ajax” concept the MHD control in a scramjet allows one to improve the scramjet performance by using the scheme of Magneto-Plasma-Chemical Engine2. Now it is more often titled as the scramjet with MHD bypass. The MHD bypass of energy in the propulsion redistributes the total flow enthalpy along the scramjet channel by means of coupled the MHD generator and the MHD accelerator. It allows one to increase effectiveness of thermodynamic cycle of the propulsion system and to increase its specific impulse and thrust. In the conventional scheme of the propulsion the MHD generator is located upstream of the combustion chamber and the MHD accelerator is located downstream of the combustion chamber. The MHD generator transforms part of the flow enthalpy into the electric power, which is transferred to the MHD accelerator for additional acceleration of combustion products. So part of the flow enthalpy bypasses the combustion chamber and it leads to decreasing the total pressure losses in the supersonic combustion chamber3. Unexpected scheme for MHD bypass in a scramjet was suggested by Dr. V.A.Bityurin. He has proposed to dispose the MHD accelerator upstream of the combustion chamber and the MHD generator downstream of the combustion chamber. Thus this scheme can be called as a reverse scheme of MHD bypass. According to Dr. Bityurin the reverse scheme of MHD bypass leads to increasing the scramjet specific impulse too. In this paper we analyze both the conventional and the reverse schemes of MHD bypass in the scramjet.

II. Model for Scramjet with MHD Bypass Figs.1a,1b shows the conventional and the reverse schemes of the scramjet with MHD bypass. In all the schemes

we assume that equilibrium conductivity of the flow upstream of the combustion chamber is negligible to produce significant MHD effect. Thus, a nonequilibrium ionization of the flow needs to be provided. We take into account that MHD generator produces the power Wg and the power Wi is spent on the flow ionization. One can see that in the conventional scheme the MHD bypass causes the total enthalpy of a flow entering the combustion chamber to decrease on the value ( )g iW W− . On the other hand, in the reverse scheme the MHD bypass causes the total

enthalpy of the flow to increase on the value gW . In order to investigate effect of the MHD bypass on the scramjet characteristics we have developed mathematical model of the scramjet with MHD bypass which combines these two schemes. Now we itemize the model approaches. Flowfield upstream of the first MHD system is calculated in two-dimensional Euler approach. At cross-section 1 the flow parameters are averaged. Downstream of the cross-section 1 the 1D approach is used. The specific heat of air cp is supposed to be constant.We use subscripts to denote parameters of a flow in corresponding cross-sections of the engine channel. For obviousness these designations are indicated in Fig. 1. Models for subsystems of the scramjet with MHD bypass are introduced below.

A. Scramjet inlet (0-1)

*Head of Department

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-1336

Copyright © 2005 by E.G. Sheikin. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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The model of the scramjet inlet coincides with the model used in Ref.3. The following characteristics are used: N is the number of shocks in an external part, θN is the total turning angle of a flow in the inlet, Md is the Mach design number Fth is relative value of the inlet throat. If an averaged temperature at the exit of the inlet (entrance of the first MHD system) takes on a value T1 the velocity v1 in this cross-section can be determined from the energy conservation law: 2 2

0 0 1 12 2p pv c T v c T+ = + . The Mach number at the cross-section 1 of the propulsion can be

calculated by the formula: ( ) ( ) ( )21 0 1 0 0 12 1 1M T T M T T γ= − − − , where γ is the specific heats ratio. Fig.2 shows

dependencies of relative values of p1/p0 and T1/T0 in the scramjet inlet upon Fth for various values of the flight Mach number M0 .

B. MHD systems (1-2 and 3-4) Set of equations for stationary MHD flow in quasi-1D approach has a form:

( )2

( )

