numerical simulation of aeroheating over blunt bodies with...

Numerical Simulation of Planetary Reentry Aeroheating over Blunt Bodies with Non-equilibrium Reacting flow and

Surface Reactions

Akshay Prakash* and Xiaolin Zhong†

University of California, Los Angeles

Thermal protection layer has been commonly used to protect the reentry vehicles

from the harsh conditions encountered at hypersonic velocities. Numerical simulations and experiments are used to predict the amount of this protective layer needed so that vehicles safely traverse the harsh zone. Prediction of ablation requires modeling of hypersonic flows coupled with reacting gas chemistry and the response of the solid protection layer to the extreme conditions. Current computational codes modeling chemistry with hypersonic flow are coupled with codes predicting the response of the protection layer. In addition there has been limited study on effects of chemical Nonequilibrium in flow the field and surface ablation on laminar-turbulent flow transition of hypersonic boundary layers. Such an integrated tool would facilitate the study of transition in chemically reacting ablative flow fields. Therefore it is our aim to develop an integrated high order code which solves the material response along with the flow with thermal and chemical non equilibrium with species ionization. In this paper we present results of shock capturing nonequilibrium solver with surface reactions for modeling ablation. The code has 11 species reaction model to account for carbon species.

I. Introduction

American Institute of Aeronautics and Astronautics

1

P rediction and study of thermal response of reentry vehicles in harsh ablative conditions encountered is very important from the point of view of safety of the vehicle and cost effectiveness of the mission. The right amount of thermal protection layer would avoid undesirably conservative designs thus allowing for more payload weights. Knowledge of the flow field, particularly the heat transfer rates to the surface of vehicle is

very crucial This depends on many factors which include thermal and chemical nonequilibrium, laminar-turbulent flow transition, radiation to name a few. Knowing the heat transfer rates is just one part of the complex problem. The other important component is to predict the amount of ablative protection needed. Prediction of the thermal response of the Thermal Protection Layer has been a subject of study since 1960s. Due to the complex nature of the physics involved the problem has not been generically solved. Earliest efforts include the CMA [30] code (Charring Material Ablation) developed by Aerotherm Corporation in the late 1960s combined with the BLIMP (Boundary Layer Integral Matrix Procedure). This approach is characterized by solving the governing equations in solid (the TPS) using codes like 1-D CMA and in the fluid region (the gaseous environment, Integral Boundary Layer approach) separately using an independent code and the coupling the two solvers loosely through boundary conditions. Kuntz et. al. [21] along similar lines developed an iterative algorithm involving SACCARA and COYOTE which results in better convergence. SACCARA is based on Steger Warming flux splitting and TVD flux function of Yee [44]. The solver is 2nd order accurate in space discretization. It includes two-temperature model of Park [32 and 33] with vibration relaxation and chemical non equilibrium with 5 species model. Murray and Russel

* Student, Mechanical and Aerospace Engineering Dept., UCLA, [email protected], student member. † Professor, Mechanical and Aerospace Engineering Dept, UCLA, [email protected], Associate Fellow AIAA.

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-1542

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

[31] used MASCC (Maneuvering Aerotherm Shape Change Code) with CMA. MASCC is based on a boundary layer scheme MEIT (Momentum/Energy Integral Technique) and is a completely general three dimensional flow field solver which uses semi-empirical procedures to determine the flow field. Milos and Chen [6, 7, 8, 9, 27, and 28 ] have been developing surface chemistry models and computer codes for both 2-D and 3-D ablation and thermal response simulations. Recently they developed a 3-D thermal response code 3dFIAT [9] for charring materials. Suzuki et. al. [39] have developed CFD methods for aeroheating problems of ablating heat shields. The CFD code is coupled with the 1-D Aerotherm CMA code for material thermal responses. Prediction of laminar-turbulent transition of hypersonic boundary layer is an important aspect of study of reentry vehicles since it drastically affects the heating rates and drag that a vehicle encounters. So far there has been limited study of transition in chemically reacting hypersonic flow fields. Menon et.al.[25] studied affects of nonequilibrium chemistry on flow transition for compressible supersonic over a flat plate. However they only considered inviscid flow. Johnson et.al. [17] studied flow transition in reacting flows with equilibrium chemistry model. Malik [23] studied effects of chemistry on boundary layer stability. Hornung et. al. [1, 12] did experiments on a 5° cone with varying enthalpy of the free stream and for different gases (CO2, air, Nitrogen). The enthalpy range for the experiment was such that the gasses dissociated in the boundary layer. One of the conclusions was that chemical reactions tend to stabilize the flow thus increasing the transition Reynolds number. A. Scope of Current Study

It is our aim to study transition on ablating surfaces with chemical and thermodynamic nonequilibrium.

