Development of an Aerodynamic/RCS Framework for the
Preliminary Design of a Hypersonic Aircraft
by
Daniel L. DiCara
Submitted to the Department of Aerospace Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Aerospace Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2006
@ Massachusetts Institute of Technology 2006. All rights reserved.
A uthor ................
......................... .................................
Department of Aerospace Engineering
May 26, 2006
A
Certified by .....
I\
Jaime Peraire
Professor
Thesis Supervisor
.
i
Accepted by.....
Jaime Peraire
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
OCT 15 2008
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Development of an Aerodynamic/RCS Framework for the
Preliminary Design of a Hypersonic Aircraft
by
Daniel L. DiCara
Submitted to the Department of Aerospace Engineering
on May 26, 2006, in partial fulfillment of the
requirements for the degree of
Master of Science in Aerospace Engineering
Abstract
The design of hypersonic airbreathing aircraft pushes the envelope of current state-ofthe-art aerospace propulsion and materials technology. Therefore, these aircraft are
highly integrated to produce adequate thrust, reduce drag, and limit surface heating.
Consequently, every aircraft component (e.g., wings, fuselage, propulsion system) is
sensitive to changes in every other component. Including Radar Cross Section (RCS)
considerations further complicates matters. During preliminary design, this requires
the rapid analysis of different aircraft configurations to investigate component interactions and determine performance trends. This thesis presents a framework and
accompanying software for performing such an analysis. The intent is to optimize a
hypersonic airbreathing aircraft design in terms of aerodynamic performance and RCS.
Computational Fluid Dynamics (CFD) and Computational Electromagnetics (CEM)
are the two main framework software components. CFD simulates airflow around the
aircraft to analyze its aerodynamic performance. Alternately, CEM simulates the electromagnetic signature of the aircraft to predict its RCS. The framework begins with
the generation of a three-dimensional computer aided design aircraft model. Next, a
grid generator discretizes this model. The flow simulation is performed on this grid
and the aircraft's aerodynamic characteristics are determined. Flow visualization aids
this determination. Then, aircraft geometry refinements are made to improve aerodynamic performance. Afterward, CEM is performed on aerodynamically favorable
designs at various aspect angles and frequencies. RCS values are determined and used
to rank the different configurations. Also, inverse synthetic aperture radar images are
generated to locate major scattering centers and aid the design refinement. The design loop continues in this fashion until an acceptable aircraft design is achieved. The
NASA X-43A test vehicle was used to validate this preliminary design framework.
Thesis Supervisor: Jaime Peraire
Title: Professor
Acknowledgments
I would like to thank MIT Lincoln Laboratory and the Lincoln Scholars Committee
for funding my graduate work and providing valuable feedback over the course of my
research. Two other people at Lincoln Laboratory I would like to thank are Dr. Jack
Fleischman and Dr. Hsiu Han. Jack was my group leader at Lincoln Laboratory when
I applied to the Lincoln Scholars Program. I cannot thank him enough for supporting
my entrance into the graduate program at MIT and providing me with a challenging
and exciting research topic. Furthermore, Hsiu was my Lincoln Laboratory advisor
during the course of my graduate work. He was an excellent resource and provided
much needed instruction on all topics having to do with Electromagnetics. Having
an aerospace engineering background, I was fairly inexperienced in this area prior to
entering graduate school. I am very grateful for his patience and effort in instructing
me in this field.
I am also thankful for the software installation and support given by William
Jones and Karen Bibb at the NASA Langley Research Center. Bill provided me with
the GridEx software that was a crucial component of my design framework. Despite
his very busy schedule, he was quick to fix any problems that came up and provide
guidance whenever necesary. Karen also took a lot of time out of her busy schedule to
provide me with the FELISA Hypersonics code, also a crucial component of my design
framework. Karen did an excellent job of modifying the code so it would compile and
run on the Aerospace Computational Design Lab (ACDL) cluster. Without this help,
simulation times would have easily taken an order of magnitude longer than using the
10 node ACDL cluster.
Last, but definitely not least, I would like to thank several members of the ACDL.
For instance, Bob Haimes and Garret Barter were invaluable in assisting me with all
of my computer related issues. Bob provided me with much needed installation and
user support for VisualS.
This tool is responsible for all of the flow visualizations
presented in this thesis. Bob also provided advice and support on everything from
ProEngineer to system backups. I really appreciate his willingness to help me with
problems that inevitably arise when trying to integrate a multitude of software into
a coherent framework.
Similarly, Garrett provided extensive time and effort into
configuring my laptop, desktop, and the cluster to accomodate my needs. Also, I had
two hard drive failures during my graduate studies, and Garrett was very helpful in
getting me back online. He also put up with all of my day to day questions about
how to print, using latex, and just about anything else you could think of. Lastly, I
am very grateful for my advisor, Professor Jaime Peraire. His encouraging advice and
enthusiasm about my research kept me motivated even when things were not going
well. I also appreciated his knowledgable guidance and his ability to convey difficult
subject matter to me in terms I could understand. Finally, Professor Peraire's friendly
nature made him a real pleasure to work with.
Contents
1
13
Introduction
1.1
Hypersonic Aerodynamics
1.2
Scramjet Propulsion
1.3
14
.........................
17
..........................
..
Engine Description .......................
1.2.2
Combustor Inlet Model .......................
20
1.2.3
Combustor Exit Model .......................
22
Radar Cross Section Reduction
25
......................
1.3.1
Radar Equation ...........................
26
1.3.2
Radar Cross Section
27
1.3.3
Scattering Mechanisms ...................
....
1.3.4
RCS Reduction Techniques ....
..
........................
. . ............
29
. .
30
33
2 Preliminary Design Framework
2.1
3D Computer Aided Design Solid Modeling . ...............
2.2
Grid Generation ..............
2.3
Flow Simulation ..........
2.4
RCS Signature Prediction
.
33
. .
. ....
. . ... . . . . . . 35
.. . .
. ....
. . ... .. . . . . 36
.........................
3 X-43A Trade Study
3.1
18
1.2.1
Compression System ............................
3.1.1
Aerodynamic Performance . . . ...............
3.1.2
RCS Performance ..........................
36
39
40
. . . 42
48
3.2
3.3
Expansion System ..............................
3.2.1
Aerodynamic Performance ...................
3.2.2
RCS Performance ..........................
Control Surfaces .....................
51
..
52
53
...........
54
List of Figures
1-1 X-43A Hypersonic Airbreathing Aircraft [8]
1-2 Scramjet Engine Stages [3] . . . . . . . . . .
2-1
Aerodynamic/RCS Framework Outline . . .
2-2
EM Signature Prediction Techniques
3-1
X-43A Flight Test Aircraft Photograph [12]
. . . . . . . . . . . . . 40
3-2
External Compression System Design . . . .
. . . . . . . . . . . . . 40
3-3
Internal Compression System Design . . . .
. . . . . . . . . . . . . 41
3-4
Total Pressure Ratio Design Comparison . .
. . . . . . . . . . . . . 42
3-5
Kinetic Energy Efficiency Design Comparison
. . . . . . . . . . . . . 43
3-6
Mach Number Visualization for IFA = 600 LEA =
3-7
Mach Number Visualization for IFA = 1350 LEA = 90 w/out Ramp
3-8
Density Visualization for IFA = 600 LEA = 90 w/Ramp . . . . . . .
3-9
Density Visualization for IFA = 1350 LEA = 90 w/out Ramp
. . . .
90
w/Ramp . . .
. . .
3-10 Pressure Visualization for IFA = 600 LEA = 9' w/Ramp . . . . . .
3-11 Pressure Visualization for IFA = 1350 LEA = 90 w/out Ramp . . .
3-12 Median RCS Design Comparison
. . . . . . . . . . . . . . . . . . .
3-13 Total Pressure Ratio Design Comparison Refinement
. . . . . . . .
3-14 Kinetic Energy Efficiency Design Comparison Refinement . . . . . .
3-15 Leading Edge Angle RCS Comparison
. . . . . . . . . . . . . . ..
3-16 Internal Ramp Configuration RCS Comparison . . . . . . . . . . . .
3-17 Lift-to-Drag Ratio
...........................
3-18 Scramjet Engine Thrust
.............
.
.
3-19 Tail-End HC Configuration ...................
......
.
......