2

=const ; ,

x x

ion

dv dpv Fdx dxd h v

v qdx

vA p R T

ρ

ρ ψ

ρ ρ

+ = ≡ ×

+= ⋅ + ⋅

=

j B

j E (1)

where ρ is the flow density, h is the enthalpy, A is the MHD channel cross-sectional area, x is the longitudinal coordinate, B is the magnetic field, E is the electric field, j is the current density, F is the Lorentz force, qion is the power density spent on a flow ionization. Substitution of qion in the right hand of Eqs.(1) signifies that the power spent on ionization in an MHD system passes into a heat due to recombination processes. By using the factor ψ we define what part of the power spent on the flow ionization will be released as additional heat in the MHD system located upstream of the combustion chamber. This factor has a value in the range: 0 1ψ≤ ≤ . In case of 1ψ < the recombination processes in the MHD channel are not complete, but in the combustion chamber they have to be completed. The flow conductivity in the MHD system located downstream of the combustor is supposed to be equilibrium. So this MHD system is described by the set of equations (1) with 0ψ = . The generalized Ohm’s law determines relations between electromagnetic components in MHD channel:

( ) ( )µ σ+ × = + ×j j B E v B (2)

where µ is the electron mobility, σ is the flow conductivity. We assume that ( )0, ,0yB=B . In considered configuration of magnetic field the current density can be determined from equation (2) by the relation:

( ) ( ) ( ) ( )( )2 21 ,0, 1x z y x z yE E B v E E B vσ β β β σ β β= + + + − − − +j , where β is the Hall parameter β µ= B . We

consider the ideally sectioned Faraday MHD generator, for which ( )0,0, zj=j , ( ),0,x zE E=E . In this case the right parts of Eqs.(1) are determined by the following expressions:

( ) ( ) ( ) ( )2 2 2(1 ) ; 1x

k B v k k B vσ σ× = × = − − ⋅ = − −j B j B j E , (3) where the load factor k is determined by the ratio ( )z x yk E v B= − ⋅ . The load factor k has a values 0<k<1 for the MHD generator and k>1 for the MHD accelerator. We assume that the load factor is constant along the MHD channel.

The power Wg produced by the MHD generator is determined by the relation:

( ) 2 2

0

1L

gW k k B v Adxσ= − ∫ (4)

where L is the length of the MHD generator. In analysis the scramjet with MHD bypass we will use specific quantities: the specific power produced by the MHD generator g gw W m= , where m vAρ= is the air mass flow in

the MHD channel and the enthalpy extraction ratio ηg=wg/w0, where ( )20 0 0 2pw c T v= + . The power Wi spent on the

flow ionization can be determined by the relation:1

0

L

i ionW q Adx= ∫ , where L1 is the length of MHD system located

upstream of the combustion chamber. Relative power spent on the flow ionization is determined by the


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ratio: i gr W W= . In using factor r, the power Wi can be written in the form: 0i gW r m wη= ⋅ ⋅ ⋅ . Self-sustained operational mode in the scramjet with MHD bypass is realized when 1r ≤ .

C. Combustion chamber (2-3) A mass flow of a fuel in the scramjet combustor is usually much less than an air mass flow, thus we will regard a

fuel supply into the combustion chamber as a heat release without injection of a mass. Set of equations for 1D model of combustion chamber in neglecting the fuel mass flow is presented here:

( )2

0

(1 )2

;

rec

dv dpvdx dxd vv h q x qdx

vA m const p R T

ρ

ρ ψ

ρ ρ

+ =

+ = + −

= = =

(5)

where q(x) is the power density releasing in the combustion chamber in result of a fuel combustion. The heat release

in the combustor due to the fuel burning can be determined by the equation ( ) ( )2

0

L

Q q x A x dx= ∫ , where L2 is the

length of the combustion chamber. When the combustion efficiency is equal to 1 we can determine Q by the relation u fuelQ H m= , where Hu is the calorific value of the fuel, fuelm - is the mass flow of the fuel. The additional

heat release due to recombination processes in the combustor is ( ) ( ) ( )2

0

1 1L

rec rec iQ q A x dx Wψ ψ= − ≡ −∫ . If recq is

assumed to be constant it can be determined by the evident expression:1

0

/L

rec ion ccq q Adx V= ∫ , where ( )2

0

L

ccV A x dx= ∫ is

a volume of the combustion chamber. Let's consider the combustion chamber working in a mode with a constant pressure. This approach is frequently

considered in analyzing the scramjet. It is evident from Eqs.(5) that modification of the flow parameters in the combustion chamber can be determined by the relations:

( )

3 2 3 2 3 2

2 23 3

2 2

0

; ;

= ; ; ;1 1

; (1 ) 1

fuel rec

u ifuel rec

p p

T T T p p v vM

M T T TT T T T

H WT T

c L mc

ρρ

ψα

= + ∆ = =

= ∆ = ∆ + ∆+ ∆ + ∆

∆ = ∆ = −+

(6)

where L0 is the stochiometric factor, α is the excess air factor (α≥1). In computations we consider H2 as a fuel. Expression for recT∆ can be rewritten in dimensionless parameters by substituting 0i gW r m wη= ⋅ ⋅ ⋅ in the

corresponding formula. It is easy to show that ( ) ( )( )20 01 1 1 2rec gT r T Mψ η γ∆ = − ⋅ ⋅ + − .

