NASA CONTRACTOR REPORT

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Henry G. Adelman and Jean-Luc Cambler

Eloret Institute

1178 Maraschino Drive

Sunnyvale, CA 94087

Prepared for

Ames Research Center

under Cooperative Agreement NCC2-388

(NASA-C R-'186 705 ) TRAHSATMOSPHERIC

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National Aeronautics and

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NASA CONTRACTOR REPORT

TRANSATMOSPHERIC VEHICLE RESEARCH

Henry G. Adelman and Jean-Luc Cambier

CONTRACT NAS2-

NCC2-388
LIMIT D

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1. Report No.

4. Title and Subtitle

TRA.NSATMOSPHERIC

2. Government Accession No. 3. Recipien_'s Catalog No.

VEHICLE RESEARCH

7. Author(s)

Henry G. Adelman

Jean-Luc Cambier

9. Performing Organization Name and Address

Eloret Institute

1178 Maraschino Drive

Sunnyvale, CA 94087

12 Sponsoring Agency Name and Address

National Aeronautics and Space

Administration, Washington, D.C.

1.5. Supplementary Notes

20456

5. Report Date

i June 1990

6. Performing Organization Code

8. Performing Organization Report No.

10. Work Unit No.

11. Contract or Grant No.

NCC2-388

13. Type of Report and Period Covered

12/i/85- o5/31/9o

14. Sponsoring Agency Code

Point of Contact. Cene P. Menees, c/o 230-2 NASA Ames Res.

Moffett Field, CA 94035

16. Abstract

Ctr.

Research was conducted into the alternatives to the supersonic combustion ramjet

("scram jet") engine for hypersonic flight. A new engine concept, the Oblique Detonation Wave

Engine (ODWE) was proposed and explored analytically and experimentally. Codes were

developed which can couple the fluid dynamics of supersonic flow with strong shock waves ,

with the finite rate chemistry necessary to model the detonation process. An additional study

was conducted which compared the performance of a hypersonic vehicle powered by a scram jet

or an ODWE. This work-included engineering models of the overall performances of the two

engines. This information was fed into a trajectory program which optimized the flight path to

orbit. A third code calculated the vehicle size, weight, and aerodynamic characteristics.

The experimental work was carried out in the Ames 20MW arc-jet wind tunnel, focusing

on mixing and combustion of fuel injected into a supersonic airstream. Several injector designs

were evaluated by sampling the stream behind the injectors and analyzing the mixture with an

on-line mass spectrometer. In addition, an attempt was made to create a standing oblique

detonation wave in the wind tunnel using hydrogen fuel. It appeared that the conditions in the

test chamber were marginal for the generation of oblique detonation waves.

17. Key Wort_,J (Suggatted'by Author(s))

National Aerospace Plane

Transatmospheric Vehicles

Pathfinder Program

Hypersonic Flight

19. Security Classif. (of this report)

Unclassified

18. Distribution Statement

Unclassified, Unlimited

20. Security ClagIf. (of this page)

Unclassified

21. No. of Page=

*For tale by the National Technical Information Service, Springfield, Virginia 22161

22. Price"
TRANSATMOSPHERIC VEHICLE RESEARCH

Final Technlcal Report

for the program period

December I, 1985 - May 31, 1990

Submitted to

National Aeronautics and Space Administration

Ames Research Center

Moffett Field, California 94035

Aerothermodynamics Branch

George S. Deiwert, Chief and Technical Monitor

NASA-Cooperatlve Agreement NCC2-388

Prepared by

ELORET INSTITUTE

1178 Maraschino Drive

Sunnyvale, CA 94087

Phone: 408 730-8422 and 415 493-4710

Fax: 408 730-1441

K. Heinemann, President and Grant Administrator

Henry G. Adelman, Principal Investigator

Jean-Luc Cambier, Co-Principal Investigator

1 June 1990
Final Reporting on the research efforts under Cooperative

Agreement NCC2-388 is in two parts. Part 1 includes primarily

the work performed by Dr. Henry Adelman during the period

12/1/85 through 5/31/90, focusing on the experimental aspects

of the Oblique Detonation Wave Engine (ODWE) project. Part 2

emphasises the numerical simulations of the ODWE experiment

and related analytical work, performed by Dr. Jean-Luc Cambier

who joined the team during 1 January to 31 December, 1989.
PART 1

OVERVIEW AND EXPERIMENTAL WORK

by Dr. Henry G. Adelman
During the period from December i, 1985 to May 31, 1990,

Dr. Adelman worked on several tasks related to the National

Aerospace Plane(NASP), Transatmospheric Vehicles(TAV),

and the Pathfinder program for planetary exploration.

This work has resulted in the publication of many papers

and several journal article.

OBLIQUE DETONATION WAVE ENGINE STUDIES

Abstract:

Dr. Adelman's research on the propulsion system for hypersonic

flight focused on alternatives to the supersonic combustion ramjet

(scramjet) engine. A comprehensive literature search showed

that very little test data or analytical modeling existed for

a scramjet or for a vehicle powered by a this type of engine. _

In addition, this data and our own analytical predictions

showed that the scramjet powered vehicle may not provide the

performance necessary for orbital missions. Therefore, Dr. Ade]_man

proposed a new engine concept, the Oblique Detonation Wave

Engine (ODWE).

The study of this new engine required both analytical and

experimental research. The analytical work was done in

cojunction with others at Ames and Eloret Institute. The

cooperative effort with Jean-Luc Cambier was to develop codes

which can couple the fluid dynamics of supersonic flow with strong
shock waves with the finite rate chemistry necessary to

model the detonation process.

An additional study was conducted which compared the performance

of a hypersonic vehicle powered by a scramjet or an ODWE.This

work included engineering models of the overall performances

of the two engines. This information was fed into a trajectory

program which optimized the flight path to orbit. A third code

calculated the vehicle size, weight, and aerodynamic

characteristics. Results of this study were presented by

Dr. Adelman at the 9th International Symposium on Airbreathing

Engines in Athens, Greece in September, 1989.

The experimental work was carried out in the Ames 20 MWarc-jet

wind tunnel. Dr. Adelman coordinated this work with personnel

from Aerojet TechSystems and the Facilities branch of NASA-Ames

RT Division. Experimental studies were begun in September, 1988

and continued through August, 1989. These studies focused on

mixing and combustion of fuel injected into a supersonic airstream.

Several injector designs were evaluated by sampling the

stream behind the injectors and analyzing the mixture with

an on-line mass spectrometer. Preliminary results were reported

at the AIAA Joint Propulsion Conference in Monterey in July,

1989.

In addition to the injection studies, an attempt was made to

create a standing oblique detonation wave in the wind tunnel

using hydrogen fuel. The results of these tests were reported
for the first time at an Agard Hypersonic Propulsion Meeting

in Madrid. It appeared that the conditions in the test

chamber were marginal for the generation of oblique detonation

waves.

Fuel Injection Experimental Studies:

Several fuel injection designs were tested for air-fuel mixing.

Since the oblique detonation wave experiment requires good air

fuel mixing, the extent of mixing had to be determined. This

was accomplished by an in-stream probe which passed gas

samples to an on-line mass spectrometer. The probe assembly

was supported on a 3-D traverse table which could span the entire

flow field of interest. Results of the fuel-air sampling

showed a narrow fuel jet which takes considerable distance to spread.

Several methods of increasing the extent of mixing were

tested including a blunt trailing edge strut. Unfortunately, this

blunt design allowed premature burning of the fuel in the wake of the

strut. Another design incorporated a bifurcated trailing edge strut.

However, this design was not tested due to the lack of time.

Detonation Wave Experimental Studies:

Several attempts were made to create a standing oblique detonation

wave. Before this was attempted, it was necessary to detremine the

state of the air in the arc-jet wind tunnel, which required a water

cooled calorimeter mounted in the stream. After the free stream

conditions were determined by the calorimeter, a wedge was placed
behind the fuel injection struts to create an oblique shock wave

that would become an oblique detonation wave.

Flow diagnostics were used to.determine the wave state including

shadowgraph and schlieren optics to allow comparisons of the

wave shapes with and without fuel injection. The results of these

experiments showed that fuel injection caused the wave to move

away from the wedge and become more normal. However, the cause of

this wave movement could not be attributed to combustion since both

hydrogen and helium created the same effects.

During one test run, a pressure rise was noted behind

the oblique wave indicating combustion. On other occassions, no

pressure rise was observed. Somedifficulties were due to the

erratic operation of the steam vacuum system which could not

maintain a constant test chamber vacuum. The cause of this

problem was later discovered to be a faulty isolation valve

on another arc-jet wind tunnel. However, due to the extended

period required to repair the leaking isolation valve and

the tight scheduling of the 20 MWarc-jet tunnel, no further

mixing or detonation wave tests could be carried out during this

period.

The wave displacement observed with inert gases was due to their

low molecular weights which create higher speeds of sound and,

therefore, lower Mach numbers. Decreasing the Mach number of the flow

causes an increase in the oblique wave angle.

Analytical Studies:
From the beginning of this program on wave combustion, it was

realized that predictions of fuel injection, mixing and combustion

phenomena would help to design the experiment and intrepret the

results. Various calculations and numerical simulations were

used for this purpose.

Fuel Injection Simulations:

The extent of fuel-air mixing was initially predicted by a

correlation developed from other studies found in the literature.

In order to verify this correlation and design the best injector,

simulations of fuel injection were begun using a 2-D code.

While this code modeled the injector as a slot, the actual injectors

consisted of 19 individual holes. These circular holes create 3-D

effects which cannot be modeled by a 2-D simultion. Therefore, the

2-D models underestimated the extent of mixing by a large degree.

The 2-D simulations were, however, usefull for predicting the

necessary conditions for combustion and detonation. They also predicte

the effects of light injected gases on the oblique wave shape and angl

This was illustrated when an unmixed jet of hydrogen encountered

an oblique wave and distorted the shape due to the low molecular

weight and low Mach number.

Detonation Wave Simulations:

Initial predictions of the existence of detonation waves at

the expected test conditions were carried out with a staedy

flow, I-D code. While this code predicted ignition delays and

combustion behind an oblique shock wave, it could not simulate
the coupling between the flame front and the wave which has

been observed with detonation waves. An attempt was made to

determine this coupling by the method of characteristics.

These calculations indicated that coupling would occur for

certain test conditions depending on the wind tunnel free

stream temperature and pressure.

Since a more accurate method of predicting detonations was needed,

the 2-D code which had been developed for the injection simulations

was extended to model combustion behind a detonation wave. Several

calculations were made which verified the trends predicted by

the I-D model. Detonations were shown to couple the heat release

and pressure rise to the oblique wave front and cause the wave to

become less oblique. Since it was possible that the fuel would not

be completely mixed with air before encountering the oblique wave,

a simulation was carried out with relatively unmixed fuel and air.

The results showed a distorted, bowed forward, "oblique" wave

which appeared almost identical to the case without combustion

discussed in the injection section. The most obvious difference

was the appearance of small areas where normal detonations occured.

The predicted wave shape distortion was remarkably similar to the shap

observed in the experiments.

Mission Studies:

In order to asses the performance potential of an Oblique

Detonation Wave Engine installed in a single-stage-to-orbit

Transatmospheric Vehicle, a mission analysis study was
performed. First, it was necessary to develop a I-D

engineering code which could predict the performance of

both an ODWEand a scramjet engine. This code calculated

specific impulses and thrust coefficients for both engines

at various flight paths corresponding to different dynamic

pressures. Engine cooling requirements were assumed to be

satisfied by heat absorption into the liquid hydrogen fuel.

If the heat loads exceeded the heat capacities of a

stoichiometric amount of fuel, then excess fuel was used

for cooling. Injecting this excess fuel into the supersonic

airstream inside the engine created lower specific impulses

and, therefore, lower engine performance. Since the ODWE

combustion zone is much smaller than that of the scramjet,

the ODWEneeded less cooling and had less performance degradation

than the scramjet due to excess fuel injection. This effect

was seen in the performance data. The specific impulse degradation

of the ODWEoccured at a higher Mach number than for the

scramjet. At lower Mach numbers, the scramjet had higher

performance than the ODWEdue to lower losses in the four

shock inlet system compared to the ODWEtwo shock inlet.

However, the results of a comprehensive mission analysis

study showed that high Mach number performance is more

important than low Mach number performance, so the ODWEwas

more efficient overall.

