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AIAA 2002-3296Evaluation of Drag Reduction of

Blunt Bodies at Supersonic Speedsby Counter-flow CombustionV.I. Golovitchev,

Chalmers University of Technology, 412 96 G oteborg,

Sweden

P.K. Tretjakov,

Institute for Pure and Applied Mechanics, 630090,Novosibirsk, Russia

C.N. Raffoul,

WPAFB, OH 45433-7251

32th AIAA Fluid Dynamics ConferenceJune 24-27, 2002/St.Louis, Missouri

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 201914344

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Evaluation of Drag Reduction of BluntBodies at Supersonic Speeds by Counter-flow

Combustion

V.I . G olovitch ev, Chalmers University of Technology, 412 96 Gotebor g, Sw ed en

P.K. Tretjakov,y I nst i tu te for Pur e and Appl ied M echani cs, 630090, N ovosibi rsk, Ru ssia

C.N. Ra ffoul,z WPAFB, OH 45433-7251

The objectiveof thisstudy is to assessthe feasibility of counterflow combustion realizedusing a blunt body with a smaller diameter pipe working asthe aerodynamic spikeinjectingcombustible gasesupstream the supersonic flow.

First of all, the experimental evidences of drag reduction by counterflow combustionin supersonic streams are presented. The hardware used in the experiments is descri-bed as well. Then, to perform the problem numerical study based on the solution of fullNavier-Stokes equations, the KI VA-3V reactive flow computer code has been modified to si-

mulate hydrogen counterflow combustion in theM=2.0 supersonic streamusingthe detailedchemistry approach. The results illustrate the considerable effect of the counterflow com-bustion on a flow structure before the blunt body. However, the intensity of heat releaseappeared to be not sufficient enough to generate a more effective air spike flow structuretypical to the powerful optical (laser) discharge. To increase the energy r elease rate, thekinetics of the gasified boron-based hydrocarbon fuel composition has been analyzed. Theimportant role of a conical tip of the spike for flame stabilization has been also demonstra-ted. Measurements of drag reduction by counterflow hydrogen combustion in M=2.0-2.5 airstreamsare presented and discussed together with the numerical predictions. These resultsconfirm that theflame spike could bean effective means of drag reduction of blunt bodiesin supersonic flows.

Introduction

The concept of structural aerodynamic spike isan effective means to reduce the pressure drag of

blunt bodies in supersonic stream s. The example

of t he concept rea lization is, e.g. , t he Trident D-5

missile wh ich fl ying distan ce wa s thus increased by

550 km. Other applications are also conceivable.

In the presence of the structural spike, the flow

st r u ct u r e is ch a r a ct er iz ed by t h e p r ese n ce o f t h e

oblique shock and the recirculation zone forming

a n a e r od y n a m i c bod y p rofi l e s i m il a r t o t h a t of a

con t o u re d bod y. I f t h e sp ik e h a s a n on -op t im a l

length, e.g. , too long, the truncated recirculation

z o n e f o r m s (se e F ig .1) , a n d a s f a r a s t h e o bliq u e

Associate Professory Head, Supersonic Combustion La b.z Aerospace P ropulsion Offi ce (AFRL /P RA)

sh ock is s t a bil ize d a bo ve t h e f r on t bou n d a r y of

t h is z on e , d r a g r e d uct ion e ff ect w il l be m o de r a -

t e d. D r a g r ed u ct i on i s m or e r el a t e d t o t h e p r o-

blem of construction of a body surface of minimum

d r a g . Am on g p ossible a n a ly t ica l so lu t ion s, in a

class of axysimmetric bodies, t here is t he solution

w it h a s in g u la r i t y o f t h e bo d y su r f a ce t h a t is , in

f a ct , a s t r u ct u r a l sp ik e. D u e t o a f or m a l sim ila r i t y

bet w e e n m om e n t u m , m a ss, a n d e n er g y con se r va -

t io n s, i t is p o ssible t o sh o w t h a t t h e d r a g r e d u c-

tion effect can be achieved by vary ing momentum,

mass, and energy, i .e. mass or energy spikes are

conceivable. The effect is dependent on t he t ype

and size of non-uniformity of the flow around the

body. The w a ke-like non-uniformit y, produced, e.g.,

by a structura l spike due t o non-slip velocity con-dit ions, forms st able fl ows wit h t he front r ecircula-

tion zones that reduces drag. On the contrary, the

jet-type non-uniformity (produced, if the body has

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a)

b)

Fig. 1 Supersonic flow, M1

=2.0, structures beforea blunt body with a structural spike. Two types(depending on the spike length) of flow separationhas been observed: a) the leading-edge and b) de-layed separations.

a recess or a blind hole on t he front surfa ce) leads

to non-steady oscillat ing flow regimes used in ac-

oustic genera tors/resona nt tubes. Some exam ples

a)

b)

Fig. 2 a) Simulation of the structural spike effectby projecting a bid upstream a supersonic M=2.0flow. b) Schlieren image illustrating T retjakov et

al. air-spike concept realization by concentratinga laser energy before the body in the M=2.0 flow.

of such a genera lized spike concept applications a re

presented below. In Fig.2a, t he effect of the str uctu-

ral spike is simulated by a bead projected upstream

t h e su p er son ic M= 2.0 flo w. Th e su b-son ic w a k e

behind the bid effectively forms the wake-like non-

uniformity of the v elocity profi le. The effect of such

a spike becomes well pronounced when t he bid re-

aches the dista nce similar to the optimal length of

the s pike.

The further development of the idea has lead re-

cently to the air-spike concept implemented in

t w o d if f e r e n t w a y s by My r a bo1 and Tretjakov, eta l. 2 The air spike can be formed by concentrated

energy (a n electr ic a rc plasma torch in the Myra bos

case, a repetit ive-pulse laser beam in the case of

Tretjakov et a l., see Fig.2b) projected forw a rd off a

moving body producing a tunnel of low density,

r e d u ce d p r e ssu r e h o t a ir in t h e sh a p e o f a p a r a -

boloid of revolution. Such a spike ha s important

a d va n t a g e s o ver a s t r u ct u r a l sp ik e d u e t o t h e f a ct

tha t a ir density behind the blast w ave is lower tha n

that behind the shock wave. The level of the drag

reduction in th e supersonic M= 2.0 flow ca n rea ch

50% of the ba seline dra g. The effect depends a lso

on the relat ive hot spot posit ion with respect to

the body, the hot spot size, and M num ber of the

free stream .