D. Nozzle (4-5) We suppose that the nozzle flow is isentropic. Thus the relationship between a relative change of a flow pressure

and a relative change of a flow temperature in the nozzle is as follows: ( ) ( )1

5 4 5 4p p T T γ γ −= (7a)

The energy conservation law in this case has the form: 2 2 25 5 4 4 0 02 2 2p p p p fuelv c T v c T v c T c T+ = + = + + ∆ (7b)

We will consider two approaches: the fully expanded nozzle, for which the exit pressure p5 is equal to the pressure p0 in the free stream; and the nozzle with a given ratio of the exit area A5 to the entrance area A0.

For the fully expanded nozzle (design nozzle) it is easy to obtain next relations from equations (7): ( )1 1

5 0 5 4 0 4

25 0 0 5

;

2 ( )p fuel

p p T T p p

v v c T T T

γ−= = ⋅

= + + ∆ − (8)


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For the nozzle with a given cross-sectional area A5 in addition to equations (7) it is necessary to use the law of conservation of mass. It is easy to show that in this case the Mach number at the nozzle exit M5 can be obtained as a solution of the equation:

( ) ( )1 1

2 1 2 12 20 005 5 4 4

5 4 4

1 11 12 2

vAM M M MA v

γ γγ γργ γ

ρ

+ +− −− − + = ⋅ ⋅ +

(9a)

Other parameters of the flow at the nozzle exit in this case can be calculated in using evident relations:

( ) ( )( )1

2 25 4 4 5

5 5 5 5 4 5 4

1 11 12 2

1 ; p

T T M M

v M c T p p T Tγ γ

γ γ

γ−

− − = ⋅ + +

= ⋅ − = ⋅

(9b)

E. Calculation of Specific Impulse and Thrust for the Scramjet with MHD Bypass When the flow parameters at the nozzle exit are known one can calculate the thrust R for the propulsion (in

neglecting the fuel mass flow) by using the relationship4: ( ) ( )5 0 5 5 0R m v v A p p= ⋅ − + ⋅ − (10a)

Specific impulse Isp for the propulsion is determined by the ratio ( )sp fuelI R m g= ⋅ . Taking into account that

0fuelm m Lα= and 0 0 0m v Aρ= , it is easy to show that

0 0 5 5 52

0 0 00

11 1spL v v A p

Ig v A pM

αγ

= − + −

(10b)

The equation (10b) allows one to calculate specific impulse for the propulsion when the exit pressure p5 and the velocity v5 are determined in using results obtained in the previous section.

III. Parametric Investigations of Scramjet with MHD Bypass In Ref.3 is shown that in a number of cases it is reasonable to investigate not the complete scheme of the scramjet

with MHD bypass, but only its part named as the combustion chamber with MHD bypass. This subsystem of the propulsion, in general consideration, consists of the MHD system (generator or accelerator), the combustion chamber and other MHD system (contrary to the first MHD system – accelerator or generator) following one after another. The key characteristic for the combustion chamber with MHD bypass is the total pressure recovery factor. The more is the total pressure recovery factor in this subsystem the greater is the thrust which can be realized in the scramjet with MHD bypass. Thus in parametric investigations it is enough to analyze only the combustion chamber with MHD bypass. Let's define the total pressure *

ip in the cross-section “i” of the propulsion shown in Figs.1 by the

well-known relations:1* 211

2i i ip p Mγγγ −− = ⋅ +

. The total pressure recovery factor in subsystem “i” of the

propulsion is determined by the relation: * *1 /i i ip pσ += . The total pressure recovery factor in the combustion chamber

with MHD bypass can be determined by the relation: ( ) ( )( )* * * * * * * *4 1 2 1 3 2 4 3 1 2 3/ / / /p p p p p p p pσ σ σ σΣ = ≡ = . Eqs.(6)

allow one to calculate the total pressure recover factor in the combustion chamber 2σ . In order to determine