Given the complexity of the problem, such a code would push to the limits of the computational algorithms and computer capabilities. However due to the advancement in recent years of CFD algorithms and computational power, we believe it is time to go beyond the current approach of loosely linking of two separate codes for aeroheating predictions. To develop a high order simulation tool it is important to adopt shock-fitting techniques which allow the use of high order difference method as opposed to shock capturing methodology which reduces to first order near the shock. For the present paper we aim to develop a high order computational tool that includes nonequilibrium chemistry, two temperature vibrational relaxation and surface chemistry. The results qualitatively agree to simulations by Keenan [18]. The results have also been compared with experimental results by Hornung [16], and simulation of Gnoffo [13]. We plan to develop a thermal response code and model surface recession of the body surface. The tool thus developed can used to simulate reentry flow with intrinsically coupled solvers for the flow and the thermal response of the heat shield to provide more accurate predictions. The tool would be very use full in study of transition in a hypersonic flow field with surface ablation. This tool could be a starting point for developing specialized codes for study of stability in reentry flows with blowing/suction, ablation, turbulence along with radiation. The code would be used to study surface roughness and mass injection induced transition in the ablative flow field. These are very complex phenomena and developing an intrinsically coupled solver involving the above mentioned processes is indeed a challenging task. Such a computational tool could provide benchmark solutions for developing more specialized code, or could be developed into a specialized code to study various complex physical phenomena during a hypersonic reentry. B. The Physical Process

Numerical prediction of ablation is challenging due to the complex multi-disciplinary physical and

chemical processes that occur. In general, when subject to a large heat flux or elevated temperatures, thermal protection materials are affected by a combination of the following processes: pyrolysis, ablation, mechanical failure. Pyrolysis or thermal decomposition is the chemical decomposition in the interior of a material that releases gaseous by-products without consuming atmospheric species. Ablation is a combination of vaporization, sublimation, and reaction (such as oxidation and nitridation) which convert liquid or solid surface species into gaseous species. The liquid species would be a result of the material melting. Mechanical failure is the loss of surface material which does not produce gaseous species such as melt flow of a surface oxide, spallation of a solid and erosion caused by shear forces of impact of particles of droplets. For the current study we assume that ‘ablation’ only comprises of gaseous mass ejected from the surface without any surface recession (if possible surface recession

would also be considered). Such a case would be valid for TPS materials like carbon phenolic and Kevlar epoxy composites which release pyrolysis gases and form carbonaceous char layer.

These processes are a result of the hypersonic flow field which surrounds the vehicle. At such speeds the air is heated to temperatures high enough that real gas effects such as chemical decomposition and possibly ionization of the air becomes a factor in the analysis. So in the boundary layer adjacent to the surface of the vehicle (not including ablation at this time) the non-equilibrium chemical reactions between constituent elements of the air mixture need to be modeled. This requires that when numerically modeling the non-equilibrium chemically reacting boundary layer flow problem, multi-species kinetics and transfer properties are included, increasing the complexity of the analysis considerably. Now including ablation, the problem becomes coupled. Not only are the chemical reactions between the different species in the pyrolysis gas mixtures important but also their reactions with the various species in the boundary layer flow must be considered.

II. Methodology

A. Governing Equations The governing equations are the Navier Stokes equations:

j vj

j j

F FU + + =wt x x

∂ ∂∂∂ ∂ ∂ (1.1)

1 1

1 i

i NS

NS 1

1 1 2j vj

2 2 3

3 3 v s

j j

v

j j

F = ; F =

T cx x

( ) TTx x

j

j ij

j NSj

j j

j j j

j j j

j jv vs

sv j

jji i vs s s s

s

uu vu vu

u u p

u u p

u u pk e D

E u

E p uu k k h v

ρρ ρρ ρρ τ

ρ δ τρ δ τρ δ

ρ

τ ρ

⎡ ⎤⎢ ⎥⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥+ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥+ ⎢ ⎥⎢ ⎥ ⎢ ⎥+⎢ ⎥ ∂ ∂⎢ ⎥+⎢ ⎥ ⎢ ⎥∂ ∂⎢ ⎥ ⎢⎢ ⎥+ ∂∂⎢⎣ ⎦ + + +⎢ ∂ ∂⎣ ⎦

∑

∑

1

0;

00

0

i

NS

T v s vs

ww

w

w

Q w e−

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥+⎢ ⎥

⎥ ⎢ ⎥⎣ ⎦⎥⎥

(1.2)

Flux is split into viscous and inviscid parts. The inviscid part is discretized by high order upwind schemes while the viscous part by high order centered schemes.

