Supersonic and Hypersonic Air-Breathing Configurations Derived from 2D Flowfields

American Institute of Aeronautics and Astronautics

1

Supersonic and Hypersonic Slender Air-breathing Configurations

Derived From 2D Flowfields

Frederick Ferguson,* and Mookesh Dhanasar

†

North Carolina A&T State University

Reginald Williams‡

NAVAIR, Paxtuxent River, MD

Isaiah M. Blankson§ and David Kankam

**

NASA Glenn Research Center

Abstract This research explores the design of supersonic and hypersonic slender air-breathing

configurations from prescribed Two-Dimensional shock waves. Through the coupled use of the

exact solutions of shock waves in an ideal gas, and the exact representations of planar and

axisymmetric geometric shapes, a series of elementary configurations are developed and analyzed.

The design process is accomplished through the use of specially developed subroutines,

programmed in FORTRAN, to manipulate and assemble these elementary configurations into

either completed vehicle configurations or propulsion system configurations. The elementary

shapes of interest to this study include the star-shaped leading edges, the caret-shaped inlets, and

cylindrical combustors, convergent and divergent nozzles and plug nozzle after-bodies. This paper

describes the generation of these elementary shapes, the aerodynamic basis for their creation and

the technical requirements used during the final configuration assembly process. As part of this

effort an existing FORTRAN code is modified and enhanced. As its output, the design code

generates the aircraft configuration and analyzes its aerodynamic performance. Further, the

algorithms used to evaluate the resulting aero-thermo-dynamic and geometric characteristics of the

resulting configurations; such as the local heat fluxes, the lift and drag, the surface areas and the

configuration volume, are based on empirical engineering correlations and strict geometric

principles. In general, the code developed as part of this research effort was used to conduct the

following studies: Generate propulsion systems configurations from prescribed 2-D shock waves;

Evaluate the resulting vehicle wetted surface area and volume; Evaluate the thrust performance of

the system; Conduct an aero-thermo-dynamic analysis of the resulting system, and; Identify the

design parameters that affect the vehicle’s overall performance and shape. The outcome of this

research can be classified in the following two categories. First, the propulsion system design and

assembly process led to the discovery of engineering parameters that directly influence the

aerodynamic performance of the resulting configuration. These parameters were manipulated to

generate configurations with superior aerodynamic and thrust properties. Second, routines were

developed that led to the design and analysis of a morphing ramjet-to-scramjet configuration.

Nomenclature

= angle of attack

= shock wave angle

Cf = skin friction coefficient

Cp = pressure coefficient

*Professor & Director, Center for Aerospace Research, and AIAA Senior Member.

†Graduate Student, Center for Aerospace Research, and AIAA Member.

‡Aerospace Engineer, NAVAIR, Patuxent River, Maryland, and AIAA Senior Member.

§Senior Scientist, NASA Glenn Research Center, Cleveland, Ohio, and AIAA Associate Member.

**University Affairs Officer, NASA Glenn Research Center, Cleveland, Ohio, and AIAA Senior Member.


2

D = Drag, force component parallel to the freestream velocity

= specific heats ratio

L = Lift, force component perpendicular to the freestream velocity

M = Mach number

= wedge angle

P = pressure

u = velocity component parallel to the freestream velocity

S = Surface area

T = temperature

OOP = Object Oriented Programming

I. Introduction

his paper is motivated by the need to rebuild the air-breathing hypersonics infrastructure in the USA by

conducting a joint, unclassified research and development program involving industry, academia, DOD and

other Government agencies. This can be achieved by focusing on the development of a manned, half global

range Mach 5 or greater waverider cruise vehicle that serves as a multidisciplinary research test bed for the

development of air-breathing sustained hypersonic flight technologies. In essence, the proposed project mimics the

highly successful X-15 program, but through the use of a manned air-breathing vehicle. In another sense, the

proposed vehicle may be regarded as a replacement for the SR-71. Moreover, the Flight Demonstration of such a

vehicle will help to develop a design database that can potentially satisfy the critical need for a fully reusable

hypersonic research vehicle. This vehicle can potentially be used to demonstrate integrated aerodynamic,

propulsion, control, and structural technologies for hypersonic vehicle design, and for reducing the risk involved in

the development of future operational hypersonic vehicles.

In general, hypersonic vehicles will operate at flight conditions very different from those experienced by

subsonic or low supersonic aircraft1-2

. Designers’ experience with wind tunnel facilities, computational capacity,

and flight research has provided the framework for the lower speed regimes. This is not the case for air-breathing

hypersonic flight, where verification and development through experiment will not be possible in ground facilities,

current or in the foreseeable future1-2

. The problems of hypersonic flight are primarily associated with the high

stagnation temperatures/enthalpies associated with very high speeds. These higher temperatures result in high heat

transfer to the vehicles, changes in the gas characteristics around the vehicles, and changes in the chemical

constituents of air, which can directly affect the classical combustion phenomena. For air-breathing hypersonic

vehicles the severe operational environment, the need to totally or partially integrate the propulsion system with the

air-frame, the ultimate disciplinary coupling of the vehicle subsystems, and the long residence times in an

environment at high levels of aerodynamic heating and dynamic pressure introduce technical problems that will be

with us for a long time to come1-2

. It may be possible, that in the Mach 4-6 range most of the needed technologies

are either conventional or of near-term maturity, making applications in this range immediately attractive. This

paper focuses on an idealized concept the can potentially lead to the development and analysis of complete

hypersonic vehicle and propulsion systems concepts. In turn, the results of this study can provide the aerodynamic

performance data necessary to guide designers in their quest to develop a Mach 5 – 7 vehicle demonstrator concept.

II. Technical Approach

A. Aerodynamic Concepts

The basic approach to the effective design of waverider configurations comes mainly from the exact solution of

supersonic flowfields. Exact solutions are available in the form of either oblique shock waves or expansion waves.

This concept is illustrated Fig. 1. Consider a shockwave in a supersonic flow that is induced by the wedge, ABC. As

indicated in Fig. 1, in the case of an inverse design approach, for a given Mach number, M, and for a given oblique

shock wave angle, β, there is a corresponding wedge deflection angle, θ, which dictates the basic geometry of the

wedge. In addition, for any point, A, on the shockwave, and for the purposes of this analysis, two lines emanate

down stream, namely, line AB, representing a free stream streamline on the wedge upper surface and line AC,

representing a streamline processed by the shock wave will be carved. In this case, the freestream streamlines will

make up the upper surface and the shock processed streamline will make up the lower surface of the wedge. In a

similar manner, a typical waverider from any prescribed shock wave is derived. Using this approach, each point

T


3

lying on a leading edge curve that lies on the shock wave can contribute to the construction of the resulting

waverider geometry. This concept is illustrated in Fig. 2 in the case of a wedge. This design concept is not limited to

the wedge configuration3-10

. In fact, an entire class of configurations can be generated as described in the following

sections of this paper.

Figure 1. 2D Waverider Design Figure 2. Wedge Construction

As part of the research efforts sponsored by the NASA URC Program and conducted at North Carolina A&T

State University7-10

, an Object Oriented Approach (OOA) is adopted in the development of a FORTRAN code that

generates and analyzes elementary aerodynamic shapes and assembling them into entire vehicle or propulsion

system configurations. In general, the elementary shapes are developed from 2-D shock and expansion waves. In

addition, aerodynamic routines capable of conducting Quasi-1D flowfield analyses with heating and friction, and

routines with elementary combustion models are also available. The code is equipped with routines that carefully

assemble these elementary shapes into completed hypersonic vehicle configurations. In this paper, the design

concept of constructing the appropriate geometries and the unique manner in which they are assembled in defining

the final vehicle configuration is detailed. Also, the algorithms behind the construction and analysis of each sub-

assemble are presented.

