GallagherFinalReport

Numerical Simulation of Arc-Jet Experiments using the Data-

Parallel Line Relaxation Method

Jason Gallagher, Graduate Student, Stanford University

Sponsor: David M. Driver, Senior Research Scientist, Experimental Aerophysics Branch

NASA Organization: APS

June 14, 2004 – September 24, 2004

Abstract

A computational fluid dynamics analysis

has been performed on various simple

geometries using the Data-Parallel Line

Relaxation (DPLR) method. Results

were obtained for arc-jet simulations of a

twenty-degree half wedge, a flat-faced

puck, a spherical calorimeter, and also a

perfect air calculation for the nose of the

shuttle in a simplified re-entry

environment. The results obtained will

be compared to actual test and/or flight

data to validate future CFD models and

their accuracy.

Introduction

The focus of this study was to obtain

numerical solutions of arc-jet

experiments and compare them with

actual test data. The arc-jet is designed

to provide ground-based hyperthermal

and hypervelocity environments in

support of NASA activities in thermal

protection materials, aero-

thermodynamics, vehicle structures, and

hypersonic propulsion and flight.

Current arc-jet experiments are being

implemented in order to test proposed

repair materials for the leading edge of

the space shuttle wing in a re-entry

environment. The types of models being

tested include a twenty-degree half

wedge and a flat-faced puck.

Developing CFD models that can

reproduce the arc-jet environment is

important for future tests. If CFD models

can be produced yielding trustworthy

results, many more test configurations

can be processed numerically without

having to suffer the cost associated with

arc-jet facility usage. To better

understand the process of developing

reliable CFD models, time was spent

modeling various geometries that have

been tested in the arc-jet in recent

months.

Three main geometries were analyzed

throughout this study. The first was a

twenty-degree half wedge. The second

model was a flat-faced puck. Last, was a

spherical geometry. All of the studies

were performed in two-dimensions using

DPLR-2D.

Methods and Materials

The Data-Parallel Line Relaxation

(DPLR) method in two-dimensions was

used to perform the CFD calculations.

The DPLR method was chosen because

it has shown particularly good

convergence properties and reaches a

steady-state solution in less time than

other methods1. Also, because of its high

parallel efficiency, it is very capable of

modeling viscous flows in a reasonable

time1, especially for smaller scale

applications such as the geometries

being studied.

In addition to the numerical solution

performed by DPLR-2D, grids were

generated using Gridgen software.

Learning the basics of Gridgen was

relatively simple. It utilizes a “bottom-

up” technique in which curves are

created first, followed by surfaces, then

volumes. Also, Gridgen allows for the

grids to be exported in the native format

of many CFD applications, which made

it easy to use with DPLR-2D.

In addition to Gridgen, another meshing

software known as the Self Adaptive

Grid codE (SAGE), was used in order to

adapt the grids to the flow field solutions

calculated using DPLR. Essentially, this

software was used mainly to adapt the

grid to the outer contour of the shock by

moving the outer boundary. This

allowed for much more efficient use of

the grid domain. Also, this software was

used to change wall spacing, which

helps resolve flow quantities near the

wall.

Twenty-Degree Half-Angle Wedge

The first grid generated in Gridgen was

for the twenty-degree half-angle wedge.

Creating the surface of the wedge and

extruding hyperbolically from the wedge

surface to create the grid produced this

computational domain (Figure 1). After

adapting the grid to the first flow

solution using SAGE, one can see the

difference in the outer boundaries of the

grid (Figure 2).

Figure 1: Original Wedge Grid (123 x

51)

Figure 2: Final SAGEd Wedge Grid

This verification case involved the

computation of a hypersonic flow field

past a wedge with a half-angle of

twenty-degrees and at a ten-degree angle

of attack. The flow field past the shock

is uniform. The leading edge of the

wedge is located at coordinates

(x=0,y=0) and is assumed to extend

indefinitely in the z-coordinate. The

half-angle of the wedge is 20 degrees

measured from the x-axis, but the flow

sees a thirty-degree inclination due to the

additional ten-degree angle-of-attack.

The computational domain was not

chosen along an axis of symmetry due to

the ten-degree angle of attack. The

inflow boundary is located at a non-

arbitrary length to the left of the wedge.

The outflow boundary is located at the

end of the wedge. The far field boundary

was placed at a distance large enough to

place it well above the oblique shock.

The surface of the wedge contained two

different materials, represented by two

different blocks in the grid. The first

block began on the underneath portion of

the wedge, traveled around the nose of

the wedge, and ended a third of the way

up the incline. This is actually a copper

surface, which was modeled as fully

catalytic with a constant wall

temperature of 300K. The latter half of

the wedge was modeled as RCG using

the catalysis model from Stewart. The

incoming flow was simulated using a 6

species (N2 O2 NO N O Ar) air model.