In equation (1.2), ijk

k

i

j

j

iij x

uxu

xu

δµµτ∂∂

−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂∂

=32

, where µ is the viscosity coefficient determined

by the Wilke’s mixing rule [42]:


3

1

, ,s s s ss

s s s

X c M cX M

Mµ

µφ s sM

−⎛ ⎞

= = = ⎜ ⎟⎝

∑ ∑⎠ (1.3)

2 114

1 8 1s srs r

r r s r

MMX

M Mµ

φµ

−⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥ ⎢ ⎥= + +⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠⎝ ⎠ ⎣ ⎦⎢ ⎥⎣ ⎦∑

(1.4) Species viscosity µs, is calculated using curve fit data [2, 14, 4]:

( )( ) ( )0.1exp ln ln ( / )s s s sA T B T C kg msµ ⎡ ⎤= + +⎣ ⎦

(1.5) Constants A, B and C are listed in appendix. The species usj velocity can be written as [2]:

sj sju v ui= +

(1.6) Note that ‘j’ denotes the coordinate variable, and ‘s’ denotes the specie, vsj is the diffusion velocity

calculated using the Ficks law:

ss sj

j

ss

cv D

x

c

ScD

ρ ρ

ρρµρ

∂=

∂

=

= (1.7)

Here Ds is the species diffusion coefficient calculated based on Schmidt number which is assumed to be constant equal to 0.5 for all species.

As mentioned in the equations above, the average velocity is then grouped with the inviscid terms and

solved using Flux splitting, while the diffusion velocity is grouped with the viscous terms. The source terms due to chemical reactions and vibrational relaxation are put separately in ‘w’. These equations are transformed into body fitted curvilinear coordinates:

(1.8)

ξ = ξ(x, y,z) x = x(ξ,η,ς,τ)η= η(x, y,z) y = y(ξ,η,ς,τ)ς = ς(x, y,z) z = z(ξ,η,ς,τ)

τ = t t = τ

⎫ ⎧⎪ ⎪⎪ ⎪⇔⎬ ⎨⎪ ⎪⎪ ⎪⎭ ⎩

The equation to be solved then is:

11 ' ' '' ' '

v v vE F GU E F G J+ + + + + + +U =J τ ξ η ς ξ η ς τ

⎛ ⎞∂ ⎜ ⎟∂ ∂ ∂∂ ∂ ∂ ∂ ⎝ ⎠∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

w (1.9)


4

A high-order explicit finite difference scheme [51] is used for spatial discretization of the governing equations, the inviscid flux terms are discretized by the upwind scheme, and the viscous flux terms are discretized

by the central scheme. For the inviscid flux vectors, the flux Jacobeans contain both positive and negative eigenvalues, a simple local Lax-Friedrichs scheme is used to split vectors into negative and positive wave fields. For example, the flux term F′ can be split into two terms of pure positive and negative eigenvalues as follows:

( ) (' ' '

' ' ' '1 12 2

F F F

)F F U F F Uλ λ

+ −

+ −

= +

= + = − (1.10) where λ is chosen to be larger than the local maximum of eigenvalues of F′:

( )2 '2

' x x x

c u cJu v w

u

ηλ ε

η η ηη

∇ ⎛ ⎞= + +⎜ ⎟⎝ ⎠+ +

=∇

(1.11)

The parameter ε is a small positive constant added to adjust the smoothness of the splitting. The fluxes F′+ and F′- contain only positive and negative eigenvalues respectively.

The first term on the right hand side of equation (1.10) is discretized by the upwind scheme and the second term by the downwind scheme. The fifth-order explicit scheme utilizes a 7-point stencil and has an adjustable parameter α as follows [51]:

3 65

63

3 2 1

1' ...6!

