assessment of an inviscid euler-adjoint solver for prediction of aerodynamic characteristics of the...

7/25/2019 Assessment of an Inviscid Euler-Adjoint Solver for Prediction of Aerodynamic Characteristics of the NASA HL-20 Lifti

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American Institute of Aeronautics and Astronautics1

Assessment of an Inviscid Euler-Adjoint Solver for

Prediction of Aerodynamic Characteristics of the NASA

HL-20 Lifting Body

Dan Almosnino1

Aerion Technologies Corporation / Desktop Aeronautics, Palo Alto, CA 94303, U.S.A

An Adjoint-based Euler solver is used to calculate the flow on NASAs HL-20 lifting body

configuration. The study covers a full Mach range from low subsonic (M=0.3) to hypersonic

(up to M=20). Longitudinal and lateral aerodynamic coefficients are calculated.

Convergence behavior of the solver is discussed with emphasis on the impact of the HL-20

base flow in subsonic and transonic Mach numbers. Hypersonic flow cases are then studied

in detail, with incidence reaching 50 degrees. Computational considerations pertaining to

hypersonic flow and the impact of modifying the specific heat ratio are discussed.

Representative numerical flow visualizations are included for each flow regime and flow

features are discussed. Computational results show good agreement with wind-tunnel dataand a second computational method. The study demonstrates the conceptual and

preliminary design power of the current Euler-Adjoint solver when applied to complex

reentry geometries across their full flight Mach range.

Nomenclature

= angle of attack

= angle of side-slip

= specific heat ratio

CA = axial force coefficient

CD = drag force coefficientCD0 = drag force coefficient at zero lift

CDBase= base drag coefficientCFL = CourantFriedrichsLewy condition value

CL = lift coefficientCl = rolling moment coefficient (based on body width, s)

Cm = pitching moment coefficient (based on body length, Lb)CN = normal force coefficient

Cn = yawing moment coefficient (based on body width, s)CY = side force coefficient

Lb = reference length for longitudinal coefficientsL/D = lift to drag ratio

M = Mach numberN = number of volume grid cells

ReL = Reynolds number (based on body length, Lb)

Sref = reference areas = body width (reference length for lateral coeficients)Xref = X coordinate of moment reference point

Zref = Z coordinate of moment reference point

1Independent Consultant, Senior Member AIAA.

AIAA Applied Aerodynamics Conference

June 2016, Washington, D.C.

AIAA

right 2016 by Aerion Technologies Corporation / Desktop Aeronautics. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

A Aviation
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I. Introduction

HIS study aims to assess computational results of GoCart 2.0, a user analysis framework that runs Cart3D-1.4.9

Euler/Adjoint solver, against experimental data and CFD results of other methods for a NASA HL-20 lifting-body configuration. Cart3D unstructured Cartesian-grid Euler-Adjoint solver is discussed in Refs. 1 to 6. Cart3D

development itself started circa 1995 (e.g. Refs. 7 to 9). The current study also helps to identify limitations of themethod and to establish its value as a conceptual and preliminary design tool.

The HL-20 Personnel Launch System was a NASA concept for manned orbital missions studied by NASALangley Research Center circa 1990. Its stated goals were to achieve low operational costs, improved flight safety,

and a possibility of landing on conventional runways. Specifically, the plans for Space Station Freedom required asmall supporting vehicle for ferrying personnel to and from the station (called the Personnel Launch System, or PLS

plan). There was also a requirement to have a vehicle permanently docked at the station to serve as an emergencycrew rescue vehicle (planned to be a small personnel-only version, called the Assured Crew Return Capability,

or ACRC plan). One of the concepts evaluated was of a lifting body type vehicle designated HL-20.10

No actualflight prototype was ever built. After completing the first extensive set of wind-tunnel tests (carried out in ten

different wind-tunnels,11-18

and performing some stability and control studies,15-22

several modifications wereproposed and tested to improve both aerodynamic and control characteristics of the vehicle, designated HL-20A,

HL-20B.23,24

In addition, a full-scale mock-up of the HL-20 was built to study systems and human factors associatedwith the vehicle.

25Other concepts (Ref. 26 for example) are not within the scope of this study.

The HL-20 lifting body case is particularly interesting for an assessment study, because it encompasses the full

range of Mach numbers, from low subsonic to hypersonic. A specific computational challenge is the handling of theHL-20 significant base area flow. Note that the sharply trimmed trailing-edges of the fins create a base-type flow aswell.