53
53
3-20 Pressure Visualization for IFA = 1200 LEA = 9' No Ramp w/out HC .
55
3-21 Pressure Visualization for IFA = 120' LEA = 90 No Ramp w/HC . . .
55
3-22 Tail End Configuration RCS Comparison . ................
56
3-23 2D and 3D Flow Visualizations
...................
3-24 Control Surface Configuration RCS Comparison . ............
...
57
58
List of Tables
1.1
Scramjet Engine Reference Station Descriptions [3]
...........
19
Chapter 1
Introduction
Preliminary aircraft design requires efficient methods for estimating aircraft performance. Important performance considerations are lift, drag, stability, control surface
authority, and propulsion system selection and integration. In military aircraft design,
Radar Cross Section (RCS) is also crucial. These design considerations are highly coupled - improving one may adversely affect the others. Therefore, refining an aircraft
design requires extensive simulation to examine trade-offs between different aircraft
configurations. Unfortunately, predicting aerodynamic performance using Computational Fluid Dynamics (CFD) is typically time-consuming. Similarly, predicting aircraft RCS using Computational Electromagnetics (CEM) takes a considerable amount
of time. As a result, low fidelity tools are generally used in preliminary aircraft design, and such tools may inaccurately predict aircraft performance, adversely affecting
crucial design decisions. Therefore, this thesis provides a framework and accompanying suite of software to rapidly perform CFD and CEM simulations for preliminary
aircraft design in terms of aerodynamic and RCS considerations.
To demonstrate the utility of this framework and the accompanying software, a
case study was performed using a baseline aircraft configuration as a starting point.
An idea underlying this thesis is to look towards the future of military aircraft design.
Most would agree that future military air vehicles will need to fly higher, farther, and
faster. The epitome of this concept is the NASA X-43A. This experimental aircraft
flies at hypersonic speeds (> Mach 5) within the atmosphere. It employs a scramjet propulsion system, which is considered the most likely candidate for hypersonic
airbreathing flight in production aircraft in the future. Additionally, the X-43A completed two successful flight tests during my graduate studies lending credence to the
viability of scramjet engine technology. Furthermore, photographs and diagrams of
the X-43A are available in the open literature and were used in producing this thesis.
Therefore, a canonical hypersonic airbreathing aircraft configuration was constructed
based on the X-43A design; wherein the configuration was refined using the preliminary design framework presented herein.
1.1
Hypersonic Aerodynamics
In Reference [5], Anderson identifies five flow phenomena that become significant as
the freestream Mach number is increased through hypersonic values. They are the following: thin shock layers, entropy layers, viscous interactions, high-temperature flows,
and low-density flows. The influence of these phenomena distinguish hypersonic flow
from other flow regimes. Firstly, thin shock layers result from the high Mach numbers
encountered in hypersonic flow. According to oblique shock wave theory, higher flow
Mach numbers produce smaller shock-wave angles. Consequently, sharp aircraft edges
in a hypersonic flow produce oblique shock waves that reside very near the aircraft's
surface. In certain instances, these shallow oblique shocks may interact with the viscous boundary layer. Alternately, blunt aircraft edges and nose cones in hypersonic
flows produce what is called an entropy layer. These blunt surfaces effectuate strong
curved bow shocks. Entropy increases across a shock and the magnitude of this increase depends on the shock strength and hence the shock-wave angle. Therefore,
the curvature of the bow shock generates an entropy gradient (layer) normal to the
aircraft surface that also interacts with the boundary layer.
Shallow oblique shock waves and entropy layers are not the only aspects of hypersonic flow that have the potential to affect the boundary layer. For instance, the
internal energy of hypersonic freestream fluid particles is small in comparison to their
kinetic energy [1]. This kinetic energy is dissipated in the boundary layer and manifests primarily as a temperature increase. This increase in temperature has two effects:
(i) it increases the viscosity of the fluid, and (ii) it decreases the density. Both effects
feed off of one another to increase the boundary layer thickness. In extreme cases,
the boundary layer may even merge with the shock wave. This interaction between
the boundary layer and the outer inviscid flow region is termed viscous interaction.
High-temperature flows are also a result of the increased temperature in the boundary
layer. If the temperature is high enough, the internal vibrational energy modes of the
fluid particles may become excited. Furthermore, dissociation of the fluid molecules
and even ionization may take place. These are often referred to as real gas effects
and they act to reduce the thickness of the boundary layer. Finally, most hypersonic
aircraft travel to the edge of the atmosphere or even into outer space. At these high
altitudes, density of the air is low enough to invalidate the assumption that air is a
continuum (continuous medium). In these instances, the field of rarefied gas dynamics
must be used to simulate the flow accurately.
The flow does not have to exhibit all of these phenomena at once to be considered hypersonic. However, as the Mach number approaches higher values, all of
these phenomena emerge and become significant. Thus, CFD codes of increasing fidelity/complexity are required. For the hypersonic airbreathing aircraft studied in this
thesis, relatively low hypersonic Mach numbers (< Mach 10) are analyzed. The reason
for this is twofold: (i) the atmosphere must be dense enough to provide adequate oxygen to the airbreathing propulsion system, and (ii) the surface temperatures on the
aircraft must be manageable for the given state-of-the-art materials employed. For a
typical flight, this requires an altitude of 100 kft where air is still considered a continuum. At this altitude, relatively low Mach numbers are necessary to achieve sustained
hypersonic flight without the aircraft overheating. Consequently, strong viscous interactions, low-density, and high-temperature flow effects have a limited significance in
the case of hypersonic airbreathing aircraft. As scramjet engine technology matures
and materials designed to operate at higher temperatures are developed in the future,
perhaps higher Mach numbers for these type of vehicles can be achieved. However,
given current materials and scramjet engine limitations for hypersonic aircraft, the
chosen freestream Mach number simulated in this thesis is reasonable.
Therefore,
the inviscid hypersonic flow solver (FELISA) utilized in this thesis provides adequate
results for preliminary hypersonic airbreathing aircraft design.
The disparity between conventional and hypersonic airbreathing aircraft configurations reflects the aerodynamic differences just described. For instance, conventional
aircraft can be broken down into distinct components (e.g., wings, fuselage, horizontal
and vertical tail, engines). In conventional aircraft design, these components can be
designed and analyzed separately with modest consideration of the interactions between the different aircraft parts. This is not true when designing hypersonic aircraft.
The components of hypersonic aircraft must be highly coupled in order to manage the
harsh hypersonic flow environment [11]. For instance, in scramjet engine design, the
airbreathing engine is typically integrated into the airframe to reduce wave drag and
take advantage of the bottom compression/expansion surfaces of the aircraft. Also to
reduce wave drag, blended wing body configurations and highly swept control surfaces
are typically employed. A design that implements these ideas is the X-43A given in
Figure 1-1.
First of all, notice that distinct wings are unnecessary for providing lift. High
pressure air behind the leading edge shock exerts enough force (lift) on the underside
of the aircraft to support its weight [5]. Furthermore, the engine is integrated into the
airframe. The under-surface of the aircraft forward of the engine has been designed
to efficiently compress the air through a series of oblique shocks. Similarly, aft of the
engine, the under-surface has been designed to efficiently expand the combustion gases
to produce additional thrust. Finally, the control surfaces are significantly swept back
to reduce wave drag. These are common traits of hypersonic airbreathing aircraft that
the trade-study will examine in this thesis.
X-43A B
NASA Dryden Flight Research Center Graphics Collection
http://www.dfrc. nasa.gov/gallery/graphics/index.html
created April 6, 2004 by Tony Landis
X-43A 3-view
Figure 1-1: X-43A Hypersonic Airbreathing Aircraft [8]
1.2
Scramjet Propulsion
The typical modern jet engine requires a compressor that consists of alternating rows of
rotating (rotor) blades and stationary (stator) vanes. The compressor provides a rise in
static pressure to the combustor inlet. This static pressure rise is necessary for efficient
combustion. A turbine residing behind the combustor also contains alternating rows
of rotor blades and stator vanes. It extracts a portion of the energy from the hot
combustion gases to power the compressor, wherein the remaining energy is discharged
as useful work in the form of thrust. An advantage of hypersonic aircraft design is
that this compressor and turbine hardware is unnecessary. A hypersonic aircraft is
designed to take advantage of normal and/or oblique shock waves in the flow that
provide adequate compression prior to the combustor inlet. This is known as the
"ram effect," and consequently, engines of this type are called ramjets. Scramjets
(Supersonic Combustion RAMJETs) are a type of ramjet in which air entering the
combustor is supersonic. For vehicles traveling at hypersonic speeds (4 Mach 6), it is
inefficient to slow the air to subsonic speeds prior to combustion. Therefore, scramjet
engines are typically the chosen propulsion system for hypersonic airbreathing aircraft.