1 1 5 51 , 9 , 45 , 0 ,12 2 4 3

i i k i ki ik i

i i i i

uu a u hhb b x

b

α

α α α α α α α α

+ +=−

± ± ±

⎛ ⎞∂= − +⎜ ⎟⎜ ⎟∂⎝ ⎠

= ± + = − = ± + = − =

∑

∓ 60i (1.12)

The scheme is upwind where α < 0 and downwind when α > 0. It becomes a six-order central scheme when α = 0.

B. Shock Fitting The solution procedure is based on shock fitting by Zhong [51]. The domain between the shock and blunt

body is discretized and solved based on the Local Lax Friedrich flux splitting. The conditions behind the shock are calculated using the Rankine Hugoniot relations:

( ) ( ) 0s s s t

yx zs

tt

F F l U U l

l i jJ J J

lJ

ηη η

η

∞ ∞

k

− • + − =

⎛ ⎞⎛ ⎞ ⎛ ⎞= + +⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎛ ⎞= ⎜ ⎟⎝ ⎠

(1.13)

The shock may be moving and its velocity (and hence the grid velocity) is calculated by differentiating the above expression in time and using the following compatibility relationships:


5

( )

( ( ( )

31 21

1 1

/0

'' '

N

' 'N s N

U J FF Fl + + + w =

τ ξ η ζ

ηl A = u +c l

J

−

− −

∂⎡ ⎤∂∂ ∂⋅ −⎢ ⎥∂ ∂ ∂ ∂⎣ ⎦

∇⋅ (1.14)

Here left eigenvector is defined as: 1Nl −

( )

( )

( )

01 1

0

0

1 .2

1 .2

1 .2

1 12 21 12 21 12 21

21

2

N n

i n

NS n

x

y

z

γl = u u h cu

γ u u h cu

γ u u h cu

γcn u

γcn v

γcn w

γ

γ

−

−⎡ ⎤− −⎢ ⎥⎢ ⎥

−⎢ ⎥− −⎢ ⎥⎢ ⎥−⎢ ⎥− −⎢ ⎥⎢ ⎥−⎛ ⎞⎢ ⎥− −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥−⎛ ⎞⎢ ⎥− −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥

−⎛ ⎞⎢ ⎥− −⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥

−⎢ ⎥⎢ ⎥⎢ ⎥−⎢ ⎥−⎢ ⎥⎣ ⎦

(1.15)

In equation (1.15) the first NS columns (NS is the number of species) represent entries due to the reacting

species. The last column represents entry due to Vibration conservation equation. Note that in absence of chemical nonequilibrium the first NS columns would reduce to one column with , heat of formation set to zero. In absence of thermal nonequilibrium the last column would vanish. The equations are discretized (inviscid terms by 5

hth order

finite difference scheme and viscous terms by 6th order central difference schemes) and solved in time using Runge Kutta or Backward Euler methods.

C. Shock Capturing 11 species model and surface reactions were implemented in shock capturing coded developed by Yee and Sjogreen [40, 41, 45, 46, 47, 48, 49, 50]. We implemented nonequilibrium model in the Harten-Yee upwind TVD scheme. The scheme can be represented by the general formula:

( )1 1 11 1 1 12 2 2 2

1 1 12 2

1

12

n n n n n n

j j j j

j jj j

u h h u h h

h f f

λθ λ θ

φ

+ + +

+ − + −

++ +

⎛ ⎞ ⎛ ⎞+ − = − − −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎡ ⎤

= + +⎢ ⎥⎣ ⎦

(1.16)

The function φ of Harten’s original modified scheme was modified by Yee using minmod and other limiters. The present calculations use explicit scheme with the minmod limiter.


6

D. Chemical Reaction

Surface reactions introduce additional C species into the flow field. Hence we have considered 11 species

model [18] with the following reactions:

3 2

2

2

2

2

22

C M C C MCO M CO O M

N M N MO M O M

NO M N O MC M C C MCO M C O MCN M C N M

+ ⇔ + +

+ ⇔ + ++ ⇔ ++ ⇔ ++ ⇔ + ++ ⇔ + ++ ⇔ + ++ ⇔ + +

(1.17)