B. Elementary Geometric Surface Concepts

This section describes the geometric principles used to generate the surfaces that make up a typical waverider

configuration. In general, the waverider configuration is

composed of intersecting planes. In this analysis, the planes and

lines of interest are described in the Cartesian system of

coordinates, x, y and z. For example a typical plane in the

Cartesian System of Coordinates is defined by the equation:

0 DCzByAx (1)

where the coefficients; A, B, C and D, represent the constants

that control the nature of the surface. It is of interest to note that

a plane is infinite in space if the values of coordinates, x, y and

z, are not restricted by certain limits. The waverider

configuration is made up of finite planes that are limited by the

results of rigid aerodynamic analysis. In this design process, the

appropriate aerodynamic analysis is conducted with the goal of

identifying the geometric requirements of the vehicle surfaces.

As an illustrative example10

, consider Fig. 3. The algorithm of generating a finite plane or a plane surface with

boundaries is explained through the use of Fig. 3. If a plane A is projected to the xy-plane, the x and y values of the

plane can be programmed based on their relationship on the xy-plane, in this case, the projection is oabc, then the z

value can be derived from the line’s equation, refer to Eq. (1). Another geometric entity of interest to this study is

the straight line. The equation of a line can be obtained from the unique solution derived from the following two

intersecting planes;

β

θ A

B

Shock wave

θ

B

A

Freestream

β A A

B

C C

B

Shock wave Shock wave

Freestream

x

y

z

A

o a

b

c

Figure 3. Projection of a Plane on xy-plane


4

0

0

2222

1111

DzCyBxA

DzCyBxA (2)

An alternative to Eq. (2) is the geometric tool used to define a straight line through the use of the following

equation:

p

zz

n

yy

m

xx )()()( 000

(3)

where the symbols, m, n and p, are non-zero constants and the coordinates, x0, y0, and z0, represent an arbitrary point

of interest on the line. Also, in this study a line is used to divide an infinite plane into smaller pieces. Using this

definition, a typical surface can be readily projected onto any of the three Cartesian planes, namely, the yz-plane, xz-

plane and xy-plane. Based on the geometric principles underlining Eqs. (1) through (3), and their derivations, a

group of subroutines were developed in FORTRAN. These routines are programmed to effectively handle the

waverider design process, by quickly generating basic planes and lines as required.

C. Vehicle Configuration Assembly Concepts

In this section, a typical Caret shaped waverider, as illustrated in Fig. 4, is generated using the principles

described earlier. Consider an oblique shock wave in a supersonic flow. In the case of a caret shaped waverider, the

shock wave is prescribed along with the leading edge lines, namely, EF and EG. Next, the equation for the line EH

is prescribed using the free stream information. The point, HL, can be calculated through the use of the shock wave

relations. Once these basic line equations are obtained the appropriate surfaces, EHG, EHLG, EHF and EHLF are

constructed through the appropriate use of the available FORTRAN routines. The illustration of a typical caret

shaped waverider constructed through the use of this process is shown in Fig. 4. It is of interest to note that the

resulting caret waverider is constructed such that it induces the prescribed shock wave. This concept was

demonstrated in Ref. 7-10. Moreover, this design approach demonstrates that a unique caret waverider can be

constructed when two leading edges on a shock wave are prescribed.

Consider a second example, that of a wedge inlet that can be used to prepare the hypersonic flow for scramjet

processing. Fig. 5 illustrates the shape of a hypersonic fore-body that was constructed using this design philosophy.

Splitting the caret waverider, which is illustrated in Fig. 4, at line EH and adding an appropriate wedge in between

can lead to the construct of this idealized forebody configuration. As demonstrated in the case of the caret

waverider, here too, a unique forebody configuration is constructed such that it satisfies the given freestream

conditions and the leading edges on the shockwave. It is of interest to note that the cross sectional area described by

the points GEFH dictates the mass flow available to the scramjet. In addition, when compared to that generated by

the caret waverider, the mass flow rate is greatly enlarged. In a similar manner the configurations illustrated in Figs.

6 and 7 are constructed. Refer to Ref. 7 – 10 for further details.

Figure 4. A Caret Shaped Waverider Figure 5. An Inlet Waverider

A

H

G

C

E

Shock wave

β

θ

B

D

F

Freestream

E

F

G

H

HL

Shock wave

β

θ

Freestream


5

E

F

G

H

HL

Shock wave II

Shock wave

Freestream

Sock wave II

Shock wave I

Shock wave

Freestream

Figure 6. A Star-shaped Waverider Figure 7. A waverider derived forebody with wings

III. Propulsion Integration Approach

A. The Generic Hypersonic Propulsion Concept and its Limitations

Typically, subsonic aircraft feature propulsion systems that are mounted as distinct components hanging off its

wings. For example, the engine pods of the Boeing 747 are easily identifiable. Even designs intended for low-

supersonic speeds, like the Concorde, feature distinct engine pods. However, in the design of hypersonic air-

breathing vehicles this is certainly not the case. Since thin shock layers are a common occurrence in hypersonic

flight11

designers must be careful to prevent the shock wave from one component of the aircraft to adversely

interfere with others. In addition, a hypersonic vehicle will more than likely utilize a ramjet or a scramjet engine for

propulsion12

. These engines are similar to turbojets except that they dispense with the compressor and turbine stages.

Instead, these engines rely on the motion of the vehicle itself to compress the incoming flow before combustion

occurs12, 13

.

The vehicle configuration and its design consideration are the most important requirements for understanding the

aerothermodynamics of the hypersonic air-breathing engines. At hypersonic speeds, the shock interactions and the

need for ideal engine operation conditions dictate that the propulsion system be highly integrated into the overall

airframe design14

. The most closely integrated engine/vehicle integration is observed in the case of a propulsion

system with a scramjet engine14

. The scramjet engine occupies the entire lower surface of the vehicle body.

Typically, the scramjet propulsion system consists of the following major components: internal inlet, isolator,

combustor, internal nozzle and the fuel supply subsystem. The vehicle fore-body is an essential part of the air

induction system while the vehicle after-body is a critical part of the nozzle component. As a result of these and

other aerodynamics considerations, it is predicted that the most promising hypersonic vehicle will be defined by

highly integrated configurations such as the one illustrated in Fig. 8a and 8b.

a) An Integrated Scramjet Concept16

b) X-43A First Free Flight15

Figure 8: Illustration of Integrated Scramjet Propulsion Systems

The scramjet propulsion system is a hypersonic air-breathing engine in which heat addition, due to combustion

of fuel and air, occurs in the flow that is supersonic relative to the engine11-13

. In a conventional ramjet engine the

incoming supersonic airflow is decelerated to subsonic speeds by means of a multi-shock intake system and


6

diffusion process. Fuel is added to the subsonic airflow, the mixture combusts and then re-accelerates through a

mechanical choke to supersonic speeds. By contrast, the airflow in a pure scramjet remains supersonic throughout

the combustion process and does not require a choking mechanism.

The scramjet engine of interest to this study is one that seamlessly makes the transition between ramjet and

scramjet during operation. Unfortunately, as important as propulsion integration is for the hypersonic vehicle,

focusing solely on integration does not lead to a realistic design. The vehicle must be capable of getting off the

ground and quickly accelerates to hypersonic speeds, with engines capable of seamlessly transitioning from one

flight regime to the next. In light of these realities, this paper focuses on a more realistic concept, such as the one

illustrated in Fig. 9, which was conceptually developed at NASA GRC. It is of interest to note that the concept

illustrated in Fig. 9 has the potential to continuous morph as it traverse the entire flight spectrum, from low subsonic

to hypersonic speeds.