II. Geometry

Figure 1a shows the schematics of a 0.07-scale HL-20 wind-tunnel model used for transonic tests,15

whereas ahigh-density mesh, digital model used in the current study is shown in Fig. 1b. The digital model is based on a

NASA-provided laser-scan of the 0.07 scale wind-tunnel model. The intersected model contains 422,554 surfacecells for the full geometry. The fins and vertical stabilizer have a round, blunt leading edge. The trailing edges are

trimmed (ending at a straight-cut angle of 90 to the fin or stabilizer surfaces). Figure 1a shows the different control

surfaces present in the wind-tunnel model, however the digital model in this study does not provide options forcontrol deflection. Table 1 provides the reference dimensions of the 0.07-scale model and the full scale vehicle.

T

a) 0.07-scale HL-20 wind-tunnel model,15

b) Shaded image of the digital model.

dimensions in inches.

Figure 1. HL-20 geometry.


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III. Sources of Experimental Data

Table 2 summarizes ten different sources for the experimental data used in the assessment of the computationalresults.

11-18The table demonstrates how extensive the HL-20 experimental effort was, but it also raises the need for

caution in data analysis, due to unavoidable differences in some flow characteristics between the wind tunnels, suchas the Reynolds number, the level of turbulence and the value of the specific heat ratio . The Reynolds numbers

quoted in Table 2 are based on the wind-tunnel model body length. Actual flight conditions for a 24.6 ft. long

vehicle would experience a much higher Reynolds number.

Table 1. HL-20 reference dimensions.

7% Model Full Scale Units Misc.

Body Width s 9.70 138.571 inch Reference Length for Lateral Coefficients

Body Length, Lb 20.63 294.714 inch Reference Length for Pitching Moment

Reference Area, Sref 152.2 31061.2 inch2

Moment Reference Point Xref 11.14 159.143 inch 0.54*Lb

Moment Reference Point Zref* -1.604 -22.914 inch Below Nose-tip

* Needed for moment coefficient calculation if model geometry definition has an x-axis going through the nose tip.

Table 2. Experimental data sources used in the assessment of the computational results.11-18

Test FacilityModelScale

MReL

(millions)

Number ofRuns

Type of Test Comments

30x60 ft. Full-ScaleTunnel

0.20.05,0.08

1.74, 2.79* 1.4 130

Force &

moment

*Estimated here using

standard sea level

conditions.

Low TurbulencePressure Tunnel

0.059 0.2, 0.33.40, 7.0, 10.3,

13.8, 22.31.4 129

7x10 ft. High SpeedTunnel

0.0590.3 to

0.83.40 1.4 184

CALSPAN 8 ft.

Transonic Tunnel0.07

0.6 to

1.26.00 1.4 244

Unitary Plan Wind

Tunnel0.07

1.6 to

4.53.40 1.4 412

20 inch M=6Hypersonic Tunnel

0.02 60.32, 1.09, 2.09,

3.781.4 126 Force &

moment,

Thermalmapping

Flow

visualization

CF4 M=6Hypersonic Tunnel

0.02 6 0.13, 0.26 1.22 73

31 inch M=10

Hypersonic Tunnel0.02 10

0.26, 0.54, 1.01,

2.01.4 83

MSFC 14 inch

Tri-Sonic Tunnel0.02

1.5 to

4.5? 1.4 28

Force &moment

(Ascent &

Abort)

Mentioned in Refs. 14, 23.

Data not used in thisstudy.

22 inch M=20

(Helium)Hypersonic Tunnel

0.02 20 1.47 1.67 26Force &Moment

Mentioned in Refs. 12, 13,14;Cm data provided in Ref.

13.


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IV. Computational Results

A. Preliminary Comments

The HL-20 case is particularly interesting because it deals with a lifting-body geometry over a full range ofMach numbers, from low subsonic (M=0.05) to hypersonic (M=20.3). The extensive wind-tunnel tests provided one

of the most comprehensive databases covering these Mach numbers. As such, the experimental data is a good

opportunity for the assessment of Euler and full Navier-Stokes solvers. On the other hand, the large base area andblunt fin trailing edges of the HL-20 present a special computational challenge for the Euler solver, especially insubsonic and transonic flows.

In reality, one would expect the HL-20 subsonic base flow to be unsteady, possibly periodical (shedding a Von-Karman like vortex street). Viscosity would tend to dampen the unsteady effects to some extent. This strong base

flow can affect the pressure field upstream (and as a result it affects the aerodynamic coefficients). The wind-tunneltest reports do not include any indication of the extent of unsteadiness (only average processed values are provided).

The wind tunnel data do provide average base pressure coefficient measurements that can be used to estimate thebase drag, but this measurement is performed at a single location (usually in a cavity where the support system

connects to the base). In subsonic and transonic flows with a large base area, the base surface pressure will in realityvary across the base, so the single point measurement needs to be considered with caution. In fully supersonic and

hypersonic flows the base pressure is almost constant across the base area and the effect of the base flow is not

propagated upstream.