Co u n t er flo w com bu st ion , a s p r oven in3 a n d i l -

lu st r a t e d in F ig .3a - c, t e n d s t o w e a k e n (o r n e a r ly

suppress) the shocks near the blunt body face, thus

reducing the dra g. In this case, th e spike is used to

be an injector through which the combustible gas

is injected upst ream th e supersonic flow. The posi-

tive effect of such a fla me spike w ill be evalua ted

both theoretically and experimentally for different

(including projectile) geometries.

Experimental Study

The supersonic wind tunnel of the Institute for

Pu r e a n d Ap p lie d Me ch a n ics o f Sibe r ia n B r a n ch

of Russian Academy of Sciences, Novosibirsk has

be e n u se d in t h e fla m e sp ik e co n ce p t va l id a t io n .

T h e d e t a i le d d e scr ip t io n o f t h e h a r d w a r e ca n be

found elsewh ere, a nd a brief description of the par-

ticular experiment s is given below.

I n F ig . 4a , i t is sh ow n t h e e xp er im en t sch em e

en a b l in g on e t o s t u d y t h e fl ow s t r u ct u r e i n t h e

p r ese n ce of t h e st r u ct u r a l sp ik e, t h e h y st e r esis

p h en om e n a - t h e t r a n sit ion f r om on e fl ow se pa r a -

tion pattern to another one when the spike length

i s v a r i ed , a s w e ll a s t h e e f fe ct s of t h e m a s s s u p-

ply through the spike and combustion on the flow

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structure a nd dra g. The spike hysteresis effect w as

specially investigate due to a possible consequence

for the moving body w ith t he spike to ha ve different

drag depending on whether the body accelerates or

decelerates.

The aerodynamic spike can be moved along the

m od e l a x is w it h t h e h e lp a coor d in a t e a p plia n ce -

the mechanism for a horizontal displacement. The

t e st ed a e r od y n a m ic sp ik es of d i ff er e n t sh a p e a r e

presented in Fig.4b. The spike supplying ga ses ma y

be argon, hydrogen and a ir. The experiments w ith

hydrogen injection followed by combustion werecarried out as well. Pressure was measured on the

face surface of the model with the help of inductive

gauges in locations along the radius and recorded

by the potentiometer. The spike gas flow rate was

measured by a standard gauge based on the diaph-

a)

b)

c)

Fig.3 The M=2.0 flow structures: a) in theabsenceof counterflow injection,b) in the presenceof inertgas injection, G

H

2

=0.002, and c) in the presence ofcounterflow combustion,

G

H

2

=0.002. The hydrogen

mass flow rate amountsto 0.2%of the air mass flowrate through the body cross section.

ra gm pressur e drop. The spike displacement s peed

a ccounted for a pproxima tely 1 mm /s. The fl ow re-

gime cha nge wa s registered with the help of optical

observation of fl ow structures th rough the windows

using Toplers device a s w ell as by pressur e measu-

rements along the model face surface.

To in it ia t e cou n t e r flo w com bu st ion , a m icr o-

ramjet pilot device (see Fig.5a) has been used as

a s ource of high temperat ure products of hydrogen-

air combustion. This device operat ed reliably wit-

hin t he ra nge of M= 2.0-2.5. The rich fl am e quen-

ching regime did not ta ke place within t he limits ofma ximal possible hydrogen mas s fl ow rat e through

t h e ig n it e r (

0.2 g/s) determined by the design

peculiarit ies. Fig.5b illustra tes t he ignit ion device

op er a t io n . I g n it ion of t h e m a in h y d r o g en in jec-

t e d f r o m t h e sp ik e w a s o ccu r e d by m e a n s o f t h e

microramjet device movement towards the hydro-

gen injection position. After h ydrogen ignition, th e

igniter wa s removed.

A few technical realizations for combustion ini-

t iat ion w ere considered. They were based on the

applicat ion of sma ll pyrotechnic ignit ion cartridge

(using silane, SiH4

) a n d a sp ecia l a p p lica t io n3 of

the resona nce-igniter concept for ga s heating in aclosed end du ct similar to th e process in the reso-

nant tubes.

Hy d r o g e n w a s t h e f u e l o f ch o ice be ca u se o f i t s

h i gh e ne rg y r el ea s e r a t e a n d b eca u s e of h y d r o-

g en ca n be f or m e d in a con sid er a ble a m o u n t in

the pyrolysis of practical hydrocarbon fuels. 4 First

of all , the posit ive effect of counterflow hydrogen

combust ion on dra g reduction in supersonic M= 2.0-

2.5 fl ow s h a s bee n d ir ect ly m e a su r e d a n d t h e d a t a

a r e s u m m a r i ze d in F i g .6. F r om t h e s e d a t a , on e

ca n con clu d e t h a t d r a g of t h e blu n t bod y w it h t h e

structural spike can be reduced to 60 %of the ba-

seline drag when using injection and combustion

of a sm all a mount of hydrogen. The relative drag

reduction in Fig.6 is presented as a function of a

parameter which is a product of the relat ive mass

fl o w r a t e G

an d the relat ive heat a ddit ionH

o

= C

p

T

o

,

w h e r eH

o

is t he combustion heat release. The po-

sitive effect of drag reduction by counterflow com-

bustion is comparable with the effect achieved with

the help of optical (laser) discha rge5 f o r t h e sa m e

flow conditions.

Th e n , a se ries of e xp er im en t s w a s ca r r ie d ou t

e n a blin g o n e t o d e t e r m in e t h e m in im u m siz e s o f

the blunt body with t he fla me spike tha t ma kes itpossible to realize t he st eady-sta te hydrogen com-

bustion in supersonic air streams with parameters

M1

= 2.0-2.5,Pt o t

= 2.5-4.5 a tm ,Tt o t

= 300 K. Thus, one

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a)

b)

Fig. 4 a) Model in a test section of the wind tunnel. Flow conditions: M=2.0-2.5, Re 107 . Notations: 1-model, 2- aerodynamic spike, 3- model aft mounting sting, 4- pilot ignition device, 5- optical window, 6-reacting gas supply, 7- towards the mechanism of a vertical displacement of the pilot ignitor, 8- towardsthe mechanism of a horizontal displacement of the spike. b) Aerodynamic spikes of different shapes:1-sharp end spike, 2- pipe, 3- pipe with a conic tip.

a) b)

Fig. 5 a) Schematic of the pilot ignition device (1- insulator, 2- ignition spark electrodes) and b) visuali-zation of its operation.

