American Institute of Aeronautics and Astronautics

1

Integrated Aero-Servo-Thermo-Propulso-Elasticity (ASTPE) Methodology for Hypersonic Scramjet Vehicle Design/Analysis

Ryan P. Starkey1

University of Colorado, Boulder, CO, 80309

Danny D. Liu2, P.C. Chen3, Ayan Sengupta4, and K.T. Chang5

ZONA Technology, Inc., Scottsdale, AZ 85258

and Falcon Rankins6

University of Maryland, College Park, MD, 20742

The objective of this wok is to create a design/analysis methodology for rapid assessment and optimization of scramjet-powered vehicle (SPV) designs and performance estimates within the multi-disciplinary considerations of an Aero-Servo-Thermo-Propulso-Elastic (ASTPE) analysis. This methodology will be housed in an ASTPE Desktop Design Environment (ADDE) to facilitate a conceptual-to-preliminary hypersonic vehicle design and optimization tool. The ASTPE approach is aimed at developing an expedient procedure to inject essential preliminary design requirements and/or feedbacks in early stages of conceptual design in order to consolidate the conceptual design feature for a scramjet powered vehicle. A design procedure is demonstrated by applying this present ASTPE on a single engine missile (SEM).

I. Introduction merging hypersonic technology from space access, global-strike vehicle to hypersonic Unmanned Air Vehicles (UAVs) demands effective hypersonic methodology for vehicle design and analysis. Air-breathing hypersonic

vehicle concepts employing scramjet engines for cruise, space access, and hypersonic strike capability are currently being developed through several ongoing R&D efforts. Notably, these include the Waverider/Single Engine Demonstrator (WR-SED/X-51) by the Air Force, the Force Application and Launch from the Continental U.S. (FALCON) by DARPA, Hyper-X (X-43) by NASA (Figure 1), and HyFly by the Navy. Most of these designs take advantage of waverider or waverider-like forebodies to either minimize pressure leakage from the lower to upper surface and/or satisfy a shock-on-cowl lip condition to achieve superior inlet flow quality at a given design condition. However, any aeroelastic or dynamic perturbations will give rise to a non-ideal inlet flowfield. This would then induce vehicle instability in terms of the interaction of hypersonic aerodynamic, aeroelastic, aeroservoelastic, and propulsive forces, let alone the important aerothermoelastic interaction.

To provide control to such types of instability in such an extreme environment with aerothermal consideration is a challenging endeavor. McRuer [2] has warranted that the integration of airframe, propulsion, control, and dynamics should be a central issue for hypersonic vehicle design whereby forbidden zones appear in the hypersonic flight/operation corridor (bounded by the 1-g-upper and the thermal-load-lower boundaries) due to control limits as shown in Figure 1. Bowcutt [3] also ranked high the importance of the vehicle control system development for X-43s, HyFly and X-51.

The development and optimization of hypersonic vehicles is a challenging endeavor with the design closure of missile-scale vehicles proving even more elusive. This complexity was extremely evident in NASA’s Hyper-X program where there was a vast difference between the vehicle design scale and the scale of the flight test vehicle. The Boeing Dual-Fuel vehicle was designed as a Mach 10, 200 foot class, global reach cruise vehicle, but was

1 Assistant Professor, Associate Fellow AIAA 2 Company President, AIAA Fellow. 3 Company Vice President, Senior Member AIAA 4 R&D Engineering Specialist. 5 R&D Engineering Specialist. 6 Research Assistant, University of Maryland.

E

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-1122

Copyright © 2010 by University of Colorado. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

American Institute of Aeronautics and Astronautics

2

Figure 1. Excluded operational regions in flight

corridor (taken from Ref. [2]).

photographically scaled down to 14 feet while preserving most of the original length scale of the scramjet engine to emerge as the NASA’s Hyper-X, Mach 7 configuration. The resulting vehicle then required silane to initiate and sustain combustion in the small-scale engine and utilized a 1000 pound block of tungsten in the forebody to balance the lift and moment. Clearly, the effort which goes into evolving and refining a complex, hypersonic vehicle design is substantial, especially when including the intricate synergy required between the disciplines of aerodynamics, propulsion, aeroelasticity, stability and control, and aerothermodynamics.

Physical understanding and formulation to account for these complex interactions for hypersonic air-breathing vehicles are lacking at present, with the

exception of a simple model suggested by Chavez and Schmidt [4]. With greatly simplified component forces and a dummy engine in their model, it can be concluded that the propulsive and aeroelastic interaction alone could indeed be destabilizing.

Although Chavez/Schmidt’s work has been widely quoted in the literature [4], few followed to tackle the interactive AeroServoPropulsoElastic (ASPE) impact on the dynamic stability of the scramjet vehicles. Their work clearly indicated that such a type of analysis can be effectively handled through a “Conceptual-Design/Analysis” (CDA) approach. This is needed because the multi-disciplinary nature of ASPE would be otherwise far too complex as a system to handle. To do so, however, requires in depth physical understanding of the mechanism and interactions of all disciplines involved. This is in fact the physical-based model that is currently established by the ZONA Team.

Previous experience in the last decade also indicates that large discrepancies exist between measured data (wind-tunnel model) and flight data. This is so because the scaling law for different sizes of scramjet inlet/engine is simply non-existent at present. It is not clear in fact whether such scaling laws can ever be established. In the presence of vehicle aeroelasticity, the ASPE interactions of a scramjet vehicle would be vastly different between that derived from the measured and the flight test. For this reason, an analytical model for rapid assessment of the ASPE interaction as to the vehicle stability and control is badly needed.

The ZONA Team has created such a “Conceptual-Design/Analysis” (CDA) tool for precisely the purpose of rapid assessment of vehicle stability and control law implementation. In almost every aspect, ZONA’s CDA model has largely refined the features of Chavez/Schmidt’s model. In particular, the essential improvements of the ZONA model over that of Chavez/Schmidt lies in the scramjet inlet/engine design feature and in the closed-loop control methodology, whereby both are lacking in Chavez/Schmidt’s model. Details of our “Conceptual-Design/Analysis” (CDA) model will be described in what follows.

II. Approach We have created a design/analysis methodology for rapid assessment and optimization of scramjet-powered

vehicle (SPV) designs and performance estimates within the multi-disciplinary considerations of an Aero-Servo-Thermo-Propulso-Elastic (ASTPE) analysis.

An expedient procedure is developed to inject essential preliminary design requirements and/or feedbacks in early stages of conceptual design in order to consolidate the conceptual design feature for a scramjet powered vehicle. The software architecture is shown in Figure 2. Different blocks are described below.

A. University of Colorado Vehicle Design and Analysis Code (UCDA)

The University of Maryland Vehicle Design Code systematically creates a vehicle/combustor geometry based on inputs for forebody, inlet, combustor, nozzle, airframe, and control surface definitions. This works in either a one-off mode or interacts with the optimization software to develop a new design. Each major component has multiple methods of describing the geometry to increase/decrease the complexity and number of design variables required.