B. The ‘Exoskeletal’ Engine Concept

Even though this research effort is geared toward the design of an entire hypersonic aircraft configuration, this

section explores the preliminary design elements associated with an “exoskeletal” engine with the goal of integrating

it into the vehicle configuration illustrated in Fig. 7 at a later stage. A schematic of this engine is illustrated in Fig. 9.

The engine is designed to operate as a combined-cycle propulsion plant from ground to Mach 6 and greater. The

‘exoskeletal’ engine concept is a revolutionary class of gas turbine engines, in which the rotating components are

mounted concentrically within a drum structure around a central core channel. This provides numerous postulated

advantages over a conventional engine, primarily because the rotating components are in compression instead of

tension. Of great interest for application to a combined-cycle engine is the fact that the central core of this engine

could function as a ramjet, and possibly even a scramjet, enabling the engine to operate on a hybrid cycle up to

hypersonic speeds.

Figure 9. NASA GRC Exoskeletal Mach 5 Turboramjet Concept

The exoskeletal design lends itself naturally to the combined cycle concept. At low speed, both the outer drum

and central core would be open; the drum would provide primary propulsion and the central core would either not be

combusting, or would be burning fuel occasionally for needed thrust augmentation. At higher speeds, flow would be

directed down the central core alone, with continuous combustion in this region providing thrust in a ramjet mode.

This central core is ideally suited for ramjet operation, and the process of closing off the compressor assembly could

be accomplished without the ducting losses of a traditional hybrid design. Another advantage is that the core and

duct nozzles can be designed and optimized separately. The combined-cycle exoskeletal engine thus holds the

promise of generating thrust from static conditions through the Mach 6 upper limit of a ramjet, with applications

ranging from rapid-response missiles, high-speed cruisers, and first stage access-to-space.

This paper focused on fostering the development of the NASA GRC exoskeletal engine with primary interest in

the ‘morphing ramjet to scramjet configuration’ design and construction issues. Once the propulsion system design

requirements are determined and a working configuration obtained, attention will be given to the integration of the

turbojet design requirements on the exterior of the ‘morphing ramjet to scramjet’.

Ramjet Only

Turbojet & Ramjet

Turbojet Inlet Compressor Turbine

Ramjet Burner Ramjet Nozzle

Turbojet Nozzle Turbojet Exhaust Duct & Afterburner


7

C. Aerophysics of Ramjets and Scramjet

At high speeds, the primary purpose of the air induction system, which comprises of the vehicle forebody and

internal inlet, is to capture and compress an appropriate quantity of air. This appropriate mass flow must then be

further processed by the other engine components16

as illustrated in Fig. 10.

Fig. 10: Isolator and Combustor Aero-Physics16

.

In conventional jet engines, the inlet works in combination with the mechanical compressor to provide the

necessary high pressure for the entire engine. For vehicles flying at high speeds, adequate compression can be

achieved without a mechanical compressor. The fore-body provides the initial external compression which also

contributes to the drag and moments of the vehicle. Typically, the internal inlet compression provides the final

compression of the propulsion cycle. In general, the fore-body and the inlet are designed in harmony to provide the

required mass capture and aerodynamic contraction ratio needed to maximize the inlet efficiency. The air in the

captured stream tube undergoes a reduction in Mach number with an appropriate increase in pressure and

temperature16

. In a well designed system, there are shock waves and reflected waves built into the flow path to assist

in the processing of the flow. However, there are non-uniformities, due to oblique reflecting shock waves, which can

influence the flow path and subsequently the combustion process. Non-uniformities in the scramjet air induction are

due to phenomena associated with the vehicle bow shock, isentropic turning Mach waves, shock-boundary layer

interaction, non-uniform flow conditions, and three-dimensional effects. Fig. 10 illustrates the flowfield associated

with the stream tube as it passes through the system of shock waves in the fore-body, inlet and through the isolator16

.

IV. Preliminary Ramjet-to-Scramjet Morphing Design

A. Forebody, Inlet and Isolator Design Requirements

As a combined-cycle powerplant, the exoskeletal engine shares similarities with existing hybrid, or combined-

cycle, engines. Hybrid engines offer the possibility of using a single engine system across a wide range of Mach

numbers. Gas turbine engines operate from zero velocity to low supersonic speeds; at higher Mach numbers, the

presence of a compressor reduces engine efficiency, and it is more effective to use available inlet ram compression

at the beginning of the cycle. In the Mach 3 and greater range, a ramjet engine, (i.e. without a compressor or

turbine), is most efficient. That means that an aircraft that is designed for flight to Mach numbers beyond 3 must

either use two separate engine systems (gas turbine and ramjet), or use one hybrid engine that can transition between

turbine and ramjet modes.

An example of an existing hybrid is the engine that powers the SR-71 Blackbird, the Pratt & Whitney JT11D-

20B bleed turbojet. This is a conventional afterburning turbojet outfitted with special bypass ducts, designed over

forty years ago for flights up to Mach 3. At low speeds, the engine performs as a conventional turbojet. At high

Mach numbers, air is bled from the front of the engine to the afterburner, bypassing the rotating compressor/turbine

assembly. In this mode, the engine essentially operates as a ramjet, taking advantage of the greater efficiency of the

ramjet cycle at higher Mach numbers. A key component of the SR-71 engine is a translating conical inlet, which

works efficiently across the wide Mach number range. The exoskeletal engine would operate in a similar manner,

though with fewer losses than the JT11D-20B, and up to higher Mach numbers.


8

A key to the success of any combined-cycle engine is minimizing the inevitable compromises that are made in

designing a single engine that can operate in different modes. Consequently, the inlet must be designed so that it

can operate across the Mach number spectrum, while accommodating the proper management of the central core and

the compressor flowfields. Shock locations and uniformity requirements must also be met, since the compressor face

is much more sensitive to the peripheral flow gradients when compared to traditional engine design. The star-shaped

fore-bodies, generated in this research effort and illustrated in Fig. 11a, 11b and 11c, meet these requirements.

a) Front View

b) Side View

12c) Isometric View

Figure 11. Star-Shaped Inlets for the Exoskeletal Ramjet-to-Scramjet Concept.

In a similar manner the inlet and isolator configurations are generated. In the case of the inlet geometry, the final

configuration is completely determined by a secondary shock wave that is reflected off of the cowl lip, such that the

inlet flow turns and enters the isolator parallel to the freestream. Illustrative examples of the inlet, highlighting the

variation of the cross-sectional geometry resulting from the secondary shock, and the accompanying isolator are

presented in Fig. 12a, 12b and 12c.