1.2.1
Engine Description
Compression
Expansion
Combustion
1
3
4
9
Figure 1-2: Scramjet Engine Stages [3]
A generic scramjet engine is illustrated in Figure 1-2. Similar to a conventional jet
engine, a scramjet performs three main functions: compression, combustion, and expansion. The unconventional aspect of scramjets is their incorporation of the vehicle's
airframe into the compression and expansion processes. Properly shaping the underside of the aircraft prior to the engine inlet and aft of the engine outlet significantly
reduces engine size and drag. In the figure, numbers are prescribed to each engine
stage and will be used to denote the location of various fluid state variables mentioned
in the discussion that follows. Furthermore, Table 1.2.1 provides a description of each
engine stage.
FELISA simulates the flow field up to the combustor entrance (station 3). Since
the flow is supersonic throughout the combustor, boundary conditions prescribed at
Stage
0
1
3
4
9
10
Description
Freestream Conditions
External Compression Begins
External Compression Ends
Diffuser Entry
Diffuser Exit
Combustor Entry
Combustor Exit
Nozzle Entry
Nozzle Exit
External Expansion Begins
External Expansion Ends
Table 1.1: Scramjet Engine Reference Station Descriptions [3]
the combustor entrance will not affect the flow. However, a thermodynamic model of
the compression system was derived to determine the desired fluid state (density, velocity, energy, pressure, and speed of sound) at the combustor entrance, as more fully
described herein. The results from the compression system model will be compared
to the CFD simulated fluid state. Then, the compression system will be iteratively
modified to achieve the desired fluid state at the combustor inlet. Otherwise, combustion will be inefficient and adequate thrust will not be produced. A description of the
compression system model will be described below.
The actual combustion process will be treated as a black box in the CFD simulation, wherein a model of the combustor has been calibrated to arrive at the desired
combustor exit fluid state. Unlike the combustor entrance, boundary conditions at the
combustor exit will influence the fluid state in the CFD simulation. Typical scramjet
engine operating conditions were gleaned, in most part, from Reference
[3].
This
design methodology will also be described below. Finally, ambient air properties were
needed to evaluate the engine modeling equations. A typical flight altitude for hypersonic aircraft is 100 kft. Therefore, properties of the "U.S. Standard Atmosphere
1976" at 100 kft were used. These properties include To = 227 K, Po = 1090 Pa,
Po = 0.0167 kg/m 3 , and ao = 302 m/s.
1.2.2
Combustor Inlet Model
Typically, a limiting factor in the design of a compression system is the cycle static
temperature ratio (4 = 1). This is the ratio of static temperature at the combustor
inlet to the ambient air temperature. For scramjet engines, acceptable combustor
inlet temperatures typically range from 1440 K to 1670 K [3]. Consequently, the cycle
static temperature ratio is 6.3 < b < 7.4. The ratio used in this model is ' = 7.
Furthermore, two assumptions that sacrifice very little accuracy are that compression
is adiabatic and the fluid is a calorically perfect gas. The adiabatic compression
assumption permits the conservation of total enthalpy during the compression process.
Furthermore, a calorically perfect gas has a constant ratio of specific heats. The ratio
used in this analysis will be > = 1.36. These assumptions help simplify the following
derivation.
Definitions of the first two fluid state variables at the combustor inlet are given
here. Speed of sound and specific internal energy are given in Equations 1.1 and 1.2,
J
respectively. The speed of sound requires the specific gas constant for air, R = 287 kgK
'
and the specific internal energy is defined using the specific heat of air at constant
volume, C,,
R
c-1
-797
J
kg.K
a3 = VyRT 3 = /R
e3 = CT
7
To
(1.1)
(1.2)
3
Deriving the velocity at the combustor can be accomplished by using the conservation of energy given in Equation 1.3.
pouoAo (ho +
) +
rhb+(hb
) +
+
p
3 U3 A 3
(h
3
+ V
(1.3)
Assuming no mass addition eliminates the summation term (Z nb = 0) and results
in the following simplification: rh = pouoAo = p3 u 3A 3 . Furthermore, the adiabatic
compression assumption eliminates the heat addition term (Q = 0). Also, since no
external work is being applied to the fluid, the work term is eliminated (W = 0). Finally, the calorically perfect gas assumption permits the replacement of enthalpy with
temperature and specific heat (ho = C,,To and h3 = CcT3 ). Applying these assumptions and rearranging Equation 1.3 gives Equation 1.4 for velocity at the entrance to
the combustor.
V3 =
(1.4)
V 2 - 2CpTo ( - 1)
Fluid velocity will be assumed parallel to the engine walls in the axial direction.
Therefore, only the x-component of velocity will be assumed nonzero resulting in the
three components of velocity given by Equations 1.5-1.7.
us = V3
(1.5)
v3 = 0
(1.6)
w3 = 0
(1.7)
Next, the static pressure ratio is defined using a compression system efficiency term,
c=
hh.
h3-ho"
This term relates the ideal (i.e. isentropic) change in static enthalpy to the
real (non-isentropic) change in enthalpy that occurs during the compression process.
This efficiency term can be reformulated to yield Equation 1.8 in terms of an ideal
temperature ratio.
c
Cpc (T3 - TX)
C, (T3 - To)
-
T
- = 0 (1 - o) + 7c
To
To
1
(1.8)
Subsequently, Gibbs equation (Equation 1.9) evaluated for an isentropic process yields
the compression system static pressure ratio given in Equation 1.10.
Tds = dh -
P3
T3
s - s = 0 = Cpcln- -R In
T,
Po
dP
dT
= ds = CpcT
p
=o
P3
P0
T3
R
I
R
=
dP
P
(1.9)
(1.10)
p1'7)'c
(1.10)
As a result of the ideal gas assumption, density is then computed as given in Equation
1.11. All the necessary state variables for the combustor entrance have now been
defined in Equations 1.1-1.2, 1.5-1.7, and 1.10-1.11.
P3
P3 =(1.11)
RT3
Two compression system figures of merit will be used to gauge the performance
of different inlet configurations.
These are total pressure ratio and kinetic energy
efficiency. The total pressure ratio is simply the ratio of total pressure at the combustor
entrance to the total pressure in the freestream.
This is given in Equation 1.12.
The kinetic energy efficiency is simply the ratio of velocity that would be achieved
in isentropic compression to the actual velocity that is achieved at the combustor
entrance. This is given in Equation 1.13. Ultimately, an efficient compression system
converts the kinetic energy in the freestream into a large pressure and density rise at
the combustor entrance, with as small a rise in temperature as is possible.
PT3
+ --1
_
+
-1C-
PTO
V=2
V20
1.2.3
1+
1
2
(1.12)
N 22 1 M20
V2 - 2Cpc (T - To)
V0
(113)
Combustor Exit Model
A few decisions were made before modeling the combustion process. For instance,
hydrogen fuel (H 2 ) was modeled in this analysis due to its high heat of reaction (hpR =
119,954 kJ/kg Fuel). Additionally, hydrogen is a typical scramjet engine fuel and was
used to power the X-43A. Next, an appropriate fuel-to-air ratio (fat) was derived using
stoichiometric (ideal) combustion in which all the available fuel and requisite oxygen
are consumed. Equation 1.14 provides this ratio for hydrocarbon fuels [3]. The fuelto-air ratio for hydrogen fuel was determined by plugging in x = 0 and y = 2 for the
number of carbon and hydrogen atoms, respectively, in molecular hydrogen.
fst =
36x+3y
103 (4x + y)
(1.14)
= 0.0291
Finally, as had been assumed in the compression process, air during combustion is
assumed to be a calorically perfect gas. Therefore, a typical value of the ratio of
specific heats for scramjet engines is Yb = 1.238. Consequently, the specific heats at
constant pressure and volume were now known: Cpb =
= 1493
-bR
J
and Cb
R1= 1206 J.
kg-K
7b-1
Combustion was modeled as a constant pressure deflagration. Therefore, pressure
at the combustor exit is immediately known.