The base flow and the extent of its impact upstream have an impact on the convergence behavior of inviscidsolvers such as Cart3D. Specific measures (tuning) may be required in order to get good results. Navier-Stokes

solvers should be able to simulate the base flow better (depending on the turbulence model and the extent ofnumerical damping).

The other challenge in the HL-20 case is in high hypersonic Mach numbers, where real-gas effects can takeplace. Cart3D does not simulate real gas effects, but it does accept variation of the specific heat ratio ().

B. The Solver and the Analysis FrameworkCart3D is a high-fidelity solver for the Euler inviscid equations of flow, being developed at NASA Ames

Research Center since the mid 90s (Refs. 7 to 9 for example). The solver is used mainly for conceptual andpreliminary aerodynamic design. It allows performing automated CFD analysis on complex geometries and supports

steady and, in its latest version (1.50), time-dependent simulations. The latest packages (current study uses version1.4.9) feature fully-integrated Adjoint-driven mesh adaptation

1-6 and also include utilities for geometry import,

surface modeling and intersection, mesh generation, and post-processing of results. Parallel computing, either shared

memory (OpenMP) or distributed memory (MPI) can be used.Cart3D input consists of a geometry model in the form of surface triangulations. The input may be generated

from within CAD packages, from legacy surface triangulations or from structured surface grids. Cart3D uses

adaptively refined Cartesian grids to discretize the space around the geometry. It carves the geometry out of theset of "cut-cells" (volume grid cells that intersect the surface triangulation). The multigrid meshes are automatically

refined on a localized basis in multiple adaptation cycles. The Adjoint solution identifies the grid cells where thecomputational error is highest and targets those for further refinement, aiming to reduce the error in aerodynamic

outputs.GoCart 2.0 is a commercial user analysis framework that runs Cart3D. The package provides graphical user

interface support and additional automation that greatly eases problem setup, convergence monitoring and post-processing (including digital visualization of the flow field and surface contours for selected flow parameters).

C. Methodology

The amount of HL-20 wind tunnel tests data accumulated in several years of research exceeds by far the scope ofthis report and the resources available for this study. The assessment is therefore based mostly on a Mach sweep (todemonstrate how well Cart3D / GoCart 2.0 handle the different aspects of the Mach range), and some polar samples

at selected Mach numbers. Important aspects of this case, such as the base flow and specific heat ratio impact arecovered as well. Solution convergence behavior and recommended tuning are discussed in detail.
http://people.nas.nasa.gov/~aftosmis/cart3d/http://people.nas.nasa.gov/~aftosmis/cart3d/


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D. Convergence and Numerical ConsiderationsThis section presents typical cases from each flow regime and discusses some of the input parameters used to

achieve the results shown. These parameters may not be the only way or combination to achieve good results for aparticular case. Different geometrical configurations may behave differently than the HL-20 configuration.

1. Subsonic and Transonic Flow Range

Convergence of the HL-20 case in subsonic Mach numbers (0.3 to 0.6) and transonic Mach numbers (0.8 to1.6) required over 8.5 million cells (10 or 11 adaptation cycles). The code had to use multiple built-in correctiveactions to overcome oscillatory behavior and convergence issues caused by the base flow. A better convergence

pattern was achieved with 5 multigrid levels (instead of 3) and 4 buffer cell layers (instead of 3) in the Adjointsettings, with CFL=1.0 (instead of 1.1). Figure 2 shows a typical subsonic convergence pattern at M=0.3 and

incidence of =8. The oscillating behavior and convergence difficulty at M=0.3 is demonstrated in Fig. 3a for a

run using default settings, and in Fig. 3b for a run that uses 5 multigrid levels and 4 buffer cell layers with

CFL=1.0. Figure 4 shows a typical transonic convergence pattern at M=0.9 and incidence of =8.

Figure 2. Typical convergence pattern of a subsonic HL-20 calculation at M=0.3 and =8.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.001 0.01 0.1 1 10

Number of Cells (Millions)

CL

CD

Half Configuration

a)Oscillatory behavior with default settings: 3 multigrid levels, 3 buffer cell layers and CFL=1.1.

b)Improved behavior with modified settings: 5 multigrid levels, 4 buffer cell layers and CFL=1.0.

Figure 3. Solution behavior of forces and moments at M=0.3, =8with different settings.