TRANS-ATMOSPHERICVEHICLE HEATINGLOADSSTUDIEs

One problem which faces airbreathing single-stage-to-orbit
vehicles is the tremendous heating loads imposed on the

airframe and engines. Several studies were conducted of

the expected heating loads on a typical TAV mission. A

chemical equilibrium program was modified for this purpose

in order to predict the composition of the air at the high

temperatures seen at the stagnation points on the nose and

the wing leading edges. Heating loads on the body were

determined for laminar and turbulent boundary layer conditions.

i

The determination of the transition from laminar to turbulent flow

was made using previously derived criteria.

Peak heating rates and integrated heating loads were calculated

for various missions with different trajectories of altitude-speed

histories. These results were presented in several AIAA conferences

and in archival AIAA journals.

INTERPLANETARY EXPLORATION STUDIES

The exploration of Mars was studied for different scenarios of

approach trajectories and earth return trajectories. A manned

mission was examined with landings and rake-offs from the

Martian surface. Vehicle sizes, weights and shapes were considered

along with aerodynamic characteristics, The ability to explore

large portions of the Martian surface was noted for certain

configurations.

References:

M.E. Tauber, G.P. Menees and H.G. Adelman, "Aerothermodynamics
of Transatmospheric Vehicles", AIAA 4th Thermophysics and Heat

Transfer Conference, Boston, June, 1986.

G.P. Menees, M.E. Tauber, J.T. Wilson and H.G. Adelman, "Ascent

Aeromaneuvering Capabilities of Transatmopheric Vehicles",

AIAA 25th Aerospace Sciences Meeting, Reno, January, 1987.

M.E. Tauber and H.G. Adelman, "The Thermal Environment of

Transatmospheric vehicles", AIAA 5th Joint Thermophysics

and Heat Transfer Conference, Honolulu, June, 1987.

J.L. Cambier, H.G. Adelman and G.P. Menees, "Detonation Processes

in Supersonic Combustion", 8th International Symposium on

Airbreathing Propulsion, Cincinnati, June, 1987.

H.G. Adelman et. al., "Analytical and Experimental Validation of

the Oblique Detonation Wave Engine", AIAA Paper 88-0097, 26th

Aerospace Sciences Meeting, Reno, January, 1988.

J .L • Cambier, H.G. Adelman and G.P. Menees, "Numerical Simulations

of an Oblique Detonation Wave Engine", AIAA Paper 88-0063, 26th

Aerospace Sciences Meeting, Reno, January, 1988.

M.E. Tauber and H.G. Adelman, "Thermal Environments of TransAtmospheric Vehicles", AIAA Journal of Aircraft, Voi.25, No.4,

April, 1988, pp 355-363.

J.L. Cambier and H.G. Adelman, "Numerical Simulations of a

Pulsed Detonation Wave Engine", AIAA Joint Propulsion conference,

Boston, July, 1988.
G•P- Menees, J.F. Wilson and H.G. Adelman, "Comparative Flight

Strategies for Ascent from Martian Surface to Orbiter Rendezvous",

Paper 89-0634, 27th Aerospace Sciences Meeting, Reno/ Jan. 1989.

H.G. Adelman et. al., "Experimental and Analytical Investigations

of Wave Enhanced Combustors", AIAA Joint Propulsion Conference,

Monterey, July, 1989, Paper 89-2787.

G.P. Menees, J.F. Wilson and H.G. Adelman, "Comparative Strategies

for Ascent from Martian Surface to Orbiter Rendezvous", Paper

89-0634, 27th Aerospace Sciences Meeting, Reno, Jan. 1989.

J.L. Cambier, H.G. Adelman and G.P. Menees, "Numerical Simulations

of Oblique Detonations in Supersonic Combustion Combustion Chambers",

AIAA Journal of Propulsion, Vol.5, No.4, July-August, 1989.

G.P. Menees, H.G. Adelman, J.L. Cambier and J.V. Bowles,

"Wave Combustors for Trans-Atmosdpheric Vehicles", Paper 1]-5,

9th International Symposium on Airbreathing Engines", Athens,

Greece, September, 1989.

J.L. Cambier, H.G. Adelman and G.P. Menees, "Numerical Simulations

of an Oblique Detonation Wave Engine", AIAA Journal of Propulsion

and Power, Vol.6, No_3, May-June, 1990, pp 315-323.

G.P. Menees, H.G. Adelman and J.L. Cambier, "Analytical and

Experimental Investigations of the Oblique Detonation Wave Engine",

AGARDPEP 75th Symposium on Hypersonic Combined Cycle Propulsion,

Madrid, Spain, May 28-June i, 1990n (Preprin% a%%ached).

N0%es Copies and/0r preprin%s of %he above papers were included

in earlier progress reports.
PART 2

NUMERICAL SIMULATIONS

by Dr. Jean-Luc Cambier
Report to Contract NCC2-388 : Jan.-Dec 1989

Part I: Numerical Simulations of ODWE Experiment

and Related Analytical Work

Jean-Luc Cambier, Research Scientist

Eloret Institute, Sunnyvale ,CA.
I: Introduction

The computational work for the ODWE research program and for the year 1989 was

divided in three parts:

• continued code development and enhancement of numerical capability

• application of TVD code (re: 'MOZART') to simulation of fuel injection process

and comparison with experimental data.

• continued validation of the code MOZART by simulation of shock induced combustion and comparison with ballistic experimental data.

In addition, some computational work was performed on another code, originally provided by D. Bogdanoff, and extensively modified, for the 1-dimensional analysis of

generic scramjet engine designs.

Complementary to this computational and analytical work, some conceptual research

was done for the creation and submission of research proposals to NASA Headquarters

for two different programs.

II: Code Development

II-A: Introduction

The code MOZART was further developed in 1989 from a 2D to a 3D capability. The

algorithm for chemical kinetics was modified to fully use the conservation of elements,

and thereby reducing the chances of error. The code MOZART is now a well-rounded
capability and few further modifications are projected. Somenumerical experiments

on an implicit version have been carried out, but the development of a fully implicit

version of the code is not planned for the immediate future. The most immediate area of

concern is the enhancement of the grid-patching capability, to accomodate grid sliding

(steady/unsteady) and grid embedding when nodal points from different grid systems

are not on the same locations. This problem occurs for highly complex geometries;

the algorithms required for the solution of this problem have been written and will be

tested in 1990. This increased capability will be similar to the 'chimera' capability in

development in the RF division.

Most of the new code development was focused on a series of TVD codes for the

simulation of non-equilibrium, multi-temperature gas and plasma codes. Three types

of codes were originally written:

• a 3-Temperature and a Nv-temperature code for neutral, non-equilibrium gas. The

3-T version was tested and compared to experimental data on shock layers and

with the 2-T code by Candler.

• a one-fluid, multi-T code for neutral and/or strongly ionized flows.

• a multi-fluid code for ionized flows.

The multi-fluid description is obtained by solving a full set of Euler equations of the

heavy component (both neutrals and heavy ions), and one for the electron component.

The various exchange terms for mass, momentum and energy between all fluid components are explicitely solved on the right- hand side. The time scales are very small, and

the code is therefore applicable for plasma flows in highly non-equilibrium, with potential charge separation. This is the case near electrodes in arc-heated flows, for example.
The one-fluid description assumesno chargeseparation, and only the mass and energy

transfers are explicitely computed. This approximation is valid for most flows, such as

high temperature shock layers. The results of both one-fluid and two-fluid versions were

observed to be consistent with one another.

The algorithms for chemical and ionization kinetics in the case of multi-T plasmas

were decisively more complex, due to several translational temperatures and the effect

on the correct computation of the energy balance. The case of strong ionizing shock

was computed and compared to an analytic solution. The case of a shock in a preionized plasma, and the dramatic effect of electron heat conduction as a precursor was

also computed and compared with known analytic solutions. It was observed that the

essential physics were well reproduced by the code.

The one-fluid code was then extended to include radiation emission/absorption and

radiative transfer. The physics of emission and absorption have been currently modelled, and are expected to be tested in the first half of 1990. These major developments

in computational capability are expected to be useful in various areas of flow modelling

for Ames, in the very near future. The simulation of strongly ionized shock layers, arcjet flows, laser-heated flows and plasma ignition of combustible mixtures will hopefully

be attempted with these codes in the future.

The plasma at low and medium temperatures is composed of three components, i.e.

the neutral particles, ions, and free electrons. Each component satisfies its own system

of conservation equations with additional coupling terms responsible for the exchange of

momentum, energy, as well as chemical and ionization/recombination reactions. Some

of the multi-fluid effects can be modelled by multiple translational temperatures, there-
fore by separately convecting the translational energies of each component. If electromagnetic effects are important or very small spatial scales must be resolved, one must

also separately solve for the momentum equation of each component. In the following,

we designate a multi-fluid description by the number of separate momentum equations

that are being solved; thus, a one-fluid description can have different ion and electron

temperatures, but only the global momentum equation is solved. The mass and momentum conservation equations for a plasma component a (=n, i or e), in the absence

of chemical reactions, ta_e the form:

0ps -. _.

--_- + V. (uc, ps) -- 0 V8 E a (1)

where Z_ is the charge of the plasma component, £ is the electric field. The force

of friction /_ accounts for the exchange of momentum through collisions with other

components of the plasma. The total energy density is transported according to:

OE_ -. -. -.

+ V(ff_(E_ + P_)) = Z_en_u_£ + n_ff_ + _ O_ (3)

while internal energies follow a linear convection rule:

0E_,_ _ _ • •

Of. + V(u,_E,,,,_) = Q,,,,,. + Q,,,. (4)

• •

The exchange terms Q_,tr, Q_,. are the coupling terms between vibration and translational/electronic modes; similar terms exist for the relaxation of the internal electronic

excitation energy 1. The conservation equations must also be supplemented on the right

hand side by the viscous terms, which axe not explicitely written here. The translational

and rotational degrees of freedom are combined, since they are at the same temperature.

The electrons having no internal structure, the system of conservation equations for the

1The electronic excitation energies and temperatures are indicated here by the * suffix, to distinguish

it from free electronic quantities with a traditional e suffix.
electron gas takes the very simple form of an ideal gaswith 7, = 5/3.

Since the pressure is governed by the translational degrees of freedom only, the equation of state, for a given component only, is:

1 2 o

P_, = n_,.RT,,.,_, = (7,.,. - 1)E,.,. = (7,.,. - 1)(E. - -_p_,u_, - Z,,,_, -- E.,_, - El,.) (5)

where "Yt.,. is the ratio of specific heats, but taking into account the translational and

rotational degrees of freedom only. E} = Z. psh_ is the heat of formation at T = 0, and

/_ is the Boltzmann constant.

The exhange terms on the right-hand-side operate at frequencies that are characteristic of the respective collision frequencies. For example, if v,i is the average collision

frequency between electrons and ions, the rate at which momentum is exchanged between these two components is given by the friction force density:

= - <)

This term represents the momentum gained by the electrons per unit of time, through

collisions with ions. A more general and systematic description of the coupling terms

can be found in Ref. [2]. Similar terms exist for collisions between heavy particles.

If the gas is substantially ionized, the coulomb collisions between charged particles

are very frequent, and lead to a more rapid relaxation of the velocity difference between

ions and electrons. In addition, such a velocity difference would induce a charge separation; the rapidly rising electric field would then restore neutrality within a time scale
characteristic of the inverseof the plasma frequency2:

(nee2 _ 1/2 = (6)

\ m,_o /

A steady-state can be reMized by bMancing the electric force with the pressure and

thermM gradients: this leads to the characteristic polarization effect at the shock discontinuity in a plasma. The momentum equation for the electrons in quasi steady state

leads to:

•..¢ ...¢ ...¢

Op,_, _ -VP, + RT + P_ - en,$ __ 0 (7)

cot -

..¢

where the inertial contribution has been neglected. P_ is the friction force due to

collisions, and/_w is the thermal friction [2,:]]"

/_T = -0.71n_/_VT_ (8)

Assuming that a steady state is achieved, the electric field can be estimated from equation (7) above, and the charge separation by solving the Poisson equation:

V. $ = --(ni- n,) (9)

_o

This method will be used in the one-fluid model to estimate the electric field and charge

separation.

By summing the momentum equations for ions and electrons, it is clear that there

is no electric or friction force appearing in the resulting equations of motion. Since

the solution of the momentum equation for the electrons may require a time resolution

comparable to the natural oscillation period of the plasma (1/wp), significant savings

in computational work can be obtained. However the method described above to estimate the steady electric properties of the plasma will, in this one-fluid model, lead

2We use here the MKSA system of units.
to inaccurate results. The one-fluid model can be used therefore in caseswhere these

electro-magnetic effectsare expectedto play only a minor role.

There arehoweverno restrictions on the number of translational temperatures, since

all energiesare separately convected. Let us also mention that the algorithm used to

compute the energyexchangeterms must be ableto provide the correct asymptotic limit

when the exchangetime scalesare not resolved. This can be very easily implemented.