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Fig. 6 Drag reduction effect of counterflow hyd-rogen combustion in supersonic M=2.0-2.5streamsfor blunt bodies of different shapes (cylinder and

hemisphere+ cylinder) with the structural spikesused as the fuel injector.

ca n se le ct t h e siz e o f t h e bo d y a n d a n d t h e sp ik e

le n g t h t o g u a r a n t e e st a ble co m bu st io n f o r g ive n

f r ee st r e a m con d it ion s. Th e r e su lt s a r e su m m a -r iz ed i n F i g .7. F i g. 7a i ll u st r a t e s t h e r e la t i on s -

hip between th e body diameter,d

, a n d t h e d im e n -

sion less len g t h of t h e st r u ct u r a l sp ik e, l = L = d

,

where L is th e spike length, in t he region of sta ble

com bu st ion . Th e bou n d a r y 3 cor r e sp on d s t o t h e

flame which is stabilized by a separation zone for-

med by a free hydrogen jet not connected w ith the

separa tion zone in front of the blunt body wit h th e

spike. The lean fl am e blow-off ta kes place when

t h e sp ik e is lon g er t h a n t h e op t im a l o n e. F ig. 7b

shows the regions of stable combustion in the G , p

p la n e : I is t h e bou n d a r y of t h e st a ble cou n t e r flo w

combustion for a free jet , II is th e sta bilizat ion re-gion for the blunt body with the spike. This region

ha s tw o boundaries marked by 1 and 2.

Th u s, on e ca n con clu d e t h a t t h e p ossibi li t y of

dra g reduction using the count erfl ow combustion in

supersonic streams realized in a form of the flame

spike is confi rmed experimenta lly. When effects of

t h e m a ss fl ow r a t e a n d t h e e n e rg y d e posit ion va r i-

at ions for the model fuel (hydrogen) were st udied,

it w as observed tha t t he blunt body sha pe does not

p la y a n e sse n t ia l r o le. Th e in t e r est in g f e a t u r e o f

the experimenta l dat a obta ined is the effect m ode-

ra tion (see Fig.6), if th e fuel am ount injected or t he

am ount of energy released w ill exceed some specifi cvalues. This effect will be discussed later on.

The a erodyna mic spike hysteresis effect is very

importa nt for pra ctical applicat ion due t o the con-

sequence tha t t he moving body with t he spike may

have different drag depending on whether the body

accelerates or decelerates. Informat ion presented

in Fig. 8 can be used to clarify th e mat ter. H ystere-

sis wa s shown to exist betw een th e tw o types of fl ow

separation caused by the presence of the spike: the

fi rst one occurs (see Fig. 8a) when t he spike ha s a n

optima l length , th e second one (see Fig. 8b) is typi-

cal of the long spike. Du e to the hy steresis (see Fig.

8c), it is possible to enter the high d rag sta te from

low dra g at the sam e spike length, although the re-

verse is not true. Da ta presented in Figs 8d-e arecha ra cterist ic of counterfl ow combustion reducing

this transit ion substantially: for

a)

b)

Fig.7 Regions(in the d , L and Po

- G planes) of hyd-rogen steady counterflow combustion in thesuper-sonic, M

1

=2.0 stream: a) the minimum diameterof the body, and the spike length; b) the hydrogenmass-flow rate and the total pressure. Boundariesof the flame blow-off: 1 - a lean flame blow-off,

( 1.0), 2- a rich flame blow-off, ( 1.0), 3 - aleanflame blow-off for a free counterflow jet.

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a) b)

c)

d) e)

Fig. 8 Spike hysteresis- M=2.0 flow structures and pressure diagram. Flow structures for a) the optimallength structural spike, b) the long structural spike, d) the short length flamespike (

G

=0.015), e) the longflame spike. I n c), it is presented the excessive total pressure on a front body surface vs spike length (inmm) record.

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Fig. 9 a) The pressure drag vs the structuralspike length for the blunt cylinder at M=2.0 flow:

1- pressure drag, 2- base drag, 3- total drag withcounterflow hydrogen combustion.

t w o fla m e sp ik e s o f d i f f e r e n t le n g t h s t h is is n o

tra nsit ion from one flow separa tion regime to anot-

her observed. This explains th e results presented

in F ig . 9 a n d i l lu st r a t e s t h e u n iq u e f ea t u r e of t h e

fl am e spike.

Theoretical Study

At first, the counterflow combustion in a superso-

nic flow wa s studied numerically w ith t he help of a

computer code described in. 2 In t his case, th e effect

of combustion ha s been simulat ed by introduction

of t h e h e a t sou r ce t e r m in t h e e n e r g y e q u a t ion .

The typical results obtained by applying the code

t o M= 2.5 a ir flo w a r o u n d a sp h er e a r e p r e sen t e d

in Fig.10. If the heat release of a suffi cient inten-

sity was localized in a small region before the blunt

body, the flow structure was considerably changed

representing a pa ttern t ypical of the fl ow structure

in the presence of the structural spike. In this case,

o n e ca n se e a d e p a r t u r e o f a n o r m a l sh o ck f r o mthe sphere and its transformation into the oblique

shock, t hus, reducing drag. The prolat e subsonic

recirculation zone was predicted (see Fig.10b) be-

f or e t h e bod y ca u se d by a cou n t e r flo w jet . Th is

phenomenon is at tr ibuted to th e effect of intensive

heat release in a supersonic flow.

T h e n , t h e a n a ly t ica l s t u d y u sin g t h e a p p r o a ch

proposed by 6 w a s ca r r i ed ou t a l l ow i n g t o con -

clu d e t h a t t h e d r a g r e d uct ion e ff ect is a ch ieved

mainly due to the formation of the wake type non-

uniformity in the incoming air stream. The init ial

non-uniformity can be formed by the fuel counter-

fl ow injection. In the presence of combustion, t his

type of non-uniformity can be reinforced or redu-

ced depending on the combustion wave propaga-

tion direction an d the combustion regime, i .e. , de-

a)

b)

Fig. 10 Calculated a) Mach number (15 isolinesranged between 0.0- 2.5) distributions and b) velo-city vector plot in front of a sphere with theenergyrelease zone placed before the body.

fl a g r a t i on or d e t on a t i on . I t i s k n ow n t h a t i n t h e

detona tion regime, combustion products move in

the direction of the propaga ting combustion w ave.

