Proceedings of the 23rd National Heat and Mass Transfer Conference and

1st International ISHMT-ASTFE Heat and Mass Transfer Conference

IHMTC2015

17-20 December, 2015, Thiruvananthapuram, India

IHMTC 2015-595

NON-EQUILIBRIUM FLOW SIMULATION OF PLASMA WIND TUNNEL TEST OF HSP CREW MODULE

Ajith M Aravindakshan Pillai L Dileep KN Sreenivas N Engineer Engineer Engineer Engineer FMTD/PRG/VSSC APLD/PRG/VSSC FMTD/PRG/VSSC APLD/PRG/VSSC ajith_mohan@vssc.gov.in l_aravindakshan@vssc.gov.in

ABSTRACT

A key element in the design of re-entry vehicle is the

characterization of the high temperature

aerothermodynamic environment around the vehicle during

its atmospheric hypersonic flight. Since the air undergoes

partially or fully ionized condition around the re-entry

body due to high temperature environment created due to

the strong shock standing in front, the air can no longer be

considered as a single gas which obeys perfect gas

relations, but as a mixture of number of species. Since it is

clear that real gas effects will play an important role in

many hypersonic applications, the aerothermodynamic

analyses of heat shield and other external surfaces of re-

entry vehicles need to take account of real gas effects.

Indeed, real gas thermodynamics, transport properties and

finite rate chemistry have a considerable effect on shock

and mach waves positions and shapes, thus affecting the

vehicle aerodynamics and its re-entry trajectory. As a

consequence, flow physics greatly influences the vehicle

re-entry performances, as well as those of its heat shield.

In the current work a theoretical methodology has

been developed to model chemically non-equilibrium and

thermally equilibrium flows for two dimensional/axi-

symmetric geometries for such high temperature

environments. Many models based on single and two

temperatures (depending on the translational, rotational and

vibrational modes of molecular excitement) are available in

the literature. In the present formulation, Park-87 model (7

species 24 reactions single temperature) has been used.

With the numerical model developed, Simulation of PWT

test of scaled down model of HSP (Human Space flight

Project) crew module has attempted.

Keywords: PWT, Fully catalytic, re-entry, equilibrium,

non-equilibrium

NOMENCLATURE

t Time ,s

ρ Density, kg/m3

V Velocity, m/s

C Molar concentration

υ Stoichiometric coefficient

Y Specie mass fraction

J Diffusion flux

S Rate of creation of species

A Exponential factor

β Temperature exponent

E Activation energy, J/kg-mol

R Universal gas constant, J/kg-mol-K

k Rate constant

µ Viscosity, kg/ms

τ Stress tensor

I Unit tensor

p Pressure, N/m2

h Sensible enthalpy, kJ

Cp Specific heat J/kg K

T Temperature, K

M Molecular weight

k1 Boltzmann constant

λ Thermal conductivity, W/mK

Subscripts

i,j Species

r Reaction number

INTRODUCTION

The aerodynamic and aerothermodynamic analyses of

reentry vehicles, as well as their heat shield design

activities, need to take account of real gas effects. These

effects, in the past, were responsible for the inadequate

prediction of body flap efficiency of the Space Shuttle[1]

While this latter aspect seems to be well understood, it

is clear that real gas effects may play an important role in

many hypersonic applications. Indeed, real gas

thermodynamics, transport properties and finite rate

chemistry have a considerable effect on shock and Mach

wave positions and shapes, thus affecting the vehicle

aerodynamics and, then, its reentry trajectory.

As a consequence, flow physics greatly influences the

vehicle reentry performances, as well as those of its heat

shield [2].

So, the risk due to an inadequate knowledge of real gas

effects is that the integrity and performance of the vehicle

may be severely compromised because of wrong design

choices as, for example, additional weight for the Thermal

Protection System (TPS).

The thermal protection material (TPM) may promote

the chemical recombination, at wall, of atomic species

produced during the flow dissociation processes taking

place when the gas passes through the strong bow shock

wave ahead of the reentry vehicle [3]. These recombination

reactions, by means of the heat of formation of the

molecular species that leave the heat shield surface,

increase the overall heat flux up to about two times or more

the one of a non-catalytic wall [4]. These phenomena

depend on both reentry energy and vehicle configuration.

Indeed, if a blunt body vehicle design is adopted, attention

to the catalytic heat transfer has to be paid, especially when

the vehicle reenters at high Angle of Attack (AoA) (i.e.

strong detached bow shock in front of the vehicle).