Let us consider a one-fluid description of a fully ionized plasma, i.e. only ions and

electrons. During the summation of the momentum equations, the body forces and

friction forces cancelout after assumingno chargeseparation (hi __n,) and no current

density (ui _- u,). An equation for the total energy of the plasma can be obtained in

a similar fashion. The energy for the electron gas is convected separately, therefore

allowing two distinct translational temperatures. When incorporated into a one-fluid

algorithm, this energy equation for electrons is a non-linear convection equation which

would require to compute the generalized Riemann invariants along the three characteristic paths (u,, u,+c,). The stability and/or accuracy becomes then severely constrained

from the large values of c,. However by using the conservation of mass and momentum for electrons, it is possible to reduce the left-hand side of this equation to a linear

convection problem:

aEo,,r - - •

0t + V. (ff, Z,,,r) = -P,V-g, + Q,, (10)

where oixly the translational energy E,,,r = 3n,f_T, is convected. The fast time scales

due to the electrostatic forces have been removed, and the transport equation can be

easily incorporated into a multiple temperature TVD algorithm. We however pay the

price of a source term on the r.h.s, written in a non-conservative form. This term will
present difficulties at a shock, where the gradients are not resolved•

II-B: One-Fluid Model

Let us consider a fully-ionized plasma, composed of n species of ions and electrons

only. The hyperbolic system we intend to solve, written in a conservative form, is:

f 01 _

P,_

P_

m

E

Ev

E,

Se,tr

OQ OF 0

+ Ox -Or

up1

upn

upe

P + pu 2

uH

uE.

uE.

uEe,tr

= RHS

where m = pu is the momentum density, and H = E + P is the enthalpy per unit

volume• The mass density of the electron gas can be convected as another specie, or

can be obtained at each time step by using the fact that there is no charge separation.

The pressure is the sum of individual plasma components:

1

P = (_,,_ - 1)(E - -_pu - E,_ - E. - Ee,t,. - E_) + (% - 1)E_,t_ (12)

The derivatives of the pressure are computed with respect to the conserved variables,

i.e. ps, m, E, E., E., E_,tr. Using the notation Pq =_)q,#qVq= ps, m, E.., and using the

definitions of the mass fractions _ = p_/p, and of the internal energies per unit mass

e,, = E,,/p, e. = Z./p and e_,_,. = E_,t,./p, we compute these derivatives as (compare

with [4,7]):

PE = --PE,, = --PE. = ;/i,t,. -- 1 , P,. = -uPs ,

^

u 2

Pp. = (9,,,_ - 1)(--_ - C,,,.Tms - h:) + R----T,,.,s Vs 7£ e,

ms

P_.,,r = %- 1 - PE

u 2

Pp. = (_'i,,,-- 1)--_-

(13)

(14)
With these definitions, one can compute the determinant of the jacobian; the speed of

sound is then obtained in the form (c,8 - Ps/P):

c 2 -- _ _.Pp. + (h - u 2 - e. - e.)PE + PE.,,.e_,t_ _-- /_ _,,,_Ti,,_ + %T_ (15)

s mi

where one recognizes the expression for the ion-acoustic speed of sound• The TVD

scheme requires the projection of our non-linear system of equations onto the characterk -1

istic eigenspace, through transformation matrices T, T -1. Let ai+l/2 = T_+I/2Ai+I/2Q

be the component of AQ in the k th characteristic direction. The jumps in characteristic

k

variables ai+l/2 and the transformation matrix T satisfy:

AQ = Ta

AF = TAa (16)

where A is the diagonal matrix whose elements are the eigenvalues of the hyperbolic

system of equations• After some algebra, we find:

O_ --"

__ Ap

Ap_

( AP +cA rn--ucA p )

2ca

( AP--eArn+ueAp)

2c 2

AE_ --e_-4f -

AE, - e,-_

A Ee,tr -- ee,tr-_-

W .__

I 1

0

u

u2_

0

0

0

u 2

0 _1 _1 0 0 0

• • • • • •

• • . • •

1 _. _. 0 0 0

u u+c u-c 0 0 0

- P-_ h+uc h-uc _PE__ _P_m,__ _PE.,,.

PE PE P_ PE

0 e,, e,_ 1 0 0

0 e. e. 0 1 0

0 ee,tr ee,tr 0 0 1

(17)

10
the fluxes, according to the original scheme by A. Harten [5].

terms are of the following form:

The rest of the numerical method follows closely the usual procedure for computing

The energy exchange

Q_i __ r E u_i(i,t,--E_,t,.) (18)

where u',_ is related to the collision frequency: u',_ = (2m,/m_)u,_. This equation has

an exact exponential solution. We choose therefore to express this term as:

I E 'a,) 6E_,t, _- _( ,,t, - E_,,,.)(1 - e-2"o' (19)

Notice that when the time scale of coupling is resolved (u',iAt << I) we obtain in this

limit the correct exchange term:

(20)

while if a large time step is used:

1 E

6E_,,,. __ _ ( ,,,,. - E_:,.)

which a/so the correct asymptotic limit (both Ti,_,and T_,,,-* T,q =

(21)

T,+T_ _ This

2 ]"

numerical scheme provides both accuracy and stability for large time steps. The same

method is used for other modes of relaxation (T-V, V-*, T-* couplings). When a shock

is propagating into a plasma, the heat conduction of electrons becomes an important

process which acts on very small time scales. The electron heat conduction is (in the

absence of magnetic field):

n_ = 3.1616 n_k_T_ "_ tc'T:/2 (22)

m e l/el

where we have isolated the temperature dependence. The heat conduction flux then

takes the form:

-, 2 .,.,_,-r,7/2

II
The jacobian term (OF/OT,) will have a TS,/2 dependence. A simple implicit algorithm

can be written for this heat conduction problem, and solved in A-form for the electron

temperature. The time step used can then be much larger: this implicit algorithm has

been compared with an explicit one. Accuracy can be maintained if the relative change

in temperature induced by the heat conduction process alone is kept to a reasonable

value (< 5%). This still allows us great savings (about 50-fold) in computational costs.

A test of the numerical method was performed by simulating the propagation of a

shock in a one-dimensional system. The plasma neutral was composed only of singlyionized atomic nitrogen N + and electrons.The free stream density was poo = 10-6kg/m 3,

or a number density3 Noo __ 7.143 10-5 moles/m 3. The free stream velocityand temperature were respectivelyUoo = 7 kln/s and Too = 275°K. Grids of various resolutionwere

used for this test case, depending whether the one-fluidor two-fluid models were used.

The free stream velocity and temperatures are too small for this test to be representaL

rive of laboratory conditions; however we are only interested at this stage in checking

the numerical method and the reproduction of the essentialphysics.

Figure I shows the temperature profilesobtained for this shock reflectingfrom the

closed end on the right-hand side. The dashed linesindicate the ion and electron temperatures obtained when the electron heat conduction is artificiallysuppressed. The

ion viscous shock is very well defined; the relaxing zone behind the shock, due to the

ion-electron energy exchange through collisons,isalso well reproduced. The electron

temperature jumps to a post-shock value Te2 "_ 1050°K, then increases due to the energy exchange. The density isshown in Figure 2 (dashed curve);the post-shock value is

N,2 _- 2.83 10-4. The solidcurves for both Figures I &: 2 indicate the temperature and

3Number densitieswith a capitalletterare expressed in moles/m s throughout the text.

12
density profiles obtained when the electron heat conduction is included. Because the

latter process is considerably faster than the ion-electron energy exchange, the shocked

electron gas is essentially isothermal. The heating of electrons prior to the ion shock

extends to considerable distances, and through energy exchange, is also responsible for

a slight heating and compression of the ionic component, as can be observed in Figures

I_2.

These results qualitatively the correct features expected in strong shocks in completely ionized plasmas. However, even in the absence of heat conduction (_ neglecting

the electron viscosity), the electron heating should be adiabatic. This implies that the

post-shock electron temperature should be given by:

= __ 690°K (23)

\ nel /

We see therefore that in the absence of resolution of the shock structure, the nonconservative term -P_XTg over-estimates the heating of the electron gas. When heat

conduction is allowed, the problem may be less serious, and the error will translate into

an error in the distance through which pre-shock heating will occur. Nevertheless, there

are situations in which this over-estimate of the electron heating may lead to significant

errors: such is the case of magnetized plasma in a transverse field, and possibly for

ionizing shocks.

Another uncertainty arises when the electric field is computed: assuming a steadystate for the electron momentum equation, the (time) asymptotic field can be expressed

as a combination of the gradient of pressure and thermal and friction forces. However,

because the shock structure is not completely resolved, the length scale that must be

used for the electron pressure gradient in the vicinity of the viscous shock must be based

13
on the shock thickness for the electrons. We have therefore two methods for computing

the electric field in this approximation. The first method uses the grid scale, and is

assumed valid in the regions of smooth variations. The second method uses the Debye

length scale 4

( eokT_ _ 1/2

= \ / (24)

as an estimate of the width of the compression region for electrons, and is expected

to yield better estimates at the shock, i.e. for the peak electric field. The results are

shown in Figure 3. It is apparent that the two methods gives very different answers, in

particular for the peak values (__ 2000 and __ 7500 V/cm respectively). In order to gain

better knowledge of the shock structure, and associated phenomena, it is necessary to

turn to the two-fluid model.

II-C" Two-Fluid Model

As explained in the previous sections, the multi-fluid description of the plasma

amounts in solving simultaneously the momentum equations for each component. Since

the electrons are very mobile, we expect large variations in the electron velocity, which

must be correctly reproduced for an accurate answer. This imposes small time steps,

such that wp/kt << 1. Because the electron gas is always subsonic, it is not necessary to

use a shock-capturing method to model this component. The scheme we use is a simple

18*-order accurate scheme, i.e. a donor-cell method based on the linearized system of

equations [6]"

Pe "¢ --¢

-k--+ = 0 (25)

COp_ue,i

V(g,p,u,,_) = -V_P, - en,g_ + RT,i + IL,,i (26) 0t

4This expression is the one-dimensional Debye length. The Debye radius, i.e. in 3-dimensions, should

include a factor 4r.

14
0t -t- V(g_Ee,,r) = -PeV_7_ - (RT -F P_)g_ (27)

The electron heat conduction is not considered here. In addition, we artificially set

(_ - 0, for clarity: this does not affect the validity of the numerical methods.

The electric field is computed at each time step by solvingthe Poisson equation

(eq. 9). The thermal and pressure forces on the r.h.s, of the momentum equation are

assumed constant during the time step. After developing the friction term, this equation

integrates to:

(p_ue)(''+1) -(p_u_)(n)e-_"'a'--F[-V(P_ _ + p_u_) end,f, -t- RT] (") -_"_' (") (') -_o,a, -- e +pe u i (1-e )

(2s)

where the convective term has been brought into the r.h.s. Essentially, the ion-electrons

collisions force the velocity to relax towards the ion velocity with the characteristic

ion-electron collision frequency v_i _- 0.51v_. This relaxation provides the damping of

plasma oscillations over large time scales. An explicit integration of the equations of

motion is performed for the same test case, over a refined grid. The time step is sufficiently small that plasma oscillations are resolved. Figure 4 shows the density profiles

for both ion and electron components. Oscillations are clearly visible for most quantities of the electron gas (including the temperature, if shown on a linear scale). These

oscillations can be artificially suppressed however by enhancing the damping through

collisions. This can be easily done in equation (29) by using larger values of the collision frequency. Setting for example v_i _- 5_'_i in eq. (29) leads to a strong damping

of the velocity fluctuations, as can be seen in Figure 5. This is sufficient to completely

damp all fluctuations in density, temperature, and other variables. In Figure 6 we show

the electric field, for both cases of naturally and artificially damped oscillations, while

Figure 7 shows the relative charge density 5n/n. Similar results are obtained if the

15
artificial increase of the damping is 10 or 20-fold.

It is clear that the artificial damping smoothes out the fluctuations, without affecting

the mean or peak values of any physical variable. This is possible because the dynamics

of the plasma depend only upon the electron gas averaged over many plasma oscillations.

Therefore the artificial enhancement of collision damping will not generate inaccuracies,

but will only filterout the time scalesof plasma oscillation.This isalso apparent during

the computation, as the time step allowed for stabilityisfound to increase by one order

of magnitude when damping isused. The density profilesare then shown in Figure 8.

The post-shock electron temperature (the relaxation isnot considered here) isfound to

be 700°K, matching closelythe adiabatic value. It was found that suppressing the joule

heating of the electrons would give the exact adiabatic value, as expected.