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2. Supersonic Flow Range

Convergence of the HL-20 case in supersonic Mach numbers (2.0 to 4.5) required at least 9 adaptation cycles

(3 to 5 million cells). The base flow did not cause significant convergence issues in supersonic flow and the basepressure coefficient is almost constant across the base area. A better convergence pattern was achieved with 5multigrid levels in the Adjoint settings. Figure 5 shows a typical supersonic convergence pattern at Mach=2.0

and incidence of =8. It was observed that the M=1.6 case converged better when using transonic regime input

settings.

3. Hypersonic Flow Range

Convergence of the case in hypersonic Mach numbers turned out to be fast, with no sensitivity to the base

flow. The incidence range (zero to 42 degrees at M=10) did not cause significant convergence issues (meaningthat the codes built-in mechanisms were able to deal with each hypersonic run without the need to tweak the

input controls). Figure 6 shows a typical hypersonic convergence pattern at M=10 and =8. Note that for all

practical purposes the aerodynamic coefficients (CL and CD) are converged already at a much lower density

grid, however the flow and surface details (such as CP distribution) are then too crude. Turning on directionalbuffering of limiters in the hypersonic calculations helped to reduce or eliminate a known numerical

phenomenon called staircasing (detailed analysis can be found in Ref. 27). The effect is to selectively widenthe stencil of the limiters near strong features (not just shocks) and smear the limiter values to prevent strong

gradients getting confined within the cells. Figure 7a shows an example of staircasing, while the effect ofusing directional buffer limiters is shown in Fig. 7b.

Figure 4. Typical convergence pattern of a transonic HL-20 calculation at M=0.9 and =8.

0

0.05

0.1

0.15

0.2

0.25

0.001 0.01 0.1 1 10


CL

CD

Half Configuration

Figure 5. Typical convergence pattern of a supersonic HL-20 calculation at M=2.0 and =8.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.001 0.01 0.1 1 10 100


CL

CD

Half Configuration


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E. Mach Sweep Results

A Mach sweep was calculated for an incidence of 8 . The choice of =8had to do with having an incidence

applicable to all Mach numbers in the experimental database. The experiments covered a Mach number range from

0.05 to 20, while the assessment covers a Mach number range from 0.3 to 20. Note that the wind-tunnel tests hadsome limitations on the angle of attack range, depending on the wind-tunnel test section, the support system, the

model size and practical aerodynamic considerations (e.g. stall onset). The experimental data sources used in Figs. 8

to 13 are from six different wind tunnels.

11-18

1. Longitudinal Aerodynamic Coefficients

Figure 8 shows the lift coefficient for a Mach sweep from M=0.3 to M=10 at =8. Both calculated and

experimental data points in this figure use a specific heat ratio of =1.4 (Table 2). The overall match is good,with some discrepancies at subsonic Mach numbers (M0.6) and a slight under-prediction at M=10.

Figure 6. Typical convergence pattern of a hypersonic HL-20 calculation at M=10 and =8.

0

0.01

0.02

0.03

0.04

0.05

0.001 0.01 0.1 1 10Number of Cells (Millions)

CL

CD

Half Configuration

a)Staircasing b) With directional buffer limiters turned on

Figure 7. "Staircasing" example at M=10 & =40 and the effect of turning on directional buffer limiters.

Figure 8. Lift coefficient Mach sweep at =8.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.0 2.0 4.0 6.0 8.0 10.0

Langley 30x60ft

tunnel

Langley 7x10ft

tunnel

Calspan 8ft tunnel

Langley UnitaryPlan tunnel

Langley 20 inch

M=6 tunnel

Langley 31 inch

M=10 tunnel

GoCart 2.0

CL

Mach


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Comparison for the drag coefficient CD should be made with caution because the Euler solver is inviscid, sothe calculated drag coefficient does not include the viscous drag contribution. One would therefore expect the

calculated drag coefficient to be somewhat lower than the corresponding experimental result for the total drag.Complicating the analysis is the fact that each wind tunnel used a different range of Reynolds numbers (creating

some inconsistency in the friction drag contribution when trying to plot all data in a single Mach sweep). This isdemonstrated in Fig. 9, where the viscous drag at zero lift is estimated with a separate tool for each Mach

number, using the actual Reynolds number from the experiment. The tool is based on the well-known flat plateapproximation with form-related and other empirical or semi-empirical corrections. It is not able to estimate the

effects of the angle of attack (pressure field change) on the local skin friction, so the correction for =8 uses thesame value calculated for zero lift. It is evident that the Reynolds number variation in the various experimental

facilities introduces a large variability in the viscous drag (roughly up to 5% of the total drag).

Figure 10 shows the drag coefficient Mach sweep at 8 incidence. The figure shows both the GoCart 2.0

original inviscid results, and GoCart 2.0 results corrected with the viscous drag estimate from Fig. 9. The

corrected results match the experimental data quite well (with some over-prediction of the total drag coefficientat lower supersonic Mach numbers).