2

2

3 2

2 3

2

2 2

2

2

2

2

2 2

2

2 2

N O NO NNO O O NC C C CC CO C OCO O O CCN O NO C

CO O O COCO C C ON C CN NCN C C NCO N CN OCO N C NO

CO CO CO CCO CO C O

CO NO CO NN O NO NO

2

+ ⇔ ++ ⇔ ++ ⇔ +

+ ⇔ +

+ ⇔ +

+ ⇔ ++ ⇔ ++ ⇔ ++ ⇔ ++ ⇔ ++ ⇔ ++ ⇔ ++ ⇔ ++ ⇔ +

+ ⇔ ++ ⇔ +

(1.18)

ONOONMNO⇔+⇔+⇔+2 Apart from these are 6 surface reactions [18], the first three (equations 1.18) are sublimation reactions, last

three (equations 1.19) are oxidation reactions:

(1.19)

( ) 1

( ) 2

( ) 2

s

s

s

C C

C C

C C

⇒

⇒

⇒

( ) 2

( )

( ) ( ) 2

s

s

s

C O CO O

C O CO

C O O C O

+ ⇒ +

+ ⇒

s+ + ⇒ + (1.20)


7

The values of reaction constants are given reference [34, 20, 24, 18]. Note that the forward reaction rates

for equations involving dissociation of species would be at a temperature that is the geometric mean of vibrational and translational temperature. All other forward rates are evaluated at translational temperature. The backward reaction rates would depend on the translational-rotational temperature for all the reactions. The forward reaction rates are calculated using the following equation:

2 2, ,N O and NO

( )exp /frm fm b r bk C T Tη θ= −

(1.21) Subscript r denotes reaction number and subscript m denotes the collision partner for first 8 equations. is

geometric average of translation-rotation temperature and vibration temperature for reactions 3, 4 and 5, and equals to translation-rotation temperature for other reactions. The backward reaction rates are calculated based on equilibrium rate constants. For reactions 3, 4, 5, 9 and 10 the equilibrium rate is calculated using Park’s curve fits:

bT

( ) 21

0 2 3 4exp ln

10000 /

meqr r m m m m

A5K A A A z A z A

zz T

⎛ ⎞= + + + +⎜ ⎟⎝ ⎠

=

z

(1.22) Subscript r represents reaction number. For other reactions rates are calculated based on free Gibbs energy using the following relations:

( )

( )( )2 43

3 52 41 7

exp 0.001

1 ln2 6 12 20

neqr u

GK R TRT

a T a T aa T a TG a TRT T

−∆∆⎛ ⎞= − ×⎜ ⎟⎝ ⎠

∆= − − − − − + −6 a (1.23)

The source terms involving chemical reactions may become stiff, i.e. the rates for some reactions maybe

orders of magnitude higher than the others. To overcome this we use implicit scheme for reacting source. For case of a well stirred reactor, the trapezoidal method of integration can be written as:

( )1

nn nWI t U U t W

U+

⎛ ⎞∂⎡ ⎤− ∆ − = ∆ ×⎜ ⎟⎢ ⎥⎜ ⎟∂⎣ ⎦⎝ ⎠

n

(1.24)

Here WU

∂∂

is the Jacobean of the source term . The oxidation reaction rates are calculated using the

following relation:

w

( )( )

( )

,

3

1 4

2

3 2

2

1.43 10 0.01 exp 14501 2 10 exp 13000

0.63 exp 1160

ww r r

s

w

w

w

RTk

M

TT

T

απ

α

αα α

−

−

=

× + × −=

+ × ×

= × −

=

(1.25)


8

Here rα is the ratio of mass fraction of oxygen atoms contained in reaction products to mass fraction of oxygen atoms reaching the wall. Reactions involving nitrogen species and are considered slow and are ignored. Mass flux in sublimation reactions are calculated using the following relations:

2CO

( ),

,

2

101300exp

ss s v s s

w

sv s s

w

Mm p p

RT

Pp

T

απ

′ = −

⎛= ⎜

⎝ ⎠Q

⎞+ ⎟ (1.26)

Here rα is experimentally determined for each species.

E. Vibrational Energy The equation for vibration energy is solved in similar way to energy equation. The vibration energy is

defined as [20, 37, 3]:

/ 1vsi v

v vs

vsi s vsivs T

i

E Eg R

Eeθ

θ

=

=−

∑

∑ (1.27) However there is only one overall vibration energy equation. It is solved and the vibration temperature is

calculated using Newton’s method. Also note that unlike the energy term there is a source term which consists of vibration energy from translational energy and due to formation of diatomic species.

