14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

Ramjet and Scramjet Engine Cycle Analysis for a GenericHypersonic Vehicle

Shahriar Keshmiri *, Richard Colgren §, Saeed Farokhi£

The University of KansasDepartment of Aerospace Engineering

Maj Mirmirani ¥

California State University, Los AngelesCollege of Engineering, Computer Science, and Technology

California State University, Los Angeles

Abstract

Horizontal take-off and horizontal landing vehicles continue to be a subject of great interest for future space

launch missions. For a hypersonic vehicle, in order to operate through all Mach regimes, a combined-cycle

propulsion system is the most promising concept. This paper describes the cycle analysis for a ramjet/scramjet

system consisting of an airbreathing core with a variable geometry inlet. This combined cycle engine model can

be used within any hypersonic vehicle conceptual design framework. The propulsion model for this

configuration study is developed using a two dimensional forebody, inlet, and nozzle. A one dimensional model

is used for the isolator and the combustor. This mathematical model of the engine is implemented in MATLAB.

The effect of the flight path angle and the angle of attack are investigated. The engine model is used in the

development of a six degrees of freedom simulation.

NOMENCLATURE

α Angle Of Attack (A. O. A.)

bi Burner inlet

BE Burner exit

DOF Degrees Of Freedom

f Fuel air ratio

Fst Stoichiometry fuel air ratio

ii Isolator inlet

ie Isolator exit

M Mach number

ni Nozzle inlet

* PhD Student, Department of Aerospace Engineering, University of Kansas, Member AIAA.£ Professor of Aerospace Engineering, University of Kansas, Associate Fellow AIAA.§ Associate Professor of Aerospace Engineering, University of Kansas, Associate Fellow of AIAA.¥ Professor of Mechanical Engineering, Chair of M. E. Department, California State University, Los Angeles,Member AIAA.

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA 2006-8158

Copyright © 2006 by Shahriar Keshmiri, Saeed Farokhi, Richard Colgren and Maj Mirmirani. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

ne Nozzle exit

ψ Static temperature ratio

πd Total pressure recovery

ηd Kinetic energy efficiency

ηb Burner efficiency

γ Ratio of specific heats

q Heat release

Cp Specific heat at constant pressure

Ramjet-Scramjet Propulsion Model

The propulsion model for this research is developed using a 2-D forebody, inlet, and nozzle code and a 1-D

isolator and burner code. The code analyzes the entire vehicle with forebody, inlet, and nozzle flows calculated

assuming a 2-D perfect gas. The burner performance characteristics are computed using a 1-D flow with liquid

hydrogen combustion. The cycle analysis of the isolator and combustor is conducted using Rayleigh flow

principles. The nozzle flow and dimensions are determined applying the method of characteristics.

Ramjet-Scramjet Compression Performance

The most challenging task in the design of a combined cycle engine for a generic hypersonic vehicle (GHV) is

to design a ramjet-scramjet engine. The performance of the hypersonic inlet is investigated using oblique shock

theory. A MATLAB code is written to calculate external and internal compression and underbody flow at

supersonic through hypersonic speeds. The total pressure recovery (ratio), πd, across the compression system is

defined as the ratio of the total pressure at the burner inlet entry Mach number (Mib) to the total pressure of the

free stream flow. The total pressure ratio is an important measure of the performance of the compression

system. Another important measure of the performance of hypersonic inlets is the kinematic energy efficiency,

ηd. The MATLAB program, EX_IN_COMP.m, is used to calculate performance factors for any hypersonic

vehicle that incorporates up to four oblique shocks. In this research, a X-43A type under body compression

system is considered. Figures 1 and 2 show the 2-D and 3-D models of the compression system (see [1] and

[2]).

Figure 1: 2-D View of Compression System

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

In the GHV model, the forebody shock impinges at the leading edge of the cowl, interacts with the local shock

wave at the blunt leading edge of the cowl, and generates a shock-shock interaction. A multi-deflection surface

is used to increase the recovery pressure ratio.

Figure 2: 3-D view of External-Internal Compression System

The following figures show the performance parameters for the compression system at 100,000 ft above sea

level. The total pressure ratio decreases dramatically with the flight Mach number. Figure 3 shows the

decreasing trend in the total pressure ratio with increasing freesteam Mach number. The inlet pressure recovery

decreases at higher angles of attack as shown in Figure 4.

Figure 3: Inlet Pressure Recovery with Flight Mach Number [α=0 degrees]

Figure 4: Effect of Angle of Attack on the Inlet Pressure Recovery with Flight Mach Number

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

At hypersonic speeds, the angle of attack is changed from 0 to 5 (degrees) and the variation of the inlet pressure

recovery is calculated and shown in Figure 5. This figure shows that inlet pressure recovery increases with

speed.