P4 = P3
(1.15)
Next, the combustor exit velocity is derived using conservation of momentum as given
in Equation 1.16.
P3 A 3 + (p 3 u 3 A 3 ) u 3 +
rnhbUb
+ F = P 4A 4 + (p 4 u 4 A 4 ) u 4
(1.16)
Devices in the combustor, such as fuel injectors and mixers, protrude into the flow
path and cause drag. This is accounted for through a burner effective drag coefficient
of the form C
A-
where A, is the wetted area of the internal combustor surfaces.
the
ASecond,
Therefore, the force in this equation is given by F = -P3u'A3Cf.
2
3
A3
o
only mass addition is fuel. Therefore, E
rhbUb
is replaced with tif uf. In addition, the
fuel-to-air ratio can be defined in relation to the combustor inlet, exit, and fuel mass
flow rates. This is given in Equation 1.17.
-
rif
m4 -
3
= .7i4 = mi (1 + f)
(1.17)
Again, assuming that all velocities are in the axial direction (u 3 = V3 , u 4 = V4 , and
Uf = Vf), Equation 1.16 can be reformulated using these considerations and the fact
that ni3 = P3 u 3 A 3 and ni4 = p4u 4 A 4 . The result of these simplifications is given in
Equation 1.18.
4 = V3
P(A3 -A4)
AV (1+-f )
1-+f.
Y'
++4
1= f+
CI
2 (1f +AA3
f
(1.18)
1)
The first term within the brackets can often be neglected. Furthermore, a reasonable
assumption for the fuel entrance velocity in comparison to V3 is -V = 0.5. Lastly, a
3
conservative estimate of the burner effective drag coefficient is Cf - - = 0.1. Velocity
at the combustor exit can now be defined using these assumptions. Equations 1.19 1.21 give the three components of velocity.
4 = V4
V4 =
= V3
1=f
C
(1+Af)
V
= 0.937V3
(1.19)
v4 = 0
(1.20)
W4= 0
(1.21)
Temperature at the combustor exit is defined using conservation of energy as given
in Equation 1.3. Unlike the compression system, combustion is not adiabatic and
includes mass addition through the incorporation of fuel. Therefore, heat addition
is given by
Q=
rbrnfhPR where
irb is the burner efficiency. A conservative estimate
of the burner efficiency is 80%. Since mass addition occurs, a reference temperature
(TO = To = 227 K) is used to accurately estimate the absolute static enthalpy. Finally,
the work term can be neglected resulting in Equation 1.22.
nA3 [Cpb (T3 -
T) +
+ m
f
[hif
+
+-brnfhhpR
= r 4
[Cpb (T 4 - TO) +
(1.22)
The absolute sensible enthalpy of the fuel entering the combustor is hf. It is often
neglected in comparison to Q which contains a much higher fuel heat of reaction term,
hpR. Rearranging Equation 1.17, assuming hf is negligible, gives an expression for
the temperature at the combustor exit in Equation 1.23.
T4
T3
+f
1+ f
1
CpbT3
fhPR +f
bT+(+fV2)
V[2
V2
K]
2
2
2V
pb
2pb
(1.23)
After computing T4 , the speed of sound, density and internal energy of the fluid at
the combustor exit can be readily defined as given in Equations 1.24-1.26. Therefore,
given the achieved fluid state at the combustor entrance from the CFD simulation, an
appropriate fluid state at the combustor exit can be computed using Equations 1.15,
1.19-1.21, and 1.24-1.26. These values can then be enforced in the CFD simulation to
accurately predict the scramjet engine's performance. The figures of merit used for
gauging such performance will be Lift-to-Drag ratio (L/D) and thrust.
a 4 = V/bRT4
P4 =
e4
1.3
P4
RT4
CvbT 4
(1.24)
(1.25)
(1.26)
Radar Cross Section Reduction
Before tackling RCS reduction techniques, a brief discussion concerning radar system
performance, RCS, and the appropriate physics involved is warranted. To begin, radar
stands for radio detection and ranging. As the name implies, a radar emits radio waves
to detect, locate, and track targets. A target in the radar beam intercepts these EM
waves and a current along the target's surface is induced. Behaving like an antenna, the
target's surface current radiates its own electric field known as the scattered field [4].
RCS (often denoted by u) is a measure of this scattered field intensity compared to
that of the radar emitted electric field incident on the target. The scattered field then
makes its way back to the radar. The radar receiver intercepts and processes this field
and depending on the Signal to Noise Ratio (S/N or SNR), a detection may occur.
Location, velocity, and other information about the target may also be obtained from
these detections. A mathematical description of this process is given by the radar
equation that follows.
1.3.1
Radar Equation
Some terms used in defining the radar equation are provided below.
* T, = Transmitter and R, - Receiver
* PT
- Transmitted Power
" PID _ Transmitted Power Density Incident on the Target
* Ps - Scattered Power at the Target
* pR E
Scattered Power Density at the Radar
* PR: - Scattered Power Incident on the Radar
The scattered power, given in Equation 1.27, is a measure of the scattered electric
field strength. In this equation, RT. is the range to the target, GT, is the gain of
the transmitting antenna, and a is the RCS of the target. The 4rR42 term in the
denominator is known as the spreading loss. The transmitted power is distributed on
the surface of a sphere centered at the radar with a radius RTX.
Therefore, power
density on the sphere decreases as distance from the radar increases. Counteracting
this effect, the gain term represents the focusing capability of the transmitting antenna
in comparison to an isotropic antenna.
Ps =PTGT
(1.27)
Extending this equation to represent the scattered power density at the radar involves
the addition of another spreading loss term. This accounts for the return trip from
the target back to the radar. The result is given in Equation 1.28.
D
PTxGTx
pD=4P
S 47 R~q
4 R
47r RX
(1.28)
The receiving antenna also has an associated gain, GR, that is incorporated into
a term coined the effective antenna aperture. This is given in Equation 1.29. The
scattered power received by the radar is then given by Equation 1.30.
Ae =
(1.29)
-
4r
PT.GTxr JAe
Pax =r47rR
4wRL
PTxGTxGIR.A
2
(1.30)
= (4)3xR
4wR2
(4) 3 4R 2R
Monostatic radars share the same transmit and receive antenna. Therefore, the following simplifications apply: RT~ = RRx = R and GTx~
=
G
= G. This reduces
Equation 1.30 to Equation 1.31 that is commonly referred to as the radar equation.
PTXG 2 aA2
PRx =
1.3.2
(1.31)
(47r)3R4
Radar Cross Section
A typical expression for RCS is given in Equation 1.32 [6]. In this equation, Es is the
scattered electric field and Ei is the radar transmitted electric field incident on the
target.
r=4R2
-2
(1.32)
To relate this back to the radar equation, it is helpful to see how electric fields are
defined. The Maxwell equations are defined below for this purpose.
V X H(-, t) = 0D(f,t) + J(F,t)
Sx
E(F, t) = -B(F-
,
t)
(1.33)
(1.34)
V - D(F,t) = p(-, t)
(1.35)
V. B(r,t)= 0
(1.36)
Equations 1.33 - 1.36 are Ampere's Law, Faraday's Law, Coulomb's Law, and Gauss's
Law, respectively [7].
*
(f', t)-
* B('F, t)-
Electric Field Strength (Volts/m)
Magnetic Flux Density (Webers/m 2 )
* H(f, t) - Magnetic Field Strength (Amperes/m)
*
5)(i, t)
* J(F, t)
Electric Displacement (Coulombs/m 2 )
= Electric Current Density (Amperes/m 2 )
* p(F',t) - Electric Charge Density (Coulombs/m 3 )
The Helmholtz wave equation given in Equation 1.37 is derived from Maxwell's
equations in source free regions where p = 0 and J = 0 [7].
V2
o00
+02
-2 = 0
(1.37)
For the RCS study performed in this thesis, the radar will be considered in the far
field of the target. Though far field is not a clearly defined concept, an approximation
is given in Equation 1.38 [2].
4L 2
Rmi = 4
(1.38)
In this equation, L is the length of the target perpendicular to the radar Line Of Site
(LOS) and A is the transmitted wavelength. A radar farther than Rmin away from the
target is considered in the far field. In the far field, the electric and magnetic fields can
be approximated by plane waves. Plane waves are solutions to the Helmholtz wave
equation, and an example is given in Equation 1.39 [4].