I n t h e d efl a g r a t i on r eg im e, a n o t h er s it u a t i on t a -kes place: gases escaping t he combustion zone are

moving directly opposite. U sing the counterfl ow

g a s in je ct ion of com bu st ible g a se s, i t is d i ffi cult

to expect that the detonation regime could be re-

a l iz ed . I f , in t h e d e fla g r a t io n r e gim e, cou n t e r flo w

combustion is rea lized by forming th e fl am e propa-

gat ing to t he body surfa ce, the fl am e spike effect

will r einforce the effect of hyd rogen injection. The

t e r m d e fla g r a t io n su m m a r iz es fl a m e p r op a g a t io n

regimes corresponding to a low branch of the Hu-

goniot curve. To simulat e this phenomenon, t he

n u m e r ica l s t u d y w a s p e r f o r m e d , a n d t h e m a t h e -

m a t ica l m o de l a n d m o difi ca t io n s of t h e K I VA-3V

computer code7 used for numerical simulation are

described in.4 In order to account the effect of tur-

bulence/chemistry intera ctions, th e P a SR (Pa rtia lly

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Stirred Reactor) model in a generalized form has

bee n in cor p or a t e d in t o a f r a m e w o rk of t h e RN G

k , turbulence model for reacting compressible

gases, to simulation hydrogen counterflow combus-

tion. The brief model description is given below.

Model of Turbulent Combustion

M os t m e t hod s i n r ea c t in g fl o w m od el in g i n -

volve numerica l solutions of the Reynolds-av erag ed

Navier- St okes (RANS) equa tions. More sophisti-

ca t e d , bu t m o r e p r o m isin g a p p r o a ch e s m a k e u seof the probability density function (PDF) technique

coupled with the large eddy simulation (LES) mo-

d e ls. O n ce t h e P D F is k n ow n , t h e m e a n ch em ica l

reaction rates can be treated in a closed form, ir-

respective of complexity of a chemical mechanism.

So m e m e t h o d s u se a p r e scr ibe d f o r m o f t h e PD F

p a r a m e t e r iz e d by i t s lo w e r st a t ist ic m o m e n t s, in

others, the function is defined by solving the evo-

lu t ion a l s in g le -p oin t P D F e q u a t ion . B o t h a p pr o-

aches become problema tic w hen a pplied t o complex

ch em i st r y. Wi t h t h e a s s u me d P D F m e t hod , t h e

ch oice o f t h e P D F f or m is q u it e a r bit r a r y , a n d , a s

the number of species grows, this technique leads

to an unlimited number of low-moment equations

w h ich m u st be close d a n d solved . F or t h e d ir ect

P DF approach, the problem a rises when th e unclo-

sed micro- mixing t erms a re modeled.

Application of another useful idea to turbulence

com bu st ion m od e lin g a ssu m es t h a t u n d er h ig h -

in t en sit y con d it ion s, t u r bu len ce e x er t s t h e m a in

impact on the mecha nism of turbulence combus-

t io n , bu t t h e in flu e n ce o f fi n it e - r a t e ch e m ist r y is

never negligible. The formation of a n archipelago

of u n bu r n t g a s p ock et s d u e t o t h e d ist or t e d fl a m e

front reconnections can be regarded as a main con-sequence of the model. I n th is case, the Pa SR (Pa r-

tially St irred Reactor) model ha s been generalized

to account for the effect of mixture imperfections on

chemical reaction rat es.

The model dist inguishes (see Fig.11a) between

t h e con cen t r a t ion (in m e a n m ola r d e n sit y ) a n t h e

reactor exit,c

1 , the concentrations in the reaction

zone,c

, and in t he feed,c

0 . To illustra te th e relation

betw een rat es of the processes I-II in t he rea ctor, let

us an alyze the Pa SR differentia l-a lgebraic problem

c

1

, c

o

= ,

c

c

;

c , c

1

m i x

= ,

c

c

;

(1)

w h e r e

is the t ime step,

c

is the chemical reaction

t im e, a n d

m i x

is the micro-mixing time. The equa-

tions above (represented gra phically in Fig.11b),

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

CC0 1

C

*

a)

c

0

c1

c

time

concentration

t t mix t c c = 0eqt mix

I

II

f (c)r

0

b)

Fig. 11 a) The concept of a partially stirred re-

actor, PaSR. The reaction zone is lined; b) Processrates diagram for the PaSR.

express the idea that combustion in the reactor is

a sequential process where mixing is followed by

ch e m ica l r e a ct io n s, a n d t h a t in a n y m o m e n t , t h e

r a t e s o f t h e in divid u a l s t e p s a r e e q u a l . Af t e r a l-

gebraic manipulations, one can yield the a na lytical

solutions of the linear problem (1):

c

c

1

=

c

m i x

+

c

(2)

The solution (2) shows that the turbulent combus-tion time is a sum of the mixing and reaction times,

if the process is expressed in terms of the reactor

ou t p u t p a r a m e t er s. Th u s, t h e m od e l is s im ila r t o

turbulent dissipation (or eddy break-up) approach,

however, a ccounting for fi nite-rat e chemistry. Fi-

na lly, th e solution (2) can be represented a s

c

1

, c

o

= ,

c

1

c

= ,

1

2

H m

c

1

c

;

c

1

m i x

;

(3)

w h e r e =

c

=

m i x

+

c

, a n dH m

i s a h a r m on i c

m e a n .

The model generalizat ion is equivalent t o a sub-

stit ution of the equa tions (1) for a set of the generalPa SR r a t e ba la n ce s

I :

c

1

,c

o

= f

r

c ;

(4)

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I I :

c , c

1

=

c

1

, c

m i x

+ f

r

c ;

w h e r e

f

r

c =

0 0

r

,

0

r

_!

r

c = t e r m

r

, t e r m

r

(5)

is the Arrhenius chemical source term separated

into production,t e r m

r

, an d destruction,t e r m

r

, r a -

tes,

0 0

r

a n d

0

r

are the stoichiometric coefficients

of the backward and forward stages, respectively.

Species indices are omitted for simplification.