Other simple checks can be performed. The wavelength of oscillations, as seen for

example in Figure 5, is __ 0.7/_, which is also the computed Debye length scale. By using

the relation: 1

= \ ) =

it is easy to observe that these are indeed the natural plasma oscillations.Similarly,

the electricpotential jump over the shock profileA_ can be estimated (using the width

at half the peak value) as: A_ __ (3 104V/m) x (2 I0-6m) __ 0.06V. According to the

Debye criterion e_ _ kT, this corresponds to a temperature jump AT __ 696°K, as

measured.

II-D: Chemical/Ionization Kinetics

As mentioned previously, we have slightly modified the algorithm for chemical kinetics

16
in MOZART to enforce the conservation of elements. This same modification is also

being used here. Let us consider an elementary reaction and its reverse f(r) and b(r):

v_AA + v_B _ v_C + V_OD

with the elementary conservation law:

1 dnA 1 dnB

VA dt VS dt

1 dnc 1 dnD

m m

m

vc dt l]D dt

for a given (one-way) reaction. Listing all reactions involving specie A in that form, the

total change in density is:

A(r)nA = _.r.v_VAl_C i_DV_ kb/k t_ _ VAnr v_A A n v_B k;f/kf, -- 72)A -- ff_AnA

The last for is conveniently used for numerical integration:

( 7)A _ e-LAZXt

AriA= f_A hA)(1 -- )

which is stable for large time steps. The integration form is not linear however, and

does not exactly conserve the elements. This would be possible only if an explicit

time integration was used, which is not desirable for its unstability. The remedy is to

stabilize by the exact exponential integration each pair (forward/reverse) of elementary

reactions. We write therefore the change due to each reaction as:

dnA r r Vr Vr

-- VAr ;_,Vc_,VD I '_C '_D kb -- nAanB sky} = z]A -

dt

and the integration leads to:

II_ nA)(1 -- e -r_A')

= -

Here after numerical integration, one can still write:

A(r)nA A(r)ns A(r)nc

17
,t

and the overM1 scheme conserve the elements while being stable at large time steps.

The formulation differs in details between dissociation/recombination reactions and bimolecular reactions, but the essential features are described above.

For ionization reactions due to electron impact, special care must be taken for the

energy balance. In the scheme used here, heavy ions have a (large) positive enthalpy of

formation, and the free electron has no zero-point energy. In the one fluid formulation,

the total energy convected is:

E = Et_ + E_ + E. + Ek + Eo + E_

which is broken down respectively into the translational/rotational, vibrational, electronic energies of heavy particles, kinetic energy, zero-point energy and free electron

energy. Considering a reaction involving heavy particles only, here atoms in the ground

state:

A+B _ A + +B+e

the conservation of total energy allows us to directly translate the change in total formation energy into temperature changes for the heavy particles. If excited atoms are

considered:

A* +B _ A + +B+e

there is also a net change of total electronic energy, mad therefore electronic temperature

which must be accounted for. The same is true for impact ionization:

A+e _-_ A + +e+e

A* +e _ A + +e+e

Consider for example the impact ionization from ground state: the positive change

in zero-point energy from the forward reaction (ionization) would lead to a decrease in

18
heavy ion translational temperature if it was not compensated. Indeed, the changein

electron energyin that caseis exactly given by the changein zeropoint energy,s.t.:

6E_ + 6Eo = 0

and this indicates that energy is removed from the thermal modes of the free electron

gas component. The complete kinetics algorithm then computes the changes in energies

due to various reaction mechanisms: AE., AE,, AE,. Note that the conservation of

total energy implies:

AE_ + AE, + AE_ + AEo = 0

The separately convected energies E., E,, E, are then modified accordingly. Note also

that if different gas components are considered at different velocities, the change in

kinetic energies zXEk must also be considered. This will be used in the future when the

kinetics algorithm is implemented in the two-fluid formulation.

Figure 9 shows the profile of a one-dimensional strong ionizing shock in Argon. The

relaxation zone is shown in detail for the temperatures, (ion and electron), ionization

fraction, and density ratio. The insert is taken from a calculation by Biberman &:

Yakubov [8], and shows fairly good agreement. This calculation was done for ionization

from ground state only. Other tests including effect of precursor excitation are being

conducted.

III: Simulation of ODWE Experiment

The focus of this work was the simulation of the flow field in the strut region. This

was done first with an Euler (inviscid) computation to obtain the position of the reflected shocks. The computations were done for a free stream Mach numbers of 4.5 and

19
5.4. Two values of the vertical separation between the struts were considered: 2/3"

and 3/4". It was apparent from the results that multiple shock interactions occured

between the struts, as well as shock impingement on the struts flat plate. It was clear

then that in the case of high stagnation enthalpy, extreme care should be taken in avoiding locally high temperatures. However, the experiment proceeded nevertheless and the

struts melted.

Another series of computations were made with greater refinement, including the

blunt leading edge of the struts, and with high gridding density. The full Navier-Stokes

were solved, for an assumed laminar case. The conditions were Moo = 5.4, Too = 42.2K,

Poo = 0.019.8 atm, ReVoo _- 2105/in. The total length of the strut is approximately

5", and one should expect transition to turbulence somewhere at the end of the strut.

However because of the leading compressive ramp (7 ° ) and of the porous (i.e. rough)

plate in the fn'st half of the flat plate section, one could expect transition sooner. There

is however no definite way to predict the transition with precision and there were no

measurements intended to measure the properties of the boundary layer on the strut.

We decided to ignore these effects for the moment. In addition, when fuel injection takes

place, the flow becomes obviously turbulent: the algebraic (Baldwin-Lomax) model is

then unable to model the correct physics, and ideally one should use a 2-equation model

at this point. The development and validation of a k-e model is one of the high priority

development for 1990.

Figure 10 shows the computed density contours in logarithmic scale for the strut flow

field prior to fuel injection. Of special significance is the boundary layer detachment on

the top and bottom surfaces,at the start of the trailingramp section. The detachment

and development of the shear layer are also clearlyvisibleon the schlieren.In addition,

20
weak recompression shocks are seen to originate from the trailing edge itself. This can

also be observed in the computed density field, although the pattern is more complex:

it appears that weak shocks are thrown off from the pairs of vortices on opposite sides

of the strut. The flow between the struts shows a regular diamond pattern from the

multiple shock intersections. There is also a recirculation region on the flat plate in front

of the first shock impingement. Because of the good resolution of bot grid systems and

numerical scheme, one can observe in detail the pattern of shocks and expansion waves,

especially near the recirculation region. Figures 11 through 19 show the development

of the flow field during injection by a time accurate simulation. This series of computations was done to provide the camera crew of the NOVA series with data for a future

PBS presentation. Notice at the end of the run (near 200 #sec) that there is a flickering

instability (better shown in the movie version) of the mixing layer at the trailing edge,

upper section of the strut. We assume that this transient dissipates at later times; this

may also happen only within the laminar flow assumption, where dissipation through

viscous effects is a slow mechanism.

Another calculation (done previous to the time-accurate one) was done for steady

state. The difference lies in the fact that the flow in each region is computed individually (or by small groups) until steadiness is achieved, using extrapolation boundary

conditions instead of grid overlaps. There is therefore a locM time variable for each grid.

In this cMculation, initiM wlues and initial boundary conditions differ from the timeaccurate version. The results are identical, except for the absence of this 'whipping'

layer at the trailing edge (Figure 20). In Figures 21 through 23, we show the temperature, Mach number and stagnation pressure. It can be seen that the fuel injection and

its associated shock lead to large drops in stagnation pressure.

21
The corresponding schlieren is shown in Figure 24: in this picture, the flow between the two strut surfacesis very complex, and there seemsto be larger areasof flow

separation and recirculation on the surfaces.It is howeverdifficult to obtain a clear experimental picture of the flow. Most of the featuresof the ttow howeverare reproduced

by the simulations, especially the strong bow shocksin front of the injectors, and the

diamond pattern of shockinteractions. The mixing obtained by astrictly 2-dimensional

simulation is very poor, and is belowthe measuredmixing. This canbe easilyexplained

by the importance of three-dimensionaleffects, especiallylongitudinal vortices. In addition, it is not clear what are the turbulence levels in the experimental flow: a more

detailed comparison could be obtained only if three dimensional computations are performed. Although this task was planned, upcoming funding difficulties for this project

make the realization of these computations in the near future doubtful.

IV: Simulation of Ballistic Experiment

The series of ballistic experiments performed in the 1970's at the Institute of SaintLouis provides us with a clean database for code validation. These experiments involved

the shooting of a projectile of simple geometry (sphere-cylinder or cone) into a pre-mixed

hydrogen-air or hydrogen-oxygen gas mixture. The problems of injection and mixing

are therefore alleviated, and one can concentrate on the validation of the chemical kinetics and the coupling between the flow dynamics and chemical kinetics. One of the

most difficult cases to reproduce is the intermediate case between detonative regime and

uncoupled shock-flame regime. In the first case, the heat release occurs immediately

behind the shock front, and it is impossible to distinguish the shock from the flame,

even looking at the experimental schlieren. The simulation of this case is easy, because

the finite size of the grid elements provides a spurious coupling between the shock and

22
flame. Indeed, if shockand flame arelocated within the samecomputational cell, or are

in neigboring cells,the inherent numerical diffusion of the algorithm will automatically

combinethe two. In fact, the situation is much worse,becauseof the sensitivity of the

width of the reaction zone to the chemical kinetics. Previous attempts at reproducing

the experimental results had partly failed becausethe numerical diffusion was too large:

the radical speciesdiffusion into the pre-ignition zoneacceleratedthe chemistry,and the

point where the shockand flame decoupledwasnot properly located. By appropriately

slowing the chemistry (by _ 30- 50%), one could compensate for this numerical effect,

bu at the expense of loosing predicting value.

Since these first attempts, we have continued the simulations, but with a much

higher grid resolution, and the results have been spectacularly good. Here, we simulate

the hydrogen-air case at Moo = 6.46, for a sphere-cylinder model. The experimental

schlieren is shown in Figure 25. The decoupling of the flame and shock is clearly shown.

The corresponding numerical result (Temperature contours) is shown in Figure 26. The

point of decoupling occurs relatively at the same position (a_ugle estimation), and this

constitutes an excellent validation of the code. In the course of this calculation, we have

revised some of the reaction rates, although the most important for flame propagation

(H + 02 ---* OH + O) or ignition delay (/-/2 _ H + H) did not change by much. We

also incorporated the effects of various 3rd-body efficiency into the kinetics algorithm,

an additional development that was long overdue. These calculations used 44 one-way

reaction steps, and 9 species (N2 inert), including HO2,H202. We would like to pursue

these validations for other cases, and plan to attempt the case of oscillating combustion,

pictured in Figure 27. This case is extremely difficult, and requires the modelling of the

interaction between chemical kinetics and sound pressure waves. We believe however

that the code has the required capabilities to reproduce this flow, with minor changes

23
"" and enhancements.This task will be pursued in 1990.

V: One-dimensional En_ineerin_ Analysis of ODWE

In addition to strict CFD, we have worked on an engineering code and provided the

engine data base for the analysis and comparison of the ODWE performance, versus

conventional scramjet. The engine data was supplied to another code for structural

and mission analysis, and the overall results were presentd at the ISABE conference in

Athens, Greece. The original code was provided to us by D. Bogdanoff, and extensively

modified by ourselves. First runs were made for a scramjet engine. After succesful

tests of the modifications, a second code version was made to model the ODWE. Both

analysis were made in one dimension, and involved many simplifying assumptions which

are common in these types of analyses. The resulting codes, as the original one, axe

very specialized, and there was no time available to attempt to make these codes more

user-friendly for future purposes. Rather than describe the work here, we refer to the

paper presented at the ISABE conference, a copy of which is provided in the Appendix.

VI: Proposal Research

During the year 1989, we have also made serious efforts in attempting to obtain funding for the project and related projects from NASA Headquarters. The first series of

attempts was made concerning the Generic Hypersonics program. Several of our proposals (ODWE, Bifurcated Spiralling Strut, Shock Impingement in Combustors) were

well received by F. Moore, who acted as technical consultant to NASA Headquarters,

and were to be funded for a total of nearly $900,000. Unfortunately, after the recommendations of F. Moore, the budget went into a state of flux, and intense competition

24
from NASA-Lewis killed most of this funding. It is not known what final arrangements

were made concerning this program, between Ames and Lewis, and Headquarters.

Another (starting) program was the High Speed Civilian Transport (HSCT): several

proposals were written and some were accepted for initial funding (plasma ignition, reacting fluid element model, new combustor concepts for low NO emission) of $150,000.

This funding was attributed to the RT branch.