The current aerodynamic design and analysis methodology for both the waverider forebody and the vehicle aftbody are detailed below. There are a number of different ways to develop a waverider forebody; wedge generated flows, conically generated flow, blended flows, and osculating cone generated flows. The simplest of these is the

American Institute of Aeronautics and Astronautics

3

analytical variable wedge angle method of Starkey and Lewis [1], while the most flexible (and computationally expensive) is the osculating cone method of Sobiesky [11].

Figure 2. Software Architecture for ASTPE

• Waverider Design

The extreme sensitivities inherent in a missile-scale, hypersonic vehicle scramjet performance relative to the inlet conditions require detailed modeling all of associated components in order to capture the true physics [5]. When coupling this combustor sensitivity with aeroelastic effects the situation becomes much more complex.

In order to reduce the complexity of the models, the vehicle will utilize a two-dimensional keel-line flowpath, similar to that used in the Hyper-X program. As detailed in Figure 3, the main aerodynamic-propulsive components to be analyzed are: a waverider forebody, a scramjet combustor, and a simple two-dimensional nozzle.

(a) Aerodynamic-Propulsive Formulation

(b) Control Surface Deflection

Figure 3. Generic Single Engine Missile Configuration

• Variable Wedge-Angle Derived Waverider

The Variable Wedge-Angle waverider methodology was developed at the University of Maryland for reduced order, modeling of hypersonic waveriders [1]. The power in this method is that the waverider forebody can be designed and analyzed analytically using only seven geometric design variables, as shown in Figure 4.

The computational fluid dynamics (CFD) validation cases shown in Figure 5 show the power of the variable wedge angle method as a quick estimate of a waverider flowfield by producing an attached shock-wave at the design

.

UCDAVehicle Design Code

• Create SEM geometry from given cruise condition

• Compute aerodynamicsproperties and trim vehicle

• Supersonic combustionwith multiple species

TPSOPTThermal protection system optimization

• Heat Flux by MINIVER• Complex Variable

Differentiation forsensitivity

• Optimization for minimum TPS weight while subjected totemperature constraint

UPTOPTrajectory Optimization

• Quasi 6 DOF spherical earthtrajectory optimization

• Using Genetic Algorithm/Gradient basedoptimization

• Capable of includingvehicle parameters as design variables

ASE Analysis

• Unsteady aerodynamics by wedge and conesolutions

•Unified flight dynamics and aeroelastic formulation

• State Space equations

MATLAB

Control system design

TPSWeight

Optimized Trajectory

• grids and panels• widths and heights of different stations

• non-structural weight

Plant State-Space Model

BUAXX +=.

SMBStructural Sizing

• Beam representation ofstructure

• Loads based on trajectory• Skin thickness sizing by

fully Stressed Design• Natural Frequencies and

mode shapes•Output EI, GJ, mass and

stiffness matricesmatrices

Control EffectorEffector

Aeroelastic TRIM Analysis

• Trim variables by complex variable differentiation

• Solve for L = W and CM = 0• Formulated based on static

aeroelastic approach

conv?

Yes

No

TPS and Structural Skin Weights

Mass and Stiffness Matrix

Trajectory

American Institute of Aeronautics and Astronautics

4

condition. Also shown is the minimal cross-flow (other than at the inflection point at the leading edge) thereby giving uniform flow into the airbreathing engine and demonstrating the applicability of strip theories to analyze the aftbody flow.

Figure 4. Variable wedge-angle waverider forebody.

(a) pressure contours,

(b) cross-flow velocity vectors.

Figure 5. CFD validation of VWA methodology,

For a Mach 8, zero degree angle-of-attack design point of the forebody, off-design performance at various Mach numbers and angles of attack is shown in Figure 6. The only discrepancy is near the zero-lift point where the absolute difference is small, but the % difference is large. Therefore, the variable wedge angle methodology is shown to be comparable to the osculating cone method and Euler CFD analysis for changes in Mach number and angle of attack.

Figure 6. L/D ratio and % difference for CFD, osculating cone,

and variable wedge angle analyses of a Mach 8 forebody.

• Osculating Cone Waverider True waveriders are generated using an inverse design method; one where the desired flowfield is chosen and the

vehicle that generates that flowfield is produced. One method of waverider generation, first conceived of by Sobieczky et al. [11], where multiple slices of a conical flowfield are placed side-by-side to build up the desired flowpath, is referred to as the method of osculating cones [12], as shown in Figure 7. The keel-line flowfield can be

American Institute of Aeronautics and Astronautics

5

generated in this manner to provide uniform flow to a two-dimensional combustor while providing the high lift-to-drag ratio (L/D) at high lift coefficient (CL) that waveriders are well known for. In addition to the compression provided by the waverider, the inlet system also utilizes a number of planar compression ramps which satisfy an on-design shock-on-lip constraint.

(a)

(b)

Figure 7. Osculating cone waverider with a) shock flowfield at combustor inlet plane and b) inlet plane compression surface generation [4].

B. Modified Shock-Expansion Method Formulation

Another innovation used in this stage of the vehicle analysis (for fast optimization studies) is a modified shock-expansion method. Shock-expansion theory is inaccurate for this application because it determines the flowfield using single Prandtl-Meyer expansions (hypersonic slender body theory) assuming two-dimensional streamlines. Due to the highly curved nature of these missile airframes, the shock-expansion method resulted in an over-prediction in peak surface pressure by as much as 50%. The modified method uses a combination of the oblique shock relations and Taylor-Maccoll cone flow equations to solve the local flow properties (for compression) while marching down a ‘two-dimensional' streamline. As with shock-expansion theory, the local flow conditions and the relative inclination angle at a point are used to calculate the properties at the next point. The blending of the properties predicted by the oblique shock and Taylor-Maccoll methods is based on the local radius of curvature in the spanwise direction. This attempts to predict the pressure relieving effects a three-dimensional body has on a two-dimensional streamline approximation to local flow conditions. Expansion regions are calculated using traditional shock-expansion theory.

A similar method using a blend of Tangent Wedge and Tangent Cone approximations to off-design flowfield predictions for osculating cone generated waveriders was developed by Grantz [13]. Grantz's method was not applicable to this study since it requires a known generating body with a known flowfield (i.e., streamline locations), such as the method of osculating cones, to determine the surface properties of the body.

Continuing with the assumption of two-dimensional flow, the surface properties at a point are solved using the known properties at the previous point and the local body angle, relative to that point. For oblique shock theory, the wedge angle used to determine the new properties, and for cone flow the cone half angle is used. For a known surface point, with initial properties, P1, T1, and M1, the relative surface angle is used to determine the new properties. Assuming only wedge flow the results are given by P2w, T2w, and M2w, with completely conical flow given by P2c, T2c, and M2c.

The local radius of curvature R is determined in the spanwise plane by:

3 221/

( y )R

y

′+ =′′

(1)

The actual surface properties for compression surfaces are found by linear interpolation in the form

( )1w cR Rλ λ λ= + − where w values are calculated from oblique-shock theory, c values are determined from solution

to the Taylor-Maccoll equations, and λ indicates each of P, T, and M at a given location. Results using this methodology have been validated using Euler CFD calculations as shown in Figure 8.