1σ and 3σ it is necessary to find solution of Eqs.(1). To solve the set of Eqs.(1) with second members of the equations in the form (3), it is necessary to know

conductivity of a flow σ in function of parameters of corresponding MHD system. In case of nonequilibrium MHD system the conductivity of a flow depends upon parameters of the ionizer and the flow. In case of equilibrium MHD system the conductivity depends only on the flow parameters. The power produced by MHD generator depends on its length, the flow conductivity, the magnetic flux density, the load factor and other parameters. In parametric stage of investigations we do not take into account real characteristics of MHD subsystems, such as its length, the magnetic flux density and the ionizer characteristics. As parameters which can be varied, we consider the enthalpy extraction ratio ηg and the relative power spent on ionization r. Analogously to Ref.5, the MHD system located upstream of the combustion chamber is considered in approach with a constant cross-sectional area. It is easy to show that in this approaches the set of Eqs.(1) can be re-arranged to one first-order differential equation in


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dimensionless quantities 1v v v= and ηg with the boundary condition: ( )0 1gv η = = . This equation for nonequilibrium MHD generator has the form:

( ){ } ( )2

1

11 1 1 0gg

dva v b r v b rd k

η ψ ψη

⋅ − ⋅ − ⋅ − − ⋅ − + ⋅ − =

, (11a)

For nonequilibrium MHD accelerator we obtain the following equation:

( ){ } ( )2

1

11 1 1 0gg

dv ra v b r r v b r rd k

η ψ ψη

− ⋅ − ⋅ + ⋅ − + − ⋅ − ⋅ − + =

(11b)

Here ( ) ( )( )2 2 21 11 2 1a M Mγ γ γ = − ⋅ + − , 1 1/b γ= − and k1 is the load factor of MHD system located upstream

of the combustor. By finding numerical solution of Eqs.(11) we determine the velocity at the exit cross-section of the MHD system depending on the enthalpy extraction ratio: ( ) ( )2 1g gv v vη η= ⋅ . Temperature at the exit cross-section 2 of the MHD systems can be obtained from the energy conservation law. For nonequilibrium MHD generator T2 is determined by the relation:

( )( ) ( )2

2 22 1 1 1

1 11 1 1 12 2g gT T M v r Mγ γη ψ η

− − = ⋅ + − − − + (12a)

For nonequilibrium MHD accelerator we obtain the following expression:

( )( ) ( )2

2 22 1 1 1

1 11 1 1 12 2g gT T M v r r Mγ γη ψ η

− − = ⋅ + − + − + + (12b)

Density, pressure and Mach number at the cross-section 2 can be determined by using evident relations:

( )2 1 1 2 2 2 2 2 1 2 1 2 1 ; ; v v p R T M M v v T Tρ ρ ρ= = =

In case of MHD system located downstream of the combustor we assume that conductivity of a flow in its channel is equilibrium and it is not required to deposit additional energy for the flow ionization. Preliminary analysis has shown that variation in geometry of a channel for this MHD system practically doesn’t influence on the specific impulse of the scramjet with MHD bypass. So in investigating the propulsion we restrict our examination by considering the MHD flow with a constant pressure in the channel of the MHD system located downstream of the combustion chamber. Modification of the flow parameters in this MHD system can be determined in using results of Ref.6. The following relations correspond to the scheme from Fig.1a, in which the equilibrium MHD accelerator is used:

( )

( )

234 3 1 1

3

2 24 3 1 1

3

1 11 12

112 12

g

p g

kT T T M r

k

rv v c T M

k

γ η

γ η

− − = + + −

−− = + +

(13a)

For the scheme from Fig.1b, which uses equilibrium MHD generator we obtain the following relations: 23

4 3 1 13

2 24 3 1 1

3

1 112

1 12 12

g

p g

kT T T M

k

v v c T Mk

γ η

γ η

− − = + +

− = − +

(13b)

Pressure and Mach number at the cross-section 4 for considered flow regime are determined by the relations:

( )4 3 4 3 4 3 4 3= ; p p M M v v T T= Thus Eq.(6) and Eqs.(11-13) allow one to calculate the total pressure recovery factor in the combustion chamber

with MHD bypass. In order to emphasize the effect of MHD bypass on the total pressure in the combustor we will present not absolute values of the total pressure recovery factorσΣ but relative ones: ( ) ( )0g gσ σ η σ ηΣ Σ Σ= = . If

the value of σΣ is greater than 1 the MHD bypass leads the specific impulse of the scramjet to increase. In analyzing the scramjet with MHD bypass we consider the inlet with fixed geometry which is characterized by the total turning angle θN=15°, the relative value of the inlet throat Fth=0.1 and Md=10. Figs.3,4 demonstrate contours of σΣ in axes k1 and ηg for conventional and reverse schemes of the scramjet with MHD bypass in idealized assuming that r=0.


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One can see that there are conditions at which MHD bypass increases theσΣ value in both the schemes. According to Fig.3, in the conventional scheme the total pressure recovery factor is monotonic function of parameters k1 and ηg. In the reverse scheme, as it follows from Fig.4, theσΣ value monotonically depends upon k1 factor and non- monotonically upon ηg factor. Positive effect of MHD bypass in the conventional scheme significantly exceeds one in the reverse scheme. This fact is more obviously demonstrated in Fig.5. Figs.6,7 show dependencies ofσΣ upon the load factor k1 at various values of ψ factor. One can see that growth of ψ factor from 0 to 1 causes the total pressure in the combustion chamber with MHD bypass to increase both for conventional and the reverse schemes. Relative effect of ψ on the σΣ value is not very significant; in considered conditions it does not exceed 5%. It follows from Fig.6 that σΣ decreases while increasing the load factor k1 in the conventional scheme of scramjet with MHD bypass. According to Fig.7 corresponding dependency for the reverse scheme has the opposite tendency. Calculations show that dependencies of σΣ on the load factor k3 in the MHD system located downstream of the combustion chamber are monotonic too. The closer the load factor k3 to unity the greater magnitude has the valueσΣ both for conventional and reverse schemes of the scramjet with MHD bypass. Fig.8 demonstrates dependencies of σΣ upon the enthalpy extraction ratio for the conventional scheme. The dependencies are shown for various values of the flight Mach number. One can see that MHD control in the combustion chamber with MHD bypass causes the total pressure to increase at M0<Md. The positive effect increases while decreasing the flight Mach number. At M0>Md the MHD bypass does not improve the scramjet performance.

Thus the parametric analysis has shown that the conventional scheme of the scramjet with MHD bypass is more effective than the reverse one. The MHD bypass is reasonable to be used at flight Mach numbers less than design Mach number.

IV. Numerical Investigations of Scramjet with MHD Bypass In this section we will analyze only the conventional scheme of scramjet with MHD bypass, since it provides

more significant positive effect on the scramjet specific impulse. Model approaches which are peculiar to parametric investigations will be defined more exactly in this section. In particular the parameters ηg and r which characterize nonequilibrium MHD generator were considered in previous section as independent variables. Here we define these parameters as functions of given characteristics of the MHD generator and the ionizer, such as the length of MHD generator L1, the magnetic flux density B, the load factor k1, the flow parameters at the entrance of MHD generator and the ionizer characteristics. The e-beam is considered as the flow ionizer. Approximation formulae from Ref.7 are used in calculating the nonequilibrium conductivity σ of a flow. According to Ref.7 the main characteristic of the ionizer is the power density qion spent on the flow ionization. It depends upon the e-beam current density, the energy of electrons in the e-beam and the flow density. In calculations we assume that qion is constant in the volume of the MHD generator. Flow parameters in channel of nonequilibrium MHD generator are calculated numerically by solving the set of equations (1,3). Free stream conditions are determined through the flight Mach number M0 and the free stream dynamic pressure q∞. Some calculated characteristics of the nonequilibrium MHD generator located upstream of the combustion chamber in the scramjet with Md=10, θN=15° and Fth=0.1 are shown in Figs.9-12. One can see that both the enthalpy extraction ratio ηg and the relative power spent on the flow ionization r are monotone increasing functions of the length of the MHD generator (Figs.9,10). In considered conditions maximal values of ηg and minimal values of r are observed for the load factor k1=0.5. Minimal values of ηg and maximal values of r are observed for the load factor k1=0.25. According to Figs.11-12 the values of ηg and r are monotone increasing functions of qion. Increasing the flight Mach number M0 causes the enthalpy extraction ratio ηg to increase and the relative power spent on the flow ionization r to decrease.