In an effort to accommodate the technical requirements explained above, an inverse design approach based on

the waverider concept outlined in Section I is explored; refer to Ref. 7-10 for greater details. This effort focused on

the design of an inlet capable of operating over a wide Mach number range, and providing high quality flow to three

distinct regions of the engine; namely, the forebody, the inlet and the isolator. Using the vehicle design methodology

described in Sections I and II, an appropriate class of star-shaped inlets was derived, and a representative of that

class is illustrated in Fig. 11. Similarly, the inlet and isolator designs are illustrated in Figs. 12a, 12b and 12c. It is of

interest to note that the FORTRAN Code developed as part of this analysis can generate star-shaped fore-bodies

with the number of blades ranging from one through eight. Illustrative views of the inlet and the isolator resulting

from the four-point star-shaped forebody are illustrated in Fig. 13a, 13b, and 13c.

a) Inlet Front View

b) Inlet Isometric View

c) Isolator Isometric View

Figure 12: Illustrative Examples of the Inlet and Isolator


9

a) Inlet Front View

b) Inlet Side View

c) Inlet Isometric View

Fig. 13 Illustrative Views of the Fore-body-Inlet Combination

B. Designing for Ramjet-Scramjet Transformation

The ramjet was designed to work at supersonic speeds. Unlike turbojets, ramjets have no moving parts. The air is

captured by the inlet and compressed by the primary shock wave. A typical ramjet configuration17, 18

is illustrated in

Fig. 14. As observed in Fig. 14, the compressed air is slowed down as it approaches the burner, and combustion

takes place in subsonic conditions. A nozzle is then employed to accelerate the hot gas back to supersonic speeds.

This mode of operation gives the ramjets a leap in speed to Mach numbers ranging from 3 – 5. It is of interest to

note that the air speed in the ramjet compressor remains high. In addition, the air in the combustor is brought to

subsonic conditions prior to burning, resulting in both high temperature and pressure in the engine with temperatures

in the range of 6,000ºF. These and other effects, force the ramjet to favor operations at low Mach numbers17-18

.

Figure 14: Schematic Diagram of the Ramjet Figure 15: Schematic Diagram of the Scramjet

In an effort to mitigate this problem designers came up with the scramjet concept, a supersonic combustion

ramjet which solved the overheating problem of the ramjet. This concept is illustrated in Fig. 15. The difficulties

associated with mixing air with the fuel at supersonic speeds, and completing combustion within milliseconds, have

both been solved as demonstrated in the two successful X-34 test flights15

. In this effort, a deliberate attempt is made

to construct a variable ‘diffuser-to-plug-nozzle’ concept that allows for the seamless engine transition from ramjet to

scramjet operation modes. This design concept was first illustrated in Fig. 9. In a similar manner, this concept was

implemented in the generation of the preliminary ramjet-to-scramjet configurations that are illustrated in Fig. 16.

The combustor accepts the inlet/isolator airflow with variations in geometric inflow profiles and provides

efficient fuel air mixing within the available combustor length16

as shown in Fig. 10. The fuel supply subsystem is

required to deliver fuel to the flow path at appropriate locations with the desired physical properties. The combustor

fuel is scheduled to stay within the engine operability limits while optimizing engine thrust potential. The expansion

system, consisting of the internal nozzle and vehicle after-body, completes the propulsion flow path and controls the

expansion of the high pressure and temperature gas mixture to produce net thrust. During the expansion process, the

potential energy generated by the combustor is converted into kinetic energy. The nozzle must process the

accumulated flow distortions generated by the air induction system, isolator and combustor. The phenomena of

importance to the scramjet nozzle design include flow chemistry, boundary layer effects, non-uniform flow


10

conditions, shear layer interaction, and three-dimensional effects11-22

. The design of the nozzle has a major effect on

the efficiency of the propulsion system and the vehicle due to its ability to influence vehicle pitching moment and

lift22

.

a) Rear View b) Front View c) Side View

d) Transparent Isometric View e) Isometric View with Cut away

Fig. 16: Illustration of A Morphing Ramjet-to-Scramjet Configuration

V. Preliminary Ramjet Analysis

A. Ramjet-Scramjet Design from 2D Flowfields

This research project is in its infancy and its immediate objectives are: to design ramjet configurations carved

from 2D flowfields, and to investigate their aerodynamic performance. For this purpose, conceptual design routines

written in an OOP using FORTRAN are developed. In general, the geometric design concept originates from the 2D

planar and axisymetric theories described in Section I of this paper.

Using the waverider theory as a starting point and the propulsion systems concept described in Ref. 12, a typical

ramjet C-sectional flowfield illustrated in Figure 17 can be derived. The details of the aerodynamic analysis efforts

related to the performance of this configuration are described in the next section. This section, however, focuses on

the construction of a 3D ramjet-to-scramjet configuration that uses Fig. 17 as its defining inputs. The geometric

points, A through G, lying on the x-axis not only define the various components of the ramjet propulsion system

such as it’s forebody, inlet, isolator, diffuser, combustor and nozzle, they also serves as the key indicators for the 3D

construction of these components.

Fig. 17: Illustration of A Ramjet-to-Scramjet Mid-Section with Morphing Design Points

Primary

Shock

Zone

A

Reflected

Shock

Zone

Isolator

Zone Diffuser

Zone

Combustor

Zone

Nozzle

Zone

B D C E F G

x


11

For example, using the information at points D and E along the x-axis and the geometric information resulting from

the star-shaped, fore-body configuration illustrated in Figure 11, an appropriate 3D configuration representing the

diffuser can be constructed. In this case, the geometry of the resulting diffuser is illustrated in Figure 18.

a) Diffuser Base View

b) Diffuser Side View

c) Diffuser Isometric View

Figure 18: Illustration of the diffuser Component Derived from a star-shaped fore-body

It is of interest to note that by choosing the design points, A – G, in the form of design parameters and

independent of each other, the resulting integrated configuration can have its E-point beyond its F-point location

with respect to the x-axis. This approach provides a great deal of flexibility in arriving at candidates with desirable

aerodynamic characteristics. In addition, when generating the 3-D configurations, the choice of the fore-body is of

great importance, since it provides the geometric information need from the third dimension. In this research, star-

shaped, fore-bodies are generated with the number of blades ranging from two to eight. Once the appropriate

forebody information is obtained, following the approach already outlined, each component of the ramjet can be

uniquely defined in 3D and constructed, using the routines already established. Examples of the types of propulsion

system components and the manner in which they are pieced together to result in an integrated ramjet configuration

are illustrated in Figure 19.

a) Side View of A Variable Geometry Ramjet Configuration

b) Isometric View of Ramjet

c) Transparent Isometric View of Ramjet

Figure 19: Illustration of Ramjet Derived from a 4-Point Star-Shaped Fore-body


12

B. Ramjet-Scramjet Analysis

The analysis of the propulsion system consists of the evaluation of the following six major components; namely, the

primary shock zone, the inlet, the isolator, the diffuser and mixing region, the combustor and the nozzle. The

evaluation of the primary shock zone, the inlet and the nozzle is straight forward and is conducted in accordance

with Ref. 11-12, 19-20. However, the evaluation of the flowfield parameters is somewhat complicated and is

conducted in accordance with Ref. 12.

The isolator, diffuser and combustor sections of the ramjet engine, illustrated in Figure 20, are modeled using a

quasi-one-dimensional analysis19-20

. The main equation describing the quasi-one-dimensional flow through these

sections includes area variation, friction and mass injection, and can be written in the following form12

:

dx

md

mM

MM

D

c

M

MM

dx

dT

TM

MM

dx

dA

AM

M

dx

dM

M h

f

1

1

124

1

1

1

11

1

212

2

2

20

02

2

2

2

2

(4)

where the parameter, M , is defined as follows:

2

2

11 MM

In Eq. (4), the symbols; M represents the local Mach number, To the total temperature, cf the skin friction coefficient,

m the mass flow rate and x the independent parameter, which represents the local distance along the ramjet

centerline. In order to integrate Eq. (4), the design parameters; such as, the cross sectional area, A(x), the stagnation

temperature, T0(x), the mass flow rate, m , and the coefficient of friction, cf, must be specified as functions of the

variable, x.

