[American Institute of Aeronautics and Astronautics 10th AIAA/NAL-NASDA-ISAS International Space Planes and Hypersonic Systems and Technologies Conference - Kyoto,Japan (24 April 2001

c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

A01 -28053AIAA/NAL-NASDA-ISAS 10th Internationa! SpacePlanes and Hypersonic Systems and TechnologiesConferenceKyoto, Japan 24-27 April 2001 AIAA 2001-1849

DESIGN AND ANALYSIS OF PAYLOAD-OPTIMIZED WAVERIDERS

Marcus Lobbia* and Kojiro SuzukitDepartment of Aeronautics and Astronautics, The University of Tokyo

7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JAPAN

ABSTRACT

A waverider is a supersonic or hypersonicvehicle with a shock wave attached along its leadingedge; this attached shock wave limits leakage fromthe lower flow region to the upper, thus allowing thepotential for high lift/drag ratios relative toconventional designs. To help expand theapplicability of waveriders to realistic aerospacemissions, implementation of a cylindrical payloadrequirement into the waverider design andoptimization process is investigated. In addition,because the inverse design process is used forconstructing waveriders in this research, the use ofComputational Fluid Dynamics in obtaining thegenerating flowfield for waverider design isdemonstrated. Finally, three-dimensional numericalsimulations are performed around waveriderconfigurations to verify that the design processimplemented is correct. These validation resultsshow good agreement with those obtained during thedesign/optimization process, and help highlight thepotential of payload-optimized waveriders in modernaerospace missions.

INTRODUCTION

High-Speed Aerospace Vehicle DesignEfficient aerodynamic design is a requirement

for modern high-speed aircraft design. As the flightvelocity for a given design increases, the dynamicpressure of the flow (and thus the drag forces actingon the vehicle) also increase; therefore a highlyefficient and optimized design is necessary foreffective application of supersonic/hypersonicvehicles to practical aerospace missions.

One measure of the aerodynamic efficiency ofan aircraft can be obtained by looking at the ratio ofits lift to drag forces (L/D). The benefits of increasing

*Graduate Student, Dept. of Aeronautics and Astronautics, GraduateSchool of Engineering, Univ. of Tokyo, AIAA Student Membert Associate Professor, Dept. of Advanced Energy, Graduate Schoolof Frontier Sciences, Univ. of Tokyo, AIAA Member

Copyright © 2001 by the American Institute ofAeronautics and Astronautics, Inc. All rights reserved.

the L/D of the design can be seen from the Breguetequation for cruise range:

,npJ^.\.d\¥± _!_, (i)( «, j (tf. JU/0Jwhere m/ is the total fuel mass, ms is the mass of thevehicle structure and payload (not including fuel), dis the cruise range, SFC is the specific fuelconsumption, and U«> is the cruise velocity. Becausethe logarithm of the mass ratio is inverselyproportional to the L/D of the design, a low L/D canexponentially increase the fuel required to cover thesame distance. Thus, for a high-speed cruise vehicleto have any chance of economic success, attaining ahigh L/D should be an important objective.l

The effective specific impulse, defined as:

Ispeff ~ ( T - D ) / ( g x m f ) , (2)

is a measure of the net thrust available; for the case ofa space plane, minimizing the drag on the vehicleincreases the effective specific impulse available.This kind of accelerator vehicle uses a relativelysmall-angle trajectory to reach orbit, thus matchingthe lift to the weight of the vehicle is desirable.1 Bydesigning the configuration for a high L/D, a heaviervehicle weight (either in the form of a larger payloador more fuel) can be considered, expanding theoperational characteristics of the space plane.

WaveridersOne class of aerospace vehicles that have

shown the ability to attain a higher L/D compared toconventional designs is waveriders. A waverider isdefined as a supersonic or hypersonic vehicle with anattached shock wave along its entire leading edge(see Fig. 1 for a conical-flow example). Theattached shock wave keeps the high-pressure flowcontained below the waverider lower surface, thusallowing the potential for high L/D ratios. Becausethe vehicle appears to be riding its own shock wave,they are thus referred to as "waveriders."