Figure 8(a) shows the missile airframe neglecting the engine flowpath, since Figure 4(b) demonstrated the two-dimensional nature of the keel-line flow. The top half of each vehicle pictured in Figure 8 is the Euler CFD solution while the bottom half is the modified shock-expansion method. As can be seen, there are only minor differences in

American Institute of Aeronautics and Astronautics

6

the solutions, but the solution run-times are many orders of magnitude apart since the analytical blending function takes only a fraction of a second to compute. Figure 8(b) is a close-up view of the peak pressure location.

(a)

(b)

Figure 8. Validation of modified shock-expansion methodology for three-dimensional pressure relieving effects along two-dimensional streamlines.

• Scramjet Combustor

The scramjet combustor is generated in a two-dimensional manner with an isolator section followed by one or more expanding sections, as shown in Figure 9(a). The fuel (and pilot agent if desired) can be injected through any number of ports in any position throughout the combustor. Figure 9(b) shows a mixing profile and burning efficiency are then applied to determine the effects of the inlet conditions, fuel, and geometry on the combustion using finite-rate chemistry computations [14].

(a)

(b) Figure 9. a) Scramjet combustor model,

b) Sample Jet-A fuel mass fraction and Mach number as a function of combustor position. The elegance of this scramjet model is in the formulation of the finite-rate chemistry inclusion in the quasi-one-

dimensional equations of fluid motion. Using this model the design sensitivities of various fuel types, chemistry mechanisms, injector locations and angles, viscous effects, and wall heat transfer can be determined in a computationally efficient manner. The inclusion of chemical kinetics allows for a prediction of fuel ignition, a finite-

American Institute of Aeronautics and Astronautics

7

rate process that inherently cannot be predicted using equilibrium methods. Chemistry also allows for off-design calculations to determine what conditions are needed for the fuel to burn, and what conditions will cause the combustor to choke. These prediction abilities are crucial in flowfield regimes where the limits of the scramjet concept are seen (i.e., hydrocarbon missile scramjets, ram/scram transition, etc.).

The series of ordinary differential equations that model the governing equations of motion are shown below. Along with a user specified cross-sectional area profile, mass and reaction mixing profile, viscous model, and a reaction mechanism, the ordinary differential equations are integrated to solve for the combustor flowfield.

Equations for continuity, momentum, state, mixture molecular weight, species conservation, and energy are shown below, respectively.

1 1 1 1dm d dU dA

m dx dx U dx A dx

ρρ

= + +

(2)

( )2 22 2

2

2 110

2

fM C Mdp M dU dm

p dx dx D m dxU

γ γ εγ −+ + + =

(3)

1 1 1 1dp d dT d MW

p dx dx T dx dxMW

ρρ

= + −

(4)

2 1 i

i i

dYd MWMW

dx MW dx

= −

∑

(5)

1i ,mix i i ,addedi iMW dmdY Y dm

dx U m dx m dx

ωρ

= + −

’

(6)

( )2 3

21 1 f p aw wi i oi i /

i ip added

C c T TdY dm hdT dm dUh h U

ˆdx c dx m dx m dx dxPr DA

− = − + − − −

∑ ∑

(7)

where

( )1p p i pi pi

addedic c m c c T

m

≡ − + ∑

(8)

and

p p pi ii

c c T c Y≡ +∑ (9)

( )2 32 3 4 52 3 4u

pi i i i ii

Rc a a T a T a T

MW≡ + + +

(10)

These equations constitute a stiff set of ordinary differential equations (ODE) due to the chemical production terms from combustion. Solution of these equations requires a stiff ODE solver which can account for differing time scales. A code named VODPK [15], developed by Lawrence Livermore National Lab, was used to accomplish this task. VODPK uses a backward differentiation formula to integrate the set of stiff ODEs. Values for the individual chemical species molecular weight, specific heat, heat of formation, and reaction rates are obtained by CHEMKIN-II [16] for a user-supplied reaction mechanism.

For this study only Jet-A fuel was investigated, although any fuel could be used. The Jet-A reaction mechanism used in this study is a subset of the full reaction mechanism from Kundu et. al [17]. The reaction mechanism consists of 17 species and 14 reactions and was chosen because it has been validated by Chang and Lewis [18]. The ambient air composition is assumed to be 78% nitrogen, 21% oxygen and 1% argon by volume.

Solving the equations for conservation of mass, momentum, energy, and the equation of state for the derivative in velocity yields:

( ) ( )21 11 1 1 1o i ii i

i i added

ˆM h / h dY dmdU dA dmh h

ˆdx A dx m dx dx m dxh

γ ε

α

+ − − = − + + − +

∑ ∑

American Institute of Aeronautics and Astronautics

8

( )22 3

21 p aw w f

/

c T T CdMWM

ˆMW dx Dh Pr Aγ

− − + −

(11)

where

221

1U

MˆU h

α γ

≡ − +

(12)

and

pˆ ˆh c T≡

(13)

Each term in the dU / dx derivative can be calculated, or is a prescribed quantity. The first term is the cross-sectional area profile dA / dx which is assumed to be prescribed by the user. The second term is the mass flow

addition term dm / dx and represents the mass mixing profile prescribed by the user. The quantity h can be

calculated using CHEMKIN-II. Solution of the change in mixture molecular weight d MW / dx is found by first solving the species conservation equation. Given the mixing profile and chemical information from CHEMKIN-II, the conservation of species is a known quantity which may then be substituted into the mixture molecular weight equation to solve for the change in mixture molecular weight. The friction terms involving the friction coefficient are all known quantities or may be calculated using CHEMKIN-II. The remaining terms in dU / dx are known quantities, quantities that have already been calculated, or quantities that may be calculated using CHEMKIN-II. Thus, the velocity derivative derived in dU / dx is a known quantity at a particular x-location in the combustor.

With knowledge of the velocity derivative, the density derivative may be found from the continuity equation. The pressure derivative may be calculated from the momentum equation. The temperature derivative is then found from the equation of state. The derivatives of all the variables are then integrated using VODPK to find the flow solution. The full engine flowfield may be calculated in a fraction of a second on a standard take-off computer. Thus, this method allows for rapid design of full vehicle concepts that include a detailed engine flowfield. The mixing model used is that of Rogers [19], tabulated by Henry and Anderson [20]

b

r fax exp( cx )

m mdx f

=+

(14)

inj

xx

L≡ (15)

where injL is the length between the start and end of the injection and the curve-fit constants are a = 1.1703, b =

0.62925, c = 0.42632, d = 1.4615, and f = 0.32655.

(a) (b)

Figure 10. Sample scramjet performance with (a) Mach number and pressure distribution, and (b) temperature and species mass fraction distributions.

The importance of using finite-rate chemistry to accurately predict the fuel ignition point and the effects of the

combustor geometry and the energy release can be seen in Figure 9. The Mach number and pressure distribution for

American Institute of Aeronautics and Astronautics

9

a sample combustor are shown in Figure 10 (a), while the temperature and species mass fractions (to show fuel burning efficiency) are shown in Figure 10 (b). In this instance, the combustor is 1.5 meters long with the constant area portion 0.75 meters long and the expansion section the following 0.75 meters. The fuel ignition occurs just before the expansion area and the interplay between the combustor geometry and heat release are evident.