Figure 20: Designation of Axial Locations for the Propulsion System Geometry

The area variation, A(x), is calculated based on the engine configuration, T0(x) is assumed constant except for the

regions where combustion is simulated through the use of Eq. (5), and as suggested in Ref. 12. Combustion is

simulated as an increase in the stagnation temperature of the flow in the combustor up to a specified maximum; this

temperature release profile is described using a rational function20

;

x

x

T

T

T

xT

1111

02

04

02

0

(5)

where the parameter, x , is defined as follows:

34

3

xx

xxx

Isolator

Reflected Shock

Ramjet Burner

Ramjet Nozzle

Primary Shock Mixing

2 3 4


13

and the symbols, x is the horizontal distance measured from the combustor starting location to its ending point,

namely, ix and 4x . On the other hand the non-dimensional parameter, , is a factor greater than 1. Typically, a

value in the range of 40 - 50 is chosen for the symbol, , in the case of subsonic ramjet combustion12

.

The local cross-sectional area and equivalent width are combined and used in the Reference Temperature

method21

, for evaluating the local skin friction, cf,. It is of interest to note that the fuel injection influence is

simulated in the mass flow rate term, m . For realistic ramjet operations, a sonic point needs to be located in the

combustor, corresponding to choking of the flow at the throat. In Ramjet mode of operations, finding the sonic point

is obvious, however, in the case of the scramjet the sonic location is found as described in Ref. 12 and 20. Using

l’Hospital’s rule in relations to Eq. (4) as the Mach number approaches unity an appropriate value for x is found at

which location the Mach number is equal to one. Once the sonic point is found, Eq. (4) is integrated backwards to

obtain the properties at the combustor entrance.

The flow through the isolator is also obtained by the integration of Eq. (4). The driving functions are again

specified in a similar manner, and the integration is performed from the isolator entrance to exit in order to obtain

the flow conditions. Although the isolator is expected to contain a ‘shock train’ that brings the flow to the subsonic

conditions required at the combustor entrance, no analytical models are available to provide the solution to such

phenomena, see Fig. 10. Therefore, a single normal shock wave is assumed to perform the same function as the

‘shock train’. The appropriate integration of Eq. (4) is conducted in an iterative manner, varying the location of the

normal shock wave until a solution is found where the isolator exit conditions match the required combustor

entrance conditions. These ideas are also described in Ref. 18, 20 and 22. After the isolator and combustor flowfield

solutions are obtained, the momentum thrust of the engine is calculated as the difference between the impulse

function at the combustor exit and the isolator entrance20

:

)()( 24 xIxIT (6)

where, the impulse function, I, is defined as,

21 MpAI

VI. Conclusion and Future Plans

This paper gives a preliminary report on efforts to design a reconfigurable propulsion system; morphing from

ramjet to scramjet mode of operation in flight. Performance requirements will almost certainly dictate the use of a

translating center body and associated outer ‘clamshell’. The design of forebody-inlet-isolator was accomplished

through the use of 2D planar flowfields. In addition, realistic ramjet-to-scramjet propulsion systems were derived

and analysis from 2D planar shock waves, expansion waves, and from Quasi-1D flows with heat addition and

friction. The next step is to redesign these components by using 2D axisymetric flowfields. This task can be

accomplished with minimum effort since the authors have already used axisymmetric flowfields to generate

waveriders7-11

. The ramjet-scramjet transition mechanism does demand a great deal of aerodynamic and structural

analysis. The current approach focused on using the ideal situation; however, phase two of this effort will improve

the analysis methods by introducing combustion and quasi-1D nozzle modules with real gas effects. Detailed

analysis of the ‘ramjet-to-scramjet propulsion systems’ performance at various Mach numbers is of interest to this

study and will form a significant element of this research project as it develops. This includes developing the

geometric concepts, calculating inlet flowfields, and estimating performance and losses at key Mach numbers;

ranging from Mach 2 up to Mach 6. Managing the shock locations on the inlet, especially to provide good flow

conditions into both the core and compressor duct, is of great interest. The inward turning diffuser concepts are

already employed in the design process, as they lend themselves to concentric engine flowfields. With the

development of a suitable inlet and ram-scramjet configuration, a detailed combined-cycle engine model will be

developed, covering the Mach number range from static to near-hypersonic and beyond. The ultimate product of

this effort will be a recommended geometry for use as a CFD and wind tunnel or flight test bed for the

demonstration of a turbine-based combined-cycle exoskeletal engine.

Acknowledgments

This work has been partially sponsored by the following agencies; NAVAIR, NASA Glenn and Langley

Research Centers. In addition, special appreciation is extended to the Space Vehicle Technology Institute at the


14

University of Maryland, one of the NASA University Institutes, with joint sponsorship from the Department of

Defense. Appreciation is expressed to Dr. Isaiah Blankson of NASA Glenn Research Center and Dr. Reginal

Williams of the Naval Airforce Base at Patuxent River in Maryland.

References 1I. M. . Blankson, et al., ‘Air-Breathing Hypersonic Cruise: Prospects for Mach 4-7 Waverider Aircraft,’ ASME

Journal of Propulsion and Power, January-April, 1994. 2I. M. . Blankson, et al. ‘Anatomy of a Hypersonic Air-breather: A Turbine Based Combined - Cycle Hypersonic

Cruise Application-Vehicle,’ International Symposium on Air Breathing Engines, ISABE Paper 1999, Florence,

Italy. Sept 1999. 3Nonweiler, T., “Aerodynamic Problems of Manned Space Vehicles,” Journal of Royal Aeronautical Society,

Vol. 67, Jan. 1963. 4Nonweiler, T., “Delta wings of Shapes Amendable to Exact Shock Wave Theory,” Journal of Royal

Aeronautical Society, Vol. 67, Jan. 1963. 5Bowcutt, Kevin G., “Optimization of hypersonic Waveriders Derived from Cone Flows Including Viscous

Effects”, Ph.D. Dissertation, Department of Aerospace Engineering, University of Maryland, College Park,

Maryland, 1986 6Bowcutt, Kevin G., Anderson, John D. Jr., and Capriotti, D.P., “Viscous Optimized Hypersonic Waveriders,”

AIAA paper 87-0272, 1987. 7Ferguson, F., “Expanding the Waverider Design Space Using Arbitrary Generating Flowfields”, Ph.D.

Dissertation, Department of Aerospace Engineering, University of Maryland, College Park, Maryland, 1993. 8Frederick Ferguson, Terry L. Corbett, Jr., Stephen Akwaboa, and Haile Lindsay, “The Development of

Waveriders From an Axisymmetric Flowfield”, AIAA 2007-847, 45th

American Institute of Aeronautics and

Astronautics Aerospace Sciences Meeting and Exhibit, Reno, NV 2007. 9Hydar Apdin and Frederick Ferguson, ‘A Design Concept for the Construction of Completed Hypersonic

Vehicles’, 13th AIAA/CIRA International Space Planes and Hypersonic Systems and Technologies Conference,

CIRCA, Italy, May 2005 10

J. Zhang and F. Ferguson, ‘Construction and Analysis of Hypersonic Vehicle Configurations’, 13th

AIAA/CIRA International Space Planes and Hypersonic Systems and Technologies Conference, CIRCA, Italy, May

2005. 11

John J, Bertin “Hypersonic Aerothermodynamics.” AIAA Education Series. ISBN: 1-56347-036-5, Published

by American Institute of Aeronautics and Astronautics, 1994 12

William H. Heiser, David T. Pratt “Hypersonic Airbreathing Propulsion.” AIAA Education Series. ISBN: 1-

56347-035-7, Published by American Institute of Aeronautics and Astronautics, 1994. 13