In order to demonstrate possibilities of MHD bypass to control scramjet performance we consider scheme of the scramjet with a fixed geometry of the combustion chamber. The nozzle is considered in using two approaches: the fully expanded nozzle and the nozzle with fixed ratio A5/ A0. Configuration of the combustion chamber is chosen from the requirement that the regime with a constant pressure is realized in the combustor at M0=Md for given value of the excess air factor αd. It is well-known that in order to sustain the constant regime of a flow in the combustor with the fixed geometry at off-design conditions it is necessary to change the excess air factor α. In particular, at flight Mach numbers M0<Md it is necessary to provide values α>αd. The MHD generator located upstream of the combustion chamber modifies the flow parameters at the combustor entrance. So it leads the excess air factor to change its value required to sustain a constant regime of a flow in the combustor. Thus in the scramjet with MHD bypass two methods can be used to sustain a constant regime in the combustor at various values of the flight Mach


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number. They are: variation of the fuel mass flow and modification of parameters of the flow entering the combustor by using the MHD bypass.

Fig.13 demonstrates dependency of the excess air factor α in the scramjet combustor on the flight Mach number. The α values are determined from the requirements that the flow regime with a constant pressure in the combustion chamber is realized at off-design conditions too. One can see that value of α significantly increases while decreasing the flight Mach number. In principle, the MHD bypass allows one to keep the regime p=constant in the combustion chamber with the fixed geometry having a constant value of α=αd at off-design conditions. Fig.14 demonstrates what power density needs to be spent on the flow ionization in the MHD generator to do it in case of M0<Md. Fig.15 show that such type of MHD control in the scramjet allows one to increase the scramjet specific impulse and the scramjet thrust at M0<Md. Here relative specific impulse (or thrust) is specific impulse (or thrust) of the scramjet with MHD bypass in which the p=constant regime in the combustor with the fixed geometry is realized at constant parameter α=αd by changing the qion value, divided by the scramjet specific impulse (or thrust) in which the same regime in the combustor is realized by changing the α value. One can see that MHD bypass increases both the scramjet specific impulse and thrust. Figs.16,17 demonstrate how the relative specific impulse and the relative thrust of the propulsion depend upon the load factor k1 at fixed value of qion. One can see that both the specific impulse and the thrust decrease while increasing the k1 value. It follows from the figures that effect of MHD bypass on the scramjet performance depends on the nozzle configuration. According to Fig.17 the MHD bypass allows one significantly (up to 2 times) increase the scramjet thrust.

V. Conclusion Parametric analysis has shown that both the conventional and the reverse schemes of the scramjet with MHD

bypass allow one to decrease the total pressure losses in the combustion chamber with MHD bypass. The calculations made shows that the conventional scheme of the scramjet with MHD bypass is more effective than the reverse one. It is proposed to use MHD bypass to control the flow regime in the scramjet combustion chamber. It is shown that MHD bypass allows one to sustain an invariable regime of a flow in the combustor with a fixed geometry at off-design conditions at constant value of the excess air factor. Such type of MHD control allows one to increase significantly the scramjet thrust at off-design conditions.

References 1Kuranov A.L., Korabelnicov A.V., Kuchinskiy V.V., and Sheikin E.G., “Fundamental Techniques of the “Ajax” Concept.

Modern State of Research,” AIAA paper 2001-1915. 2Fraishtadt V.L., Kuranov A.L., and Sheikin E.G., “Use of MHD Systems in Hypersonic Aircraft,” Technical Physics Vol.