Although there are many ways of designing awaverider, the inverse-design method adopted for thisresearch is to specify the lower surface curve in thebase plane. From this curve, the streamlines aretraced upstream, defining the lower surface of the

American Institute of Aeronautics and Astronautics


waverider. The leading edge of the waverider isdetermined when the streamlines intersect thegenerating shock. The upper surface is thenconstructed by tracing downstream from the leadingedge in the freestream direction, and terminated whenthe base plane is reached.

Research ObjectivesSince their conception in the late 1950's,

waveriders have been researched for potential roles ina variety of aerospace missions2. Initially, inviscidresults showed extremely promising performancecharacteristics, but it was not until the late 1980's thatthe incorporation of the viscous forces into the designprocess led to more realistic results. Theseviscous-optimized waveriders, in particular, haveshown applicability to a variety of aerospace roles.3

Thus, the major objective of this research is toexpand the potential of waveriders to variousmissions by implementing payload considerationsinto the design/optimization process. Cylindricalpayloads are very common in aerospace missions(e.g., satellites, cargo bays); incorporation of thispayload into the optimization and design process canyield practical mission-orientated configurations.

Additionally, the use of Computational FluidDynamics (CFD) in solving the generating flowfieldis investigated. Successful application of CFD in thedesign process can help expand the design space forwaveriders, allowing non-conical (even fullythree-dimensional) supersonic/hypersonic flows to beused in waverider construction.

Finally, three-dimensional CFD simulationsare performed around various waveriderconfigurations to verify the performancecharacteristics obtained during the design process.Comparison of these results can help validate thedesign process used.

COMPUTATIONAL METHOD

IntroductionThe computational process used for this

research is split into two sections: design andvalidation. Thus, the design process is describedinitially, including optimization and performanceestimation techniques. After obtaining an optimizedwaverider design, validation is necessary to ensurethat the design is correct (e.g., the shock wave isattached to the leading edges of the waverider atdesign conditions) - the use of CFD for this processis described. A flow chart of this entire process isshown in Fig. 2.

Design: Generating FlowfieldIn much of the research dealing with

waveriders, conical flowfields are popular for use as

the generating flowfield for waverider design. Thereason for this is that the analytical solution forsupersonic conical flow can be expressed by theTaylor-Maccoll equation:

de2 dedu_de1

(3)

where u and v are the flow velocities in the r and 6directions, respectively, and a is the local speed ofsound. Because this is an ordinary differentialequation, it can be solved relatively quickly andeasily using a numerical integration technique (e.g.,4th-order Runge-Kutta algorithm).

Although the Taylor-Maccoll solution is easyto implement into a waverider design program, itlimits the generating flowfield to axisymmetricconical flow only. Thus, the use of CFD is alsoinvestigated for use in waverider design. The Eulerequations in particular are suited to the waveriderdesign philosophy - since the boundary conditions foran Euler solution assume tangential flow at the bodysurface, this relates well with the idea of tracingstreamlines to form the lower surface of a waverider.

In this research CFD is used as the primarymethod for solving the generating flowfield forwaverider design. The two-dimensional axisymmetricEuler equations are solved in conservation form; theassumption of a perfect gas is used to relate theinternal energy to the other flow variables.

These equations are solved using theBeam-Warming algorithm. Time integration isperformed implicitly, and the fluxes are calculatedusing Yee's Symmetric TVD scheme (2nd-orderspatial accuracy). Local time stepping is used toaccelerate the solution to steady-state.4'5

Design: Waverider ConstructionWaveriders are commonly constructed using

the inverse design process; the waverider is designedinversely from a simple supersonic or hypersonicflowfield (e.g., cone, wedge flow).