When the vehicle traveling below Mach number of

about 6, the temperature inside the shock layer is about

2000K and deviations from perfect gas behavior are

negligible. So the perfect gas equation of state is sufficient

for flows when the peak temperature is below this limit.

But at higher temperatures, perfect gas equation of state is

no longer valid and one must consider the changes in the

thermodynamic and transport properties caused by

chemical reactions.

Chemically reacting flows can be broadly classified

into three categories. Frozen, Non-equilibrium(Finite rate

chemistry) and equilibrium depending on the chemical

reaction rate in relation to the flow time. Reaction times in

turn depend on the air density and temperature. At

relatively high densities, the inter molecular collision rate

is very high, and reactions proceed to equilibrium very

rapidly. Under such conditions, the flow is considered to be

in chemical equilibrium spatially. As the density decreases

at higher altitudes, the chemical relaxation time increases

and eventually becomes significant compared to the flow

convection time. This creates a flow field that is in a

chemically equilibrium, non-equilibrium or frozen state as

it traverses the body.

Another problem usually encountered in reacting

flows is the wall catalycity. Normally the wall is

comparatively cool, therefore the atomic species recombine

near the wall releasing large amounts of energy. In

addition, the wall itself can be catalyst ie. the wall itself

can promote recombination reactions , as in the case of an

ablating material, enhancing the wall heat transfer. The

wall can be fully or partially catalytic depending on the

fraction of atoms recombining at the wall. If the flow is in

chemical equilibrium, the reaction rates are so fast that no

catalyst is required to promote reactions at the wall. One

can, therefore expect the equilibrium wall heat transfer to

be more or nearly equal to the non-equilibrium heat

transfer for the fully catalytic wall. To bring down the heat

transfer rates, the wall is normally coated with antioxidants

like silicon carbide or zirconium oxide, to make it nearly

non-catalytic.

METHODOLOGY AND GOVERNING EQUATIONS

The computational fluid dynamics calculations are

performed using the viscous Navier stokes code, where the

fluid has been modelled as a reacting gas in thermal

equilibrium and chemical non-equilibrium. The flow is

assumed to be laminar. The governing equations are as

follows.

Continuity equation

𝜕𝜌

𝜕𝑡+ ∇. 𝜌𝑉 = 0 (1)

Species equation

𝜕𝜌𝑌𝑖

𝜕𝑡+ ∇. 𝜌𝑉𝑌𝑖 + ∇. 𝐽𝑖 = 𝑅𝑖 + 𝑆𝑖 (2)

Momentum equation

𝜕𝜌𝑉

𝜕𝑡+ ∇. 𝜌𝑉𝑉 + ∇p = ∇. 𝜏 (3)

Where

𝜏 = 𝜇 ∇𝑉 + ∇𝑉𝑇 −2

3∇. 𝑉𝐼 (4)

Energy equation

𝜕𝜌𝐸

𝜕𝑡+ ∇. 𝑉 𝜌𝐸 + p = ∇. 𝜆∇𝑇 − ℎ𝑖

𝑖

𝐽𝑖 + 𝜏 . 𝑉

(5)

Where

𝐸 = ℎ −𝑝

𝜌+

𝑣2

2

ℎ = 𝑐𝑝 ,𝑗𝑑𝑇𝑇

𝑇𝑟𝑒𝑓

The ideal gas equation of state is used

𝑝𝑖 = 𝜌𝑖𝑅𝑖𝑇 (6)

𝑝 = 𝑝𝑖

𝑖

As mentioned earlier the fluid which is air surrounding

the re-entry vehicle is at a high temperature due to kinetic

energy dissipation and shock wave. The high temperature

causes air to dissociate and even ionize. The temperature in

the nose area of Apollo re-entry was about 11,000 K at a

Mach number of 35[5]. The constant specific heat

assumption becomes invalid at those temperatures. In the

current model the specific heat is used as a function of

temperature and is calculated from curve fits as 𝐶𝑝

𝑅𝑖

= 𝑎1 + 𝑎2𝑇 + 𝑎3𝑇2 + 𝑎4𝑇

3 + 𝑎5𝑇4 + 𝑎6𝑇

5 + 𝑎7𝑇6

+ 𝑎8𝑇7 (7)

Where a1,a2...,a8 are constants and T is the

temperature. The above curve fit is valid for temperature

range 100 to 20,000.The value of the constants are given in

Table 1 and are taken from Ref [6].