#= -(, t) = Re [ oei(r-wt)]
E(r = oe'"
(1.39)
Therefore, PD can be defined in terms of E1 or Es as given in Equation 1.40. Cancelling terms and rearranging gives the original equation for RCS, Equation 1.32. Note
that 71o is the characteristic impedance of free space as given in 1.41.
D
=
2.
--
47rR 2
P
"-4'R2,
Rx1
20
rl
a = 4rR2
= 4
E S 2
Ii2
(1.40)
lo8.85
4r x 10-7H
0
10- 12m
C E6o
8.85 x 10-m
377Q
(1.41)
Given this definition of RCS, a mention of units is appropriate. From dimensional
analysis, RCS is measured in units of length squared. Furthermore, since an aircraft's
RCS changes significantly with target aspect, it is appropriate to represent RCS in
decibels. Therefore, RCS is typically given in units of dBsm as shown in Equation
1.42 [4].
UdBsm =
1.3.3
0loglo(a)
(1.42)
Scattering Mechanisms
Understanding what influences scattering is essential in trying to reduce it. Hence,
scattering mechanisms will be examined before proceeding to RCS reduction. Scattering mechanisms are affected by four processes: reflections, diffractions, surface waves,
and ducting [4]. Reflections are the strongest mechanism and include specular scattering from surfaces normal to the radar LOS. Surfaces that are encountered are either
flat, singly-curved, or doubly-curved. Furthermore, scattering strength is inversely
proportional to the Gaussian curvature of the surface [6]. For instance, flat surfaces
produce the strongest scattering, whereas spherical surfaces produce weaker returns.
Alternatively, scattering strength persistence varies directly with Gaussian curvature.
For instance, as aspect deviates from normal incidence to a flat surface, scattering
strength decreases rapidly (the maximum scattering strength at normal incidence does
not persist in aspect). Alternately, scattering strength is virtually constant as aspect
to a spherical surface changes; therefore, a trade-off must be performed.
Diffractions are caused by discontinuities that launch scattered fields. Edge and
vertex discontinuities typically give rise to strong diffractions. For instance, aircraft
wing leading and trailing edges can contribute significantly to RCS. Other discontinuities that give rise to diffractions include gaps, ridges, and seams. Every gap, ridge,
and seam will most likely increase aircraft RCS. Therefore, minimizing the occurrence
of such characteristics is important.
Two types of surface waves are creeping waves and traveling waves [6]. Creeping
waves are spawned at shadow boundaries. Such waves follow surface geodesics, shedding energy and emitting a scattered field as they travel along smooth closed surfaces
shadowed from the incident radar energy. When these waves re-emerge on the illuminated side of the target, they emit a weakened scattered field directly back at the
radar. A common example involves a sphere in which a current wave is induced at the
top shadow boundary. The wave will "creep" along the shadowed side of the sphere,
emitting a scattered field and losing energy as it progresses. Then it reappears at the
bottom shadow boundary emitting a scattered field directed back toward the radar.
Alternately, traveling waves traverse illuminated surfaces and edges. Traveling waves
suffer from little attenuation and may even increase in strength, a common example
being waves generated along an aircraft's wing. The incident electric field induces a
traveling current wave along the chord of the wing. Similar to the creeping wave, this
wave constantly radiates a scattered field. Nonetheless, the wave may increase in intensity since it is constantly illuminated by the incident field. When the wave hits the
trailing edge discontinuity, it reflects and contributes to trailing edge diffraction. The
reflected wave continues to radiate a scattered field. Therefore, creeping and traveling
waves could significantly contribute to RCS [6].
Ducting is related to partially closed structures such as engine intakes/exhausts,
antenna radomes, infrared sensor windows, etc. Incident radar waves enter these
structures and bounce off internal surfaces undergoing little attenuation. They often
exit these structures directed back toward the radar. Therefore, engine cavities and
similar structures can produce large returns over broad aspects [4]. Next, body shaping
techniques for reducing scattering caused by these different scattering mechanisms are
discussed.
1.3.4
RCS Reduction Techniques
While difficult to achieve in practice, an ideal aircraft is low observable from all aspects. However, most attention is devoted to reducing RCS in a threat region centered
about the nose of the aircraft. For instance, the threat region is often defined as a
solid cone that extends 120 degrees in yaw and 60 degrees in pitch [6]. To achieve
reasonable simulation times, the threat region analyzed in this thesis was reduced to a
waterline RCS prediction including 60 degrees in yaw. Taking this threat region into
consideration when performing target shaping for RCS reduction is important. For
instance, singly and doubly curved surfaces have lower maximum RCS values than
flat surfaces. However, their sidelobes are higher and more persistent. Therefore, flat
aircraft surfaces angled such that they scatter outside of the threat region is sometimes
preferable [6].
This approach can be used for wing and control surfaces. For instance, wings are
often swept back such that normal incidence to their leading and trailing edges is
outside of the threat region [6]. This reduces scattering caused by edge diffractions.
The same can be done with horizontal and vertical tail sections. Moreover, planform
alignment is a practice of angling these surfaces and their leading/trailing edges in
similar directions. Although this increases the magnitude of the aircraft's RCS in a
few directions, it significantly reduces the persistence of these high RCS flashes, and
thus enhances the low-observability footprint of the aircraft [6].
Also, engine inlets are usually exposed to the threat region. This is problematic for
conventionally powered aircraft that have large rotating parts exposed in the engine
cavity that can significantly contribute to RCS. However, the lack of moving parts
in scramjet engines is probably beneficial when considering RCS reduction. It should
be noted here that accurate modeling of the internal scramjet combustor components
and hot combustion gases was beyond the scope of this thesis. Therefore, the face
of the combustor entrance was modeled simply as a perfect electric absorber in the
CEM simulation.
Nonetheless, the internal compression ramps leading up to the
combustor inlet face were modeled and adjusted appropriately to try and reduce the
RCS of the engine inlet. One RCS reduction technique could have been placing the
engine inlets on top of the aircraft, thereby using the body of the aircraft to shield
the inlets from the radar. Since the X-43A does not employ such a design, this
particular technique will not be explored in this thesis to keep geometry modifications
and their attendant aerodynamic/RCS implications more straightforward. The main
body shaping concepts for RCS reduction that were employed in this thesis have now
been discussed. Next, an overview of the framework and accompanying software will
be given.
Chapter 2
Preliminary Design Framework
The Aerodynamic/Radar Cross Section Framework proposed for the preliminary design of a hypersonic aircraft is outlined in Figure 2-1. As shown, the framework begins
by developing a notional aircraft design on paper. The design is then generated in
the computer using Computer Aided Design (CAD) software. The next step in the
process is to discretize the air vehicle and its domain for use as input to the CFD and
CEM codes. Based on certain figures of merit, CFD results are evaluated. Depending
on the evaluation, the design is either modified to improve its aerodynamic qualities or
passed on to the CEM code for simulation. Inverse Synthetic Aperture Radar images
are then produced from the CEM results to examine and evaluate the main scattering centers on the aircraft. Air vehicle geometry can than be modified to reduce the
major scatterers and the design loop continues until satisfactory aerodynamic/RCS
performance is obtained.
2.1
3D Computer Aided Design Solid Modeling
Pro/ENGINEER' (ProE) CAD software is the starting point of the preliminary hypersonic aircraft design framework. Using this tool, any three-dimensional (3D) air
vehicle solid model can be generated. A key to the design is parameterization of the
1Information about ProE may be found on their website at www.ptc.com.
- GrIdEx
- FELISA
solid model. This parameterization allows easy modification to air vehicle geometry
for improving aerodynamic and RCS performance. Essentially, ProE provides the user
with the ability to create associations between primitives. These associations allow
the model to remain consistent when modifications are made. For instance, most air
vehicles are symmetric. In ProE, geometry can be mirrored across a plane of symmetry. When modifications are made to one portion of the model, ProE automatically
updates its mirrored counterpart. Similarly, reference planes may be created in ProE.
Points, curves, and solids may be associated with these reference planes. If translating
a reference plane is desired, all associated geometry will be translated along with the
reference plane. These are just two examples of the parametric associations available
in ProE that provide easy and consistent ways of modifying air vehicle geometry. Most
importantly, a ProE *.prt file can be read directly into the Grid Generator, GridEx.