Figure 9. Estimated viscous drag contribution at zero-lift, based on the Mach and Reynolds numbers

of each experiment.

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5 6 7 8 9 10

Langley 7x10ft tunnel

ReL=3.4 million

Langley 7x10ft tunnel

ReL=22.3 million

Calspan 8ft tunnel ReL=6.0

million

Langley Unitary Plan tunnel

ReL=3.4 millionLangley 20 inch M=6 tunnel

ReL=1.01 million

Langley 20 inch M=6 tunnel

ReL=3.78 million

Langley 31 inch M=10

tunnel ReL=1.01 million

CD0Viscous

Mach

Figure 10. Drag coefficient Mach sweep at =8.

0

0.05

0.1

0.15

0.2

0.25

0.0 2.0 4.0 6.0 8.0 10.0

Langley 30x60ft

tunnel

Langley 7x10ft

tunnel

Calspan 8ft tunnel

Langley Unitary

Plan tunnel

Langley 20 inch

M=6 tunnel

Langley 31 inchM=10 tunnel

GoCart 2.0

GoCart2.0+Viscou

Correction

CD

Mach


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Another factor that affects the calculated drag results is the base drag. The inviscid Euler code cannot providethe exact base flow features which in reality are complex (showing unsteadiness, especially in transonic and

subsonic Mach numbers, and also dominated by viscous effects). Figure 11 shows attempts to estimate the basedrag coefficient. For GoCart 2.0 the estimate is done by roughly integrating the base pressure coefficient over the

base areas, while for the experimental data the estimate is done by using the single-point of measured pressurecoefficient. No base corrections were made to the experimental drag data. The supersonic and hypersonic base

pressure is almost constant across the base area, but this is not the case in subsonic and transonic flows.Therefore the base drag estimates are probably less accurate at subsonic and transonic Mach numbers. The

experimental data did not include base pressure measurement for the hypersonic Mach numbers.

Based on Fig. 11, GoCart 2.0 drag coefficients in Fig. 10 can be corrected for the estimated difference in base

drag, at least in the supersonic zone where fidelity is better, as shown in Fig. 12. Results are then compared tothe wind-tunnel data (ReL=3.4 million). The largest discrepancy of GoCart 2.0 results with viscous drag

correction from the experimental data is at M=1.6 (~9% over-prediction). With corrected base-drag thediscrepancy is reduced to ~5%, gradually diminishing to ~0% as the Mach number is increased to 4.5. Both

viscous and base drag corrections, as well as the experiment base drag, are only estimates.

Figure 11. Estimated GoCart2.0 and experimental base drag coefficient at =8, normalized to Sref.

0

0.05

0.1

0.15

0.2

0.25

0.0 1.0 2.0 3.0 4.0 5.0

Experiment

GoCart2.0

CDBase

Mach

Figure 12. The effect of base drag and viscous drag corrections on GoCart2.0 supersonic results, =8.

0.00

0.05

0.10

0.15

0.20

0.25

1 2 3 4 5

Langley Unitary Plan tunnel,

ReL=3.4 million

GoCart 2.0 inviscid

GoCart 2.0 with Viscous Drag

Correction

GoCart 2.0, Corrected for Bas

Drag Difference

GoCart2.0 with Base andViscousDrag Corrections

CD

Mach


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Figure 13 shows the pitching moment coefficient, Cm, for the same Mach sweep and conditions. The overallagreement between the calculated results and experimental data is good, with slight discrepancy at low Mach

numbers (M0.6) and around the transonic dip.

2. Lateral Aerodynamic Coefficients

The lateral coefficients Mach sweep was calculated at =0and =4. Experimental data sources are from the

same wind-tunnels detailed in Fig. 8.

Fig. 14 shows the variation of the side-force coefficient, CY, with Mach number. The overall agreement withthe experimental data is good, with more deviation in the transonic zone (0.9


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a practically zero yawing moment coefficient. One possibility that may explain the discrepancy at the lowerMach numbers could be the asymmetric base pressure (in the y direction) developing in yaw. Such asymmetry

can cause a yawing moment, especially with the HL-20 wide base. It is possible that the inviscid code does notpredict this base pressure asymmetry accurately enough.

Figure 16 shows the variation of the rolling moment coefficient Cl with Mach number. The overallagreement is good, with some deviations. The prediction of the trend is correct, showing a negative yawing

moment coefficient across the Mach range with a negative peak around M=1.2 that decreases gradually inabsolute value with increasing Mach number in the supersonic zone.