The r-react ion progress va ria ble _! r c is calcula-ted from the ma ss-action law

_!

r

c = k

f

r

T

N

s

Y

i = 1

c

i

0

r i

, k

b

r

T

N

s

Y

i = 1

c

i

0 0

r i

;

where T is th e temperature,k

f

r

a n dk

b

r

a r e t h e r a t e

coefficients for the forwa rd a nd backwa rd sta ges of

the reaction, andN

s

is t he tota l num ber of species

in the mixture.

The first equation of the system (4) represents

the chemical step of the operator split t ing proce-

d u r e a p pl ie d t o t h e s p eci es m a s s b a l a n ce. Th e

second one is th e time dependent species ma ss con-

s er v a t i on e q ua t i on a n a l og ou s t o t h a t i n t h e P S R

model, w hen the residence t ime is replaced by the

micro-mixing time. From matching the systems (1)

a n d (4) f ol low s t h a t t h e y a r e a n a lo gou s, i f t h e se -

cond equation in the system (4)is taken in a steady-

st a t e f or m . F in a l ly, o n e ca n g et t h e g e n er a l r a t e

expression

c

1

s

, c

o

s

= f

r

c

1

s

=(6)

=

1

2

H m

c

o

s

f

o

r

c

o

s

+ t e r m

r

;

c

o

s

f

o

r

t e r m

r

0

m i x

con t a in in g n o r e a ct ion z on e p a r a m e t e r sc

, w h ich

cannot be resolved on a computational grid, but re-

p la cin g t h e ir e f f e ct w it h t h e r a t e m u lt ip l ie r =

c

=

c

+

0

m i x

;

0

m i x

= 1 = 2 H m t ;

m i x

. Th e s u-

perscript o d en ot e s t h e v a l u es a t t h e s t a r t of t h e

t im e in t e g r a t io n , w h ile t h e su bscr ipt s r e f e r s t o

the r eference species w hich are equivalent t o the

l im it in g sp e cies of t h e cla ssic Ma g n u ssen ED C-

model. The formal introduction to the concept of

reference species facilitating calculations of reac-

tion rates in the multi-stage chemical mechanism

ca n be f o u n d in .8 I f

m i x

! 0, t h e m o d e l r e d u -

ce s t o t h e q u a si-la m in a r a p p r oa ch w it hc

1

cin

t h e r ea ct ion r a t e t e r m s. Sim ila r ly t o Eq . (3), t h e

a r g u m e n t s o f t h e h a r m o n ic m e a n f u n ct io n in Eq .

(6) a r e t h e r e a ct ion r a t e a n d t h e e d dy d issip a t ion

r a t e , r e sp ect ively. I n t h e l im it o f f a st ch e m ist r y,

i.e.,t e r m

r

c

o

s

= t e r m

r

c

1

s

, t h e d issip a t ion r a t e in

Eq.(6) reproduces the classic eddy break-up rate,

c

1

s

, c

o

s

=

0

m i x

. The correct defi nition of the m icro-

m ix in g t im e is o f a m a t t e r o f im p o r t a n ce f o r a n y

ED C turbulent combustion m odel.

Definition of micro-mixing time

If the RNGk ,

model is employed, the t urbulent

viscosity related to k, the turbulent kinetic energy,

a n d , the dissipation rate of k, is given by the ge-nera l expression.

t

=

l

1 +

s

c

k

2

=

l

2

=

l

+

s

t

+ 2

p

l

s

t

;

(7)

w h e r e

s

t

is t h e st a n d a r d k -

value of the kinema -

tic viscosity.

The a bove expression represents cont ribut ions of

three mechanisms of diffusion transport , molecu-

la r, a ve r a g e t u r bu len t , a n d t h e a d d it ion a l on e r e -

sponsible for micro-mixing. The model is assumed

t o be va l id a cr oss a f u ll r a n g e o f flo w con d it ion s

from low t o high Reynolds numbers, if k a nd a red e t er m in ed f r om t h e g e n er a l iz ed t r a n sp or t e q u a -

tions,

D k

D t

= P , + r

t

P r

k

r k (8)

D

D t

= c

1 3

r U +

k

c

1

P , c

2

(9)

+ r

t

P r

r ;

w h e r eP

is the production term, given by

P =

t

S ,

2

3

r U

2

,

2

3

k r U ;

a n dS

is t h e m ea n st r a in r a t e , d efi n e d a s

S =

1

2

@ U

j

@ x

i

+

@ U

i

@ x

j

2

P rovided tha t t he fi rst t wo terms in (7) contribu-

ted to the conventional diffusion transport, the geo-

metrical mean term in the expression can be used

t o d e fi n e t h e ch a r a ct e r ist ic t im e sca le f o r m icr o -

mixing in t he tu rbulence/chemistry intera ction mo-

del, if writ t en in a form,

m i x

= 2

p

l

t

s

1 = 2

= 2 c

1 = 2

k

k

1 = 2

; (10)

w h e r ec

= 0.09,

k

=

l

=

1 = 2 is t h e K o lm og or ov

time.

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Thus, the sequence of diffusion processes is re-

presented by different, gra dient a nd n on-gradient,

a p p r oa ch es. Eq . (10) ca n be r ew r it t e n u sin g t h e

eddy break-up time definition

m i x

k

= c

= R e

t

1 = 2

k =

(11)

This leads to a correct dependence of

m i x

o n t h e

Ret

=

t

s

=

l

, b u t i t s a c t u a l v a l u e h a s t o b e op t im i -

zed. For a typical Ret

10 3 case, the value is a bout

0.01k =

used in the modeling. If smallest eddies are

enlar ged to be resolved by a comput er grid, i.e.,

l

s g s

=

Z

1

1 =

d k k

, 1

E k =

Z

1

1 =

d k E k

s g s

=

Z

1

1 =

d k k

, 1

k

, 1

E k

1 = 2

1 = 3

4 = 3

;

a n o t h e r d e fi n it ion of t h e m icr o-m ixin g t im e h a s

been used.

m i x

2 = 3

, 1 = 3 (12)

w h e r e

is th e minimal scale resolved on the gr id,

E k = C

2 = 3

k

, 5 = 3

is t he K olmogorov energy spect-rum. The formula (12) renders the model a quality

of the SGS (sub-grid scale) approach.