Figure 5: Variation in Pressure Recovery with Angle of Attack at Hypersonic Speeds

Figures 6 and 7 show the performance of the compression system at supersonic and hypersonic speeds. As

expected from the compression process, the static temperature ratio (ψ) increases with increasing Mach number.

The burner entry Mach number (Mbi) is shown in Figure 6 as a function of flight Mach number. The combustion

takes place at supersonic speeds (scramjet) if the efficiency of underbody compression system is assumed to be

very high. In reality this curve (the burner inlet Mach number) is shifted down in the y axis direction. The

kinetic efficiency of the underbody flow2

20

iiV

V

in the moderate hypersonic speeds changes a little and higher

flight Mach number does not increase the overall kinetic efficiency (ηd) of the compression system

significantly.

Figure 6: Static Temperature and Burner Inlet Mach Number with Flight Mach Number

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

Figure 7: Performance Characteristic Coefficients with Flight Mach Number

Ramjet-Scramjet Frictionless Constant Pressure Burner

In this model, hydrogen is used as the fuel. Air is used as the oxidizer. The equation for complete combustion

(stoichiometry), and the stoichiometry fuel air ratio, are given in equation 1.

( )( ) ( )

( ) ( )( )

x y 2 2 2 2 2

st

st

st

y 79 y 79 yC H x O N x CO H O x N (1)

4 21 2 21 4

36x 3yf

103 4x y

36 0 3 2For hydrogen :x 0 & y 2 f

103 4 0 2

f 0.0291 or 2.91%

+ + + → + + +

+=+

+= = ⇒ =

+

=

In ramjet engines two throats are required. The first throat brings subsonic flow into the burner. The second

throat is used to chock the flow and accelerate it into the exhaust nozzle. Unlike ramjet engines, scramjet

engines have no throat, since the flow Mach number never becomes subsonic. To avoid needing two engine

types the concept of a dual mode combustion system, which was proposed by Curran and Stull [3], is used.

When the vehicle operates at subsonic flight speeds, this concept provides subsonic flow either upstream or

downstream of the combustor without using throats. The flow is supersonic in the burner. As described above,

both subsonic and supersonic combustion are possible using the same scramjet engine geometry. The isolator

and burner schematic are shown in Figure 8.

Figure 8: The Isolator and Burner

Isolator

Burner

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

The back pressure in the isolator is generated either by chemical energy release in the burner or obstruction of

the fuel injector (or a combination of both). Depending on the burner back pressure, the flow has two different

patterns in the isolator. If Mii<3 in the isolator inlet, then the pattern known as a normal shock train occurs. The

normal shock train provides subsonic flow at the entrance to the burner during supersonic flights. In contrast for

flows with Mii>3, the shock train generates the mechanism for a supersonic flow which adjusts the static back

pressure in the burner [1]. The impulse function at isolator exit is given by:

2ie ie ii ii ii ii ie ie ii ie ie ieI P A V A V P A A V (2)= + ρ = + ρ

The Mach number at the isolator exit is given by equation 3 [1].

12

2 2 2bb ii ii

bie ie bi2

2 2 ieb ii

ii

1M 1 M

12M where M M (3)

2P1 M

P

− γ + γ + γ − = − =

+ γ −

Both temperature and pressure increase in the burner. In order to keep the pressure constant the area ratio needs

to be increased. For a quasi-one dimensional frictionless heat addiction at a constant pressure, the axial variation

of Mach number is given as follows [1]:

( ) ( )( )

( )( )

( ) ( )

t _ burner

t _ ii

biburner

2 2b bbi bi

2 2b bbi bi biburner

T xx (4)

T x

MM x (5)

1 1x 1 M M

2 2

1 1A x A x 1 M M (6)

2 2

τ =

=γ − γ − τ + −

γ − γ − = τ + −

A MATLAB program is used to model the isolator and the burner cycle called Burner.m. This program uses the

EX_IN_COMP.m outputs and does the cycle analysis quickly and accurately. The burner area profile required

to maintain a constant pressure is proportional to τ(x). The burner model is checked at a few different area ratios

and for different temperature profiles at multiple altitudes. Figures 9 and 10 show the results for each case with

different technical specifications. The variation in the flight Mach number versus the fuel air ratio and the exit

Mach number at different altitudes is not remarkable. The variation in the area ratio of the burner is large at

about fifteen percent (see Figure 11). In order to keep the pressure constant throughout the burner using a

variable area ratio, a control system with a very fast response is needed. The input to the control system is the

flight Mach number and the total pressure. The variable area ratio needs to be controlled using fast actuators.