The freestream conditions for this

condition were:

Mach 4.85

Pressure (Pa) 987

Temperature (K) 2078

Angle-of-Attack (deg) 10

Angle-of-Sideslip (deg) 0

Table 1: Arc-Jet Freestream

Conditions

Flat Faced Puck

The analysis of the puck involves the

computation of a hypersonic flow field

with a freestream Mach number of 4.85

and the same conditions as shown in

Table 1.

The geometry of the puck is simple. The

origin is located at the center of the

puck. The flat surface extends two

inches in the vertical direction before the

corner is reached. The puck then extends

horizontally. The puck is assumed to

extend infinitely in the z-direction. The

computational domain was chosen along

an axis of symmetry since a zero degree

angle of attack was approaching the

puck. The inflow and outflow

boundaries were originally placed well

beyond the location where the shock will

form. One particular area of interest is

the puck corner. Because of the sharp

radius of curvature it is important to

refine the mesh here. For this reason,

more grid points were clustered in this

region. For the puck analysis, two main

corner radii were analyzed, 0.25 and

0.0625 inches.

Due to the fact that the CFD solution is

very sensitive to the geometry of the grid

being used, two main grids were

analyzed. The first was a grid generated

by Danesh Prabhu. This grid was

generated using Gridpro software and

can be seen in Figure 3. The second grid

was generated using Gridgen software

(Figure 4) and subsequently SAGEd to

fit the flow field features (Figure 5).

Figure 3: Puck grid using Gridpro (65

x 97)

Figure 4: Original Puck grid using

Gridgen (65 x 84)

Figure 5: Final SAGEd Puck Grid

from Gridgen

The puck itself was modeled as a surface

with a catalytic, radiative equilibrium

wall using the RCG model from Stewart.

Spherical Calorimeter

The analysis of the spherical calorimeter

was the last simulation ran using arc-jet

conditions (Table 1). The goal of the

calorimeter validation is to measure the

predicted quantity of heat exchanged to

the surface of the calorimeter and

compare it to actual heat exchange data

obtained from placing a calorimeter into

the flow of the arc-jet. This involves a

very simple model.

Figure 6: Original Sphere Grid (60 x

60)

In two-dimensions, the sphere is

modeled as a half circle. The

computational domain was made by

hyperbolically extruding from the

surface of the sphere (Figure 6). After

adapting the grid to the flow field using

SAGE, the grid was much more compact

and aligned with the flow field

characteristics (Figure 7).

Figure 7: Final SAGEd Sphere Grid

Spherical Shuttle Nose

The goal of simulating the shuttle nose

in a flight environment was to compare

the results to actual flight data. By doing

this, confidence could be built by

producing results similar to what is

recorded in flight. The shuttle nose was

chosen because of its simple geometry

and because there is sufficient flight data

that is obtained and recorded for each

flight.

The geometry of the shuttle nose is the

same as the calorimeter (Figure 6),

except that the radius is 24 inches

instead of 1.5. However, the freestream

flight conditions and surface properties

are different. The surface of the shuttle

nose was modeled as a catalytic,

radiative equilibrium wall using the

RCG model from Stewart. The

freestream conditions were modeled

using a single-species perfect air model

and were as follows: Mach 23

Pressure (Pa) 9

Temperature (K) 200

Angle-of-Attack (deg) 0

Angle-of-Sideslip (deg) 0

Table 2: Shuttle Nose Freestream

Conditions

Results

Twenty-Degree Half-Angle Wedge

Figure 7 shows the main features of the

flow field for the half-angle wedge. As

the flow meets the leading edge of the

wedge, an oblique shock is formed as the

flow turns to become tangent with the

wedge surface. The flow field past the

shock is uniform. While the results

obtained for the wedge were not

explicitly compared to experimental

data, they were in agreement with

similar wedge flow solutions obtained

by CFD specialists. The following plots

represent the final solutions obtained for

the twenty-degree half-wedge at a ten-

degree angle of attack.

Figure 8: Mach Contours for Wedge

The surface temperature distribution

across the wedge is shown in Figure 8.

The surface temperature distribution

indicates the “cold wall” boundary

condition for the first block with a

dashed line. At the material transition,

the temperature rises quickly to reach a

maximum of approximately 2050 K

(3230 F) and then retains a temperature

of roughly 1960 K (3070 F) to the end of

the wedge.