2.2
Grid Generation
Utilizing GridEx 2 to generate a grid that may be used in subsequent steps of the
analysis is the next step in the design framework. This interactive software tool was
developed by the NASA Langley Research Center Geometry Laboratory. It provides a
Graphical User Interface for the control and generation of unstructured surface/volume
meshes. This tool provides the necessary geometry input files for the CFD and CEM
codes. The actual mesh generation in GridEx is performed using the advancing front
technique. This technique was developed as part of the FELISA CFD package that
will be used for the flow computation as part of this thesis. It produces unstructured
triangular/tetrahedral meshes for arbitrary geometries.
Furthermore, the FELISA
package contains a mesh adaptation utility that can be used in collaboration with
GridEx. This utility uses a computed flow solution to perform an error analysis based
on first or second derivatives of either density, pressure, or Mach number. It produces
a new spatial distribution of mesh parameters that are read by GridEx. An adapted
2Information about GridEx may be found on their website at geolab.larc.nasa.gov/GridEx/.
mesh is then generated using this information. The result is a higher fidelity mesh
that better captures important flow phenomena such as shocks.
2.3
Flow Simulation
FELISA is a Finite Element Method Euler based flow solver for the simulation of three
dimensional steady compressible inviscid flows [10]. Since its inception, FELISA has
been updated to include improved algorithms for the simulation of hypersonic flows.
It has also been parallelized using the Message Passing Interface Standard to enhance
simulation efficiency. This code has been validated and is currently being used by
NASA. For instance, FELISA played a roll in the Columbia Accident Investigation [9].
The main output from FELISA is a file containing the non-dimensionalized fluid state
variables (density, velocity, specific internal energy, pressure, and speed of sound) at
each node in the mesh. This file can be read by either Visual3 or Tecplot. These two
tools permit the visualization of the various fluid state variables in the flow field about
the aircraft. Further post-processing utilities compute the aerodynamic coefficients
and the achieved fluid state at the engine entrance and exit. These tools are used
to determine the aerodynamic characteristics of the vehicle and guage performance.
Only the aircraft configurations with realistic flight characteristics are promoted to
the RCS Signature Prediction design stage.
2.4
RCS Signature Prediction
There are numerous methods for RCS signature prediction. They are arranged into
two main categories: exact techniques and approximate techniques. These two categories and some of their corresponding techniques are illustrated in Figure 2-2. The
hypersonic aircraft being examined in this thesis was improved based on its RCS as
seen by a high-frequency (C-Band: 5-7 GHz) radar. To perform high-frequency RCS
predictions of complex aircraft configurations, approximate techniques are usually em-
ployed. Though exact techniques are more accurate, they currently require computing
power and time for the given complex aircraft configuration that is not considered
commensurate for the improvement in results over approximate techniques, except in
special cases where the accuracy requirement is high. This is especially true in the
preliminary aircraft design stage. Therefore, Xpatch was used for the RCS signature
prediction component of this framework.
The particular method employed by Xpatch is a ray tracing approach called the
Shooting-and-Bouncing-Ray (SBR) method. This is a microwave optics technique
that is valid for electrically large targets in which the characteristic target dimension
is much larger (> 10) than the incident radar wavelength [4]. The principles behind
this technique are closely related to reflection and refraction in optics. Median and
maximum RCS values were determined from the Xpatch results and used as figures
of merit. Furthermore, Inverse Synthetic Aperture Radar (ISAR) images were generated. These images are formed by using a Fast Fourier Transform to convert the
frequency/angle space of the results into downrange/crossrange space. By overlaying
the aircraft mesh on top of the ISAR image, the major scattering centers on the aircraft can be identified. Geometrical modifications can then be made to those locations
on the aircraft. At this point, the preliminary design framework can be iterated upon
to refine the aircraft. A trade study illustrating this framework is given in the next
chapter.
•
m
Approximate Techniques
Exact Techniques
* Limited Phenomena
* Computationally Fast
• High Frequency
* Limited Geometry
SAll Phenomena
0
Cla!ssical
Sol itions
* Few geeometries
* Rigorciusly Exact
Series Solutions
1Hybrid
Numerical
Methods
*Computationally Slow
* Low Frequency
Integral
Formulations
Method of Moments (MoM)
Rayleigh-Ritz
Model Matching
Fast Multipole Method
K-Space/Spectral Iterative (SIT)
Conjugate Gradient (CG)
CGSIT/CGFFT
Hybrid
Formulations
HFEM
UNIMOMENT
FEM-EBCM
Methods
MoMIUTD
MoM/PO
MoM/GO
Surface Integral
Approaches
* Single scattering
* Unlimited Geometries
Physical Optics (PO)
Physical Theory of
Diffraction (PTD)
Differential
Formulations
Finite Element
Finite Difference-Tin ie Domain (FD-TD)
Finite Diference-Fre quency Domain (FD-FD)
Ray Tracing
Aprproaches
• Multiple Scattering
* Often Liimited to Canonical
• Geomet ries
Geometlrical Optics (GO)
GO/PO
Geometlrical Theory of
Diffrac tion (GTD)
Shootin g and Bouncing
Rays (,SBR)
Chapter 3
X-43A Trade Study
A photograph of the X-43A is given in Figure 3-1.
This was the first hypersonic
scramjet-powered aircraft to be successfully flown. Therefore, it was used as a baseline
configuration for demonstrating the utility of the preliminary aircraft design framework discussed in the previous chapter. This was accomplished by varying different
aspects of the air vehicle's geometry and examining the aerodynamic and RCS consequences. First, the compression system was parameterized into three components:
Leading Edge Angle (LEA), Inlet Face Angle (IFA), and Internal Compression Ramp
Layout (ICRL). These parameters were varied to examine their affect on scramjet inlet
performance. Then, aerodynamically viable designs were promoted to the RCS signature prediction design stage. The number of candidate aircraft configurations was
reduced again based on RCS performance. Next, the expansion system was examined. First, engine outflow conditions were computed using the simulated fluid state
at the combustor inlet and the combustor modeling equations given in Section 1.2.3.
Once the appropriate boundary conditions were applied at the engine exit, realistic
lift, drag, and thrust predictions were obtained. Based on these results, an optimal
configuration was determined from the pool of candidate aircraft that were modeled.
IPe~
NASA Dryden Flight Research Center Photo Catlection
htp',hAww ~frc nasa gov/galleryiphotainoex html
NASA Photo. EC99-45265-1 1
Date December 1999
Photo by Tom Tschida
X-43A Vehicle During Ground Testirg
Figure 3-1: X-43A Flight Test Aircraft Photograph [12]
3.1
Compression System
I FA
-
I galinn FrInar
Annnl
-am
V-
I
IFA - Inlet Face Angle
Figure 3-2: External Compression System Design
Figure 3-2 illustrates the two external compression system parameters that were
varied: LEA and IFA. Two leading edge angles (7' and 90) and seven inlet face angles
(450, 600, 750, 900, 1050, 1200, and 135 ° ) were chosen. The X-43A LEA and IFA
were difficult to determine using a protractor on the drawing given in Figure 1-1.
Nonetheless, the X-43A configuration is believed to have LEA 1 8' and IFA r 900;
therefore, the simulated configurations bound the actual X-43A design. Figure 3-2
also illustrates that two external compression ramps are modeled. The actual X-43A
appears to have three ramps, but only two were modeled here for simplicity. The
second ramp closest to the engine inlet was set at 250 from the horizontal. Since the
position of the engine remained the same as the LEA was varied, the 25' ramp became
elongated when the LEA was reduced from 90 to 7'.
Equal Top/Bottom Wall Compression Ramps
2x Top Wall Compression Ramp
Bottom Wall Compression Ramp Eliminated
Figure 3-3: Internal Compression System Design
Figure 3-3 illustrates the two different internal compression system layouts. Scramjet engines employ top and/or sidewall internal compression ramps. In this study, only
the top and bottom wall compression ramps were modified. In the case referred to
as "Ramp", both top and bottom wall compression ramps were equal. This case is
illustrated at the top of Figure 3-3. The case referred to as "No Ramp" is illustrated
at the bottom of this figure and employs only a top wall compression ramp. Therefore,
the top wall ramp was increased by a factor of two to maintain a constant combustor
inlet area.