E. T. Curran and S.N.B. Murthy, “Scramjet Propulsion”, Vol. 189, AIAA, 2000. 14

Kuchemann, D. “The Aerodynamic Design of Aircarft”, Pergamon Press, New York, 1978. 15

NASA Dryden Flight Research Center, PAO, “NASA’s X-43A Proves Hypersonic Scramjet Flight, March 27,

2004. 16

Dean Andreadis, “Scramjet Engines Enabling The Seamless Integration Of Air & Space Operations”, Pratt &

Whitney Space Propulsion, Hypersonics, West Palm Beach, FL. 17

Hill, P., and Patterson, C., ‘Mechanics and Thermodynamics of Propulsion’, Addison-Wesley Publishing

Company, 1992. 18

Billig F. S.; “Research on Supersonic Combustion” Journal of Propulsion and Power, Vol. 9, No 4, July-Aug

1993 19

John D. Anderson “Fundamentals of Aerodynamics” Third Edition, McGraw-Hill, New York, 2001. 20

Marcus Lobbia and Kojiro Suzuki, Numerical investigation of Waverider-Derived Hypersonic Transport

Configurations’, AIAA Paper 2003-3804 21

White. F. M., ‘Viscous Fluid Flow’, McGraw-Hill, New York, 1974. 22

O’Neil, M, K. and Lewis, M. J., “Design Tradeoffs on Scramjet Engine Integrated Hypersonic Waverider

Vehicles,” Journal of Aircraft, Vol. 30, No. 6, 1993, pp 943-952.

7/25/2014 46th AIAA Aerospace Sciences

Meeting and Exhibit

1

Hypersonic Vehicle Design

Mookesh Dhanasar

PhD Student, CAR

North Carolina A&T State University

January 9th 2008

7/25/2014 2

Outline

1. Justification For Hypersonic Technology Development

2. A Brief Review of the Waverider Concept

3. Hypersonic Vehicle Design from 2D Flowfields

4. Propulsion Systems Design from 2D Flowfields

4i: Geometric Design

4ii: Thrust Analysis

5. Conclusion

7/25/2014 3

Justification for Hypersonic Technology Development

Section 1: Introduction

7/25/2014 4

Hypersonic Technology Applications

• Access to Space

– Transportation on Demand to ISS, Lunar Base, etc

• Civilian Transatlantic, Transpacific Transport

– Transportation for long hauls/flights (flight times reduction, potentially reduces >12hrs to <3hrs)

• Military Applications

– Missiles, etc

What are the potential benefits of hypersonic technology?

7/25/2014 5

Characteristics of Hypersonic Flows

Hypersonic Flow (M = 5) is defined as the flight regime where the following flow phenomena gets progressively more important as the Mach number increases:

Thin Shock Layers

Entropy Layer

Viscous Interaction

High Temperature Effects

Low Density Flow

7/25/2014 6

Integrated Hypersonic Vehicle Designs

Flight Performance Data:

Justification for the Integrated Hypersonic Vehicle Design

Observation and Independent study

7/25/2014 7

Integrated Hypersonic Vehicle Designs

Flight Performance Data:

Justification for the Integrated Hypersonic Vehicle Design

Kuchemann

7/25/2014 8

Idealized Hypersonic Vehicles • Idealized Hypersonic Vehicles

7/25/2014 9

Propulsion Systems & Their Capability

This is what is known about various propulsion systems.

7/25/2014 10

Propulsion System Driven Configurations

Ultimately, the Aircraft Mission & the Propulsion System drive the configuration of the Hypersonic Aircraft

7/25/2014 11

A Brief Review of the Waverider Concept

Section 2: Hypersonic Vehicle Design

7/25/2014 12

Background

A waverider is any hypersonic vehicle that uses its own shock

wave to improve its overall aerodynamic performance

What are Waveriders?

Re-entry Vehicle with High Lift Capabilities

Terence Nonweiler, UK, 1959

Star shaped Bodies with Minimum Drag Capabilities

Maikapar, Russia, 1959

2-D plane shockwave

7/25/2014 13

Deriving Waveriders from Arbitrary Generating Shockwaves

r

Shock Wave

Free Stream Alt, M, p, ρ

Leading Edge Defined by base curve

Typical Base Curve (Upper or Lower)

Axisymmetric shockwave

7/25/2014 14

Coupled Inviscid Streamline & Boundary Layer Theories

Solid Streamline

Calculation of the Local Shear Stress & Local Heat Flux

0

n

P

Boundary Layer

streamlinesolidedgeBL PP ,

Inviscid Streamline

h, Cf

LTransition

transitionturbstH

transitionlamstH

H

transitionturbst

transitionlamst

LLengthLocalC

LLengthLocalCC

LLengthLocal

LLengthLocal

,

,

,

,

,,

,,

,

,

stst

sttrTransition

VL

*

*Re

641.2*0001209.0421.610Re

Me

tr

Viscous effects

7/25/2014 15

• Force due to Pressure, P

• Force due to Shear stress, FFF p

kzdSjydSixdSSd

S

SdF

S

SpdpF

i

j

k

• Integrate over the whole wetted surface to obtain the components

F

Sd

P

Aerodynamic Analysis Objective: To calculate L, D, and L/D

kGjLiDF

The force vector is a function of pressure and shear stress F

7/25/2014 16

Cone-Derived Waveriders

Reviewing

7/25/2014 17

1=Flat Upper 2=Flat Lower 3=Upper Opt. 1 4=Lower Opt.1

5=Upper H’bolic 6=Lower H’bolic 7=Upper Opt.2 8=Lower Opt. 2

Illustrations of Waverider Generated from Conical Flowfields

7/25/2014 18

9=Upper Elliptical 10=Lower Elliptical 11=Upper P’bolic 12=Lower P’bolic

13=Upper Circular Arc

14=Lower Circular Arc

15=Upper Opt. 3 16=Lower Opt. 3


7/25/2014 19

17=Upper Opt. 4 18=Lower Opt.4 19=Upper Min. Drag

20=Lower Min. Drag

21=Upper Fixed Base to Width Ratio

22 = Lower Fixed Base to Width Ratio

23=Bat Wing


7/25/2014 20

Results

4.5

4.7

4.9

5.1

5.3

5.5

5.7

5.9

6 8 10 12 14 16 18 20

Mach Number

L/D

Flat Bottom Lower Circular Arc

Bat Wing Kuchemann

7/25/2014 21

Waverider Design Validation

Reinforces the waverider design process

7/25/2014 22

Hypersonic Vehicle Design from 2D Flowfields

Section 3: Research Plans

Plane or axisymmetric

7/25/2014 23

Characteristics of Hypersonic Vehicles

Integrated Configurations Air-breathing Propulsion Systems

Favorable Dynamic Pressure Environments

reviewing

7/25/2014 24

Hypersonic Vehicle with Morphing Capability

An NCAT-CAR Proposed Concept

Agard

Complex

7/25/2014 25

Ramjet Only

Turbojet & Ramjet Turbojet Only

Turbojet Inlet Compressor

Burner

Turbine


Turbojet Nozzle Turbojet Exhaust Duct

& Afterburner

A NASA-GRC Proposed Concept

Hypersonic Propulsion System with Morphing Capability

Exo-Skeletal Engine Concept The engine is design to operate as a combined-cycle propulsion plant from

ground to Mach 6 and greater. The ‘exoskeletal’ engine concept is a revolutionary

class of gas turbine engines, in which the rotating components are mounted

concentrically within a drum structure around a central core channel. This

provides numerous postulated advantages over a conventional engine, primarily

because the rotating components are in compression instead of tension. Of great

interest for application to a combined-cycle engine is the fact that the central

core of this engine could function as a ramjet, and possibly even a scramjet,

enabling the engine to operate on a hybrid cycle up to hypersonic speeds.