Figure 9: Surface Temperature

Distribution

Figure 10: Surface Heat transfer

Distribution for Wedge

Figure 11: Surface Pressure

Distribution for Wedge

The surface pressure and heat transfer

plots both show relatively constant

trends across the RCG material surface.

The heat transfer remains approximately

88 W/cm2 while the pressure remains

approximately 13000 Pa.

Flat-Faced Puck

As the flow approaches the surface of

the puck, a bow shock is formed in front

of the puck. Along the centerline, the

flow travels through a normal shock and

subsequently enters a large subsonic

flow region. As the flow travels around

the edge of the puck, the shock becomes

more oblique and the downstream Mach

number increases behind the shock. The

flow field past the shock is uniform.

Computationally, the puck was the

hardest solution to obtain. Due to

problems that have not currently been

resolved, the puck with a corner radius

of 0.0625 inches will not be presented.

Two solutions for the 0.25-inch corner

radius will be presented and compared

with one another. The first is the solution

obtained from the grid produced in

Gridpro (Figure 3), and the second will

be the results from the grid produced in

Gridgen (Figure 5). It is important to

note that the dimensions of the grid from

Gridpro are 65 x 97 and the grid from

Gridgen is 65 x 83. The initial wall

spacing chosen for each grid was 1e-4

before applying SAGE to the grid.

Figure 12: Mach Contours from

Gridpro Grid

Figure 13: Mach Contours from

Gridgen Grid

The Mach contours from the Gridpro

grid extend further towards the end of

the puck than the Gridgen grid. For

example, the Mach 2 contour extends to

0.02 meters in the x-direction in Figure

11 but not as far in Figure 12.


Distribution (Gridpro grid)


Distribution (Gridgen grid)

The surface temperature distributions

indicate different trends, particularly

along the centerline. However, the

centerline and peak values are within

reasonable error limits. For instance, the

centerline temperatures for the Gridpro

and Gridgen grids are 2540 K and 2620

K, respectively. This indicates an

approximate error of 3%. Similarly, the

maximum temperatures are within

approximately 3% error of one another.

Whether or not either one of them is an

acceptable solution is the more

important matter. This will be clearer

when the results are compared to

experimental data.

Figure 16: Surface Heat Transfer




An observation of the heat transfer

distributions for the two different grids

show dissimilarity in trend as well as in

quantity. One can see that the centerline

trend is much different for the Gridpro

grid. The noticeable difference leads to

the question of what in the grid causes

the solution to act accordingly, and how

one might fix it. It is likely that the

subsonic region just behind the shock is

responsible for a large amount of the

numerical differences. Ways in which

this may be resolved is by reclustering

the grid around the shock or increasing

the number of grid points in the i-

direction. The quantitative difference in

centerline and maximum heat transfer is

15% and 13%, respectively. This is

expected due to the fact that heat transfer

is proportional to the temperature to the

fourth power. In percentages, this would

equate to a factor of 4, which is

approximately what we see. This is a

significant amount of disagreement

between grid solutions and needs to be

explored further.





Both of the surface pressure distributions

are in close agreement with one another.

Their distributions follow similar trends

along the entire puck surface and

quantitatively are less then 3% in error

from one another.

Spherical Calorimeter

Using the grid presented in Figure 7 the

analysis of the calorimeter was

performed. The resulting flow field

Mach contours can be seen below:

Figure 20: Mach Contours for

Calorimeter

At this high Mach number the bow

shock wave is forced close to the front of

the body. The flow is subsonic behind

the part of the bow wave that is ahead of

the sphere and over its surface back to

about 45 degrees. The flow is

completely symmetric about the x –axis

of the sphere, which is expected. One

can see slight waves in the shock front

near the end of the sphere. This is due to

the fact that at this point the shock is in

between two adjacent grid cells. As it

moves from one cell to the other, a jump

is seen in the shock. This does not affect

the surface quantities on the sphere due

to the fact that the region of influence

downstream of that point is not a part of

the computed flow field.


Distribution for Calorimeter

The purpose of the calorimeter is simply

to measure the amount of heat

exchanged between the flow and the

surface of the calorimeter. This

distribution is smooth along the

centerline and symmetric as expected.

The maximum heat transfer to the

surface is 783 W/cm2. This data has yet

to be compared with actual calorimeter

data obtained during an arc-jet

experiment.

Spherical Shuttle Nose

Due to some unresolved errors, the

results for the spherical shuttle nose

model has only been ran once through

DPLR-2D. In particular, the model was

not able to run on the GINKGO

computer cluster but ran successfully on

the REDWOOD computer cluster.