VII" Conclusions

The code development has focused principally in 1989 on non-equilibrium flows, at

high temperature. This development was originally intended to provide a numerical capability for the simulation of arc-jet flows, in which the ODWE experiment was taking

place. However several spin-off applications can be derived from such a capability, and

we feel that it may be used in the future to considerably extend the scope of the overall

numerical capability of ELORET and Ames RTA division.

Continued validation of the MOZART code was succesful in reproducing a shockflame interaction. This work will continue in 1990, on more difficult cases yet.

The simulation of the strut flow field in the ODWE experiment provided great detail

on the shock-shock interactions and shock-boundaz3r layer interactions. Notably, the

flow structure near the injector is particularly detailed (barrel shock, roach disk, etc..).

The results agree reasonably well with the experimental schlieren, despite the uncertainty in turbulence levels.

25
The work completed in 1989shows the excellent capabilities of the code MOZART,

but also its limitations, namely in the area of turbulence modelling. For this reason

the development of k - e and multi scale capabilities will be an essentiM focal poim for

1990. This is especially important since, due to enormous ffmding, other centers such

as Lewis, have finally developed capabilities of the same type and same accuracy. It

is crucial that the lead in code development must be kept intact, otherwise Ames will

loose another area of dominance, and therefore area of funding. For that reason, we

intend to focus on new developments in several areas of flow physics.

26
References

[1] J.L. Caxnbier & G.P. Menees, 'A Multi-Temperature TVD Algorithm for Relaxing

Hypersonic Flows', AIAA 89-1971. Presented at the 9 *h AIAA Conf. on Comp. Fluid

Dynamics, Buffalo, New-York, 1989.

[2] J.M. Burgers, Flow equations for Composite Gases, Academic Press, 1969.

[3] S.I. Bragiinski, in Reviews of Plasma Physics, vol. 1, Consultants Bureau, 1965.

[4] S. Eberhardt & K. Brown, 'A Shock-Capturing Technique for Hypersonic, Chem.

Relaxing Flows', AIAA 86-0231.

[5] A. Haxten, J. Comp. Phys., vol 49 (1983), pp. 357-393.

[6] A. Kauffman, in Plasma Physics in Theory and Application, W.B. Kunkel ed., Mc

Graw-Hill, 1966.

[7] P.A. Gnoffo, R.N. Gupta & ,I.L. Shinn, 'Conservation Equations and Physical Models

for Hypersonic Air Flows in Thermal and Chemical Nonequilibrium', NASA TP-2867,

1989.

[8] L.M. Biberman & I.T. Yakubov, 'Approach to Ionization Equilibrium behind the

Front of a Shock Wave in an Atomic Gas', Soy. Phys. - Techn. Phys. (engl. transl.),

8, 1001 (1964).

27
Figure 1" Temperature profiles for 1-fluid model. Solid line includes electron heat

conduction, dashedline is without conduction.

25.0

20.0

15.0

10.0

5.0

0.0

with elec. l_c.

--w/o ele'c, b.c.___

I

0.0 I00.0

I

f

\

'w

s

s

s

s

s

/

s

#

i=

200.0 300.0

.1

400.0 500.0

x (microns)

28
Figure 2- Density profile for 1-fluid model. Solid (dashed) line is with (without)

conduction.

ICD

35.0

30.0

25.0

Z 20.0

15.0

10.0

with elec. h.c.

_-wZ/° elec. b.c.

5.0 I I I I

0.0 100.0 200.0 300.0 400.0 500.0

x (microns)

29
Figure 3: Electric field for 1-fluid model. Estimates usegrid-scale (dashed) or Debye scale (solid) in computation of gradients.

f.0

-f.0 I I

Debye length scale

.. _r_._. _nat_..s_ .....

0.0 I00.0 200.0

I I

300.0 400.0 500.0

x (microns)

3O

I
Figure 4: Density profiles for 2-fluid model, no artificial damping. Distance in microns.

_-_ 3.0

Z

2.0

1.0

Ni

Ne

0.0 I I I

I0.0 12.5 15.0 17.5 20.0

X

31
Figure 5: Electron velocity. Solid line without artificial damping. Dashed line obt

tained for u_i = 5 x u_i.

,,,-I 10.0

5.0

0.0

-5.0

-10.0

10.0

xl

x5

I

12.5

I

17.5 20.0

X

32
Figure 6: Electric field obtained for 2-fluid model.

daxnpedsolution (x5).

Dashed line is for artificially

2.0

0.0

-2.0

-4.0

xl

x5

-6.O I I

10.0 12.5 15.0 I7.5 20.0

X

33
Figure 7" Relative charge density, 2-fluid model. Naturally and artificially damped

solutions.

0.50

xl

x5

0.25

-0.25

)

-O.5O __________I___

10.0 12.5 15.0 17.5 20.0

X

34
Figure 8: Density profiles for damped (×5) solution. Smoothing of oscillations does

not affect the plasma dynamics.

3.0

2.0

Z

1.0

0.0

Ni

Ne

IO.O 20.0

X

35
Figure 9: T_, T,, c_, N2/N1 for strong ionizmng shock in Argon. Insert is copied from

ref. [8]. Ionization from ground state only, no precursor.

U

Ttr

- 0.15

(X

T/I

0.10

0.05

2

x (om)

1.0

0.00

0.0

36
Figure 10: Density contours (logl0 scale)for cold flow prior to ionization (t=0).

37
Figure 11: Density contours during injection, t=25 _tsec.

38
k_

J_

Figure 12: Density contours at t=50 #sec.

39
Figure 13: Density contours at t-75 #sec.

40
a4.

Figure 14: Density contours at t=100 #sec.

41
•" ._r

Figure 15: Density contours at t=125 #sec.

42
.D Figure 16: Density contours at t=150 #sec.

43
I\

.b

Figure 17: Density contours at t=175 #sec.

44
Figure 18: Density contours at t=200 #sec.

45
Figure 29: Density contours at t=225 #sec.

46
Figure 20: Density contours for steady-statecalculation.

47

ORiGiNAL PAGE IS

OF POOR QUALITY
Figure 21: Temperature contours for steady-state calculation.

48

oRIG_,I_,L PAGE IS

OF pOOR QUALITY
Figure 22: Mach number contours for steady-state calculation.

49

ORIGINAL PAGE iS

OF POOR QUALITY
Figure 23. Stagnation pressure (atm) steady-state.

5O

OffYG_NAL PAGE _S

OF POOR QL:A_.;Ty
Figure 24: Schlieren for hog flow, fuel injection.

OF POOR QUA L_T_
Figure 25: Schlieren of ballistic experiment H2-air at M=6.46.

decoupling shown.

Shock and flame

52

ORIGINAL PAGE !$

OF POOR QUALITY
Figure 26. Computational results of Temperature contours for same case. Position

of shock-flame decoupling almost identical.

53

" ",_'_- |S

OF PO_R QUALITY
Figure 27: Schlieren of ballistic experiment for oscillating (unstable) combustion.

54
APPENDIX

ISABE 11-5

WAVE COMBUSTORS FOR

TRANS-ATMOSPHERIC VEHICLES

Gene P. Menees

NASA-Ames Research Center, Moffett Field, CA

Henry G. Adelman and Jean-Luc Cambier

Eloret Institute, Palo Alto, CA

Jeffrey V. Bowles

NASA-Ames Research Center, Moffett Field, CA

9TH INTERNATIONAL SYMPOSIUM ON

AIRBREATHING ENGINES

September 4-8, 1989 / Athens, Greece

55
WAVE COMBUSTORS FOR TRANS=ATMOSPHERIC VEHXCLES

Gene P. Menees*

NASA-Ames Research Center, Moffett Field,California

Henry G. Adelman t

Jean-Luc Cambier:

Eloret Institute,Palo Alto, California

JeffreyV.Bowles§

NASA-Ames Research Center, Moffett Field,California

Abstract

The Wave Combustor is an airbreathing hypersonic

propulsion system which utilizesshock and detonation

waves to enhance fuel-airmixing and combustion in supersonic flow. In this concept, an oblique shock wave

in the combustor can act as a flameholder by increasing the pressure and temperature of the air-fuelmixture

and thereby decreasing the ignitiondelay.Ifthe oblique

shock is sufficientlystrong, then the combustion front

and the shock wave can couple into a detonation wave.

In this case, combustion occurs almost instantateously

in a thin zone behind the wave front. The resultis a

shorter, lighterengine compared to the scramjet. This

engine, which iscalledthe Oblique Detonation Wave Engine (ODWE), can then be utilizedto provide a smaller,

lightervehicle or to provide a higher payload capability

for a given vehicle weight. An analysisof the performance of a conceptual trans-atmospheric vehicle(TAV)

powered by an ODWE is given here.

Nomenclature

CT

/,p

L/D

LEO

Uh

ODWE

M

q

TAV

rl

¢

= thrust coefficient

= specificimpulse

= lift-to-dragratio

= Low Earth Orbit

= combustor length-to-heightratio

= Oblique Detonation Wave Engine

= mach Number

= dynamic pressure

= "l_an_Atmo6pheric Vehicle

= fueltotal temperature

= equivalence ratio

tR_,x:h

_Ra_arch

IR_eazv.h

Scientist, Associate Fellow, AIAA

Scientist, Member AIAA

Scientist, Member AIAA

Selentist, Member, AIAA

Introduction

Investigationsof wave enhanced supersonicmixing and

combustion have been pursued forseveraldecades. Detonation wave engines were reported in the 1940% I,and

studies of engines using moving and stationarydetonationwaves followed2-7. Enhancement offuelmixing and

combustion by shock waves has been investigatedmore

recentlys,9.

The experimental and analytical program at NASAAmes Research Center on wave enhanced mixing and

combustion has been reported previously 1°-12. Experimental mixing and combustion studies are being carried

out in a 20 MW arc heated wind tunnel. Analytical

studies include computer predictions of fuel injection,

mixing and combustion using a 2-D, viscous fluid dynamic simulation with finite rate chemistry. In addition, candidate vehicle designs are studied using design

codes for aerodynamics, structures, thermal protection

systems, propulsion and trajectories.

Propulsion Modeling

A propulsion system model has been constructed to provide ODWE and scramjet engine performance data for

the vehicle design and trajectorycodes. This propulsion model provides inlet-to-nozzledetails. The inlet

compression process is modeled with multiple oblique

shocks, including the bow shock. The inletoperates

at the bow shock-on-cowl-lipdesign point for allMach

numbers. This ismade possibleby moving the cowl forward and aft during flight.A constant area combustor

is also assumed.

For the scramjet case,the inletoperates in a fourshock

mode which givesgood performance over allflightconditions.However, for the ODWE case,the oblique detonation wave acts as a diffuser,so fewer inletshocks are
needed. In thismode, two inletshocksare sufficient.

The shock system forboth casesisshown inFigurei.

The viscousand pressuredrag forcesfrom nose-to-tail

on the underbody or enginesideof the vehicleare accountedforin the two engineperformanceparameters,

specificimpulseand thrustcoefficient. The thrustcoefficientisdefinedasthe thrustnomalizedby theproduct

of dynamic pressureand capturearea.Engine specific

impulseisobtainedby dividingthrustby thefuelweight

flowrate.The remainingvehicledragnot accountedfor

in the thrustcoefficient, which includesthe top,sides,

cowl bottom surfaceand controlsurfacesisassignedto

thevehicleaerodynamic characteristics.

For the low speed flightregime , below Mach 6, a hypotheticalairbreathingenginewith an averageeffective

specificimpulseof 1000 s and a thrust-to-weightratio

of 20 isused. Effectivespecificimpulseisobtainedby

dividingthe effectivethrust(thrustminus vehicledrag)

by the fuelweight flow rate. At high Mach numbers

and altitudes,where the air-breathingenginethrustis

diminished,a rocketengine with a thrust-to-weightratioof1.5providesthe finalinjectionintoorbit.

The efflciencyof thepropulsionsystem depends on variousfactorsincludingthe flightMach number, dynamic

pressure,forebody shape, fueltemperatureand equivalenceratio.These factorsarediscussedin the results

section.

Vehicle Modeling

Performance and sizing estimations were made using a

hypersonic vehicle synthesis code for trans-atmospheric

designs. This code was orginally developed at NASAAmes to model hypersoniccruiseaircraftIs and ithas

sincebeen modifiedto studytran_atmosphericdesigns.

Estimatescan be made of aerodynamic characteristics,

aero-thermalheating,propulsionsystem performance

and structural/subsystemweights.An automated vehicleclosurealgorithmiteratesthe trajectoryanalysis

to closethe designon both vehicleweightand volume.