Results and Discussions

At fi r s t , t h e fl o w s t r u ct u r es cor r es pon d in g t o

counterflow hydrogen injection and combustion are

presented in Figs 12-13. Da ta presented in Fig.12

co r r e sp o n d t o t h e ca se o f t h e in e r t je t , in F ig .13

- t o t h e ca se of cou n t e r flo w com bu st ion . Th e se

dat a were obta ined with the help of schlieren pho-

t o gr a p h s o f t h e flu id st r u ct u r e. G e om e t r ica l ch a -

racterist ics of both, inert a nd rea cting counterfl owjets are well generalized using the dimensionless

p a r a m e t e r : a r a t io o f t h e t o t a l p r e ssu r e in t h e jet ,

P

o j

to the pressure behind the normal sh ock at the

p a r a m e t e r s o f t h e f r e e st r e a m ,P

o

0 . The effect of

combustion is w ell pronounced: for t his case, the

dista nce to the norma l shock 3 and the conta ct sur-

face radius 2 a re longer tha n for the inert case due

t o t h e lo w e r d e n sit y in t h e r e cir cu la t io n z o n e o f

t h e r e a ct ive flo w. Th is a lso m ea n s t h a t t h e sh o ck

w a ve in cl in a t io n f o r t h e ca se o f t h e r e a ct ive flo w

becomes less tha t testifi es to dra g reduction caused

by counterflow combustion.

To account for th e hy drogen/oxygen dist ribu tion

and combustion after hydrogen counterflow injec-

tion, both mixing a nd ignition/combust ion proces-

ses has to be be simulated. To simulate t he effect

of combustion, the reaction mechanism of hydro-

g en o x id a t io n in a ir h a s bee n con st r u ct e d . Most

of t he rea ctions have been studied experimenta lly,

a n d t h e m e ch a n ism h a s p r eviou sly be en u sed f or

hydrogen propulsion modeling.9 U s i n g t h e r ea c -

tion mechanism developed, the calculat ed ignit ion

delay t imes for st oichiometric hydr ogen a ir mixtu-

res at different init ial pressures and temperatures

were calculated a nd compared with the sh ock-tube

experiments. G ood agr eement ha s been achieved

a s i l lu st r a t e d in F ig. 14. Th e m a in g oa l in u sin g

the detailed mechanism of hydrogen combustion isto correctly reproduce ra th er ill-ignition condit ions

above the so-called extended second explosion limit

for hydrogen/a ir mixtu res. This effect is w ell pro-

n ou n ce d in t h e d a t a p r ese n t ed in F ig . 14. D u e t o

this effect , the ignit ion delay for higher pressure

which is shorter than the ignit ion delay for lower

p r e ssu r e a t t e m p e r a t u r e s h ig h e r t h a n t h e e x p lo -

a)

b)

Fig. 12 a) Gasdynamic M=2.0 flow structure forthe inert cointerflow jet: 1- bow shock, 2- con-tact surface, 3- shock of the jet, 4- region of flowexpansion, 5- re-attachment shock, 6- flow separa-tion zone, 8- injector. b) Dependence of the main

geometrical parameters of the inert jet on the gasinjection pressure.

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a)

b)

Fig. 13 a) Gasdynamic M=2.0 flow structure for

the reacting cointerflow jet: 1- bow shock, 2- con-tact surface, 3- shock of the jet, 6- flow separationzone, 7- flame, 8- injector. b) Dependence of themain geometrical parameters of the inert jet onthe gas injection pressure.

0.70 0.80 0.90 1.00 1.10 1.20

1000/T, K

101

102

103

Ignitiondelaytime,sec

Experiment, 1 atm

Experiment, 2 atmCalculation, 1 atm

Calculation, 2 atm

SiH4=5%, 1 atm

SiH4=5%, 2 atm

=1

Fig. 14 Validation of H2

/air ignition chemistry by

calculation of ignition delays. Simulation of igni-tion promotion and moderation of its dependenceon pressure for the stoichiometric mixture by ad-ding a small amount of silane.

sion limit temperature, becomes longer, if t he ini-

t ia l t e m p er a t u r e s a r e low e r t h a n t h e l im it . Th is

is w hy, one can see the intersection of tw o experi-

ment a l (for different pressures) curves presented in

Fig. 14. This phenomenon is likely responsible for

deterioration of drag reduction efficiency observed

in th e experiments (see Fig. 6), if lar ger am ounts of

hydrogen were injected. As a result , this can lead

to the increa sed pressure level in t he ignition zone,

thu s, w orsening a uto-ignition conditions. To mode-

rat e th e ignit ion delay dependence on pressure, it

ha s been assum ed in10 to make use of silane a s theignit ion promoter. The mea sure facilita tes t he ig-

nit ion process w hich, in t his ca se, becomes n early

hypergolic.

The result s of 2-D count erfl ow combust ion simu-

lations using the KIVA3 computer code modified to

a ccount for d eta iled chemistry hydr ogen/a ir com-

bu st ion a r e pr e se n t ed in F ig. 15. I n t h e a x isy m -

metric simulations, a part of a cylinder body of a

size 2x2 cm w ith a str uctura l spike of a lengt h 2 cm

was placed in a computation region of a size 8x20

cm . Th e st r u ct u r a l sp ik e w a s a p ip e of t h e in n e r

ra dius 0.25 cm, a nd the outer radiu s 0.5 cm. Hy dro-

gen ha s been injected th rough the pipe w ith a speedof 50 m/s. The fr ee air st rea m v elocity corresponded

t o M= 2.0 a n d Po

= 1.0 a t m . Hy d r o g en ig n it ion h a s

be e n in i t ia t e d by t w o h o t sp o t s : t h e fi r st o n e w a s

placed inside the pipe (for a short t ime), and the

second one - 0.5 cm below the spike end in the re-

circulation zone. Transient calculations continued

t i l l t h e st e a d y -st a t e w a s a ch ieve d (bu t n ot lon g e r

than 10 ms). All this time, hydrogen injection con-

tinued, but t he externa l hot spot wa s supported by

t h e e n e r g y sou r ce in t h e cou r se of 1 m s. Wit h in

the ignit ion w indow, the specifi c internal energy in

the specified mesh cells was increased on each time

step. If the temperature in the ignit ion cell was in

excess of 2000 K before the end of th e ignition w in-

dow, then, in t his point , the energy deposit ion w as

t e r m in a t e d .