F. Typical Flow PatternsThe following are a few selected views of calculated flow patterns (Mach contours). Figures 17A-17C show

calculated Mach contours on the symmetry plane (side view) and the mid-body plane (top view, half configuration)

at M=0.9, 1.2 and 3.0 for 8incidence. The model surface mesh is turned on for better distinction between the model

surface and the surrounding flow. The center fin blunt trailing-edge wake adds to the base flow in the side views.

Note the side shocks and the large base flow area in the top views. Selected x-cuts are shown, one at M=1.2 (Fig.18), the other at M=3.0 (Fig. 19). Note the lateral shock in Fig. 18 and the complex pattern in Fig. 19.

Figure 15. Yawing moment coefficient Mach sweep at = 0 and =4.

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.0 1.0 2.0 3.0 4.0 5.0

Experiment

GoCart 2.0

Cn

Mach

Figure 16. Rolling moment coefficient Mach sweep at = 0 and =4.

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.0 1.0 2.0 3.0 4.0 5.0

Experiment

GoCart 2.0

Mach

Cl


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Figure 17. Mach contours of transonic to supersonic shock system evolvement (side and top views).


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Figure 18. Mach contours at M=1.2, =8, x/L=0.85 (half configuration).

Figure 19. Mach contours at M=3.0, =8, x/L=0.80 (half configuration).


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G.Hypersonic Behavior

1. Aerodynamic CoefficientsAs real gas effects cannot be simulated using Cart3D, the question is how far the solver can be pushed into

the hypersonic zone. Yet it is also good to remember that hypersonic wind-tunnel tests have their ownlimitations. The huge volume of flow usually dictates small test cross sections and as a result the model scale

needs to be small (0.02 in the HL-20 case). This in turn, results in small Reynolds numbers, much smaller than inthe full-scale aircraft. Real gas effects are also difficult to simulate in wind-tunnel tests (as part of the

phenomenon is related to interaction with the boundary layer, heat transfer and model-surface wall temperature).Figure 20 shows the normal force coefficient (CN) variation with angle of attack at M=10. Computational

results are compared to experimental data from NASA Langley's 31 inch M=10 wind tunnel tests13

. Theexperiments were performed using air (=1.4) at a Reynolds number of 1.01x10

6(see Table 2). The

computational results (using =1.4)match the experimental data very well across the whole incidence range (=0

to =40). The computational data also exhibits the same non-linear trend that shows in the test data. Shown in

this figure are also the computational results of a structured-grid, thin-layer Navier-Stokes code (LAURA -

"Langley Aerothermodynamic Upwind Relaxation Algorithm", developed at NASA Langley.28, 29

The LAURAcode is a point-implicit, finite-volume solver based on the upwind-biased flux-difference splitting of Roe

30. The

scheme utilizes Yee's symmetric total variation diminishing discretization to achieve second-order spatialaccuracy and incorporates Harten's entropy fix. LAURA is capable of modeling Euler and Navier-Stokes flow

for a host of different air chemistry assumptions: perfect gas, equilibrium, chemical non-equilibrium, and

thermochemical non-equilibrium. In addition, any gas or gas mixture can be addressed as long as there is anadequate model for the thermodynamic and transport properties of the gas in question. The LAURA codesupports a number of boundary conditions: In addition to the usual no-slip conditions at the wall, the code

supports the specification of non-catalytic, fully catalytic, and finite-rate catalytic boundary conditions. Also, thewall temperature may be specified as a constant value, fixed distribution, or values based on a radiation

equilibrium wall condition. According to Refs. 13 and 30 the code was run in inviscid (Euler) mode to get theM=10 results in Figs. 20 to 26. The agreement of the LAURA data with the experimental results for CN is very

good (but LAURA results cover a more limited incidence range, from 15to 35).

Figure 21 shows a similar comparison for the axial force coefficient, CA. The overall agreement is

reasonable, as Cart3D results do not account for the viscous drag contribution. If the viscous component is added

(same figure), then the calculated results under 15 incidence get closer but somewhat overshoot the

experimental data. The viscous correction is calculated for zero lift and does not account for angle of attack

influence (changes in the surface pressure distribution). Therefore there is no point using the viscous correctionat higher incidence. LAURA results in this case (in inviscid mode) are roughly 100 counts lower than the GoCart

Figure 20. HL-20 Normal force coefficient vs. angle of attack at M=10, =1.4.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-5 0 5 10 15 20 25 30 35 40 45

Experiment - Langley 31 inch

tunnel (ReL=1.01 million)

GoCart 2.0

LAURA solver (inviscid mode)

CN

Alpha, degrees


15/21


2.0 inviscid results within the incidence range it covers (15 to 35). At high incidence, both GoCart2.0 and

LAURA show an almost flat slope for CA, while the experiment shows a small negative slope.