There are several different methods for obtaina unique design for a given flowfield; the methodadopted in this research is to specify the lowersurface curve of the waverider in the base plane (seeFig. 3). This is performed by generating a series ofcubic splines through 4 control points; the slopes atthe end of the curve and the normalized height of thecurve are also specified. The lower surface of thewaverider is created by the tracing the streamlines inthe generating flowfield upstream from the basecurve; the leading edge of the waverider isdetermined when the shock wave in the generating



flowfield is reached. The upper surface is thenformed by tracing in the freestream direction from theleading edge back to the base plane.

In determining the shock wave location (andthus the leading edge for the waverider), a pressuredifference based on the flow properties before andafter the shock wave in the generating flowfield isused. When tracing the streamlines to form the lowersurface of the waverider, the pressure change ischecked each increment; when this change exceedsthe specified value, it is assumed that the shock wavehas been reached.

Design: OptimizationAlthough waveriders can be designed

arbitrarily from a given flowfield by specifying thelower surface base curve, an optimization procedureis implemented to try and find the "best" designbased on a specified objective function. For thisresearch, the designs were optimized for acombination of L/D, volumetric efficiency, andpayload efficiency; the objective function:

(4)payV

is minimized by varying seven parameters describingthe shape and location of the base curve. The variableV describes the total volume of the waverider and A isthe surface area; the constants a, b, and c control theinfluence of the L/D ratio, volumetric efficiency (r]vof),and payload efficiency (rjpay)7 respectively, in theoptimization process. By adjusting the constants ofthe objective function, the process can be weighted toobtain a design with the desired characteristics (e.g.,high L/D versus volumetric efficiency).

The volumetric efficiency is an indication ofthe volume of the waverider relative to its surfacearea; this parameter is often incorporated intowaverider optimization programs to maintain abalance between usability (high volume) vs.aerodynamic performance (high L/D). The payloadefficiency is introduced as a refined indication of theuseful volume of the waverider. The payload issimply a cylindrical volume (Vpay) that can be placedinside the waverider; the size is specified beforehand,and it is implemented both in the objective function(i.e., to design a waverider with high payloadefficiency) and as a constraint on the design process(i.e., the payload is required to be able to fit into thewaverider).

The optimization procedure used is thedownhill simplex method of Nelder and Mead.6 Inthis algorithm, 1) N+l configurations are initially

generated, 2) a new configuration is generated basedon the best N configurations, and 3) the newconfiguration replaces the worst. Steps 2 and 3 arerepeated until the difference between the best andworst configurations reaches a specific tolerance. Forthis research, N-l parameters describing the shapeand location of the lower surface base curve (see Fig.3) are allowed to vary in the optimization process.

Design: Aerodynamic PropertiesIn order to estimate the aerodynamic

characteristics of the design, the properties of thegenerating flowfield are applied at the lower surfacepoints of the waverider. Since the upper surface isparallel to the freestream direction, it is assumed tobe at freestream conditions. The pressure force actingon the base of the waverider is also obtained byassuming freestream flow properties at the base.Using these values, the pressure forces can beintegrated over the waverider surface. Because this isan inviscid calculation, the skin friction drag actingon the waverider is estimated using the referencetemperature method7 (with the assumption of a fullyturbulent boundary layer based on the highfreestream Reynolds number of approximately2.2xl08 for a 60 m long waverider in Mach 10operation at 30 km altitude). This calculationtechnique is relatively efficient to implement duringthe optimization process.

Additionally, because the value of the skinfriction drag depends on the length of the design, allwaveriders are scaled to the same length to allowaccurate comparisons.

Validation: Grid GenerationA finite-volume CFD technique is used to

numerically simulate the flow around a waverider;thus a distribution of grid cells around theconfiguration is required. This distribution can beobtained by specifying the boundaries of the grid(including the waverider surface), and then using anelliptic grid generation technique to obtain theinterior grid points.