Figure 11. Combustor temperature contours for off-

baseline conditions.

The sensitivity of the combustor performance relative to the ignition point is detailed in Figure 11. By varying a few of the combustor design conditions slightly off of baseline, the performance degraded very quickly with most of the variations resulting in thermally choked flow. Only two conditions did not result in a choked flow state: 1) lowering the mixing efficiency from 90% to 85% (lowering the heat release), and 2) increasing the mixing length from 0.5 meters to 0.55 meters (delaying ignition until after the mechanical throat). The only off-baseline condition which retained a moderate amount of performance was the lower mixing efficiency case, otherwise the engine would unstart.

Although some of the design conditions were altered to determine the sensitivity, similar results occurs for off-design flight performance, especially once angle-of-attack exceeds a few degrees or the Mach number increases much past the design point (both causing increased inlet pressure). Alleviating these concerns can only be done through bleeds, spillage, bypass, or geometry variations [5,21].

• Nozzle Following the combustor are the internal and external nozzle sections, which are calculated using the frozen,

non-rotational, two-dimensional method of characteristics, as shown in Figure 12. Since part of the nozzle is utilized as a control surface in this configuration the combustor flowfield directly effects the vehicle trim state.

Figure 12. Sample method of characteristics nozzle design showing pressure contours.

Using the design fuel equivalence ratio as the combustor state, the control surface effectiveness can be

determined, as shown in Figure 13. The trim state in this instance is at a slightly downward control surface deflection, as shown in Figure 14.

American Institute of Aeronautics and Astronautics

10

Figure 13. Control surface effectiveness at the design

fuel equivalence ratio.

Figure 14. Baseline vehicle configuration.

C. University of Maryland Parallelized Optimization Tools (UMDOPT) Although random-based evolutionary methods are generally praised for their ability to find global optima, their

efficiency as the objective function approaches the optimum typically decreases significantly. In the near-optimal space, the classical gradient-based optimization techniques excel. This leads to the concept of hybrid optimization techniques that combine the strengths of the two disciplines.

Madavan [26] provides an overview of efforts to hybridize differential evolutionary schemes, and also shows increased performance by combining DES with dynamic hill climb (DHC). The current work uses the Design Optimization Tool (DOT) package [27]; more specifically calling the sequential quadratic programming (SQP) routine. SQP is an efficient constrained optimization technique that minimizes a quadratic approximation to the objective function subject to linearized constraints. Details of the method are available throughout literature and included in the DOT manual [27]. For the purposes of the current work, a front-end code was written to scale the constraints in order to better condition the optimization problem. Further, the front end adjusted the scaling and automatically restarted the SQP routine after the first pass. Experience showed that this helped make DOT more effective at finding the optimal solution.

When combining the two optimization techniques, a method for triggering the local search is required. For the DES-SQP method, two switchover methods were examined with various threshold settings. The first method simply calls DOT after the DES had progressed a given number of generations (1,5,10,100). The second method, following Madavan [28], calls DOT when the ratio of the population coefficient of variation (CV, or the ratio of the population mean to the population standard deviation) between successive generations exceeds a threshold value (1.0, 1.2, 1.5). In both methods, the DES sends the best performing population member to DOT, unless that member has not improved since the last time the local search was performed, in which case a random member is sent. Also, in all cases that the local search is triggered, the gradients are scaled and DOT is called twice, as described above.

The current work has shown that coupling SQP with DES provides an effective method of optimization that is more powerful than either method alone. The results obtained from the hybrid method show a consistency and reliability which is greatly desired in optimization work, since it may reduce the amount of tuning required when examining a new problem.

• University of Maryland Parallel Trajectory Optimization Program (UPTOP)

The University of Maryland Parallel Trajectory Optimization Program (UPTOP) is a generalized atmospheric and near-earth orbit trajectory optimization program written in Fortran 95. UPTOP relies on a differential evolutionary scheme (UMDOPT) to provide optimal results without requiring a feasible initial condition, which can limit the usefulness of gradient-based optimization packages. UPTOP is capable of optimizing multi-stage trajectories where the vehicle may have multiple engines and fuel tanks. Input to the code consists of two simple input decks and interpolation tables to define the aerodynamic characteristics and engine performance. The current capabilities of the code also allow for elementary sizing studies and provide the user with the ability to optimize vehicle parameters such as fuel weight and reference areas. Additionally, the user can define a set of relationships between the vehicle parameters so that the effects of a change in one vehicle parameter will be accurately reflected in the vehicle's performance. Users can also define new variables to be tracked or used thoughout the trajectory optimization. UPTOP is a modular code written with expansion into in mind, and provides a solid base for delving

American Institute of Aeronautics and Astronautics

11

into guidance and control issues. UPTOP has been validated against sample problems solved by POST with good agreement, and although it makes sacrifices in computational time, UPTOP guarantees a thorough examination of the entire design space while searching for the optimal solution. • Vehicle Dynamics

Although UPTOP currently only models flight in a vertical plane, development of a 6-DOF version is nearly complete (see Section 9). The equations of motion for rigid-body flight are given by

dpV

dt= (16)

1b

dVB F g

dt m= + (17)

( )1 1

b b bd

J J J Tdt

ω Ω ω− −= − + (18)

f

dm dm

dt dt = −

(19)

1

2 qdq

qdt

Ω= − (20)

where the position p , velocity V , and gravity g , vectors are specified in an inertial reference frame. Vehicle

rotation rates ω , are defined in the local aircraft coordinate system, and J is the vehicle inertia matrix.

Quaternions q , are used to track vehicle orientation using the standard update matrix qΩ , which is dependent on

vehicle rotational rates. Further details can be found in standard vehicle dynamics texts. B is the direction cosine matrix that rotates the external force vector bF , and torque vector bT , from the body axes to the inertial reference

frame. bF consists of the vehicle lift, drag and thrust, which are defined in terms of their respective force

coefficients in equations similar to LL qC S= , where S is the appropriate reference area. The torques are similarly

defined as coefficients, with the addition of an appropriate reference length. Vehicle orientation, rotational rate, force and torque vectors are all reported in the 3 reference frames, oriented as

follows: 1. Earth Centered Inertial - positioned at planet center; 1- North; 2- 0 deg longitude; 3 - 90 deg longitude 2. Local Horizon - positioned at A/C c.g., serves as local horizon; 1 - North; 2 - East; 3 – Down 3. Aircraft Body Coordinates - position at A/C c.g.; 1 - A/C nose; 2 - A/C right wing; 3 - completes right-hand

frame (down, with respect to pilot in level flight) UPTOP uses a 4th order Runge-Kutta routine to propagate the equations of motion while minimizing numerical

inaccuracies. The user must specify a time-step (which may be set to different, constant values throughout different segments of a simulation) and a maximum allowed time to aid in memory allocation.