Figure 22 shows a similar comparison for the pitching moment coefficient, Cm. The agreement between the

calculated results and the experimental data is good across the whole incidence range, including the non-lineartrend. The LAURA solver inviscid results for Cm are on par with Cart3D results, with slight differences in the

slope.

Figure 23 shows a comparison of the L/D ratio for the same case. Note that the calculated drag does notinclude the viscous contribution, so the calculated L/D should be higher than the corresponding experimental

one. The overall agreement is good, and indeed the calculated L/D is higher than the experimental L/D up to

~30incidence. Beyond that the calculated values seem identical to the experimental ones, meaning that if the

viscous contribution is added then the calculation slightly overshoots the experiment in the high incidence

region. The maximum L/D predicted by the calculation is ~1.45 at ~20 degrees incidence, matching closely theexperimental data. In this context, one of the main reasons for suggesting aerodynamic improvements to the

original HL-20 configuration was the poor L/D ratio. The LAURA solver results in inviscid mode are very closeto the Cart3D results (predicting a maximum L/D of ~1.5). The peak L/D ratio is sensitive to Reynolds number

Figure 21. HL-20 Axial force coefficient vs. angle of attack at M=10, =1.4.

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

-5 0 5 10 15 20 25 30 35 40 45



GoCart 2.0 (inviscid)


GoCart 2.0 with Zero-Lift

Viscous Drag Correction

CA

Alpha, degrees

Figure 22. HL-20 Pitching moment coefficient vs. angle of attack at M=10, =1.4.

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

-5 0 5 10 15 20 25 30 35 40 45



GoCart 2.0


Cm

Alpha, degrees


16/21


as shown in Fig. 24a, taken from Ref. 13. The figure shows that the higher the Reynolds number (within thelimited number tested), the higher the peak. The inviscid flow is supposed to be an asymptotic limit for this

trend. In the reported experimental results of Ref. 13, neither CN nor CL show much sensitivity to Reynoldsnumber and the scale of the CD graph precludes clear conclusions. However Fig. 24b, taken from Ref. 13, shows

that the higher the Reynolds number, the lower the axial force coefficient. It is reasonable to suspect that the lowReynolds number wind-tunnel experiments (1.01 million) do not best-simulate the actual flow conditions of a

full scale flight vehicle, showing higher axial force and a lower L/D peak than in the case of a full scale vehicle.

Figure 25 shows the pitching moment coefficient variation with angle of attack for Mach=20 with =1.67,

ReL=1.47 million (experiments performed in NASA Langley's 22 inch hypersonic Helium tunnel, Ref. 13). The

experimental data indicates almost identical CM magnitudes of the M=20 and M=10 cases up to about 15

incidence. Cart3D results for M=20 follow the experimental data well up to about 10incidence (then curving

down more strongly than the experimental data). It is not evident that the Euler solver reaches its limits at that

Figure 23. HL-20 L/D ratio (untrimmed) vs. angle of attack at M=10, =1.4.

-1

-0.5

0

0.5

1

1.5

2

-5 0 5 10 15 20 25 30 35 40 45

Experiment, Langley 31 inch


GoCart 2.0 (Inviscid)

LAURA solver (inviscid

mode)

Alpha, degrees

L/D

a) L/D ratio b) Axial force coefficientFigure 24. L/D peak and CA dependency on Reynolds number at M=10, =1.4 from Ref. 13.


17/21


point, because at low incidence the match is good. Another factor to consider is that at M=6, Ref. 13 shows thatat high incidence the HL-20 pitching moment coefficient decreases with increasing Reynolds number (Fig. 26).

The inviscid solution is expected to resemble a high Reynolds number flow. Indeed the inviscid-mode LAURAresults in Fig. 26 are closer to the highest Reynolds number experimental results (3.78 million).

2. Hypersonic Flow Patterns

Figures 27 to 30 show selected computational visualizations of hypersonic cases, for Mach numbers of 6 and10, and angles of attack of =8 and 40. The figures plot density contours, selected for showing high sensitivity

to flow features in the hypersonic flow regime.

Figure 25. Pitching moment coefficient vs. angle of attack for M=20, =1.67.

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.080.1

-5 0 5 10 15 20 25 30 35

Experiment -

ReL=1.47 million

GoCart2.0 - Inviscid

Cm

Alpha (degrees)

Figure 26. Pitching moment coefficient vs. angle of attack for different Reynolds numbers at M=6,

air, =1.4, from Ref. 13.