Also note that the total energy term includes vibration energy and chemical energy terms. The total energy

can be written as:

01

2s vs i i v s ss i

E C T u u Eρ ρ= + + +∑ ∑ ∑ hρ (1.28)

The exchange between vibration and translation energy can be calculated using [26, 35, 36, 37, and 38]:

( ) ( )v vT V s

s s LT

chem s vss

e T e TQ

Q w e

ρτ−

−=

=

∑

∑

v

(1.29)

Where s LTτ is the Landau Teller vibration relaxation given by [22, and 26]:

( )[ ])/(,1016.1

;,42.18015.0exp1

;/

3/42/13

4/13/1

rsrssrvssrsr

srsrsr

r srr

r rs

MMMMA

atminpTAp

XX

TL

TL

TL

+=×=

−−=

=

−

−−

−

− ∑∑

µθµ

µτ

ττ


9


10

III. Results

The code is in development phase. Here we present the validation cases run for the current code. We developed a five species code first with thermal and chemical non equilibrium with shock capturing and shock fitting [51] methodologies. We validated the reaction model with simulating Hornung’s experiments on nitrogen flow over cylinders, and Gnoffo’s [13] simulation of Hornung’s experiments. Then we present PANT cases run on a 2D geometry (cylinder). Here the shock standoff distance is not supposed to match the actual experimental value but we get the same profile for temperature and species mass fractions along the stagnation line. We are developing the 3D version of the code. A. Nitrogen Flow over Cylinders [16]: 1. Hornung, 1 inch diameter cylinder

This is one of the experimental cases of Hornung (1972) [16] where partially ionized nitrogen flows over

cylinders of various radiuses were studied for various free stream dissociations of Nitrogen. The free stream temperature for this case was 1833K, free stream density was 4.98 x 10-3 kg m-3 and free stream mass fractions of nitrogen molecule and atom were 0.927 and 0.073 respectively. For simulations we used isothermal wall at 1000K and non catalytic boundary conditions.

We simulated the flow over 1 inch diameter cylinder and compare the shock standoff distance as given in

the experimental photographs in Fig 1. The agreement between computational and experimental data is excellent. The shock standoff distance at stagnation region is matched exactly while there is little discrepancy near the edge of the computational domain. The figure also shows temperature contours. The temperature rises sharply behind the shock to about 12000K and then due to chemical and thermal relaxation, drops to about 8000 K for most of the flow field. The wall temperature is set to 1000K. In Fig 2 and 3 computed fringe patterns are compared to experimental fringe pattern. In figure 2 we plot computational fringe contours with experimental contours. We get the same qualitative pattern as the experiment. Note the dark and light patterns match roughly through most of the region except at the very edge where they are slightly off. In figure 3 we compare the fringe number along stagnation line with the experimental values. The agreement is very good. Near the shock the fringe number falls off a little rapidly than experiment which can be attributed to the dissipation in the numerical scheme. Near the surface the fringe number rises sharply due to the sharp rise in density which is due to the isothermal wall condition of 1000K. Figure 4 shows the variation of translation and vibration temperatures along the stagnation line. For this case the vibration energy attains equilibrium with translation-rotation energy very quickly and for most of the flow field in the stagnation region the two temperatures are equal. At the wall the vibration temperature is set equal to translation temperature value of 1000K. However away from the stagnation region the temperature are different as shown in figure 5. The maximum translation temperature reached in about 13000K while the maximum vibration temperature reached is about 11000K. Figure 6 shows the variation of mass fractions of nitrogen along the stagnation line. This case appropriately illustrates the difference between equilibrium and nonequilibrium simulations. Note that immediately behind the shock temperature is about 13000K but nitrogen is hardly dissociated. If equilibrium were assumed the nitrogen would be much more dissociated and the predicted temperatures would have been lower.

X

Y

0 0.05-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

T12497.411664.210831.19997.899164.748331.587498.426665.265832.14998.954165.793332.632499.471666.32833.158

Fig. 1: Shock standoff compared with experimental values of Hornung.

Fig. 2: Fringe pattern compared with experimental results


11

Distance from shock (inch)

Frin

geN

umbe

r

0 0.05 0.1

0

1

2

3

4

5

Current computationHornung Experiment

Fig. 3: Fringe along stagnation line compared with Hornung’s experimental values.

X (m)

Tem

pera

ture

-0.025 -0.02 -0.0151000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

TTv

Fig. 4: Temperature profile in stagnation region.