The specific heat of the mixture is calculated as a mass

fraction average of the pure species heat capacities

𝐶𝑝 = 𝑚𝑗𝑐𝑝 ,𝑗

𝑗

The density-based solver solves the governing

equations of continuity, momentum, energy and species

transport simultaneously . The system of governing

equations solved in vector form is given by

𝜕

𝜕𝑥 𝑊𝑑𝑉 + [𝐹 − 𝐺]. 𝑑𝐴 = 𝐻𝑑𝑉

𝑉𝑉

(8)

The inviscid flux vector F in Eqn 8 is computed using

a flux-vector splitting scheme Advection Upstream

Splitting Method (AUSM) . The spatial discretization is

specified using a second order upwind scheme. Time

discretization is accomplished using an explicit method

CHEMICAL REACTION MODEL For high temperature ionized air, there are seven

primary species, which are N2,O2,NO,N,O,NO+,and e-

.The possible chemical reactions between these species are

N2+M <=> 2N+M

O2+M <=> 2O+M

NO+M <=> N+O+M

N2+O <=> NO+N

NO+O <=> O2+N

N+O <=> NO++e-

Where M represents any species. The first three sets

of reactions are Dissociation, the next two are Exchange

reactions and the last one is the Association and there are

24 reactions in total.

Chemical non-equilibrium assumption says that the

characteristic chemical reaction time is same as the

characteristic time of fluid motion. The laminar finite-rate

model in current model computes the chemical species

production rate using modified Arrhenius equation. The net

source term of chemical species i is computed as

𝑅𝑖 = 𝑀𝑖 𝑅𝑖,𝑟 (9)

𝑁𝑅

𝑅=1

The net rate of creation of species i in reaction r is

given by

𝑅𝑖,𝑟 = Γ 𝑣"𝑖 ,𝑟 − 𝑣′

𝑖 ,𝑟 𝑘𝑓 ,𝑟 𝐶𝑗 ,𝑟 𝑣′

𝑗 ,𝑟

𝑁

𝑗 =1

−𝑘𝑏 ,𝑟 𝐶𝑗 ,𝑟 𝑣"𝑗 ,𝑟

𝑁

𝑗 =1

(10)

The forward rate constant for reaction r is modelled

using the Arrhenius expression

𝐾𝑓 ,𝑟 = 𝐴𝑟𝑇𝛽𝑟𝑒𝑥𝑝 −

𝐸𝑟

𝑇 (11)

The backward rate constant for reaction r is computed

from the forward rate, where Kr is the equilibrium constant

for the rth

reaction.

𝐾𝑏 ,𝑟 =𝐾𝑓 ,𝑟

𝐾𝑟

(12)

Table 1

Table2

K = exp(A1+A2Z+A3Z2+A4Z

3+A5Z

4) (13)

with Z=10000/T

Constants A1A2...A5 is given in table 2.

For the reaction constants, the Park's Model consisting

of 7 species and 24 reactions is used. The values of various

constants of Park's model are taken from Ref[7] are shown

in table 2 .In [7] the Park model is used with the

assumption of thermo-chemical non-equilibrium whereas

in this work it is used with the assumption of thermal

equilibrium and therefore it is assumed that all the internal

energy modes are in equilibrium at temperature T.

TRANSPORT PROPERTIES The transport properties of the species are obtained from

the kinetic theory of gases [8] . The fluid viscosity is

defined using kinetic theory as

𝜇𝑖 =2.67 𝑋 10−6 𝑀𝑖𝑇

𝜎𝑖2Ωμi

(14)

Table 3

Species 𝝈 𝜺 𝒌𝟏,

N2 3.681 91.5

O2 3.433 113

NO 3.470 119

N 3.298 71.4

O 3.05 106.7

NO+ 4 100

e- 4 100

Where

Ωμ = Ω𝜇 𝑇∗

𝑇∗ =𝑇

𝜀/𝑘1

values of σ and Ώ are given in table 3. The thermal

conductivity of a pure gas is defined using kinetic theory as

𝜆𝑖 =15

4

𝑅

𝑀𝑖𝜇

4

15

𝐶𝑝𝑖 𝑀𝑖

𝑅+

1

3 (15)

The mass diffusion coefficient is defined using kinetic

theory as

𝐷𝑖𝑗 = 0.00188 𝑇3

1

𝑀𝑖+

1

𝑀𝑗

1/2

𝑃𝜎𝑖𝑗2Ω𝐷𝑖𝑗

(16)