7/25/2014 26

NASA GRC Exo-Skeletal Engine Concept

Duct In which the Ram-Scramjet is Constructed

7/25/2014 27

Ramjet Only

Turbojet & Ramjet

Turbojet Inlet Compressor

Turbine


Turbojet Nozzle Turbojet Exhaust Duct

& Afterburner

Propulsion System Design Challenge

Identify The Engineering Design Parameters as Functions of the Mach

Number that optimally morphs the ramjet into the scramjet as the propulsion

System traverse the Mach range of 3 to 8.

1. Exoskeletal Turbine Cycle Concept, NASA GRC

2. Ramjet-Scramjet Morphing Concept, NASA GRC, NCAT

7/25/2014 28

Propulsion Systems Design from 2D Flowfields

4.i: Geometric Design

4.ii: Thrust Analysis

Section 4: Ramjet-Scramjet Concept

7/25/2014 29

1. AERODYMANICS REQUIREMENTS DRIVES THE GEOMETRIC SHAPES

MORPHING RAMJET-SCRAMJET DESIGN CHALLENGES

2. THE GEOMETRIC SHAPES DRIVES THE AERO-PROPULSION ANALYSIS

Lower M require a nozzle to simulate the thermal Throat.

7/25/2014 30

Primary

Shock

Zone

A

Reflected

Shock

Zone

Isolator

Zone Diffuser

Zone

Combust

or

Zone

Nozzle

Zone

B D C E F G

x

GEOMETRIC DESIGN ASPECTS

A 2D Ramjet-Scramjet Cross-Section is Constructed, using a

parametric approach

The engineering design parameters are chosen such that the

Cross-Sectional Geometry Changes from Ramjet to Scramjet

Modes.

Based on the Waverider-Design Approach, a 3D Forebody/Inlet is

carefully chosen.

The Fore-body introduces the 3rd Dimension need for the

construction of the Closed Geometrical Shape of the

Morphing ‘Ramjet-Scramjet’ Configuration.

Develop a FORTRAN code

7/25/2014 31

2

2 5 3 4 6 7 1

A

B

C D

E F

G

H

I

J

K

Illustration of the RAMJET-SCRAM Design Coordinates

(Data for Two-Shockwaves Design Concept)

7/25/2014 32

11,M

2

1,

M

22,M

11,M

2

1,

M

22,M

22cos2

12sin2cot2tan

1

1

11

)β(γM

βMβθ

1

1,1

sin

nMM

2

1

211

2,

2,

21,

n

n

n

M

M

M

)sin( 1, MMn

Vehicle Forebody Design Procedures

1

2

1

2

1

2

1

2

y

x

A C D B

H = Alt

M = Mach

E

1. Geometric Construction Methods

2. Aerodynamic Analysis Methods

7/25/2014 33

GEOMETRIC DESIGN ASPECTS

Figure 11: Star-Shaped Inlets for the Exoskeletal Ramjet-to-Scramjet Concept

Fig. 11c: Front View Fig. 11b: Isometric View Fig. 11a: Side View

A Sample of Possible Forebodies

For Simplicity the 4 Star-Shaped Fore Body is Chosen

Y

X

Z

Frame 001 14 Feb 2007

X Y

Z

V4

4068.21

4036.09

4003.97

3971.85

3939.72

3907.6

3875.48

3843.36

3811.23

3779.11

3746.99

3714.86

3682.74

3650.62

3618.5

Pressure Distribution

Penetrator

Frame 001 14 Feb 2007

7/25/2014 34

ILLUSTRATION OF AN INLET WITH A REFLECTED SHOCK

Using the 4-Point Star-Shaped Body, and Two-Shocks:

E

F

G

H

HL

Shock wave II

Shock wave

Freestream

1

2

h

LCowl L2

H2

2 4

3

1

2

3 3

2

7/25/2014 35

Primary

Shock

Zone

A

Reflected

Shock

Zone

Isolator

Zone Diffuser

Zone

Combust

or

Zone

Nozzle

Zone

B D C E F G

x

3D Geometric Construction from Prescribed 2D C-Section & Forebody Shapes

7/25/2014 36

Rear View Front View Side View

Transparent Isometric View Isometric View with Cut away

Fig. 16: Illustration of A Morphing Ramjet-to-Scramjet Configuration

3D ILLUSTRATION OF THE RAMJET-SCRAMJET

Derived from Prescribed 2D C-Section & Forebody Shapes

7/25/2014 37

Propulsion Systems Design from 2D Flowfields

4.i: Geometric Design

4.ii: Thrust Analysis

Section 4: Ramjet-Scramjet Concept

7/25/2014 38

The Ideal Ramjet Engine Thermodynamic Analysis

The ideal engine thrust is given by (Hill, Paterson):

where f is the fuel-air ratio, uexit and u3 velocities at locations 3 and the exit.

Isolator

Reflected Shock

Ramjet Burner

Ramjet Nozzle

Primary Shock

Mixing

2 3 4 Exit

33 1 uufmT Exit

)1()(

)()(

2

3

MpAxI

xIxIT exit

Alternate Form for Thrust,

Impulse function

7/25/2014 39

Isolator

Reflected Shock

Ramjet

Burner

Ramjet

Nozzle

Primary Shock Mixing

2 3 4


dx

md

mM

MM

D

c

M

MM

dx

dT

TM

MM

dx

dA

AM

M

dx

dM

M h

f

1

1

124

1

1

1

11

1

212

2

2

20

02

2

2

2

2

2

2

11 MM

where the parameter, M , is defined as follows: mand the mass flow rate

1. Mach Number Evaluation:

The cross sectional area, A(x), is obtained from the design inputs.

The skin friction Coefficient, cf , is evaluated using the Reference Temperature method.

2. Skin Friction Coefficient:

The stagnation temperature, T0(x) is computed as follows:

34

3

02

04

02

0 ,5040,11

11xx

xxx

x

x

T

T

T

xT

3. Stagnation temperature Evaluation:

7/25/2014 40

PRELIMINARY RESULTS

ISP vs Mach Number

(4-Point Star Configuration)

2000

3000

4000

5000

6000

2 4 6 8 10 12

Mach Number

ISP

7/25/2014 41

Discussion

ISP vs Mach Number

(4-Point Star Configuration)

2000

3000

4000

5000

6000

2 4 6 8 10 12

Mach Number

ISP

7/25/2014 42

CONCLUSION

• When looking at hypersonic technology development

there is :

– Need for an integrated vehicle design:- Waverider concept.

– Need for an integrated propulsion system: Combine cycle

concept.

• Preliminary results are encouraging but needs

validation.

7/25/2014 43

Thank You!

Any Questions?

7/25/2014 44

Back-up Slides

7/25/2014 45

7/25/2014 46

7/25/2014 47

Thin Shock Layers Thin Shock Layers

As the Mach number increases, the shock angle becomes smaller, as illustrated in the figure below. The resulting flowfield between the surface and shock is often referred to as a shock layer. This thin layer can produce many complications in vehicle design, e.g. the shock layer may merge with the boundary layer at low Reynolds numbers to form a fully viscous shock layer.

Shock waves and streamlines over a 20° half-angle wedge at (a) Mach 2 and (b) Mach 20 [from Anderson, 2000]

At high Reynolds numbers, the shock layer can be treated as inviscid (meaning there is no friction). In the limit as Mach number goes to infinity, the shock layer forms an infinitely thin, infinitely dense sheet, or, essentially, a flat plate. The infinite flat plate is the most efficient lifting surface at hypersonic velocities, and the inviscid shock layer can therefore be used to develop simplified theories to predict hypersonic aerodynamic properties.