A fully three-dimensional elliptic gridgeneration technique is computationally expensive,and ensuring grid conservation (i.e., planar cell faces)is difficult. Thus, the three-dimensional grid isdivided into a series of two-dimensional planes, andthe grid distribution is obtained for each plane. Thetwo-dimensional Poisson equation can be expressedin generalized coordinates as:

,-2b

(5)

drj2



where the nonlinear parameters a, b, and c aredefined as:

dn J *.}(». (6)

^The source terms represent parameters used tocontrol orthogonality and clustering at the bodysurface. Because Eq. (5) is nonlinear, lagging ofcoefficients is used to obtain the parameters a, b, andc. The line-SOR technique is implemented tonumerically solve Eq. (5).8

In order to obtain an interior grid distributionusing this technique, the boundaries of the grid mustbe specified initially. Thus, the waverider surface datais read into the grid generation program, and thedesired grid distribution (for the CFD simulation) isobtained by interpolating the surface points from thedesign data. The outer boundary is specified to be ofcross-sectional elliptic shape. Because the waveriderconfigurations exhibit a sharp leading edge, each gridplane is split into two regions (corresponding to theupper and lower surfaces of the waverider); Eq. (5) issolved in each region separately.

Finally, at design conditions the flow around awaverider is half-symmetric; thus only half of theconfiguration is simulated.

Validation: Computation Fluid DynamicsIn order to accurately simulate the

three-dimensional flow around a waveriderconfiguration, a shock-capturing CFD technique isused. The three-dimensional Euler equations can beexpressed in generalized coordinates as:

dU dF dG dH n__ I __ I __ i __ _ f\dt dg dr] d£

U-U/J,

pupu2 +p

puvpuw

(e + p)u

vppvu

pv2 +p

pvwH =

(7)

pw

pwupwv

pw2 +p(e + p)w

Eq. (7) is solved using the Beam-Warmingalgorithm. Time integration is performed implicitly(2nd-order temporal accuracy), and the fluxes are

calculated using Yee's Symmetric TVD scheme(2nd-order spatial accuracy). Local time stepping isused to accelerate convergence to steady state.4'5

The boundary conditions for the simulation areapplied assuming flow tangency on the body; thesurface contravariant velocities U and W areextrapolated, and the pressure and density on thebody are obtained using second-order extrapolation.The symmetry planes are extrapolated assuming noflow in the transverse direction. The outer ellipticboundary and inlet plane are set to freestreamconditions, and the exit plane is obtained usingzeroeth-order extrapolation.

Validation: Aerodynamic PropertiesThe results from the CFD simulation can be

used to calculate the aerodynamic performance of thewaverider configuration. Thus, the pressure isintegrated over the waverider surface in the samemanner as in the design case. However, this time theupper and lower surface flow properties are takenfrom the CFD solution; because the base was notsimulated it is assumed to be at freestream conditions.The Euler equations describe inviscid flow, thus theskin friction is again calculated by the referencetemperature method using the same technique as inthe design case.

Using this method, the aerodynamiccharacteristics of the waverider can be verified, andcompared with the results obtained during the designprocess.

RESULTS

Generating Flowfields used in Waverider DesignIn order to verify the validity of using CFD to

obtain the generating flowfield for waverider design,two non-optimized waveriders were generated from aconical flowfield (6=10 deg cone at a freestreamMach number of 10). The first waverider wasdesigned using a CFD-solved generating flowfield;the second was designed using a conical flowfieldsolved using the Taylor-Maccoll equation. In eachcase, the lower surface base curve is identical, andbecause the Taylor-Maccoll solution is interpolatedonto the same grid used for the Euler CFD solution,any differences in the shape and characteristics ofeach waverider result from differences in thegenerating flowfields.

The non-optimized waveriders designed usingboth CFD-solved and Taylor-Maccoll-solvedflowfields are shown in Fig. 4 and 5, respectively;Table 1 gives a comparison of the characteristics ofeach design. As is evidenced by the results, there areslight differences between the two, but the overallshapes are similar, and the aerodynamic propertiesare reasonably close. It can be inferred that one of the



causes of these discrepancies is the absence andpresence of the conical flow assumption, respectively,for the Euler CFD and Taylor-Maccoll solutions usedto generate the waveriders. Additionally, the differenttreatments of the shock wave in the generatingflowfield (shock-fitting for the Taylor-Maccollequation versus shock-capturing for the Euler CFD)cause slight variations in the determination of thewaverider leading edge, which can affect the overalldesign in each case.