• Planet Modeling

UPTOP assumes a rotating, ellipsoidal earth, specified using a flattening parameter. Geodetic latitude, geocentric latitude, and longitude are all tracked. A fixed point iteration is used to determine vehicle altitude based on the inertial position and latitudes. For most simulations, the US standard 1976 atmosphere used by UPTOP is adequate. For altitudes above 88km, UPTOP also includes the NRLMSISE-00 standard atmosphere model. • Variables

UPTOP currently provides up to 200 default output variables, providing information on vehicle states and orientations, atmospheric states, orbital elements, etc. User-defined variables can also be integrated into the code, allowing for easy addition of heating or weight analysis, for example. Additionally, simple tracking operations, such as average, max/min, or standard deviation, can be performed on all variables.

All input and user-defined variables can be specified in one of 5 methods: 1. Constant definition 2. Curve Fit - user defines the independent variables, dependent variables, and order of a polynomial curve fit

that defines the input variable. Dependencies between the individual variables in the table can also be formed (for example, point 4 can occur 20 seconds after point 3)

American Institute of Aeronautics and Astronautics

12

3. Interpolation Table - user includes a linear interpolation table with up to 10 independent variables to define the input variable

4. Event Driven - user specifies independent variable-driven events that trigger changes in the dependent variable

5. Neural Network - user includes a feed-forward artificial neural network architecture to define the input variable. The network size, weights and activation functions must be specified, and weighted-hybrid networks are acceptable.

All trajectory input values and vehicle parameters can be included in the optimization process, unless they are specified as an interpolation table or neural network. Further, relationships between the vehicle parameters can easily be built in order to perform elementary sizing studies.

• Implementation

Due to the large amounts of data recorded in the course of a simulation, UPTOP makes use of dynamic memory allocation. Further, the user has the ability to turn-off the calculation of blocks of output variables irrelevant to their work (i.e., orbital elements in a subsonic cruise problem), thereby helping to speed the computation.

Since UPTOP relies on an evolutionary-based optimization scheme, it is well suited towards parallelization. UPTOP incorporates MPI to facilitate its use across multi-computer networks, and uses a self-scheduling job controller to ensure the best use of resources.

Figure 15 shows the excellent agreement in the optimal ascent profiles as determined by POST and UPTOP. This sample problem is solved by POST relatively quickly using the projected gradient method. Also shown on Figure 15 is the initial trajectory given in the POST input deck, which, considering the potentially wide bounds of the design variables (each vehicle pitch point was allowed to vary from 0 to 90 deg) is clearly in the near neighborhood of the optimal solution. In general, gradient-based optimizers require an initial set of design variables, and a clear, uninterrupted path

Figure 15. Comparison of POST to UPTOP results.

between the initial and optimal designs. Although these exists numerous methods of extracting the optimizer from local optima or even overcoming discontinuities in the design space, these methods generally increase the amount of problem-specific user tuning. D. Thermal Protection System Optimization (TPSOPT) Code

The development of TPSOPT was supported by a two-year AFRL contract with the goal to develop an automated design software for Thermal Protection System (TPS) optimization of hypersonic flight vehicles. TPSOPT consists of three major submodules; namely a POD/RSM module for rapid aerodynamic data generation, an aeroheating module for heat flux computation, and a TPS optimization module for minimum weight of the TPS. • POD/RSM Module

The POD/RSM module constructs a response surface of the flow eigenmodes by applying the Proper Orthogonal Decomposition (POD) technique on a set of flow solutions that are either computed by the high fidelity CFD codes or low fidelity panel codes. Once the response surface is obtained, the POD/RSM module can rapidly provide the aerodynamic data such as pressures and velocity components over the entire configuration at any given flight condition along a trajectory of the flight vehicles.

For a complex configuration of X-34, POD/RSM is found to provide accurate aerodynamic solutions with the lee-side aerodynamics resulting from stringent high angle of attack conditions. Figure 16 shows POD/RSM solutions versus direct CFL3D solutions on X-34 at Mach 10.0, where excellent correlation can be seen. Further, each POD/RSM solution performed on-line requires only a few seconds of computing time demonstrating its solution accuracy and computational efficiency.

American Institute of Aeronautics and Astronautics

13

Figure 16. Comparison of Pressure Coefficients between POD/RSM and

CFL3D Solutions on a X-34 at M = 10.0. • Aeroheating Module

The aeroheating module computes the time history of the heat flux of a given trajectory over the entire configuration. Based on the velocity components provided by the POD/RSM module, it first calculates the steamlines by a step-marching method using the flow velocity on the tangential plane of the surface. Then, along each steamline, a 2D boundary layer analysis is performed for heat flux generation. The aeroheating module loops all points along a given trajectory and consequently generates a time history of the heat flux for TPS design. • TPS Optimization Module

The objective of the TPS optimization module is to minimize the TPS weight while satisfying the thermal protection constraints and other physical constraints. All function evaluation of the constraints are performed by a transient heat transfer analysis using the time history of the heat flux as the input. The optimization solution is achieved using a gradient-based optimization technique. The sensitivities of constraints with respect to the design variables, namely the thickness of each layer of the TPS, are derived using a complex variable differentiation technique that operates

Figure 17. Design Patched Defined over TPS

on the X-34. on the complex version of the transient heat transfer analysis.

The TPS optimization module includes a TPS material library and built-in TPS structural arrangement concepts such as slab, radiation, gap, honeycomb, corrugated standoff, Z-standoff, ablator subliner, etc. to reduce the user’s burden for input set-up. The TPS optimization module assumes that the whole surface of the vehicle can be divided into several patches; within each patch a different TPS structural arrangement concepts and material can be selected.

X Y

Z0.140.121250.10250.083750.0650.046250.02750.00875

-0.01

X Y

Z0.030.02450.0190.01350.0080.0025

-0.003-0.0085-0.014

X Y

Z0.0190.0148750.010750.0066250.0025

-0.001625-0.00575-0.009875-0.014

X Y

Z

0.140.121250.10250.083750.0650.046250.02750.00875

-0.01

X Y

Z

0.030.02450.0190.01350.0080.0025

-0.003-0.0085-0.014

X Y

Z

0.0190.0148750.010750.0066250.0025

-0.001625-0.00575-0.009875-0.014

CFD

PODAoA 2 AoA 15 AoA 30

1

3

46

7

8

11

9

5

10

12

13

2

14

American Institute of Aeronautics and Astronautics

14

To ensure the smoothness of the thickness distribution of the optimized TPS, it is assumed that the thickness distribution is represented by several shape functions. Thus, the design variables of the optimization are the coefficients of the shape function, not the thickness of the TPS. This then significantly reduces the number of design variables.

For demonstration, TPSOPT is applied to the full configuration of the X-34 whose surface is divided into 14 patches as shown in Figure 17. Two types of TPS structural arrange concepts are selected; one called TPS(A) for those patches located on the nose and leading edges and the other called TPS(B) for those patches on the fuselage and wing surfaces. These structural arrangement concepts are shown in Figure 18. In Figure 19, it can be seen that the final optimization thickness of TPS on patches in the nose region (Patches 1 and 2) is about one order of magnitude thinner than its initial thickness. The optimized total TPS weight is found to be reduced by 22% terminated after the 20th design cycle while satisfying all TPS temperature constraints (Figure 20).

Figure 18. Two TPS Structural Arrangement Concepts.

Figure 19. Optimal Thickness for Patches 1 and 2.