12

X (m)

Tem

pera

ture

-0.0125 -0.01 -0.0075 -0.0051000

2000

3000

4000

5000

6000

7000

8000

9000

TTv

Fig.5: Temperature profile near the edge of computational domain.

X (m)

Mas

sfra

ctio

n

-0.025 -0.02 -0.015 -0.01

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

N2N

Fig. 6: Mass fractions along stagnation line.


13


14

2. Hornung, 2 inch diameter cylinder

This is another one of the experimental cases of Hornung (1972) [16]. The free stream temperature for this case was also 1833K, free stream density was 4.98 x 10-3 kg m-3 and free stream mass fractions of nitrogen molecule and atom were 0.927 and 0.073 respectively. The diameter for this case however is 2 inches. This case was also computed by Gnoffo [13]. For simulations we used isothermal wall at 1000K and non catalytic boundary conditions.

Figure 7 shows the comparison of shock standoff distance with Gnoffo’s computations and Hornung’s

experimental value. We get excellent agreement. The shock shape also agrees well with the data. Figure 4 also shows temperature contours. Immediately behind the shock the temperature rises to about 11000K and then due to chemical and thermal relaxation reduces to about 7000K for most of the flow field. The wall temperature was set at a constant value of 1000K. Figure 8 shows vibration temperature contours. Figure 9 shows variation of temperature along stagnation line. Like in the previous case, vibration and translation-rotation mode of energies come in equilibrium quickly in the stagnation region so that for most of the flow field vibration and translation temperatures are equal. However near the edge of the computational domain the two temperatures remain different as is shown in figure 10. For this case the highest temperature is about 11000 K just behind the shock, however through most of the flow field temperature is about 8000 K.

Figure 11 shows the computed fringe patter compared with experimental fringe pattern of Hornung. The

pattern is qualitatively similar though there are slight discrepancies. Figure 12 shows the variation of mass fractions of nitrogen along stagnation line. Here again the nonequilibrium of chemical species is evident. At temperatures of about 10000K there should be sufficiently large dissociation of nitrogen if equilibrium composition is assumed, however that is not the case here. Figure 13 compares normalized shock standoff distance for Hornung’s 1inch and 2inch cases. For the 1 inch case the standoff distance is slightly larger than that predicted for the 2inch case. Since the distance is normalized by respective nose radii, actual distance for the two inch case would be larger than (about 2 times) that for 1 inch case. Also shown in the figure are velocity contours. In the stagnation region the velocity drops to very low values which increase as we go away towards the edge of the domain. Figure 14 compares the variation of fringe number along the stagnation line. The present calculations in red line match the experimental values of Hornung (black squares) except near the shock. This discrepancy can be attributed to the dissipation of the numerical scheme which smoothes the shock.

X

Y

-0.05 0 0.05 0.1

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

T11249.910566.69883.279199.948516.627833.297149.966466.635783.35099.974416.643733.313049.992366.661683.33

Fig. 7: Shock standoff distance compared with Gnoffo’s computational values (black squares) and

Hornung’s experiments (white squares).

X

Y

-0.05 0 0.05 0.1

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Tv9032.538497.037961.527426.026890.526355.025819.525284.024748.514213.013677.513142.012606.5120711535.5

Fig. 8: Vibration temperature contours.


15

X (m)

Tem

pera

ture

-0.04 -0.031000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

TTv

Fig. 9: Vibration temperature and Translation temperature along stagnation line.

X (m)

Tem

pera

ture

-0.02 -0.015 -0.011000

2000

3000

4000

5000

6000

7000

8000

TTv

Fig. 10: Vibration temperature and Translation temperature at the edge of computational domain.


16

Fig. 11: Computational Fringe patter (bottom) compared with Hornung’s experimental fringe

pattern (top).

X (m)

Mas

sfra

ctio

ns

-0.04 -0.03

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

N2N

Fig. 12: Computational Fringe patter (bottom) compared with Hornung’s experimental fringe

pattern (top).


17

X

Y

0 2 4

-2

-1

0

1

2 u5244.384894.754545.134195.53845.883496.253146.6327972447.382097.751748.131398.51048.88699.25349.625

Fig. 13: Shocks compared for the above two cases. The 1 inch case has slightly larger normalized

shock standoff distance (normalized by nose radius).