The block-structured mesh KIVA-3 code used, in

the m odeling, might be considered of only a mo-

derate accuracy for aerodynamic calculations, but

such an a ccuracy seems to be sufficient to simulate

the effects of counterflow combustion on the super-

son ic flo w st r u ct u r e. F r om t h e r e su lt s p r ese n t ed

in Fig. 15, one can conclude tha t the t ypical shock

str ucture (see Fig. 15a ) formed in front of the blunt

bod y a t t h e in i t ia l m o m en t w a s sm o ot h e d la t e r o nwh ile combust ion process w a s developing (see plots

Fig. 15b-c). The predictions are in agreement with

the experimenta l observation. F rom temperature

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a) t= 0.4 ms b) t= 0.5 ms c) t= 0.7 ms d) t= 1.6 ms e) t= 2.5 ms

Fig. 15 Time development of couterflow H2

/air combustion for the pipe-spike. Plots a)-e) correspond topressure distributions at different moments.

a) t= 0.2 ms b) t= 0.6 ms c) t= 0.7 ms d) t= 0.8 ms e) t= 1.0 ms

f) t= 1.2 ms g) t= 1.4 ms h) t= 1.7 ms i) t= 2.0 ms j) t= 2.5 ms

k) t= 0.6 ms l) t= 0.7 ms m) t= 0.8 ms n) t= 1.0 ms o) t= 2.5 ms

Fig. 16 Time development of couterflow H2

/air combustion for the conical tip spike. Plots a)-i) corre-

spond to temperature distributions at different moments; the plot j)- to the distribution of water vapor.Plots k)-o) correspond to temperature distributions for the case of injection velocity is equal to 250 m/s.

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d ist r ibu t io n s, o n e ca n se e t h a t t h e fla m e w a s st a -

bilized in the frontal recirculation zone formed in

the presence of t he str uctural spike. The distribu-

tions of intermediate (hydrogen peroxide) species

a n d m a in (w a t e r va p o r ) co m bu st io n p r o d u ct s a s

w e ll a s a h ig h co n ce n t r a t io n o f H- r a d ica ls sh o w

t h a t t h e h e a t r e le a se t a k e s p la ce o n ly in t h is r e -

gion, effectively forming t he fl am e spike structure

of the counterflow combustion. The temperature in

the r eaction zone w as predicted to be only

1300

K . T h e p r e d ict e d fla m e sh a p e a n d p o sit io n t e st i-

fi e s t o t h e f a ct t h a t com bu st ion t a k e s p la ce in t h ele a n m ix t u r e , a n d t h e d e fla g r a t io n r e g im e is r e a -

l iz e d w it h t h e fla m e f r o n t m o vin g t o w a r d s t o t h e

bod y su r f a ce. I n t h is ca se , t h e r e a ct ion p r o du ct s

ar e moving in the sa me direction as t he injected ga-

ses, thu s, increas ing t he positive effect of injection.

As a h ig h t e m p er a t u r e level in t h e r e a ct ion z on e

was not achieved at modeling conditions, special

measures should be ta ken to enha nce an d sta bilize

combustion. To stabilize the fl am e in the experi-

m e n t s, a con ica l t ip o n t h e sp ik e en d w a s u sed .

Thus, t he spike geometry wa s m odifi ed in t he mo-

deling to account for the presence of the t ip, and

the computa tion results a re presented in Fig. 16.In t his modeling, the spike length wa s increased by

1.5 cm , f r om w h ich 0.5 cm w a s a sh e a r o f t h e co-

nical t ip. The pipe inner diameter was reduced to

0.2 cm, that allowed to specify a higher injection

velocity (200 m/s) w ithout substa ntia l increasing

of t h e h y d r og e n m a ss fl ow r a t e . Th e sim u la t ion

scena rio was also changed: hydrogen injection a nd

ignition (see Fig.16a ) took place in th e quiescent a t-

mosphere. Then, at the moment t = 0.5 ms t he air

wa s set in m otion corresponding t o M= 2.0 a nd the

total pressure Po

= 1. 0 a t m . Th e a i r s t r ea m p a r a -

m e t e r s w e r e ca lcu la t e d u sin g t h e ise n t r o p ic flo w

r el a t i on s f o r a p er f ect g a s . Th e a i r s t r ea m f or -

med the region of elevated pressure and tempera-

ture which interacted with the developed hydrogen

fl am e as can be seen in Fig.16b-c. As t he result of

t h e in t e r a ct ion , t h e fl a m e f r o n t w a s t r a n sf or m in t o

a t y p ica l f or m o f a bu t t er fly , t h e sh a p e o f w h ich

wa s observed in the experiments. Then, incoming

a ir flo w ble w t h e fla m e a lm o st a w a y , a n d co m bu s-

tion continued only in t he pipe. La ter on (see Fig.

16d-e), t he h ydrogen combustion in th e supersonic

st r e a m w a s r e - e st a blish e d , a n d t h e r e a ct io n z o n e

structure rebuilt the configuration typical of the de-

veloped fla me spike (see Fig. 16f-i). These result si llu st r a t e a n im p or t a n t r ole of t h e t ip in t h e fla m e

stabilization. The higher temperature, 1420 K, was

predicted in the r eaction zone.

Th e sim u la t io n r e sult s , w h e n t h e h y d r og en in -

jection velocity wa s increased up t o 250 m/s ar e

presented in Fig.16 k)-o). As a result , t he com-

bustion zone beca me m ore extended (see Fig.16 k),

bu t a ch a r a ct er o f t h e fl a m e f r on t in t e ra ct ion w it h

t h e a ir s t r e a m r e m a in u n ch a n g e d , e.g. , a t fi r st , t h e

fl a m e b u t t er fl y s t r u ct u r e w a s f or m ed , t h en , t h e

fla m e w a s a lm o st e x t in g u ish e d , a n d r e g e n e r a t e d

once a ga in (see Fig.15 l)-o). The t emperat ure ma x-

im u m in t h e r e a ct io n z o n e r e a ch e d 1840 K , a n d

combustion wa s w ell stabilized in t he recirculation

zone behind th e t ip. One can expect tha n t his ten-dency could be extra polat ed to the higher h ydrogen

injection velocit ies. However, it requires further

reduction of the pipe inner size arising the mesh

resolution problem in moderate accuracy simula-

tions.