Figure 20. Iteration History of the Objective

Function during Optimization Process.

E. Structural Model Base: Beam

A free-free beam model called the SMB model is developed to represent the mass and EI distribution of the whole vehicle. The purpose of the SMB model is to provide the “first-cut” generalized masses, natural frequencies, and mode shapes to the ASPE model builder for the inclusion of aeroelastic effects in the state-space equations.

The EI distribution of the SMB model can be determined by a simple stress-ratio technique using the critical shear and bending moment distribution along the vehicle generated by UCDA. The mass distribution of the SMB model is taken from the weight estimator embedded in UCDA.

It should be noted that because the aerodynamic forces computed by UCDA are all based on analytical equations there is no requirement for the mode shape transferal between the structural and aerodynamic models. This also

0.08163 inThin skinRTV-560

0.09984 inSlabAB312 Fabric

2.04122 inSlabQ-Felt

(3.5 PCF)

0.17198 inSlabAB312 Fabric

0.11645 inThin skinHRSI Coating

0.08163 inThin skinRTV-560

0.09984 inSlabAB312 Fabric

2.04122 inSlabQ-Felt

(3.5 PCF)

0.17198 inSlabAB312 Fabric

0.11645 inThin skinHRSI Coating

TPS (A) TPS (B)

L=118 in.

TPS-(A)

(1)

T/L

(2)

(3)

(4)

(5)

(1)

(2)

(3)

(4)

Position

0.0061

0.0052

0.0041

0.0048

(6)

(5)

0.0049

(6)0.0046

Optimization Cycle

N

on

-dim

ensi

on

al W

eig

ht

American Institute of Aeronautics and Astronautics

15

suggests that the SMB model can be easily replaced by a finite element model in the preliminary design phase. Typical output from SMB module can be summarized in Figures 21 through 23.

Figure 21. Thickness, EI, and GJ distributions for SEM optimization.

Figure 22. SEM mode frequencies

Figure 23. SEM mode shapes

F. Trim Module

• Sensitivity Computations with Complex Variable Differentiation (CVD)

In the Complex Variable Differentiation (CVD) technique the variable x of a real function f(x) is replaced by a

complex one, x+ih. For small h, f(x+ih) can be expanded into a Taylor’s series as follows:

( ) ( )2 2 3 3 4 4

2 3 42 6 24

df h d f h d f h d ff x ih f x ih i

dx dx dx dx+ = + − − + + (21)

The first and second derivatives of the above equation can be expressed as:

( )( ) ( )2

Im f x ihdfO h

dx h

+= + (22)

( ) ( )( ) ( )

22

2 2

2 f x Re f x ihd fO h

dx h

− + = + (23)

where the symbols “Im” and “Re” denote the imaginary and real parts, respectively. From Eqs. (22) and (23), it can be seen that the derivatives using the complex variable approach only require function evaluations. This feature is very attractive particularly when the function is complicated, in which case to obtain an analytic derivative is cumbersome and error-prone. Furthermore, unlike the finite difference method where the accuracy of the derivative depends on the step-size due to magnification of errors introduced by subtraction of very close function values, Eq. (22) shows that the first derivative obtained by CVD does not involve differencing two functions. Therefore, no cancellation errors exist for the first derivative in the use of the complex variable technique; and hence, the first derivative becomes step-size independent. Note that the second derivative in Eq. (23) is prone to cancellation errors,

American Institute of Aeronautics and Astronautics

16

but is not used here. Because CVD does not introduce cancellation error for the first derivative, the step-size h can be as small as the machine zero; for instance, h = 10-30. Based on equation (22), since the truncation error due to Taylor’s series is in the order of h2=10-60 that becomes a machine zero in a 32 bit computer, CVD does not introduce any numerical approximation and therefore can be considered as a numerically exact

differentiation technique. To incorporate CVD into an existing code for sensitivities all variables in the code must be declared as complex. The sensitivities are obtained from analysis runs, where each design variable in turn is augmented by a small imaginary part (ih ≈ i * 10-30). First-order sensitivities are obtained by division of the imaginary parts of results by h (Eq. 22).

Figure 24. Sensitivity of Axial force (Fx) with respect to Angle of Attack, Altitude,

Mach Number and Control Surface deflection

Typical results of the new UCDA are shown in Figure 24-26. Figure 24 through 26 compare sensitivities of Axial force, Lift force and Pitching moment respectively with respect to Angle of Attack, Control surface deflection, Mach number and Altitude for SEM at its design condition. Clearly, CVD compares well with Finite Difference (FD) for at least one choice of difference in independent variable in each case. This goes to show that for a highly nonlinear flow as prevalent in hypersonic aerodynamics, CVD is a good choice of finding the right derivative because different choices of the difference parameters for independent variables can lead to different derivatives, making FD a non reliable method of evaluating derivates.

American Institute of Aeronautics and Astronautics

17

Figure 25. Sensitivity of Lift force (Fz) with respect to Angle of Attack, Altitude,

Mach Number and Control Surface deflection

The difficult point to convert the UCDA code to a complex variable version is the combustor part. Because multiple chemical reacting rates are involved, the combustion part uses DOUBLE prevision data structure with several long external developed combustion subroutines. Great effort has been spent to convert the combustor part into DOUBLE COMPLEX type, but that approach failed to stabilize sensitivity. To bypass this problem, we take the following approach. We treat the combustion part as a black box, and use DOUBLE precision data structure for the combustion part as usual, but we use the following relations to estimate the properties at the combustor exit:

𝜙𝜙(ℎ + 𝑖𝑖Δℎ) = 𝜙𝜙(ℎ) +𝜕𝜕𝜙𝜙𝜕𝜕ℎ

𝑖𝑖Δℎ

𝜙𝜙(ℎ + Δℎ) = 𝜙𝜙(ℎ) +𝜕𝜕𝜙𝜙𝜕𝜕ℎ

Δℎ

First we compute 𝜙𝜙(ℎ), then 𝜙𝜙(ℎ + Δℎ) with the second equation; next we subtract these two properties to obtain (𝜕𝜕𝜙𝜙/𝜕𝜕ℎ)Δℎ; at the end we reconstruct 𝜙𝜙(ℎ + 𝑖𝑖Δℎ) by adding 𝑖𝑖 ∙ (𝜕𝜕𝜙𝜙/𝜕𝜕ℎ)Δℎ and 𝜙𝜙(ℎ) we can obtain the properties at the combustor at the exit. By doing so, the flow field with small complex variable perturbation can continue along the

American Institute of Aeronautics and Astronautics

18

Figure 26. Sensitivity of Pitching moment (My) with respect to Angle of Attack, Altitude, Mach Number and Control Surface deflection

nozzle and elevator part. The advantages of this approach are: we can treat the combustor as a black box, and the computation time is short. • Derivation of Trim Equation

After we have calculated necessary sensitivities using CVD as described earlier and new updated weight from TPSOPT and SMB module, we can trim the vehicle. The derivation of the trim equation is given below.