18/21


a) M=6.0 b) M=10.0Figure 27. Hypersonic density contours at =8 (symmetry plane side view).

a) M=6.0 b) M=10.0

Figure 28. Hypersonic density contours at =40 (symmetry plane side view).

a) x/L=0.34 b) x/L=0.85

Figure 29. Hypersonic density contours at M=6 and =8 (half configuration).


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3. The Effect of Modifying the Specific Heat Ratio in Hypersonic Computations

As explained before, Cart3D / Adjoint does not account for real-gas effects or heat-transfer. Within itsunderlying assumptions it does allow however the modification of the specific heat ratio, . The following

discussion examines the effect of modifying on GoCart 2.0 results in order to get some idea of the sensitivity

of the solution to this parameter. The calculations were performed at M=20 and =28, with being the only

input parameter changed. The results are shown in Fig. 31, after well-converged 11 adaptation cycles (~5 million

cells). There is no comparison to experimental data because these also depend on Reynolds number.The normal force coefficient in Fig. 31a is not sensitive to the change in within the range used; however the

axial force coefficient clearlyslopes down as increases. With =1.22CA is ~3.3% higher than with =1.4,while with =1.67 it is ~6.2% lower than with =1.4. In Fig. 31b, the pitching moment coefficient Cm shows a

very small sensitivity to the change in .For completeness, the Log of the final number of cells, N, created through the mesh refinement process is

also shown in Fig. 31b for the different values. Note the Adjoint solution sensitivity to the change in . Thenumber of cells did not change much between =1.22 and =1.4, but it grew from 5,086,883 for =1.4 to

5,434,108 for =1.67.

a) x/L=0.28 b) x/L=0.85

Figure 30. Hypersonic density contours at M=6 and =40 (half configuration).

Normal force coefficient Axial force coefficient

Figure 31a. Sensitivity of Cart3D / Adjoint computation to the specific heat ratio at M=20 and =28.

0

0.1

0.2

0.3

1 1.2 1.4 1.6 1.8

CN

0

0.01

0.02

0.03

0.04

1 1.2 1.4 1.6 1.8

CA


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V. Conclusions

GoCart 2.0, that uses Cart3D 1.4.9 with Adjoint solution, can be used successfully to calculate the aerodynamics

of reentry, lifting-body vehicles across the full range of Mach numbers, from subsonic to hypersonic.The method is able to tackle the large base flow of the HL-20, giving reasonable estimate for the base drag

contribution for conceptual and preliminary design purposes. The HL-20 large base introduces computationalinstability and oscillatory behavior, especially in subsonic and transonic flows. Modification of some input

parameters is needed to get converged results. A simple viscous drag estimate may be added to the inviscid results toallow better assessment of the total drag coefficient and the overall L/D ratio.

The inviscid GoCart 2.0 results generally simulate high Reynolds number flow conditions. This makes GoCart agood tool for conceptual and preliminary design of a full-scale vehicle, but caution must be used when comparing

the computational results to wind-tunnel data taken using a small scale model at relatively low Reynolds numbers.GoCart 2.0 predicts very well the hypersonic aerodynamic coefficients of the HL-20 for angles of attack up to 50

degrees. Discrepancies at high incidence are attributed to the relatively low Reynolds number used in the wind-tunnel experiments.

GoCart 2.0 hypersonic results for the normal force and pitching moment coefficients agree very well withcomputational LAURA results run in inviscid mode. LAURA predicted inviscid drag is somewhat lower than

GoCart 2.0 prediction, resulting in a slightly higher corresponding inviscid L/D ratio. There is some sensitivity ofthe computed axial force results to the specific heat ratio () within the hypersonic Mach range used (M20) andvalues between 1.22 and 1.67.

The use of tools such as GoCart 2.0 / Cart3D can significantly reduce the number and related cost of wind-tunnel

experiments needed for conceptual and preliminary design of reentry vehicles such as the HL-20. In the HL-20 case,10 different wind-tunnels were used for the investigation of the base HL-20 model. The results necessitated

subsequent modifications to the model (to increase L/D and improve stability and control characters), requiring asignificant number of additional wind tunnel tests.

AcknowledgmentsThe author wishes to acknowledge the great cooperation and help of Andrew S. Hahn (NASA Langley Research

Center) and Robert A. McDonald (California Polytechnic State University) for their help with creating the digitalmodel of the NASA HL-20. In addition, the author wishes to thank Stephen C. Smith, NASA Ames Research Center

retired, for reviewing this paper and making useful suggestions that enhanced its contents.

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Figure 31b. Sensitivity of Cart3D / Adjoint computation to the specific heat ratio at M=20 and =28.

-0.008

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-0.002

0

1 1.2 1.4 1.6 1.8

Cm

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assessment of an inviscid euler-adjoint solver for prediction of aerodynamic characteristics of the...

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