Sect 3.1

7/25/2014 48

Entropy Layer Entropy Layer Shock theory tells us that entropy increases across a shock, and the entropy increase becomes greater as the shock strength increases. Since flow near the nose passes through a nearly normal shock, it will experience a much greater change in entropy compared to flow passing through the much shallower shock angle further from the body centerline. Thus, strong entropy gradients exist near the leading edge generating an "entropy layer" that flows downstream along the body surface.

Entropy layer formation [from Anderson, 2000]

The classical boundary layer grows within this entropy layer and may be greatly affected by the entropy gradients. In addition, the entropy layer is a region of strong vorticity that can generate large gradients in the velocity flowfield near the surface, a phenomenon called "vorticity interaction." The large velocity and thermodynamic gradients induced by the sharply curved oblique shock become troublesome when attempting to predict aerodynamic performance, heat transfer results, and boundary layer shape for a hypersonic vehicle.

Sect 3.1

7/25/2014 49

Viscous Interaction Viscous Interaction When a body travels through the air, a thin region near the body surface called the

"boundary layer" is formed. In this layer, the air slows down from the "freestream" velocity of the airflow to zero at the surface. At subsonic speeds, the thickness of the boundary layer tends to become smaller as velocity increases because the thickness is inversely proportional to the Reynolds number:

• For compressible flow (or flow at high speeds), however, increasing flow temperature

(due to friction heat) near the body surface causes the boundary layer to become thicker as speed increases. The two primary factors driving this boundary layer growth are an increase in viscosity of the fluid and a decrease in density. The result of these factors is that boundary layer thickness varies as the square of the Mach number:

• Thus, as Mach number increases, the boundary layer can grow rapidly resulting in very

high drag. Should the boundary layer become thick enough, it may affect the inviscid flowfield far from the body, a phenomenon called viscous interaction. Viscous interaction can have a great influence on the surface pressure distribution and skin friction on the body thereby affecting the lift, drag, stability, and heating characteristics of the body.

Sect 3.1

7/25/2014 50

High Temperature Flow High Temperature Flow Any body traveling at high speeds in air produces friction and heat. Part of the kinetic

energy of the body's motion is absorbed by the air and carried away from the body through a process called viscous dissipation. However, hypersonic vehicles create so much heat and such high temperatures that they can actually cause chemical changes to occur in the fluid through which they fly. The most notable changes air undergoes as temperature increases are summarized below.

High Temperature Effects on Air As temperature increases, assumptions about the properties of the air are no longer valid

and the vehicle is said to be traveling through a chemically reacting boundary layer. When the properties of the working fluid change, namely density and heat transfer properties, the aerodynamic characteristics and heating properties of the body can change drastically.

Temperature [K] Chemical Change

800 Molecular vibration

2000 Oxygen molecules (O 2) dissociate

4000 Nitrogen molecules (N 2) dissociate

Nitric oxide (NO) forms

9000 Oxygen and nitrogen atoms ionize

Sect 3.1

7/25/2014 51

Low Density Flow Low Density Flow Most hypersonic vehicles are intended to cruise at high altitudes in low density fluids. In

low density flows, air can no longer be considered to be a continuum because the distance between individual particles of air becomes so great that each particle begins to affect the aerodynamic properties of a body. Under these conditions, common aerodynamic relations, like the Euler and Navier-Stokes equations, break down. Instead, aerodynamic properties must be analyzed using the kinetic theory. Some of the most important differences between low density flows and continuous flows include

– Velocity slip: The viscous no-slip condition that says the velocity of air particles going past a body must be zero at the body surface, fails. Since friction is negligible in low density, the flow velocity at the body surface is no longer zero.

– Temperature slip: The assumption that gas temperature at the body surface becomes equal to the temperature of the body surface material fails.

Sect 3.1

Drag coefficient of a sphere at hypersonic speeds transitioning from continuum to free-molecule flow [from Anderson, 2000]

7/25/2014 52

Calculating Shear Stress & Stanton Number (cont’d.)

2*2

1, ststE VstQ

stEstfst QC ,, *

• Local Dynamic Pressure at the edge

• Local Shear Stress

45.210 eRlog176.0

sturbtS

21

2, 158.032.00.1

Re

664.0

T

TMC w

s

lamf

2132 RePr332.0 slamtS

2.0,eR

0592.0

s

turbfC

svsRe

sv

seR

• Local Skin Friction Coefficient

• Local Reynolds Number

• Local Stanton Number

7/25/2014 53

Shape Generation

• Two-Dimensional Flowfield in terms of x and r

• Waverider Shape needs to be Three-Dimensional

• Third Dimension introduced with Shape Angle

7/25/2014 54

Shape Generation (Shape Angle)

y

z

Streamline Coordinates

Azimuthal Angle, f(r)

Conical Shockwave

Waverider Base f

7/25/2014 55

Models : The Ideal & Real Ramjet Engine

The ideal engine thrust is given by (Hill, Paterson):

where f is the fuel-air ratio, uexit and u3 velocities at locations 3 and the exit.

ExitEExit AppuufmT 333 1

Schematic Diagram of a Typical Ramjet. (Hill, Peterson)

7/25/2014 56

i. Since the compression phases are dictated by two oblique shock waves. The

total pressures across these waves can be calculated as described in Anderson,

Oblique Shockwave Theory.

ii. Assuming that combustion occurs at constant pressure, the stagnation pressure

does not change across and through the nozzle.

iii. Assuming that the fluid properties, R and gamma, do not change in any of the

processes, we can relate the pressure at station 3 and the exit to the Mach

numbers representative at those points, as shown in the following equations:

The Ramjet Engine Thermodynamic Analysis

03,0 PP Exit

1

23

3

3,0

2

11

M

P

P

1

2,0

2

11

exit

Exit

ExitM

P

P

Ideal Case:

Real Case:

Nozzle

Combustor

Combustor

DiffuserExitExit

P

P

P

P

P

P

P

PPP

,0

,0

,0

3,0

03

,0

03

,003,0 ;

7/25/2014 57

In the case of an ideal ramjet engine, the enthalpy of the incoming fuel is neglected.

The energy equation then becomes:

where QR is the heating value of the fuel. Assuming a constant specific heat, we can state that the fuel-air ratio now becomes:

Combining several of these equations we can get the thrust per unit mass flow to be:


03,0 PP Exit

Ideal Case:

fQhhf R 02041

020402

0204 1

TTTcQ

TTf

pR

12

111

212

0204222

MTTfRTMm

T

7/25/2014 58

Combining several of these equations we can get the thrust per unit mass flow to be:

The ‘Real Ramjet’ Engine Thermodynamic Analysis

Real Case:

Nozzle

Combustor

Combustor

DiffuserExitExit

P

P

P

P

P

P

P

PPP

,0

,0

,0

3,0

03

,0

03

,003,0 ;

The departure of isentropic processes leads to significant changes in the

compression, combustion and expansion segments of the ramjet. Stagnation

pressure ratios can be formulated for each of these and are as follows:

020402

0204 1

TTTcQ

TTf

pR

12

11

1

21

2

02

,022

2

Exit

ExitExit

p

p

p

pMM

ExitEExit Appm

uufm

T3

33

3

11

7/25/2014 59

Supersonic and Hypersonic Air-Breathing Configurations Derived from 2D Flowfields

Documents

Transcript of Supersonic and Hypersonic Air-Breathing Configurations Derived from 2D Flowfields