The aero-thermal analysis consists of a series of performance estimates based on Mach number regime. For

subsonic,transonic,and low supersonicspeeds (below

the criticalMach number), a setofempiricalrelations

are used which are based on overallvehiclegeometric

characteristics.In the mid to high supersonicregime,

realgas tangentcone/wedge models are used. Newtonian flow isassumed to determinethe hypersonicpressure coefficient.Skin frictionand heat transfermodels

arebased on a referencenthalpymethod 14.

Structuralanalysisisbased on simplifiedbeam theory,

using the aero-inducedloadsto compute the longitudinalbending moment distribution.Longitudinaland

internalpressureloads are alsoaccountedfor in the

structuralstresses.Additionalcheckson buckling,localinstabilityand minimum gauge constraints,coupled

with non-optimum fractureare then used to compute

the requiredstructuralweight.The thermalprotection

systemissizedaccordingtothemaximum temperatures

and integratedheat loadsover the mission.The high

heatingloadson thenose and wing leadingedge willrequireactivecoolingsystems15.

The trajectoryanalysisisthen used to compute the requiredfuelfractionforthe vehicle.The equationsof

motion areintegratedoverthe specifiedMach numberaltitudeflightpath to determinetotalfuelrequirements

and missionduration.Vehiclegrossweightand volume

arethen iteratedtofindthe closurepoint,thatiswhere

the requiredfuelfractionand the availablefuelfraction

areequal.

To sizethe vehicles,a missionwas selectedwhich carrieda payloadof 15,000pounds intoa Low Earth Orbit(LEO) of120 nauticalmilesaltitude.A horizontal

takeoffin the easterlydirectionfrom Kennedy Space

Centerwas assumed,with an on-stationdurationofsix

hours. Two ascenttrajectorieswere studied,with dynamic pressuresof1000 and 2000 pounds persquarefoot

(psf).The flightpath was constrainedto give100 psi

duct pressureatlowersupersonicMach numbers and a

maximum mean surfaceequilibriumradiationtemperatureof 2000 F (1367 K) forhigh Mach numbers. The

speed atwhich the airbreathingenginethrustwas augmented by a rocketwas optimizedtominimizethegross

takeoffweight. A descenttrajectorywas flown near

peak L/D to maximize the descentcross-rangecapability.Fuel reservesof2% ofmissionfuelwere assumed

forthe landingmaneuver.

Results

General Vehicle Design

The generalvehicleconfiguration,shown inFigure2,is

a liftingbody with aftmounted horizontaland vertical

tails.Planformshape isa power-lawconfigurationwith

a fore-bodylowersurfaceangleof5.5degreesand a nozzlechordangleof9.5degrees.The cross-sectional shape

consistsofupper and lowernear elliptical sectionswith

_2
major- to-minor axis ratios of 4 for the upper surface and

2 for the lower surface. The vehicle break-point (transition from forebody to aftbody) isat 65% ofthe body

lengthand the fatnessratio(maximum crosssectional

area toplanform area)is9.7%. Engine width is67% of

the maximum width which providesadequateroom for

themain landinggear.The totalpropulsionsystemconsistsoftwo airbreathingengines,one forMarianumbers

below 6,and a scramjetor an ODWE fortheremaining

part ofthe Right. In addition,a rocketengineisused

in conjuctionwith the air-breathingengineforthehigh

altitude,high Mach number portionof the trajectory.

Liquidhydrogen isthe fuelforallengines.

Aero-thermodynamic characteristics ofthe vehiclewere

computed usingthe synthesiscode methods. The structuraldesignincorporateda cool integraltank concept

where the tank carriesboth the nero-inducedbending

loadsas well as the internaltank pressureloads.Sufficienthermal insulationisused tomaintain the tank

materialtemperaturelimitsand minimizethehydrogen

boil-off.With a designconditionof2.0g'sat Mach 6,

the unit structuralweightwas somewhat lessthan 4.0

Ib/ft2.

General Engine Perfomance

The resultsofthe engineperformancecalculationsshow

that specificimpulse and thrustcoefficientsdepend on

dynamic pressure,combustion efficiency,fueltemperature and equivalenceratio.Certaintrendscan be observed.As shown inFigure 3,itisevidentthat higher

heat recyclingfrom the engine leadsto higherinjected

fueltemperaturesand largervaluesofspecificimpulse

and thrustcoefficient.We assume that the fuelisinjectedat a constantMach number of2.5.As more heat

isadded to increasethe stagnationtemperature,significantmomentum can be gained from the fuelinjection.

However, fueltemperatureislimitedby the amount of

heat which can be absorbed from the structureand by

the temperature limitsof the materialsused to store

and transportthe fuel.Illthisstudy,we willassume

that 90% ofthe heat loadshave been absorbedby the

fuel.The fuelisthen heated to a limitingtemperature

of 1100 K (1520 F),which isrepresentativeofthe currentmaterials available for fuel storage and transport.

Ifthistemperature limitisexceeded,then an amount

of fuelin excessof stoichiometricmust be used. The

resultingequivalenceratioversusMach number scheduleforthescramjetisshown inFigure4 forvariousfuel

temperaturelimits.

Sincethe ODWE combustor isshorter,a stoichiometric

mixturecan be maintainedto a Mach number of 17.5

compared to 14 forthe scramjet,fora fueltemperature

of 1100 K. While heat recycleincreasesengineperformance forstoichiometricmixtures,theeffectofusingexcessfueltomaintaina specifiedtemperaturelimitmay

increasethe thrustcoefficientsbut willlowerthe specificimpulsesas shown in Figure5. Itisclearthatthe

coolingrequirementseriouslyaffectthe performanceof

the engineathigh Mach numbers.

Flighttrajectorieswere assumed forconstantdynamic

pressuresofI000 and 2000 psi"which bracketthe range

expected for airbreathingvehicles. Higher dynamic

pressures,above 2000 psi',provideslightlygreaterapechicimpulsesand thrustcoefficients, but may impose

higherheatingloadson the vehiclewhich couldincrease

thermalprotectionsystem weights,or exceedthe 2000

F temperaturelimit.

Engine performanceisalso influencedby combustion

and mixing efficiencies.Combustion efficiencyislimitedby the amount of fuelwhich can be convertedto

waterattheconditionsinthecombustor.This isdetermined by the hydrogen-oxygen-water equilibriumconstant.Combustion efficiencies atstoichiometricair-fuel

ratiosrange from 93.5% at Mach 8 to 86.8% at Mach

20. Higherequivalenceratiosprovideexcessfuelwhich

lowerscombustiontemperaturesand raisescombustion

efficiencies. However, whilespecificimpulsevaluesdecrease,thrustcoefficientsincreasedue to the factthat

thereismomentum recoveredfrom the hot excessfuel.

Combustion efficiencycan be increasedifthereisrecombinationofthedissociatedproductsinthenozzle.Since

the amount ofrecombinationwas not a subjectofthis

study,we have assumed that itissubstantialand we

have assignedan overallcombustionefficiencyof100%

to thepropulsionsystem.

The extentof mixing mad combustionwilldepend on

theinjectordesignmad the combustor length.We have

selecteda combustor lengthto heightratio(i/h)of 10

inthisstudy forthe sczamjetand an [/hof 1.5forthe

ODWE. Due to the lackof extensivemixing and combustiondata,mixing and combustion efficiencies were

assumed to be 100% forboth enginesatallequivalence

ratios.

Scrax_et Engine Performance

The calculatedperformanceof the scrsmjetengine is

shown in Figure 6 as a functionof Mach number for

a dynamic pressureof2000 psfand an equivalenceratioschedulewhichmaintainsthefueltemperaturebelow
1100 K. It can be seen that the specific impulse begins

to drop at Mach 14 due to the rise in equivalence ratios necessary to maintain the 1100 K fuel temperature

limit.

ODWE Performance

The ODWE performance was also calculated for dynamic pressures of 1000 psi" and 2000 psf. In Figure

6 we compare the performance of both the scrsmjet and

ODWE for the q-2000 psi" case. It appears that the

ODWE has a better performance than the scramjet at

high Mach numbers, but has lower specific impulse below Mach 15. The reduced performance at low Mach

numbers is due to the steep wave angle of an oblique

Chapman-Jouguet (CJ) detonation, and therefore to

higher shock losses. The wave angle can be reduced

if either the Mach number is increased or the ChapmanJouguet Mach number is decreased (i.e. the static temperature prior to the detonation wave is increased or _b

is decreased). Therefore, the ODWE favors operation

at high Mach numbers.

The ODWE alsotakesadvantage ofa shortercombustor which requireslesscoolingand lessexcessfuelat

higherMach numbers than the scramjet.Itcan be seen

in Figurefithat the knee in the specificimpulsecurve,

which indicatesthestartofthe excessfuelingschedule,

beginsata higherMach number fortheODWE than for

the scrsmjet.Sincetheproblems ofmixingand ignition

delayimpose a long combustor forhigh Mach numbers,

itisclearthat increasingthe combustor lengthforces

the performanceofthe scrarnjetto drop atlowerMach

numbers, when the fuelmust be injectedin excessof

stoichiometric.

For the ODWE, the benefits of a shortercombustion

chamber, which resultsin a shorter,lighterenginewill

alsobe evidentin the vehiclesizeand weight calculationswhich are discussedlater.

Scramjet Vehicle Performance

A scrsmjetpowered vehiclewas modeled usingthepredictedengine performance data. The vehicleweight

breakdowns are shown in Table 1 forthe trajectoryof

constantdynamic pressureq-2000 psi'.Sincethescramjetisvery inefficientbelow Mach 6, a hypotheticalenginesystem with an averageeffectivespecificimpulseof

1000 s was used to propel the vehiclefrom horizontal

takeoffto Mach 6. Since the effectivespecificimpulse

takesinto account the aero-dynsmic drag on allsurfaces(notjust the inlet,combustor and nozzle),itis

significantly lessthan theenginespecificimpure. Aerodynamic heatingconsiderationsrequiredthat the dynamic pressureofthe flightpath,as shown in figure7,

beginsto drop below thespecifiedvalueof2000 psf at

Mach 17 to about 250 psi"at Mach 22. This low dynamic pressurerequirementathigh Mach numbers necessitatesrocketpower angrnentationwhich beginsat

Mach 18.The amount ofthrustprovidedby the rocket

islargerthan thethrustproducedby thescramjet,and

therocketthrustfractioncontinuestoincreaseuntilorbitalspeedsarereached.

The vehiclewhich fliesa 2000 psf trajectoryweighs

460,512pounds and carriesa 15,000payload intoorbit.The scrsmjetengine,low speed engineand rocket

motors comprise8.6% ofthe takeoff"weight.For comparativepurposes,a vehiclewhich fliesa 1000 psftrajectorywas alsostudied.ThisTAV isheavierat623,000

pounds. The main reasonfortheincreasedweightisthe

lowermass captureper unitareaofinlet,whichrequires

a larger,heavierengineand associatedstructure.Also,

the lowerthrust-to-weightratioresultsina longerflight

time toorbitwhich consumes a greateramount offuel.

ODWE Vehicle Performance

The hypersonicvehicleusing the ODWE has somewhat differentweight characteristics asshown in Table

2. Sincethe ODWE offerssuperiorperformanceabove

Mach 15,thepointofrocketturn-onisdelayedto Mach

19. The ODWE can operateat higherMach numbers

than the scramjet,and continuesto providea higher

fractionofairbreathingthrusttoorbitalspeeds.Therefore,lessrocketthrustisneeded and a lowermass fractionof LOX isconsumed, 12.5% versus15.9% forthe

scramjet. This representsa weightsavingsof 22,000

compared tothescramjet.Inaddition,theshortercornbustorlengthprovidedby the ODWE allowsa shorter,

lighterengine which savesabout 5,000pounds. The

ODWE represents3.7% ofthe grossweight,compared

to 4.4% for the baselinescramjetengine. While the

fuelweightfractionishigherforthe ODWE, the actual

fuelweightis14,000pounds lower.As a resultof all

thesefactors,the ODWE configurationweighs409,500

pounds, some 51,000pounds lessthan the scrsmjetvehicle(forq=2000 psf),and carriesthesame payloadof

15,000pounds to orbit.Note that the payloadweight

fractionisincreasedfrom 3.3% ofthetakeoffweightfor

the scramjetto 3.7% fortheODWE.

Conclusions

The ODWE powered hypersonicvehicleshows different

_4
performance characteristics than the scramjet powered

vehicle:

. The ODWE trades a better engine performance

above Mach 15 for a lower performance below Mach

15. This trade-off still favors the ODWE overall.

. The better performance of the ODWE at higher

Mach numbers allows a delay of the rocket augmentation mode, and results in a lower mass of LOX

required for orbit insertion.