Payload-Optimized Waveriders: Design ResultsIn order to demonstrate the effects of

incorporating payload considerations into thewaverider design process, two optimized waveriders(60 m in length) were generated from a conicalflowfield (6=10 deg cone at a freestream Machnumber of 10). The first design was optimized forL/D and volumetric efficiency only (optimizationconstants 0=7, b=2, and c=0). The second design isoptimized with the inclusion of a cylindrical payload(2.5 m radius, 20 m length) that is inserted into therear of the waverider - this payload was includedboth in the optimization process (constants 0=7, &=2,and c=4) and as a constraint on the design.

The shapes of the payload-optimized andnon-payload-optimized designs are shown in Fig. 6and 7, respectively; even though the optimizationprocess for each design was started from the sameinitial conditions, the final designs are quite different.The aerodynamic characteristics (obtained during thedesign process) of the configurations are shown inTable 2. It can be observed that although thewaverider optimized without payload considerationsexhibits a slightly larger design L/D of 3.54, thepayload-optimized waverider contains over 20% ofits volume in usable cylindrical form (see Fig. 8 for aside view of the payload-optimized configuration),while maintaining a relatively high L/D of 3.39.

Payload-Optimized Waveriders: Validation ResultsThe above two designs were validated by

numerically solving the three-dimensional Eulerequations around each configuration at designconditions. For this purpose, a 61x41x41 grid wasgenerated around each configuration (see Fig. 9 and10). Because the shock wave is expected to beattached at the leading edge of each design, mildclustering was implemented in this region (see Fig.11 for an example of the grid distribution near theleading edge in the base plane). Convergence wasassumed when the \^ norm decreased by 10"6 from itspeak value.

For the payload-optimized design, the densitycontours in both the base and mid planes are shownin Fig. 12 and 13, respectively. The same results forthe non-payload-optimized configuration are shown

in Fig. 14 and 15, respectively. Additionally, theexpected design results are also shown forcomparison on the right-hand side in each figure. Theaerodynamic characteristics of each design (both theCFD and design results) are compared in Table 3 and4, respectively, for the payload-optimized andnon-payload-optimized configurations.

As can be observed from the density contoursfor each design, some leakage is apparent at theleading edge of each waverider. This may be partlydue to the coarseness of the grids used for the CFDsolutions, and the fact that the shock wave is spreadover a few grid cells. However, the overall conicalshape of the attached shock wave is visible, and theaerodynamic characteristics of the two designsexhibit relatively close agreement with those obtainedduring the design process. Thus, from these results, itcan be inferred that the two configurations aresuccessfully validated at design conditions.

DISCUSSION

Shock-Capturing versus Shock-FittingFirst, it should be noted that when CFD

shock-capturing is used to solve the flowfieldsutilized in waverider generation, there is a slightsmearing of the shock over several grid points.However, the Taylor-Maccoll equation describes theanalytical solution for conical flow, and its solutionmethodology is a shock-fitting approach; thus theshock is infinitely sharp, and it is relatively easy todetermine the leading edge location for waveriderdesign using this method. An example illustrating thedifferences resulting from these two approaches isshown in Fig. 16; the slight smearing of the shockover several grid points is readily obvious in theshock-capturing results. Increasing the number ofpoints used in the CFD solution can help alleviatethis problem, but some shock-smearing will still bepresent.

This problem can also have effects on thethree-dimensional CFD simulations around waveriderconfigurations. Because of the numerical viscositypresent in the CFD algorithm, the shock is spreadover several grid cells, and this can cause some flowleakage to be present near the leading edge ofwaverider designs. Physical viscosity (inherent inNavier-Stokes simulations) might also affect theshock wave and its location in the leading edgeregion, leading to results different than those obtainedby solving the Euler equations. Regardless, more gridpoints and stronger clustering is required to provideaccurate results, especially in the leading-edgeregion.