3.1.1
Aerodynamic Performance
A total of 28 flow simulations were performed (every combination of leading edge angle,
inlet face angle, and internal compression ramp layout). Then, the total pressure ratio
and kinetic energy efficiency were used as figures of merit to guage the aerodynamic
performance of each configuration. Furthermore, two constraints were imposed. Since
scramjet engines require supersonic flow throughout, the first constraint required the
combustor inlet Mach number to be greater than one. The second is a static temperature constraint. As stated in Section 1.2.2, a typical maximum combustor inlet
temperature for scramjet engines is 1670 K. Therefore, combustor inlet temperatures
below this limit were required. Results from the 28 cases are illustrated in Figures 3-4
and 3-5. The markers on the plot that are not filled represent those cases where one
or both of the constraints were violated. Furthermore, the target total pressure ratio
and target kinetic energy efficiency were computed using the combustor inlet modeling equations given in Section 1.2.2 with an assumed compression system efficiency of
r/c = 80%.
Total Pressure Ratio
0.11
Target
0.1
A LEA = 7 Ramp
U
0.09
0
0
LEA=7 No Ramp
LEA =9 Ramp
LEA = 9 No Ramp
c
•
120
135
.2 0.08
0.07 ,
0.06
0.05
- 0.04
0.03
-O
0
A
90
105
O
0.02
0.01
3(
0
45
60
75
150
Inlet Face Angle (Deg)
Figure 3-4: Total Pressure Ratio Design Comparison
Kinetic Energy Efficiency
U
o
o
y:
LU
o
o
uJ
0)
50
Inlet Face Angle (Deg)
Figure 3-5: Kinetic Energy Efficiency Design Comparison
Some trends are apparent in these two plots. Firstly, fixing the leading edge angle
and internal ramp layout, pressure ratio and efficiency improve with increasing inlet
face angle when IFA > 75'. This is likely due to the fact that the inlet capture area
increases as the bottom inlet lip extends more forward. As more high pressure air is
captured by the inlet, performance improves. Similarly, the hierarchy of results are
.
fairly consistent for IFA > 750 In other words, the LEA = 90 configurations are
.
consistently better than LEA = 70 for IFA > 750 This is consistent with oblique
shock wave theory, wherein larger LEAs produce stronger shocks that increase the
pressure and density of air behind the shock. This too increases the inlet capture
area, because the higher the air density is, the more air that can fit through a given
inlet geometry. One caveat is that a stronger shock produces a greater entropy and
static temperature rise. Therefore, a trade-off must be performed to determine the
point at which increasing the ramp angle (and shock strength) becomes detrimental.
A comparison of the Ramp and No Ramp configurations with LEA = 7' does
not show a strongly correlated result from which to draw conclusions. However, the
LEA = 9' configurations show a strong correlation.
For example, the No Ramp
cases consistently outperform the Ramp cases. This is likely due to two effects: (i)
a stronger expansion fan on the top internal surface and (ii) a stronger shock on the
bottom internal surface. First, the internal top wall ramp angle is smaller for the
Ramp configurations. Therefore, the transition from the external 250 ramp to the
internal ramp produces a stronger expansion fan in the Ramp configurations. This
stronger expansion is detrimental. Second, the bottom internal ramp increases the
turning angle of the flow as compared to the No Ramp cases. This increases the shock
wave strength, and consequently increases the entropy and static temperature rise
across the shock. This is also detrimental. Therefore, the No Ramp case produces
a weaker expansion on the top internal surface and a weaker shock on the bottom
internal surface, resulting in consistently better performance. It should be noted that
complex 3D interactions are also taking place. For instance, the interactions taking
place between sidewall and top/bottom wall compression are difficult to envision.
This is an excellent reason why simulation is worthwhile. Furthermore, some of the
ambiguities seen in the results are probably due to these complicated 3D interactions
that are difficult to interpret.
Flow visualizations of Mach number, density, and pressure were generated using
Visual3 to corroborate some of the assertions made above. The best and worst case
were chosen based on Figures 3-4 and 3-5 (IFA = 135°/LEA = 90 /No Ramp and
IFA = 60 0 /LEA = 90 /Ramp).
Figure 3-6 reveals a couple inferiorities with this
particular configuration. For instance, the Mach number at the combustor inlet is
subsonic. Furthermore, the inlet face angle is too shallow and a significant amount of
the air compressed by the leading edge shock is diverted beneath the engine (this is
termed spillage). On the contrary, Figure 3-7 illustrates that the leading edge shock
impinges on the bottom lip of the inlet. Therefore, the inlet captures most of the air
compressed by the shock with very little spillage. Furthermore, the Mach number at
Figure 3-6: Mach Number Visualization for IFA = 600 LEA = 9' w/Ramp
Figure 3-7: Mach Number Visualization for IFA = 135' LEA = 9' w/out Ramp
Figure 3-8: Density Visualization for IFA = 600 LEA = 90 w/Ramp
Figure 3-9: Density Visualization for IFA = 135' LEA = 9' w/out Ramp
Awl.
Figure 3-10: Pressure Visualization for IFA = 60' LEA = 90 w/Ramp
Figure 3-11: Pressure Visualization for IFA = 1350 LEA = 90 w/out Ramp
the combustor inlet is supersonic as required. The density plots given in Figures 3-8
and 3-9 and pressure plots given in Figures 3-10 and 3-11 tell a similar story.
3.1.2
RCS Performance
Median RCS
-9
Target
-10
A LEA= 7 Ramp
-11
N LEA =7 No Ramp
* LEA = 9 Ramp
LEA = 9 No Ramp
O
90
105
-12
-13
-14
-15
6
-1;7 -1 8 -
-2(
75
120
135
Inlet Face Angle (Deg)
Figure 3-12: Median RCS Design Comparison
Based on Figures 3-4 and 3-5, only 11 of the 28 configurations satisfied the combustor inlet Mach number and temperature constraints. Therefore, the RCS signature
prediction was limited to these 11. Figure 3-12 gives the median RCS values for each
of these configurations. The top three candidate aircraft configurations in terms of
aerodynamics were also the top three in terms of their median RCS. ISAR images
were generated for four of these configurations to compare the affect changes to LEA
and ICRL had on RCS. Figure 3-15 compares the two LEA configurations for an IFA
of 135'. Based on Figure 3-15, it appears that the 70 LEA case deflects more of the
incident radar energy into the engine cavity. Due to the effect of ducting discussed
Total Pressure Ratio
0.11
Target
A LEA= 7 Ramp
0.1
0 LEA= 7 No Ramp
* LEA= 9 Ramp
-
LEA = 9 No Ramp
0
O 0.09
£ 0.08
I)
. 0.07
S0.06
\
0.05
E
A
00 .75
4z
75
I
I
105
120
I
w
Inlet Face Angle (Deg)
Figure 3-13: Total Pressure Ratio Design Comparison Refinement
Kinetic Energy Efficiency
92
o
Target
LEA=7Ramp
M LEA = 7 No Ramp
LEA = 9 Ramp
LEA = 9 No Ramp
0
SA
92.5
o 91.5
o
.-
> 90.5
0)
r- 90
9
89.5
S89
88.5
I
75
105
120
Inlet Face Angle (Deg)
Figure 3-14: Kinetic Energy Efficiency Design Comparison Refinement
IFA = 135 LEA = 7 No Ramp
IFA = 135 LEA = 9 No Ramp
--
-10
-10
?CE
00
0.5
D
0.5
Cross-Range (m)
Median RCS: -11.52 dBsm
Maximum RCS: 6.06 dBsm
0.5
0
0.5
Cross-Range (m)
Median RCS: -18.92 dBsm
Maximum RCS: -2.33 dBsm
Figure 3-15: Leading Edge Angle RCS Comparison
IFA = 120 LEA = 9 Ramp
IFA = 120 LEA = 9 No Ramp
-10
E
o
iCE
EU
co a.
3
0r
0
Cross-Range (m)
0.5
D
0,5
Cross-Range (m)
Median RCS: -12.91 dBsm
Maximum RCS: 4.70 dBsm
Median RCS: -16.92 dBsm
Maximum RCS: -0.29 dBsm
0.5
0
05
Figure 3-16: Internal Ramp Configuration RCS Comparison
in Section 1.3.3, a large portion of this energy is re-emitted from the engine cavity
and directed back towards the radar. A reduction of approximately 8 dBsm in both
median and maximum RCS is achieved by using a LEA of 90 as opposed to 7.