3. The smaller ODWE allows another direct weight

reduction of __ 5,000 Ibs.

o The overall higher performance of the ODWE resalts in a weight savings of 51,000 pounds and a

higher payload weight fraction of approximately

12%.

Since the scramjet has better performance below Mach

15, and the ODWE above Mach 15, a combination of

these two engines may be ideal. This hybrid engine

would use a two-shock diffuser for the whole Mach range.

At low Mach numbers, the mixing length and ignition

requirements are less severe, and a relatively short combustor can be used in a scramjet mode. At higher Mach

numbers, the diffusing shocks would move aft into the

combustor. The engine would operate in the oblique

detonation mode in the aft section of the combustor.

Therefore, cooling is required only for a fraction of the

combustor, and the drop in performance due to cooling requirements would still occur only at very high

Mach numbers. The design of such a hybrid engine

would require more sophisticated, two-dimensional analysis. Work in that direction is progressing.

Aknowledgement

The authors wish to thank Dr. D.W. Bogdanoff for proriding an initial version of a one-dimensional analysis

code forscramjetengineperformance,which was subsequentlymodifiedforour study.

P,_'e]L'P.._ ce s

I.Roy M., Comptes Rendus a l'Academy des Sciences,

Feb.,1946.

2.SargentW,M. and Gross,R.A.,"A DetonationWave

HypersonicRamjet", AFOSR TN 59-589,1959.

3. Townend L.H., "Detonation Ramjets for HypersonicAircraft",RAE TechnicalReport 70218,November 1970.

4. MorrisonR.B.,"Evaluationofthe ObliqueDetonationWave HypersonicRamjet", NASA ContractorReport 145358,January 1978.

5.MorrisonR.B.,"ObliqueDetonationRamjet",NASA

ContractorReport 159192,January 1980.

6. Cambier J.L.and Adelman, H.G.,"PreliminaryNumericalSimulationsof a Pulsed DetonationWave Engine',AIAA paper 88-2960,July 1988.

7. NicholsJ.A. et. al.,"IntermittantDetonationas

a Thrust-ProducingMechanism", JetPropulsion,May,

1957,pp. 534-541.

8. Kumar A. et. al.,"A Mixing Augmentation Technique for HypervelocityScramjets',AIAA paper 87-

1882.

9. Marble F.E.,Hendricks,G.J. and Zukowski,E.E.,"

Progress Toward Shock Enhancement of Supersonic

Processes",AIAA paper 87-1880,June,1987.

10. Cambier J.L., Adelman, H.G. and Menees, G.P.,

"Numerical Simulations of Oblique Detonations in Supersonic Combustion Chambers", AIAA Journal of

Propulsion and Power, vol. 5, No. 4, July-August 1989,

pp. 482-491.

11. Adelman H.G. , Cambier, J.L. , Menees, G.P. and

Balboni, J.A., "Analytical and Experimental Validation of the Oblique detonation Wave Engine Concept",

AIAA paper 88-0097, January 1988.

12. Cambier J.L.,Adelman, H.G. and Menees, G.P.,"

Numerical Simulationsofan ObliqueDetonationWave

Engine",AIAA paper 88-0063,January 1988.

13.GregoryT.J.et.al.,"HypersonicTransportPreliminaryPerformanceEstimatesforan All-BodyConfiguration",AIAA paper 70-1224,October 1970.

14. Eckert,E.R.G.,"Survey on Heat Transferat High

Speeds", AeronauticalResearch Laboratories,UniversityofMinnesota,ARL 189,December, 1961.

15. Tauber M.E. and Adelman, H.G., "Thermal Environments of Transatmospheric Vehicles", AIAA Journal

of Aircraft, vol. 25, No. 4, pp. 355-363, April 1988.

_5
.e

Component

Empty Weight

Structure

Propulsion Systems

Fixed Equipment

LH2

LOX

Payload

Weight fraction

28.0%

18.4%

8.6%

1.1%

51.8%

15.9%

3.3%

Table h Scramjet vehicle data for fixed payload of

15,000 lbs. Fractions are relative to total take-off.weight

of 460,512 lbs for q=2000 pd trajectory.

Component Weight fraction

Empty Weight

Structure

Propulsion Systems

Fixed Equipment

LH_

LOX

Payload

27.9%

18.8%

8.0%

1.1%

54.8%

12.5%

3.7%

Table 2: ODWE vehicle data for fixed payload of 15,000

lbs. Fractions are relative to total take-off weight of

409,500 lbs for q=2000 psf trajectory.

SCRAM JET

SHOCK_

INLET -,._ = = NOZZLE

t

COMBUSTOR

ODV_E

SHOCK SYSTEM DETONATION WAVE

I: Schematic of shock structure for scrsmjet

_gine and ODWE, including detonation wave.

_6

Figure 2: SchematicsofgenericTAV conceptused in

thisstudy.

3000.0

2500.0

2000.0

Isp,S

18oo.o

looo.o

600.0

'"" ".:,

'.._

%°°'°°'°''''" 100_o

-....

".o...

"-oo..°

0.0 I I I I 1

5.0 7.6 10.0 12.5 15.0 W.5 20.0

Figure 3: SpecificimpulseversusMach number for

scramjetengine(q=2000 psi',_b= I).Casesshown are

for0%, 50% and 100% ofthe heat loadsabsorbed into

thefuel.
L|

1.e

L4

12

1.0

SCI1AM / T! = I100K

ODWE /

//T!=I3OOK

/_ Ti = II00K

......,...,....."'°*"::°"

OoB ! I

I0.0 18.0 20.0 3,6.0

M

l_gm-e 4: Equ/valence r_tio versus M_ number l'or

scr_njet and ODWE engines at q-2000 psi'. ODWE

results are shown for a fuel temperature limit of 1100

K, wh;le scramjet results _re shown for a temperature

range from 1100 to 2000 K (1520 to 3140 F).

!

2000.0

Isp,S

lS00.0

1000.0

0.0

e.0 8.0 10.0 12.0 14.0 18.0 18.0 20.0 22.0

M

Figure 6: Comparison of scramjet _nd ODWE performance ch_scteristic_. Shown axe I,_ and CT profiles for

q=2000 psi', 90% of heat loa& carried by fuel _-d II00

K fuel temperature limit.

1.0

0.8

CT

0.8

0.4

0.2

2800.0

2OOO.O

Isp,S

1800.0

1000.0

TI = 2000K

.--:-:-::-:-:

T! = 1600K

2"! = 1300K

7"I ,- ll00K

_._ -,: ........

lO0.O I , .. I . I I l

I1.0 10.0 12.0 14.0 le.0 1B.0 20.0

Figure 5: Specific impulse versus Msch number for

scrsmjet engine at q=2000 psf. P_tsaze for fuel temperature limits from 1100 to 2000 K (1520 to 3140 F).

200.0

]80.0

160.0

_ _4.0.0

X

•- 120.0

.--t

.<

100.0

00.0

60.0

I I I I I I ,I

8.0 10.0 12.0 14.0 18.0 18.0 20.0

M

Z2.0

Figure _': Comparison of flight trsjectories at q=2000

pd for ODWE and scrsmjet vehicles.
Paper 26

Analytical and Experimental Investigations of the

Oblique Detonation Wave Engine Concept

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

H.G. Adelman, Eloret Institute, Palo Alto, CA

J.L. Cambier, Eloret Institute, Palo Alto, CA

AGARD PEP 75th Symposium

Hypersonic Combined Cycle Propulsion

Madrid, Spain, May 28-June 1, 1990
ANALYTICAL AND EXPERIMENTAL INVESTIGATIONS

OF THE OBLIQUE DETONATION WAVE ENGINE CONCEPT

Gene P. Menees*

NASA-Ames Research Center, Moffett Field, CA

Henry G. Adelman _

Eloret Institute, Palo Alto, CA

Jean-Luc Cambier t

Eloret Institute, Palo Alto, CA

ABSTRACT

Wave Combustors, which include the Oblique Detonation Wave Engine (ODWE), are attractive propulsion concepts for hypersonic flight. These engines utilize oblique shock or detonation waves to rapidly mix, ignite and combust the air-fuel mixture

in thin zones in the combustion chamber. Benefits of these combustion systems include shorter and lighter engines which will

require less cooling and can provide thrust at higher Mach numbers than conventional scramjets. The Wave Combustor's ability

to operate at lower combustor inlet pressures may allow the vehicle to operate at lower dynamic pressures which could lessen

the heating loads on the airframe.

The research program at NASA-Ames includes analytical studies of the ODWE combustor using Computional Fluid Dynamics

(CFD) codes which fully couple finite rate chemistry with fluid dynamics. In addition, experimental proof-of-concept studies

are being carried out in an arc heated hypersonic wind tunnel. Several fuel injection designs were studied analytically and

experimentally. In-stream strut fuel injectors were chosen to provide good mixing with minimal stagnation pressure losses.

Measurements of flow field properties behind the oblique wave are compared to analytical predictions.

NOMENCLATURE

Ct = Thrust coefficient

Isp = Specific impulse

M -- Mach number

ODWE = Oblique Detonation Wave Engine

p = pressure

q -- dynamic pressure

R_ -- Reynolds Number

T = Temperature

TAV --- Trans-atmospheric Vehicle

V = velocity

X -- lateral distance from centerline of strut

Y = vertical distance from nozzle floor

Z = axial distance fron trailing edge of strut

¢ = equivalence ratio

Subscripts

t = total

oo = free stream value

INTRODUCTION

The use of detonation waves to initiate and enhance combustion has been proposed since the 1940's 1. Some analyses have

been made using both normal and oblique waves 2'3. Normal waves are hard to stabilize and they produce higher stagnation

*Research Scientist, Associate Fellow AIAA

?Research Scientist, Member AIAA

Research Scientist. Member AIAA
Q

is evident that higher heat recycling from the engine leads to higher injected fuel temperatures and larger values of specific

impulse and thrust coefficient. We assume that the fuel is injected at a constant Much number of 2.5. As more heat is added to

increase the stagnation temperature, significant momentum can be gained from the fuel injection. However, fuel temperature is

limited by the amount of heat which can be absorbed from the structure and by the temperature limits of the materials used to

store and transport the fuel. In this study, we will assume that 90% of the heat loads have been absorbed by the fuel. The fuel

is then heated to a limiting temperature of 1100 K (1520 F), which is representative of the current materials available for fuel

storage and transport. If this temperature limit is exceeded, then an amount of fuel in excess of stoichiometric must be used.

The resulting equivalence ratio versus Much number schedule for the scramjet is shown in Fig. 3 for various fuel temperature

limits.

Since the ODWE combustor is shorter, a stoichiometric mixture can be maintained to a Much number of 17.5 compared to 14

for the scramjet, for a fuel temperature of 1100 K. While heat recycle increases engine performance for stoichiometric mixtures,

the effect of using excess fuel to maintain a specified temperature limit may increase the thrust coefficients but will lower the

specific impulses as shown in Fig. 4. It is clear that the cooling requirements seriously affect the performance of the engine at

high Much numbers.

Scram jet Engine Performance

The calculated performance of the scramjet engine is shown in Fig. 4 as a function of Much number for a dynamic pressure of

2000 psf and an equivalence ratio schedule which maintains the fuel temperature below 1100 K. It can be seen that the specific

impulse begins to drop at Much 14 due to the rise in equivalence ratios necessary to maintain the 1100 K fuel temperature limit.

ODWE Performance

The ODWE performance was also calculated for dynamic pressures of 1000 psf and 2000 psf. In Fig. 4 we compare the performance of both the scramjet and ODWE for the q=2000 psf case. It appears that the ODWE has better performance than the

scramjet at high Much numbers, but has lower specific impulse below Much 15. The reduced performance at low Much numbers

is due to the steep wave angle of an oblique Chapman-Jouguet (C J) detonation, and therefore to higher shock losses. The wave

angle can be reduced if either the Much number is increased or the Chapman-Jouguet Much number is decreased (i.e. the static

temperature prior to the detonation wave is increased or ¢ is decreased). Therefore, the ODWE favors operation at high Much

numbers.

The ODWE also takes advantage of a shorter combustor which requires less cooling and less excess fuel at higher Much numbers

than the scramjet. It can be seen in Fig. 4 that the knee in the specific impulse curve, which indicates the start of the excess

fueling schedule, begins at a higher Much number for the ODWE than for the scramjet. Since the problems of mixing and

ignition delay impose a long combustor for high Much numbers, it is clear that increasing the combustor length causes the

performance of the scramjet to drop at lower Much numbers, when fuel must be injected in excess of stoichiometric.