Considering angle of attack, control surface deflection and generalized coordinates as the dependent variables, the total force at a particular time on a flying vehicle can be summed up as

0TF F F F Fα δ ηα δ η= + + + (24)

where FT is total force, F0 is force at the mean flight condition, Fα , Fδ and Fη are forces due to small perturbations in angle of attack α, control surface deflection δ and generalized coordinate η. In terms of the deflection of the structure, the force FT can also be written as

TF KX= (25)

where K is the stiffness of the structure and X is the deflection in generalized coordinates. Also, deflection of the structure can be written as,

X ηφ η= (26)

where ϕη is mode shape in generalized coordinates.

Pre-multiplying Tηφ with Eq. (25) and using Eq. (24), we arrive at

0T T T T T T

TK F F F F Fη η η η η α η δ η ηφ φ η φ φ φ α φ δ φ η = = + + + (27)

The generalized stiffness can be defined as

American Institute of Aeronautics and Astronautics

19

2TK K mη η η η ηφ φ ω= = (28)

where ωη and mη are generalized frequency and generalized mass respectively. Combining Eq. (27) and Eq. (28), we get

0T T T TK F F F Fη η η η η α η δφ η φ φ α φ δ − = + + (29)

Now if we consider

T

aeK K Fη η ηφ = − (30)

Then,

1

0T T T

aeK F F Fη η α η δη φ φ α φ δ− = + + (31)

Putting Eq. (8) in Eq. (1), we have,

1 1 1

0 0T T T

T ae ae aeF F F F F K F F K F F K Fα δ η η η η α η η δα δ φ φ α φ δ− − −= + + + + + (32)

Eq.(9) can be rewritten as,

[ ] [ ] [ ]0TF I A F I A F I A Fα δα δ= + + + + + (33)

where

1 T

aeA F Kη ηφ−= (34)

Now, for trim condition, we satisfy two equations:

TZ T ZL F Wφ η= = (35)

and

0T

R TM Fφ= = about Center of Gravity (C.G.) (36)

where L is Lift, M is Pitching Moment, W is weight of the vehicle, TZφ is unit vector along direction of lift, T

Rφ is a

vector containing pitching moment arm and Zη is a factor that depends on the vertical acceleration the structure is

withstanding for a particular flight condition. For a level flight, 1Zη = .

Using (33), we finally arrive at the following 2 X 2 linear system of equations

[ ] [ ][ ] [ ]

0

0

T T TZ Z Z ZT T TR R R

I A F I A F W AF

I A F I A F AF

α δ

α δ

φ φ η φαδφ φ φ

+ + − =

+ + − (37)

Because the stability derivatives are nonlinear in UCDA hypersonic aerodynamics, iterating the linear trim equation to achieve the trim condition is required. At each current trim position, aerodynamic stability derivatives are recomputed for the next trim iteration. G. AeroServoElasticity (ASE) Analysis

The trim conditions are used to obtain AeroServoElasticity (ASE) matrices. Again, CVD technique is used to find the necessary stability and other derivatives. The derivation of ASE matrix follows below.

For longitudinal dynamics, there are three rigid body modes, namely Tx for fore-aft mode, Tz for plunge mode and Ry for pitch mode. The elastic mode is bending mode η. Thus the deformation can be expressed as

Flight Dynamics Model with Bending Mode Induced Aerodynamics Effects

𝑋𝑋 = 𝜙𝜙𝑥𝑥 𝜙𝜙𝑧𝑧 𝜙𝜙𝜃𝜃 𝜙𝜙𝜂𝜂

𝑇𝑇𝑥𝑥𝑇𝑇𝑧𝑧𝑅𝑅𝑦𝑦𝜂𝜂

(38)

Introduce a state vector, 𝑋𝑋𝑎𝑎𝑎𝑎 𝑇𝑇 = 𝑇𝑇𝑥𝑥 𝑇𝑇𝑧𝑧 𝑅𝑅𝑦𝑦 𝜂𝜂 𝑇𝑇𝑥 𝑇𝑇𝑧 𝑅𝑅𝑦 𝜂 (39)

The state space equation of the flight dynamic model including bending aeroelastic effects is

[ ] [ ] .

ae aeX A X B δ

= +

(3)

where

American Institute of Aeronautics and Astronautics

20

[𝐴𝐴] = 04𝑋𝑋4 𝐼𝐼4𝑋𝑋4

−𝑀𝑀−1[𝐾𝐾 + 𝑞𝑞∞𝐴𝐴𝑠𝑠0]4𝑋𝑋4 −𝑀𝑀−1 𝐶𝐶 + 𝑞𝑞∞𝑉𝑉∞𝐴𝐴𝑠𝑠1

4𝑋𝑋4

(40)

[𝐵𝐵] = 04𝑋𝑋𝑛𝑛𝑐𝑐

−𝑞𝑞∞[𝑀𝑀]−1[𝐴𝐴𝑐𝑐0]4𝑋𝑋𝑛𝑛𝑐𝑐 (41)

where c is the reference chord 𝑞𝑞∞ is the dynamic pressure and 𝑉𝑉∞ is the freestream velocity. 𝑛𝑛𝑐𝑐 is the number of control inputs

0 0 0

0 0 0

0 0 0

0 0 0

yy

m

mM

I

mη

=

(42)

2

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0

K

mη ηω

=

(43)

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 2

C

mη ηω ζ

=

(44)

where m is the mass of the vehicle Iyy is the moment of inertia about Y axis mη is the generalized mass of the bending mode ωη is the natural frequency of the bending mode and ζ is the damping ratio of the bending mode As0, As1, Ac0 are the aerodynamic stability derivative matrices

( )( )

0

0

0

0 0

0 0

0 0

0 0

D L D

L D L

s symm M

T T

mgS C C C Sq

S C C C SA

ScC C Sc

FFq q

α η

α η

α η

ηαη ηφ φ

∞

∞ ∞

− − − −

− + − = − − − −

(45)

where Fα is the aerodynamic force due to ϕθ Fη is the aerodynamic force due to ϕη CDη, CLη, CMη are the non-dimensional drag, lift and pitch moment coefficients due to ϕη

American Institute of Aeronautics and Astronautics

21

( ) ( )

( ) ( )

( )

0 0

0 0

0

12

0

2 0.5

2 0.5

2 0.5

2 0.5

u q

u q

u q

D D D L D D D

L L L D L L L

S sym

M M M M M M

quT T T T

S C C S C C Sc C C C S

S C C S C C Sc C C C S

ASc C C ScC Sc C C C Sc

FFF F Fc

q q q q

αα η

αα η

αα η

ηαη η η ηφ φ φ φ

∞ ∞ ∞ ∞

+ − − + −

+ + − + −

= + − + −

+ − −

(46)

where Fu is the aerodynamic force due to unit change in forward speed u F0 is the aerodynamic force at trim Fq is the aerodynamic force due to q

DCη, LC

η

, MCη

are the drag, lift and pitch moment due to 𝜂.

𝐹𝐹𝜂 is the aerodynamic force due to 𝜂.

0

D

L

c sym M

T

SC

SCA cSC

Fq

δ

δ

δ

δηφ

∞

−

− = − −

(47)

Fδ is the distributed aerodynamic forces due to unit change of control surface deflection δ .