Distance from shock (inch)

Frin

genu

mbe

r

0 0.1 0.2

0

1

2

3

4

5

6

7

8

Fig. 14: Fringe numbers along stagnation line compared with Hornung’s experimental values of

Hornung.


18

B. Reentry flow with Surface reactions (PANT test case)


19

∞ = 5.486 / ,U km∞

PANT (Passive Nosetip Technology) tests were conducted on 0.635 cm nose radius graphite models [43, 18]. The tests consisted of tests done in Flight Dynamics Laboratory (AFFDL) 50 MW Rent arc Plasma generator and in AEDC Aero ballistic Range G. Of the various configurations used in tests we simulated the 11 species program for free stream conditions of 0.02 ,P atm s= 293T K∞ = . Since we do not have the thermal response code yet, we fixed the wall temperature to a constant value of 2000 K and tested our surface reaction model. The test was done on a 2D shock capturing code. We present the results here for the code. We are in the process of implementing the surface reactions in 3D shock fitting code.

In figure 15 we see that surface reactions add carbon species into the flow field. CO2, O2, CO and N2 are

the prominent species near the boundary. However CO and CO2 quickly drop off to trace quantities and mixture consists predominantly of N2, O2, NO, O and N. In figure 16 the variation of species along surface is shown. In the stagnation region the mass fractions of CO and CO2 are comparatively higher. As we progress along the surface the concentration of the concentration of carbon species falls and Nitrogen and Oxygen are the main components. Note that the y axis is plotted in log scale. Figure 17 shows the variation of temperatures along the stagnation line. The temperature profiles are similar to Keenan’s [18] calculations. The thermal relaxation is very fast and vibration temperatures come to equilibrium with translation-rotation temperature quickly. For most of the stagnation region both temperatures are same. The maximum translation-rotation temperature goes to about 11000K while maximum vibration temperature is about 8000K. The wall temperature was set to 2000K. Figures 18 and 19 show temperature and vibration temperature contours in the flow field. Both temperatures are at about 7000K for most of the flow field. Hence considering ionization may not be crucial for this test case. In figure 18, translation temperature rises sharply to about 11000K behind the shock and fall off rapidly to about 7000K for most of the flow field.

X (m)

Mas

sfra

ctio

ns

-0.0075 -0.007 -0.0065 -0.00610-3

10-2

10-1

100

C3CO2N2O2NOC2COCNNOC

Fig. 15: Species mass fractions along stagnation line.

X (m)

Mas

sfra

ctio

ns

-0.006 -0.004 -0.002 010-11

10-9

10-7

10-5

10-3

10-1

C3CO2N2O2NOC2COCNNOC

Fig. 16: Species mass fractions along surface.

X (m)

Tem

pera

ture

-0.009 -0.008 -0.007

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

TTv

Fig. 17: Stagnation line temperature variation.


20

X

Y

0 0.01 0.02 0.03

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

T10372.29700.289028.328356.357684.397012.436340.475668.514996.554324.593652.622980.662308.71636.74964.779

Fig. 18: Temperature contours: Max temperature reaches to about 10000K near the shock.

X

Y

0 0.01 0.02 0.03

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Tv7645.427155.266665.16174.935684.775194.614704.454214.293724.133233.972743.812253.641763.481273.32783.161

Fig. 19: Vibrational Temperature contours.


21


22

IV. Conclusion

We aim to develop a high order 3D Navier Stokes Solver intrinsically coupled with a 3D thermal response code to study transition in ablative flow fields. As a next step we would develop our own version of thermal response code which can then be intrinsically coupled with the Navier Stokes solver. We aim to include surface recession and radiation model into the final version of the coupled code. Other models like turbulence could be added as needed. We aim to study the stability of the flow during reentry as it is effected by various processes like pyrolysis gas injection, mass spallation, if possible surface roughness to name among a few. Any simulation for actual size vehicle would require the code to run on multiple processors. Hence the code will have to be restructured to run parallel on multiple processors.

Acknowledgement: The research was supported partially by AFOSR USAF, under AFOSR Grant # FA9550-07-1-0414 monitored by Dr. John Schmisseur and partially by DOE office of Science as part of a SciDAC (Scientific Discovery thorough Advanced Computing) project with “Science Application” in Turbulence. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements either expressed or implied of AFOSR or US Govt.


23

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numerical simulation of aeroheating over blunt bodies with...

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