Waverider OptimizationComparing the non-payload-optimized and



payload-optimized waveriders, it can be argued thattaking into account the mission payload requirementscan yield much more useful designs. In particular,when optimizing waveriders exclusively for L/D, thedesigns tend to become very thin and wing-like. (SeeFig. 17 for an example of a waverider designed usingthe optimization constants 0=7, 6=0, and c=0; thisdesign exhibits a design L/D of 3.73.) Incorporatingthe volumetric efficiency into the optimization yieldsmore practical designs, but control over whether thedesign can effectively be used for specific missions isstill somewhat ambiguous. Thus, full implementationof a payload constraint into the optimization processensures that the designs will meet themission-specific requirements.

Applications of Payload-Optimized WaveridersAs is mentioned previously, cylinder-shaped

objects are very common in aerospace applications.The space shuttle, for example, regularly uses itscylindrical payload bay to launch satellites intolow-earth orbit. Obtaining waverider designsoptimized with payload considerations (in addition toperformance ones) can extend their usefulness tosimilar missions (e.g. space planes).

A more down-to-earth example of theusefulness of payload-optimized waveriders is shownin Fig. 18. This is a photo of a Mach 3.5 waveridermodel designed for a design validation experimentconducted recently at the Institute of Space andAstronautical Science Mach 4 supersonic wind tunnel(located in Sagamihara, Japan). The dimensions ofthe sting balance attachment for the model wereknown in advance; these parameters were thenimplemented as a cylindrical payload during theoptimization process, making it easy to ensure that anoptimal design that fit the wind tunnel would begenerated. The results of this experiment are plannedfor publication in a future paper.

CONCLUSIONS

The implementation of payload considerationsinto the design and optimization of waveriders wassuccessfully performed. A payload-optimized Mach10 waverider realized over 20% of its volume in theform of a cylindrical payload, while still maintaininga relatively high L/D at design conditions.

The use of CFD for obtaining the generatingflowfield for the inverse design of waveriders wassuccessfully demonstrated. Comparison of two Mach10 cone-derived waveriders (one designed from aTaylor-Maccoll-solved flowfield, the other from anEuler CFD-solved flowfield) showed similarconfigurations and performance characteristics.

Finally, the three-dimensional Euler equationswere successfully solved around two waverider

configurations. These results validated theperformance characteristics obtained during thedesign and optimization process, and verified that thedesign method implemented is correct.

REFERENCES

1. M. K. L. O'Neill and M. J. Lewis, "DesignTradeoffs on Scramjet Engine IntegratedHypersonic Waverider Vehicles," Journal ofAircraft, Vol. 30, No. 6, pp. 943-952, 1993

2. Nonweiler, T. R. F., "Aerodynamic Problems ofManned Space Vehicles," Journal of the RoyalAeronautical Society, Vol. 63, pp. 521-528,1959

3. Bowcutt, K. G, and Anderson, J. D., Jr.,"Viscous Optimized Waveriders," AIAA87-0272, Jan. 1987

4. Yee, H. C, "A Class of High-ResolutionExplicit and Implicit Shock-CapturingMethods," NASATM-101088, Feb. 1989

5. Pulliam, T. H., and Steger, J. L., "RecentImprovements In Efficiency, Accuracy, andConvergence for Implicit ApproximateFactorization Algorithms," AIAA 85-0360, Jan.1985

6. Nelder, J. A., and Mead, R., "A Simplex Methodfor Function Minimization," Computer Journal,Vol. 7, pp. 308-313,1965

7. Eckert, E. R. G., "Engineering Relations forHeat Transfer and Friction in High-VelocityLaminar and Turbulent Boundary-Layer FlowOver Surfaces with Constant Pressure andTemperature," Transactions of the AmericanSociety of Mechanical Engineers, Vol. 78, No. 6,pp. 1273-1283,1956