However, running on REDWOOD had

to be done at the mercy of other

engineers, and thus, it was

unsuccessfully attempted to get a second

run on REDWOOD with a SAGEd grid.

The SAGEd grid can be found waiting to

be ran on the PINE workstation in the

directory /users/apsdplr/gallagher/NOTWORKING.

The Mach contours, as can be seen, are

somewhat bumpy due to the coarseness

of the initial grid.

Figure 22: Mach Contours for Shuttle

Nose


Distribution for the Shuttle Nose

The surface temperature along the

shuttle nose reaches a maximum

temperature of 1771 K (2728 F).

However, at this stage in the process, the

grid is too coarse to properly capture the

surface temperature distribution along

the centerline of the shuttle nose. The

first step in correcting this problem

would be to rerun the SAGEd grid

through DPLR-2D to see whether that

corrects the temperature distribution or

not.

Since the heat transfer is directly

proportional to the temperature raised to

the fourth power, one would expect to

see a similar distribution for the heat

transfer.


Distribution for Shuttle Nose

Last, the surface pressure distribution

was calculated for the shuttle nose.


Distribution for Shuttle Nose

Summary

The validations of the two-dimensional

CFD models have not yet been

completed. The results for the wedge

and calorimeter models seem to be

numerically valid, while the puck and

shuttle nose models are somewhat

questionable. Inconsistencies in

numerical solutions were most apparent

in the quarter-inch radius puck

geometries. Of the two grids that were

analyzed, the temperature and heat

transfer distributions varied the most.

The quantitative results for each of the

four models can be seen in Table 3: Twenty-Degree Half-Angle Wedge RCG

Maximum Surface Quantities

Temperature (K,F) 2050, 32230

Heat Transfer (W/cm^2) 88.2

Pressure (Pa) 13030

Puck from Gridpro Surface Quantities

Centerline Temperature (K,F) 2540

Maximum Temperature (K,F) 2600

Centerline Heat Transfer (W/cm^2) 206

Maximum Heat Transfer (W/cm^2) 230

Centerline Pressure (Pa) 33775

Puck from Gridgen Surface Quantities

Centerline Temperature (K,F) 2620, 4256

Maximum Temperature (K,F) 2683, 4370

Centerline Heat Transfer (W/cm^2) 238

Maximum Heat Transfer (W/cm^2) 261

Centerline Pressure (Pa) 32864

Spherical Calorimeter Maximum Surface Quantities

Temperature (K) 300

Heat Transfer (W/cm^2) 783

Pressure (Pa) 33300

Spherical Shuttle Nose Maximum Surface Quantities

Temperature (K, F) 1771, 2728

Heat Transfer (W/cm^2) 49.68

Pressure (Pa) 5890

Table 3: Results Summary

Throughout the course of this project,

many different grids were generated and

ran using DPLR-2D. Solutions were

often surprising and sometimes led to

questions about the robustness of the

DPLR method. It was soon discovered,

after many trial runs, that CFD codes, in

general, are only as good as the grids

that are being used to run them on. This

placed an extreme importance on mesh

quality throughout the course of these

simulations.

Mesh quality is where the CFD analyst

has the largest impact on solution. A

high quality mesh increases the accuracy

of the CFD solution and improves

convergence relative to a poor quality

mesh. Therefore, it's important for a

mesher to have tools for obtaining and

improving a mesh. This area in

particular likely requires a great deal of

intuition, which is developed over many

years of CFD analysis. Due to lack of

intuition and experience on the meshers

part, the grids developed in this project

may be one of the primary sources for

discrepancies in numerical solutions.

Thus, they should be one of the first

objects scrutinized in determining why a

solution does not meet the expected

values or trends.

In particular, there was a significant

amount of disagreement between grid

solutions for the puck geometry. If time

permitted, this would be explored

further. However, the results themselves

will be clearer when compared to

experimental data.

In the end, it was not trivial to develop

models with the given geometries and

replicate arc-jet experimental data. To

date, there is work left to be done on the

puck and shuttle nose models in order to

obtain valid solutions and further

validate the DPLR method for these

particular flow fields.

Acknowledgements

The author would like to thank David

Driver for the opportunity to work on

this project at NASA Ames. In addition,

to all the people who helped with

various technicalities: Jack Atchison,

George Raiche, Dean Kontinos, Mike

Wright, Ryan McDaniel, Jeff Brown,

Tahir Gokcen, and Danesh Prabhu.

References

1. Wright, M.J., Candler, G.V., and

Bose, D., “A Data-Parallel Line

Relaxation Method for the Navier-

Stokes Equations,” AIAA Journal,

AIAA Paper No. 97-2046, June 1997.

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