Transformation from the body axis to airframe axis is done by [ ] ae AX T ξ= (48)

where

T

ae x z y x z yX T T R T T Rη η

=

(49)

T

x u h qξ α θ η η

=

(50)

[ ]

1 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 0 1 0

0 1 0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 1

AT

V V∞ ∞

− = −

−

(51)

So, the state space equation can be written as

A Bξ ξ δ = +

(52)

where

[ ] [ ][ ]1A AA T A T

− = (53)

and

American Institute of Aeronautics and Astronautics

22

[ ] [ ]1AB T B

− = (54)

Acknowledgments The present work is supported by the AFOSR/STTR Phases I/II contracts. The AFOSR contract monitors are

Dr. Victor Giurgiutiu, and Dr. John Schmisseur. The POC at AFRL are Dr. Ray Kalonay and Mr. Ed Pendleton.

References [1] Starkey, R.P., and Lewis, M. J., “Simple Analytical Model for Parametric Studies of Hypersonic

Waveriders,” AIAA Journal of Spacecraft and Rockets, Volume 36, Number 4, July-August 1999, pages 516-523.

[2] McRuer, D., “Design and Modeling Issues for Integrated Airframe/Propulsion Control of Hypersonic Flight Vehicles,” Paper WP7, 1991 American Control Conference, Boston, MA, 1991. pp. 729-735.

[3] Bowcutt, K. G., “Hypersonic technology Status and Development Roadmap,” AIAA HyTASP Program Committee, Technical Fellowship Advisory Board Study, December 18, 2003.

[4] Chavez, F. R., and Schmidt, D. K., “Analytical Aeropropulsive/Aeroelastic Hypersonic-Vehicle Model with Dynamic Analysis,” Journal of Guidance, Control & Dynamics, Vol. 17, No. 6, November-December 1994, pp. 1308-1319.

[5] Starkey, R. P., and Lewis, M. J., “Sensitivity of Hydrocarbon Combustion Modeling for Hypersonic Missile Design,” AIAA Journal of Propulsion and Power, Vol. 19, No. 1, Jan-Feb 2003, pp. 89-97.

[6] ZONA Technology, Inc. and University of Maryland, “Integrated Aero-Servo-Thermo-Populso-Elasticity (ASTPE) for Hypersonic Scramjet Vehicle Design/Analysis,” AF STTR Phase I Proposal, Topic # AF05-T027, Proposal # F054-027-0129, Submitted August 10, 2005.

[7] Mirmirani, M., Wu, C., Clark, A., Choi, S., and Colgren, R., “Modeling for Control of a Generic Airbreathing Hypersonic Vehicle,” AIAA 2005-6256, AIAA Guideance, Navigation, and Control Conference and Exhibit, 15-18 August 2005, San Francisco, CA.

[8] Boldender, M.A., and Doman, D.B., “A Non-Linear Model for the Longitudinal Dynamics of a Hypersonic Air-Breathing Vehicle,” AIAA 200-6255, AIAA Guideance, Navigation, and Control Conference and Exhibit, 15-18 August 2005, San Francisco, CA.

[9] Baker, M.L., Munson, M.J., Hoppus, G.W., Alston, K.Y., “The Integrated Hypersonic Aerometchanics Tool (IHAT), Build 4,” AIAA 2004-4565, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, August 30, 2004.

[10] Johnson, D.B., Thomas, R., and Manor, D., “Stability and Control Analysis of a Wave-Rider TSTO Second Stage,” AIAA-01-1834.

[11] Sobieczky, H., Dougherty, F. C., and Jones, K. D., “Hypersonic Waverider Design from Given Shock Waves,” Proceedings of the First International Hypersonic Waverider Symposium, University of Maryland, College Park, Oct. 17-19, 1990.

[12] Chauffour, M., “Shock-Based Waverider Design With Pressure Corrections and Computational Simulations”, Master Thesis, University of Maryland, Department of Aerospace Engineering, 2004.

[13] Grantz, A.C., “Calibration of Aerodynamic Engineering Methods for Waverider Design,” AIAA Paper 94-0382, 1994.

[14] O'Brien, T. F., Starkey, R. P., and Lewis, M. J., “Quasi-One-Dimensional High Speed Engine Model With Finite Rate Chemistry,” AIAA Journal of Propulsion and Power, Vol. 17, No. 6, Nov-Dec 2001, pp. 1366-1374.

[15] Byrne, G.D., Hindmarch, A.C., and Brown, P.N., “VODPK: Variable-Coefficient Ordinary Differential Equation Solver with the Preconditioned Krylov Method GMRES for the Solution of Linear Systems,” Lawrence Livermore National Lab,. Livermore, CA, 1997.

[16] Kee, R.J., Rupley, F.M., And Miller, J.A., “Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics,” SAND 89-8009B, Sandia National Labs, Livermore, CA, 1989.

[17] Kundu, K.P., Penko, P.F. and Yang, S.L., “Reduced Reaction Mechanism for Numerical Calculations in Combustion of Hydrocarbon Fuels,” AIAA Paper 98-0803, Jan. 1998.

[18] Lewis, M.J., and Chang, J.S., “Joint Jet-A/Silane/Hydrgoen Reation Mechanism,” Journal of Propulsion and Power, Vol. 16, No. 2, 2000. pp.365-367.

American Institute of Aeronautics and Astronautics

23

[19] Rogers, R.C., “Mixing of Hydrogen Injected from Multiple Injectors Normal to a Supersonic Airstream,” NASA TN D-6476, Sept. 1971.

[20] Henry, J.R., and Anderson, G.Y., “Design Considerations for the Airframe-Integrated Scramjet,” NASA TM X-2895, Dec. 1973.

[21] Starkey, R. P., “Off-design Performance Characterization of a Variable Geometry Scramjet,” ISABE-2005-1111, 17th International Symposium on Airbreathing Engines, September 4-9, 2005, Munich, Germany.

[22] Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., “Aeroelasticity,” Addison-Wesley Publishing Company, Inc. Reading, Massachusetts, 1957, Ch. 4.

[23] Stevens, B.L. and Lewis, F.L., “Aircraft Control and Simulation,” John Whiley & Sons, 2nd Ed., 2003. [24] Wright laboratory Report WL-TR-96-3099, “Application of Multivariable Control Theory to Aircraft Control

Laws,” Wright-Patterson AFB, OH 45433-7562, May 1996.

[25] Enns, D., Bugajski, D., Hendrick, R., and Stein, G., “Dynamic Inversion: An Evolving Methodology for Flight Control Design,” Int. Journal of Control, 1994, Vol. 59, No.1, pp. 71-91.

[26] Madavan, N. K., ``On Improving Efficiency of Differential Evolution for Aerodynamic Shape Optimization Applications,'' AIAA Paper No. 2004-778, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, Aug 2004.

[27] Vanderplaats Research & Development, Inc. DOT Users Manual, version 5.0. Colorado Springs, CO, 1999. [28] Madavan, N. K., ``Aerodynamic Shape Optimization Using Hybridized Differential Evolution,'' AIAA Paper

No. 2003-3792, 21st Applied Aerodynamics Conference, Orlando, FL, June 2003.