8. Hoffmann, K. A., Computational FluidDynamics for Engineers, Copyright ©1989,Engineering Education System

ConfigurationGenerating Body

A [m2]V[m3]Tlvol

CL

CDLID

A6-10° cone

Euler21432293

0.0811

0.02190.00639

3.43

B6=10° cone

Taylor-Ma ccoll22372600

0.0845

0.02670.00722

3.70

% Differenceof Euler

4.413.44.2

21.913.07.9

Table 1: Comparison of Waveriders Designed withDifferent Generating Flowfields


c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

ConfigurationrivoiVpay

CL (Design)CD (Design)LID (Design)

Payload0.08430.220

0.02210.00652

3.39

No Payload0.0842

NA

0.02300.00650

3.54

Table 2: Comparison of Design Characteristics forPayload-Optimized and Non-Payload-OptimizedWaveriders

CL

CDLID

Design0.02210.00652

3.39

CFD0.0227

0.006063.74

% Difference of CFD2.8-7.010.5

Table 3: CFD ValidationPayload-Optimized Waverider

Results for

CL

CDLID

Design0.02300.00650

3.54

CFD0.02340.00617

3.79

% Difference of CFD1.6-5.17.1

Table 4: CFD Validation ResultsNon-Payload-Optimized Waverider

for

CONE

CONICAL SHOCK

WAVERIDER

Fig. 1: Derivation of a Waverider from a ConicalFlowfield

START

Solve Generating Flowfield(CFD or Taylor-Maccoll)

Define Initial DesignParameters

-*"̂ Yes

Generate Finite VolumeGrid

Solve Three-DimensionalFlowfield (CFD)

Calculate AerodynamicCharacteristics

FINISH

Fig. 2: Flow Chart of Research Methodology

(XI, Y1), M1

(X4, Y4), M4

BASE CURVE PARAMETERS:• Normalized Point Coordinates:

Z2, Y2, Z3, Y3, Y4• Normalized Baseline Height:

H• Slope:

M1Fig. 3: Base Curve Parameters


c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

Fig. 4: Non-Optimized Mach 10 WaveriderGenerated from CFD-Solved Fiowfield

Fig. 7: Mach 10 Non-Payload-Optimized Waverider

Fig. 5: Non-Optimized Mach 10 WaveriderGenerated from Taylor-Maccoll-Solved Fiowfield

Fig. 6: Mach 10 Payload-Optimized Waverider

Fig. 8: Side View of Mach 10 Payload-OptimizedWaverider

Fig. 9: Finite Volume Grid Distribution forPayload-Optimized Waverider

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Fig. 10: Finite Volume Grid Distribution forNon-Payload-Optimized Waverider

20 -

>- 0

-20 -

-20

Fig. 11: Grid Distribution in Base Plane forPayload-Optimized Waverider

20 -

> 0 -

20

Fig. 12: Density Contours in Base Plane forPayload-Optimized Waverider

Fig. 13: Density Contours in Mid-Length Plane forPayload-Optimized Waverider



>. o -

-20 -

20

Fig. 14: Density Contours in Base Plane forNon-Payload-Optimized Waverider

body surface

PRESSURE DISTRIBUTION

shockDISTANCE FROM SURFACE

freestream

Fig. 16: Example of Shock-Capturing vs.Shock-Fitting Solutions

Fig. 17: Mach 10 Waverider Optimized for L/D only

Fig. 15: Density Contours in Mid-Length Plane forNon-Payload-Optimized Waverider

Fig. 18: Photograph of Mach 3.5 Waverider Model

10American Institute of Aeronautics and Astronautics

Documents

[American Institute of Aeronautics and Astronautics 10th AIAA/NAL-NASDA-ISAS International Space Planes and Hypersonic Systems and Technologies Conference - Kyoto,Japan (24 April 2001