43, No. 11, 1998, pp. 1309-1314. 3Sheikin E.G., and Kuranov A.L., “Scramjet with MHD Bypass under “AJAX” concept,” AIAA Paper 2004-1192. 4Abramovich G.N. , “Applied Gas Dynamics,” Nauka, Moscow, 1976 (in Russian). 5 Kuranov A.L., and Sheikin E.G., “MHD Control by External and Internal Flows in Scramjet under “Ajax” Concept,” AIAA

Paper 2003-0173. 6Sheikin E.G., “Analytical Solution of the System of MHD Equations in the Quasi-one-dimensional Approximation for

Regimes in which the Flow Parameters Vary Monotonically along the Channel,” Sov. Phys. Tech. Phys. Vol. 37, No. 12, 1992, pp. 1133-1136.

7Kuranov A.L., and Sheikin E.G., “Magnetohydrodynamic Control on Hypersonic Aircraft under “Ajax” Concept.,” Journal of Spacecraft and Rockets, Vol. 40, №2, March-April 2003, pp.174-182.

Fig.1a The conventional scheme of scramjet with MHD bypass

Fig.1b The reverse scheme of scramjet with MHD bypass


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Fig.2 Relative temperature and pressure increase in the scramjet inlet as a function of relative value of the inlet throat Fth. The flight Mach numbers are shown in the figure. N=2, θN=15°, Md=10

Fig.3 Contours of factor σΣ for the conventional scheme of scramjet with MHD bypass. M0=6,α=1.5, r=0, k3=1.1.

Fig.4 Contours of factor σΣ for the reverse scheme of scramjet with MHD bypass. M0=6, α=1.5, r=0, k3=0.9.

Fig.5 Comparison of conventional and reverse schemes of scramjet with MHD bypass at M0=6, α=1.5, r=0.25, ψ=0.5. In the conventional scheme k1=0.5, k3=0.9; In the reverse scheme k1=4, k3=0.9.


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Fig.6 Factor σΣ depending on the load factor k1for the conventional scheme of the scramjet with MHD bypass. M0=6, α=1.5, r=0.25, ηg=0.05, k3=1.1.

Fig.7 Factor σΣ depending on the load factor k1for the reverse scheme of the scramjet with MHD bypass. M0=6, α=1.5, r=0.25, ηg=0.05, k3=0.9.

Fig.8 Factor σΣ depending on the enthalpy extraction ratio ηg for the conventional scheme of the scramjet with MHD bypass. α=1.5, r=0.25, ψ=1.0, k1 =0.6, k3=1.1.

Fig.9 Characteristics of nonequilibrium MHD generator in scramjet with MHD bypass at M0=6, q∞=40 kPa, qion=1W/cm3, B=4T.


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Fig.10 Characteristics of nonequilibrium MHD generator in scramjet with MHD bypass at M0=6, q∞=40kPa, qion=1W/cm3, B=4T.

Fig.11 Characteristics of nonequilibrium MHD generator in scramjet with MHD bypass at q∞=40 kPa, B=4T, k1=0.5, L1=2m

Fig.12 Characteristics of nonequilibrium MHD generator in scramjet with MHD bypass at q∞=40 kPa, B=4T, k1=0.5, L1=2m

Fig.13 The excess air factor α in the scramjet, determined from the requirements that the flow regime with a constant pressure in the combustion chamber is realized. Md=10, θN=15°, Fth=0.1, q∞=40 kPa, αd=2.


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Fig.14 The power density spent on the flow ionization in the MHD generator to sustain a constant pressure in the scramjet combustion chamber with fixed geometry with α=αd at off-design conditions. Md=10, θN=15°, Fth=0.1, q∞=40 kPa, αd=2, B=4T, k1=0.5, L1=2m.

Fig.15 Relative specific impulse and thrust in the scramjet with MHD bypass with a constant pressure in the scramjet combustion chamber at α=αd. Md=10, θN=15°, Fth=0.1, q∞=40 kPa, αd=2, B=4T, k1=0.5, k3=1.1, L1=2m.

Fig.16 Relative specific impulse of the scramjet with MHD bypass with a constant pressure in the scramjet combustion chamber. M0=6, Md=10, θN=15°, Fth=0.1, q∞=40kPa, αd=1.25, B=4T,L1=2m,k3=1.1, qion=10W/cm3.

Fig.17 Relative thrust of the scramjet with MHD bypass with a constant pressure in the scramjet combustion chamber. M0=6, Md=10, θN=15°, Fth=0.1, q∞=40kPa, αd=1.25, B=4T, L1=2m, k3=1.1, qion=10W/cm3.

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