For the ODWE, the benefits of a shorter combustion chamber, which results in a shorter, lighter engine will also be evident in

the vehicle size and weight calculations which are discussed later.

Scram jet Vehicle Performance

A scramjet powered vehicle was modeled using the predicted engine performance data for the trajectory of constant dynamic

pressure q=2000 psf. Since the scramjet is very inefficient below Much 6, a hypothetical engine system with an average effective

specific impulse of 1000 seconds was used to propel the vehicle from horizontal takeoff to Much 6. Aerodynamic heating considerations required that the dynamic pressure of the flightpath begins to drop below the specified value of 2000 psf at Much

17 to about 250 psf at Much 22. This low dynamic pressure requirement at high Much numbers necessitates rocket power

augmentation which begins at Much 18. The amount of thrust provided by the rocket is larger than the thrust produced by the

scramjet, and the rocket thrust fraction continues to increase until orbital speeds are reached.

The scramjet powered vehicle which flies a 2000 psf trajectory weighs 460,512 pounds and carries a 15,000 pound payload into

orbit. The scramjet engine, low speed engine and rocket motors comprise 8.6% of the takeoff weight. For comparative purposes,

a vehicle which flies a 1000 psf trajectory was also studied. This TAV is heavier at 623,000 pounds. The main reason for the

increased weight is the lower mass capture per unit area of inlet, which requires a larger, heavier engine and associated structure.

Also, the lower thrust-to-weight ratio results in a longer flight time to orbit which consumes a greater amount of fuel.

ODWE Vehicle Performance

The hypersonic vehicle using the ODWE has somewhat different weight characteristics. Since the ODWE offers superior performance above Much 15, the point of rocket turn-on is delayed to Much 19. The ODWE can operate at higher Much numbers than

the scramjet, and continues to provide a higher fraction of airbreathing thrust to orbital speeds. Therefore, less rocket thrust is
andtemperatures areraisedbyfactorsof 2.4and1.3respectively. These higher pressures and temperatures will shorten the

ignition distance behind the oblique wave. The pressure field due to combustion should influence the oblique shock wave and

create a detonation. In reality, the hydrogen injection will create shock waves which will cause higher stagnation losses than

predicted by this analysis along with higher static pressures and temperatures.

While the increased pressures will shorten ignition delays behind the oblique wave, raising the temperatures may create preignition problems prior to the wave. One consideration for injector design and location is premature ignition of the fuel. A

study was made of the effects of introducing fuel at various locations inside the wind tunnel nozzle. The results indicated that

fuel must be introduced at a location in the nozzle somewhere downstream of the point where the area ratio is 10. However,

extensive modifications would be required to inject fuel in the existing nozzle. This result led to the study of strut type injectors

which would be located at the exit of the nozzle.

Injection Simulations

In order to verify some of the simplified analyses of fuel injection and combustion behavior, a more sophisticated computer

simulation was employed. This code is described in detail elsewhere 13'14. Many different simulations were performed to validate

the fluid dynamic and chemical kinetics portions of this code. Once the code was validated, it was used to guide the experimental

program. The first simulation consisted of wall injection through an orifice normal to the air stream. This configuration, which

could model injection from a flat plate resulted in an oblique shock ahead of the injected fuel. Unfortunately, the penetration

of the fuel jet was poor. A similar result has been observed experimentally, where fuel jet penetrations appeared to peak at a

value of about five times the orifice diameter 15.

In an effort to improve the fuel penetration, a projection or finger was added downstream of the fuel orifice. In this case, fuel

was forced over the projection further into the air stream. However, a normal shock was also formed upstream of the injector

which reduced the flow velocities to subsonic values. Since a detonation can only exist in supersonic flows, this geometry would

preclude the establishment of an oblique detonation wave downstream of the injector. A third configuration was examined

where the finger was modified to include a ramp on the upstream side. Fuel penetration remained good and the fuel injection

shock became oblique. Most of the flow remained supersonic except for a small recirculation zone behind the leward side of

the projection. While this configuration appeared to provide improved penetration and supersonic flow downstream of the

injection point, this design would have to be installed on a wall where the high temperatures in the boundary layer region could

prematurely ignite the fuel. In addition, the boundary layer might decrease the fuel penetration. For these reasons, it was

decided to examine strut type fuel injectors located outside the nozzle. Here fuel could be injected by multiple struts into the

core flow region where viscous effects are reduced.

In order provide a better model of the detonation process, a 2-dimensional combustion code was also developed. This code

uses the same Total Variation Diminishing (TVD) algorithm as the injection model to capture strong shocks without smearing

or oscillations. Temperature oscillations could incorrectly predict premature ignition and invalidate the detonation conditions.

Finite rate chemistry is incorporated in order to model the heat release of the detonation process. The chemistry is fully coupled

to the fluid dynamics so that heat release will couple to the shock front and show the correct rotation of the detonation wave.

The fluid dynamics and chemical kinetics parts of this code were verified using many existing data sets and conditions 13.

Simulation of ODWE Experiment

The focus of this work was the simulation of the flow field in the strut region. This was done first with an Euler (inviscid)

computation to obtain the position of the reflected shocks. The computations were done for free stream Mach numbers of 4.5

and 5.4. Two values of the vertical separation between the struts were studied (0.67 inches and 0.75 inches). It was apparent

from the results that multiple shock interactions occured between the struts, as well as shock impingement on the flat surfaces

of the struts. It was clear that in the case of high stagnation enthalpy, extreme care should be taken in avoiding locally high

temperatures. In order to model the strut injection and mixing, a series of computations were made with greater refinements,

which included blunting the leading edge of the struts and providing a high grid density. The full Navier-Stokes equations were

solved for an assumed laminar case. The conditions were Moo = 5.4, Too = 42.2K, poo - 0.0128 atm, Reoo "-' 2x105 per inch.

The total length of the strut is approximately 5 inches and transition to turbulence should occur somewhere at the end of the

strut. However, because of the leading edge compressive ramp (7 ° ) and the porous transpiration plate in the first half of the flat

strut section, transition could be expected sooner. There is, however, no definite way to predict the transition with precision

and there were no measurements to determine the properties of the boundary layer on the strut. In addition, when fuel injection

takes place, the flow obviously becomes turbulent and the algebraic (Baldwin-Lomax) model is then unable to model the correct

physics. Ideally a 2-equation model should be used at this point. The development and validation of such a model which uses

the turbulent kinetic energy equation is one of the high priority development areas.

An example of the injection patterns for two struts is shown in Fig. 5. This design indicated hot spots on the center strut which

caused the fuel to ignite immediately after injection. In fact, it was necessary to inject nitrogen at the tip of the strut to cool the

mixture and decrease the oxygen content of the boundary layer 14 . The strut design is discussed in more detail in the next section.
Test Body

The oblique waves will be created by a water cooled wedge located approximately one foot downstream of the struts in the test

section. Optical access is provided by 12 inch windows on either side of the test section and a schlieren system will provide

photographic records of the wave angle with and without fuel. Pressure and temperature transducers on the wedge will be used

to assess the state of combustion behind the oblique wave.

Mixing Studies

A series of mixing studies were carried out in the hypersonic wind tunnel. The first set of tests were made with two injection

struts spaced from 0.5 in to 0.75 inches apart, the extent of fuel mixing was measured by an on-line mass spectrometer. Gas

samples were obtained by a probe which was mounted on a traversing table that allowed motion in all three dimensions. Some

results of the fuel-air determinations are shown in Fig. 12 for two locations, 0.5 inches and 12 inches behind the strut trailing

edge. While mixing is poor at 0.5 inches, it is significantly improved at 12 inches. The further location was representative of the

proposed position of the wedge for the detonation tests. Note that the fuel distribution at 0.5 inches resembles the simulated

case of Fig. 5 with relatively unmixed jets. The experiment verified the concerns about thermal fMlure at the areas of shock

impingement on the struts. Further mixing tests with multiple struts were carried out only with cold flow to avoid overheating

while hot flow tests were run with a single strut.

Oblique Detonation Wave Studies

After the mixing studies were completed, the wedge test body was installed in the wind tunnel. While the original plan was to

locate the wedge 12 inches downstream of the struts, this required the fabrication of new doors for the wind tunnel test section

to place the windows in the proper location for viewing. Unfortunately, there was insufficient time to fabricate these doors, so

the wedge was located in the field of view with the struts. Only 1.0 inches separated the trailing edge of the strut and the front

edge of the strut. While this placed the strut in a relatively unmixed region, it was thought that combustion could occur behind

the oblique bow shock of the wedge.

Tests were run with both helium and hydrogen injection to determine the effects on the wedge shock. The effects of fuel

injection can be seen by comparing Figs. 13 and 14 for the cases of no injection and injection, respectively. It was observed

that the injection of either combustible or inert gases caused a similar displacement of the bow shock. This was due to the low

molecular weights and high speeds of sounds of hydrogen and helium. The effect is to lower tl_e Mach number of the flow and

cause the oblique wave to be more normal. During one test run, an increase in pressure was observed on the wedge with hydrogen injection, indicating combustion. However, in the limited time remaining for the tests, this phenomenon was not repeated.

CONCLUDING REMARKS

An experimental and analytical program has been undertaken to study the characteristics of stable oblique detonation waves in

a NASA-Ames arc-jet wind tunnel. The analytical models have been used extensively to aid in the experimental design and to

ensure a successful experiment.

The existance of stable oblique detonation waves has been predicted previously for premixed hydrogen-air in supersonic flows.

However, complete mixing of the fuel and air streams is not possible within reasonable distances in supersonic combustors.

Therefore, it is necessary to introduce the fuel in a manner that provides good mixing in short distances with minimal losses.

Several injector designs were examined analytically and a strut type was chosen for its ability to introduce the fuel in the nozzle

free jet. The mixing characteristics and the effects of incomplete mixing on the detonation wave are still being studied.

The simulation of the strut flow field in the ODWE experiment provided great detail on the shock-shock interactions and

shock-boundary layer interactions. Notably, the flow structure near the injector is particularly detailed (shock, Mach disk). The

results agree reasonably well with the experimental schlieren records.

A mission analysis study compared the performance of vehicles powered by a scramjet or an ODWE. The results showed that

the ODWE had better overall performance than the scramjet. The increased performance allowed the ODWE powered vehicle

to weigh less than the scramjet powered vehicle for the same payload weight.

REFERENCES

1 Roy, M., Comptes rendus a l'Academy des Sciences, February, 1946.
Fig. 1. Schematic of generic hypersonic

trans-atmospheric vehicle used in mission

analysis study.

3000.0

2500.0

2000.0

Isp,S

1500.0

1000.0

500.0

0.0

" ....'_

100%

..... "--.. 50%

0%................ "....

i

i

I

I I I I J

5.0 7.5 10.0 12.5 15.0 17.5 20.0

Fig. 2. Specific impulse versus Mach number for

scramjet engine (q=2000 psf, ¢=1). Cases

shown are for 0%, 50% and 100% of the heat

load absorbed into the fuel.

1.8

1.5

1.4

1.2

1.0

0.8

SCRAM / T, = 1100K

............... ODWE /

/T/=1300K

/_ 2",= nook

...,'""""""'""'i

I I

I0.0 15.0 20.0 25.0

Fig. 3. Equivalence ratio versus Mach number for

scramjet and ODWE engines at q=2000 psf. ODWE

results are shown for a fuel temperature limit of

1100 K while scramjet results are shown for a range

from 1100 to 2000 K (1520 to 3140 F).

3000.0

2600.0

2000.0

Isp,S

1500.0

1000.0

500.0

0.0 I

5.0

I I I I I I

1.2

1.0

0.8

CT

0.6

0.4

0.2

8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0

M

Fig. 4. Comparison of scramjet and ODWE performance

characteristics. Shown are Isp and CT profiles

for q=2000 psf, 90% of heat loads carried by fuel

and 1100 K fuel temperature limit.
Q

Fig. 7. Math number contours for non-reacting

stoichiometric air-fuel mixture flowing over

a wedge at Mach 4.2.

Fig. 8. Mach number contours for reacting

stoichiometric air-fuel mixture flowing over

wedge at Mach 4.2. The rotation of the wave

with combustion indicates a detonation.

Fig. 9. Mach number contours for relatively

unmixed fuel jet flowing over wedge.
Fig. 13. Schlieren photograph of a shock wave created by a wedge in Mach 4.5 flow.

A single strut fuel injector is positioned slightly below the wedge centerline. No

fuel is injected in this case.

Fig.14. Schlieren photograph of an oblique wave created by a wedge in Mach 4.5 flow.

Fuel is injected from a single strut. Note the displacement of the lower

portion of the wave compared to the previous figure.

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