106

105

104

103

102

Time, s

108

107

106

105

104

103

102

101

100

MoleFractio

n

Autoignition o H2Boronair Mixture

(Po=1.0 bar, T

o=800 K, H

2:B

2=3:1)

B2O

3

B

B2O3(L)B(L)HH

2

OH

a)

106

105

104

103

102

Time, s

0.0

1000.0

2000.0

3000.0

4000.0

Temperature,

K

Autoignition of H2Boronair Mixture

(Po=1.0 bar, T

o=800 K, H

2:B

2=3:1)

po=1.0 bar

po=5.0 bar

po=5.0 bar, pure H2

b)

Fig. 17 a) Selected concentrations of combustionproducts vs time histories, b) illustration of re-duced ignition delay and increased heat release

when compared with parameters of similar sto-ichiometric hydrogen/air mixture.

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As a conceivable measur e of temperature incre-

ase in the combustion zone could be considered an

addition of boron to hydrogen injected through the

spike. The boron effect on the hydrogen combustion

has been studied using the t ime-dependent reac-

tion code Senkin 11 of the Chemkin library, and the

results of computa tions are presented in Fig. 17.

The comprehen sive mecha nis m of h ydr ogen/boron

a)

b)

Fig. 18 The pressure drag as a function of a rela-tive mass flow rate, G, for fuel compositions withdifferent heat release in combustion; a) for the

spike geometry: 1- H u =120 MJ /kg, 2- H u =16.7MJ /kg,3- H

u

=13.4 MJ /kg, b) for model blunt bodies: 1-H

u

=16.7 MJ /kg, 2- Hu

=13.6 MJ /kg, 3- Hu

=9.0 MJ /kg.Low heat values correspond to solid propellantsused in the nose gas generator.

com bu st ion con sist s of 64 e le m en t a r y r e a ct ion s

between 22 species including B, B2

, B O , B O2

, B2

O,

B2

O2

, B2

O3

, B2

O3

(L), B(L), L denotes the liquid

pha se. The a uto- ignition of H2

/boron mi xt ur e (3:1,

in m o le n u m be r s) w a s st u d ie d w it h in t h e in i t ia l

temperature ra nge of 700- 900 K, an d t he pressure

ran ge of 1- 5 bar. In the Fig.17 a), one can see that

the concentration of B2

O3

in th e gas phase exceeds

t h a t of B2

O3

(L) at the equilibrium st at e. However,

there is a moment in th e development of the aut o-

ignit ion process development, when these phases

are predicted in comparable quantities. Such a pre-

sence of the liquid phase in combustion products

can reinforce the effect of the flame spike.

The results present ed in Fig. 17 b) illustra te th a t

combustion of H2

/boron composition h a s essentia l

adva nta ges, if compared w ith combustion of H2

/a ir

mixtures: the ignit ion delays a re by a order of mag-

nitude shorter, a nd the t emperat ure of combustion

products is by 1000 K higher. I t is in order to re-

ma rk tha t t he use of silane does not affect the heat

release in the reactions. In contrast to H2

/a ir mix -

t u r e s, t h e in cr ea se in t h e in i t ia l p r essu r e u p t o 5bar does not affect much the auto-ignition process.

Hig h e n e r g y r e le a se m a t e r ia ls , a s ca n be se e n

in F ig s 18a -b, a r e ben e fi cia l of t h e a p p lica t ion t o

increase the positive effect of the counterflow com-

bu st io n o n d r a g r e d u ct io n o f t h e blu n t bo d ie s in

supersonic streams. Polynitrogen and nitrogen rich

materials have high energy densit ies and are, the-

refore, promising high energetic mat erials for use

for such a purpose.

CONCLUSIONS

Theoretical and experimental study of counter-

flow combustion in supersonic streams confirms the

fact that the flame spike can be considered as an

effective means t o reduce the pressure dra g of blunt

bodies. Direct measurements of pressure drag have

been carr ied out in the supersonic, M= 2.0-2.5 air

st r e a m s w h e n t h e fla m e sp ik e h a s be e n f o r m e d

with the help of counterflow combustion of hydro-

gen injected through the small pipe playing role of

the structura l spike. The spike with a conical t ip

h a vin g be t t e r fla m e st a bil iz a t io n ca p a bil i t ie s h a s

bee n a lso st u d ied . Th e m a in m e ch a n ism o f d r a g

r e du ct ion h a s bee n a n a ly z e d w it h t h e h e lp of n u -merical simulat ions.

In experiments, the regions of stable counterflow

combust ion of hydr ogen in t he d (the blunt body di-

am eter) - L

(the dimensionless length of the spike)

a n d G

(the dimensionless hydrogen ma ss fl ow ra te)

- Po

(free stream stagnation pressure) planes have

been determined. The ma in elements of the fl ow

structure a round the blunt body in the presence of

inert and reactive injection have been resolved and

measured.

With the help of theoretical an alysis, it ha s been

established that the mechanism of drag reduction

is mainly at tr ibuted to formation of the wake-type

non-uniformity in the free stream init iated by in-

jected hydrogen and reinforced by motion of com-

bustion product behind th e fla me front propaga ting

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downstream in the deflagration regime of combus-

t ion . Wh e n p r e ssu r e in t h e r e a ct ion z on e in cr e-

a s e s ( it ca n h a p pen w i t h a n i n cr ea s e of t h e f u e l

m a ss flo w r a t e o r w it h a n in cr e a se o f f r e e st r e a m

pressure), the hydrogen combustion becomes slo-

w e r a n d less in t e n sive t h a t r e sult s in r e d uct ion

of t he posit ive effect of th e fl am e spike. To pre-

vent t his consequence, the modera tion of pressure

dependence of hydrogen combust ion above t he se-

cond extended limit of explosion is proposed using

silan e or boron. In th e case of boron, one can expect

m or e r a p id com bu st ion a s w e ll a s m u ch st r o n ge rh e a t r e le a se e ff ect . B o t h f a ct or s a r e be n efi cia l o f

the drag reduction effect.

T h e r e s u l t s o f t h i s s t u d y i l l u s t r a t i n g t h a t t h e

compara ble effi ciency in dra g reduction can be ac-

h ieved in t h e sa m e w in d t u n n e l u n d e r t h e sim ila r

flow conditions by using two different energy depo-

sit ion methods - the optical (laser) discharge and

counterfl ow hydrogen combustion. I n th e past , t he

phenomenon of dra g reduction in the case often w a s

at tr ibuted t o the specifi c effect of ionized ga s. Thus,

it may be argued that the phenomenon of drag re-

duction of blunt bodies in supersonic flows by con-

centra ted energy release a t at mospheric conditionsis not plasma specifi c.

Acknowledgments

Finan cial support of E OARD under the contract

SP C 00-4011 is gra tefully recognized.

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