The burner exit Mach number changes through different flight altitudes. This makes the nozzle design process

very challenging.

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

Figure 9: Fuel to Air Ratio

Figure 10: Burner Exit Mach Number

Figure 11: Area Ratio for a Constant Pressure Burner

Expansion Nozzle and Specific Thrust

The nozzle performance is investigated at different values of the exit Mach number. As the exit Mach number is

increased, the height ratio of the nozzle increases along with the flow turning angle. The rate of change of the

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

nozzle height ratio is logarithmic. Figures 12 and 13 show how the height ratio of the nozzle and the flow

turning angle change with the exit Mach number.

Figure 12: Maximum Turning Angle in the Nozzle

The variation in the turning angle of the flow decreases when the exit Mach number increases.

Figure 13: Ratio of Entry to Exit Height

Unlike subsonic exhaust nozzles, the exhaust nozzles of hypersonic vehicles are 2-D or planer rather than

circular or axisymmetric. The nozzles of hypersonic vehicles are relatively heavy. Changing their geometry is

not easy. In most hypersonic engines the flow enters the nozzle supersonically. This makes analytical

calculations much easier. The nozzle is designed based on the isentropic flow assumption or the assumption of

ideal expansion. The effects of underexpansion are investigated in this research, and are represented in the

following subsection. A separate MATLAB routine, Expansion.m, is written analyze the behavior of the burner

exit flow though the nozzle for both subsonic and supersonic cases.

Case Studies

Using MATLAB routines different cases are investigated at different design points. The following Figure 14

shows the result of the cycle analysis and the resulting specific thrust values.

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

Figure 14: Specific Thrust

To generate a constant thrust value over a long flight, the air mass fuel rate needs to be increased continuously

with the flight Mach number.

Summary

This paper covered the development of a cycle analysis for a ramjet/scramjet engine consisting of an

airbreathing core with a variable geometry inlet. This analysis includes underbody compression, the isolator-

burner, and the expansion nozzle. This modeling process is used within a hypersonic vehicle conceptual design

framework. The vehicle geometry’s and efficiency parameters can be adjusted for new vehicle concepts. The

model and simulation are developed to support conceptual design studies of hypersonic vehicles using multiple

cycle engines.

References

[1] Heiser, William H., and Pratt, David T., “Hypersonic Airbreathing Propulsion,” AIAA, 1994.

[2] Saeed Farokhi, “Airbreathing Jet Engines,” Aerospace Engineering Department, The University of Kansas,

Lawrence, Kansas, 2005.

[3] Curran, E. T., and Stull, F. D., “The Utilization of Supersonic Combustion Ramjet Systems at Low Mach

Number,” Aero Propulsion Laboratory, RTD-TDR63-4097, Jan. 1964.

[4] S. Keshmiri, R. D. Colgren, and M. Mirmirani, “Development of an Aerodynamic Database for a Generic

Hypersonic Air Vehicle,” AIAA 2005-35352.

[5] Shahriar Keshmiri, Maj D. Mirmirani, Richard Colgren, “Six-DOF Modeling and Simulation of a Generic

Hypersonic Vehicle for Conceptual Design Studies,” AIAA-2004-4805, August 2004.

[6] Leitmann, G., “Optimization Techniques,” Academic Press, 1962.

[7] Peter H. Zipfel, “Modeling and Simulation of Aerospace Vehicle Dynamics,” AIAA Educational Series,

2000.

[8] Frank L. Lewis and Brian L. Stevens, “Aircraft Control and Simulation,” Wiley, 1992.

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA-2006-8158

[9] Jan Roskam, “Airplane Flight Dynamics and Automatic Flight Control, Part I,” DAR Corporation, 1997.

[10] E. T. Curran and S. N. B. Murthy, “Scramjet Propulsion,” Department of the Air Force (Editor), Purdue

University.

[11] “Conceptual Design of the OREAD EXPRESS: TransAtmospheric Cargo (TAC) Vehicle,” The University

of Kansas Propulsion Design Team, 1991-1992 AIAA Air Breathing Propulsion Competition, June 1992.

[12] John H. Blakelock, “Automatic Control of Aircraft and Missiles,” Wiley, 1991.

[13] Paul Dierckx, “Curve and Surface Fitting with Splines,” Oxford University, 1995.

[14] Philip George, “Numerical Methods of Curve Fitting,” Cambridge [Eng.] University Press, 1961.