Figure 3-16 compares the two internal compression ramp layouts for an IFA of
1200. Including an internal bottom wall ramp proves detrimental not only to the
aerodynamics, but also in terms of RCS. As shown, approximately a 4 dBsm drop in
median and maximum RCS is achieved by eliminating the bottom wall ramp. Therefore, it appears that the ducting effect is exacerbated by including a bottom wall ramp
as opposed to increasing the top wall ramp and eliminating the bottom ramp. Another notable aspect of the ISAR images given in Figures 3-15 and 3-16 is the edge
diffraction present at the tail-end of the aircraft. In examining the expansion system
in the next section, a geometry alteration will be applied to this region to reduce this
scattering.
3.2
Expansion System
The pool of candidate aircraft has been reduced to three favorable configurations
based on compression system performance and RCS. After extracting the combustor
inlet fluid state from each corresponding CFD simulation, boundary conditions for
the combustor exit were computed using the combustor modeling equations given in
Section 1.2.3. These boundary conditions were then applied to new CFD simulations
performed to accurately model the scramjet engine. Consequently, lift, drag, and
thrust were determined and utilized to guage expansion system performance. Similar
to the compression system analysis, the expansion system geometry could have been
parameterized and multiple configurations evaluated.
Instead, the tail-end of the
aircraft was modified to reduce edge diffraction. The baseline configuration has a flat
tail-end with a 900 edge. This is replaced with a Half Cylinder (HC) thus smoothing
the edge and reducing the scattering that is occurring there. The implications of this
modification on L/D and thrust were examined and the best performing configuration
was determined.
3.2.1
Aerodynamic Performance
Lift-to-Drag Ratio
3.5
*
0
3.4
3.3 -
LEA= 9
LEA = 9
LEA = 9
LEA = 9
Ramp
No Ramp
Ramp HC
No Ramp HC
O 3.2 M3.1
I
o 2.91 2.8
2.7
2.6
2.5
105
120
135
150
Inlet Face Angle (Deg)
Figure 3-17: Lift-to-Drag Ratio
L/D and thrust are the two expansion system figures of merit used in this study.
Furthermore, a constraint that thrust be greater than drag was imposed. Fortunately,
all configurations satisfied this constraint by a fair margin, and this margin is believed
to be large enough to counterbalance the additional drag due to viscosity that isn't
being simulated. L/D and Scramjet Engine Thrust plots are given in Figures 3-17 and
3-18, respectively. In addition to the three configurations selected based on the compression system analysis, three new HC configurations are represented in these plots
that will be discussed in the following section. Although the IFA = 1200 configuration
has a slightly lower L/D than the IFA = 1350 No Ramp configuration due to a small
increase in drag, it is clearly the best performer when thrust is considered. From the
pool of candidate aircraft, scramjet engine efficiency is optimal for this configuration.
Scramjet Engine Thrust
2500
*
LEA=9Ramp
0LEA= 9 No Ramp
SLEA= 9 Ramp HC
LEA= 9No Ramp HC
2450
2400
2350
S4-
2300
LEA = 9 Ramp and
LEA = 9 Ramp HC
Overlapping Here
2250
2200
2150
2100
2050
2000
105
I
I
120
Inlet Face Angle (Deg)
Figure 3-18: Scramjet Engine Thrust
Next, a modification intended to reduce the RCS of these configurations is made to
examine the implications on L/D and thrust.
3.2.2
RCS Performance
Half Cylinder
-.-
IW
D
I
IFA - Inlet Face Angle
Figure 3-19: Tail-End HC Configuration
The tail-end of the X-43A, and consequently the CFD model used in this trade
study, is a flat surface with a 900 edge. As discussed in Section 1.3.3, this promotes
trailing edge diffraction that can significantly contribute to RCS. Furthermore, the
ISAR images given in Figures 3-15 and 3-16 illustrate this effect. To mitigate this
scattering, smoother edges can be employed. As shown in Figure 3-19, an HC replaces
the flat tail-end section in three new configurations that correspond to the three configurations discussed in the previous section. Not surprisingly, Figure 3-18 illustrates
that thrust is minimally affected by this design change. However, Figure 3-17 illustrates that L/D declines, and thus aerodynamic performance is reduced, for the HC
configurations. This is a consequence of the increased pressure drag generated by the
HC configurations as illustrated by comparing Figures 3-20 and 3-21. Nonetheless,
this negative consequence is acceptable for the reduction in RCS that is achieved.
The largest reduction in maximum and median RCS was seen in going from the IFA
= 1200 configuration with a flat tail-end to the IFA = 1200 configuration with the
HC tail-end. Fortunately, this was also the best candidate aircraft in terms of aerodynamic performance. A comparison between the flat tail-end and the HC tail-end
configurations is given in Figure 3-22. It is apparent that this method is effective at
reducing RCS and a . 1 dBsm reduction in median and maximum RCS is achieved.
This IFA = 1200 with HC configuration will now be augmented with control surfaces.
3.3
Control Surfaces
To complete this trade study, control surfaces were added to the design.
Ideally,
different control surface shapes/sizes would be configured and simulated with varying
degrees of deflection to investigate control authority and stability. Instead, horizontal
control surfaces were added to the design and their affect on L/D, thrust, and RCS
was determined. Therefore, a CFD simulation was performed on a new model with
control surfaces. CFD results predicted a decline of 42% in L/D and a decline of .a1%
in thrust as compared to the same aircraft configuration without horizontal control
surfaces. Furthermore, thrust was greater than drag as required. Fortunately, these
results indicate that this is a viable aircraft configuration. Density, Mach number, and
pressure flow visualizations are illustrated in Figure 3-23. Also, 3D flow visualizations
Figure 3-20: Pressure Visualization for IFA = 120' LEA = 90 No Ramp w/out HC
Figure 3-21: Pressure Visualization for IFA = 1200 LEA = 90 No Ramp w/HC
Flat Tail End
IFA = 120 LEA = 9 No Ramp
Half Cylinder Tail End
IFA = 120 LEA = 9 No Ramp
-1D
-10
-15
-15
1
-20
-25
0
C
3D
OF
C
35
0.5
0
0.5
0.5
0.5
0
0
05
0.5
Cross-Range (m)
Cross-Range (m)
Median RCS: -16.92 dBsm
Maximum RCS: -0.29 dBsm
Median RCS: -17.47 dBsm
Maximum RCS: -1.22 dBsm
Figure 3-22: Tail End Configuration RCS Comparison
are provided in this figure to demonstrate some of the functionality of the visualization
tool (Visual3).
Next, an RCS simulation was performed, and a comparison between the designs
with and without control surfaces is illustrated in Figure 3-24.
Since the control
surfaces are angled out of the threat region mentioned in Section 1.3.4, they contribute
only a small amount to the RCS of the aircraft. For instance, the wingtips do appear on
the ISAR image, but their contribution is small. Therefore, adding horizontal control
surfaces has not significantly degraded the design in terms of its RCS signature. The
next step in the preliminary design process would be to deflect the control surfaces and
experiment with different control surface shapes/sizes until the design was satisfactory.
Further refinement would be achieved by modifying the different components of the
full aircraft configuration to examine component interactions in an attempt to improve
aerodynamic and RCS qualities. The design loop would be iterated in this fashion until
an aircraft with acceptable aerodynamic and RCS characteristics was achieved.
Figure 3-23: 2D and 3D Flow Visualizations
No Control Surfaces
IFA = 120 LEA = 9 No Ramp
C
E0 1
Control Surfaces
IFA = 120 LEA = 9 No Ramp
-10
-10D
-15
-15
-20
-20
-25
-25
o
cn
C
C
oC
m
35
-']
305
3
o
Q
35
05
D
05
Cross-Range (m)
Cross-Range (m)
Median RCS: -17.47 dBsm
Maximum RCS: -1.22 dBsm
Median RCS: -17.37 dBsm
Maximum RCS: -0.92 dBsm
0.5
0
0.5
Figure 3-24: Control Surface Configuration RCS Comparison
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[2] Asoke K. Bhattacharyya and C.L. Sengupta. Radar Cross Section Analysis and
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