Where 𝜎, Ω are the constants used in Chapman-Enskog

formula . The mass diffusion coefficient of species i in the

mixture is defined as

𝐷𝑖𝑚 =1 − 𝑋𝑖

𝑋𝑗 /𝐷𝑖𝑗 𝑗

The mixture values of μ and k for the chemically

reacting gas is defined using Wilke’s rule [8]

𝜇 = 𝑋𝑖 𝜇𝑖

𝑋𝑗𝜙𝑖𝑗𝑗𝑖

𝜆 = 𝑋𝑖𝜆𝑖

𝑋𝑗𝜙𝑖𝑗𝑗𝑖

Where

𝜙𝑖𝑗 =1

8 1 +

𝑀𝑖

𝑀𝑗

−1/2

1 + 𝜇𝑖

𝜇𝑗

1/2

𝑀𝑗

𝑀𝑖

1/4

2

17

The code has been applied to a number of problems

like high enthalpy re-entry flows, Plasma wind tunnel tests

etc. which are available in the literature and the current

methodology has been validated. Since the problem of

interest is related to PWT test of scaled model of crew

module, results obtained with one PWT test is explained

here.

VALIDATION STUDIES

The key to perform reliable flow simulations is

the aerothermodynamic validation of the theoretical

models describing the high temperature effects in

hypersonic gas flow, using wind tunnel and free flight

experimental data. To this purpose, in order to assess the

capabilities of model catalyticity effects in high enthalpy

flow conditions, the tests of ELECTRE model in PWT

have been considered as benchmark evaluations [9].

Therefore, some experimental activities performed in wind

tunnel with this standard model have been duplicated

numerically through CFD evaluations.

ELECTRE test article (see Fig. 1) consists of a blunt

conical surface with total length of 0.4 m, semi aperture

cone angle of 4.6 degree, and hemispherical nose with a

radius of 0.035 m. It was tested in flight and in wind

tunnel, becoming a standard reference model to study non-

equilibrium hypersonic flow past blunt-body

configurations [9].

FIGURE 1. ELECTRE TEST ARTICLE

GEOMETRY AND AXI SYMMETRIC

COMPUTATIONAL DOMAIN (110 X 175).

Table 4

Table 5

The computational domain employed for CFD

analyses is shown in Fig. 1. It consists of 110×175 cells

with a minimum normal wall spacing of 2e-6 m. Test

conditions are summarized in Table 3. They correspond to

the operating conditions of the HEG wind tunnel located at

DLR Gottingen [9]. In correspondence with these test

conditions two different test cases were run considering

alternatively the specimen wall as NC, and FC for N and O

species. Numerical computations have been performed for

fully laminar non-equilibrium flow conditions with model

temperature fixed to Tw=300 K. Farfield conditions are as

shown in table 4.

Figure.2 shows the mach number contour around the

probe body. Fig 3 shows the coefficient of pressure along

the probe wall surface. As expected there is no change in

pressure distribution along the wall for catalytic and non

catalytic wall boundary condition and it shows a good

agreement with the measurement except near the end of the

specimen.

FIGURE 2. MACH NUMBER CONTOUR

The heat flux distribution (Fig. 4) shows an agreement

with the numerical FC solution on the nose of the test

article whereas on the rear part of cone there is a mismatch

between experimental data and CFD results, as already

seen in the case of pressure coefficient (Fig. 3).

FIGURE 3. COMPARISON OF COEFFICIENT OF

PRESSURE ALONG THE WALL

Both these mismatches could probably be caused by

flow field perturbations due to the support of the

experimental model that is located at the end of the test

bed. Since the heat flux results and pressure measurements

are showing good agreement with the numerical results

,this code with the same methodology has been used for

analysing the PWT test of scaled model of HSP crew

module.

FIGURE 4. HEAT FLUX COMPARISON WITH

THE EXPERIMENTAL RESULT

NON EQUILIBRIUM FLOW ANALYSIS ON SCALED MODEL OF HSP CREW MODULE

With the validated code and methodology, flow field

around the 1:33 scaled model of HSP crew module is

attempted. The PWT nozzle is working under plasma

chamber pressure of 3.2 bar and a stagnation temperature

of 7870K. Area ratio of the nozzle is 150.Test chamber

pressure is maintained at 0.4mbar.Test article is kept at a

distance of 1.1De from the nozzle exit, where De is the

nozzle exit diameter. Fig 5 shows the axi-symmetric

computational domain of the scaled model of HSP crew

module

It consists of 0.203million cells with a minimum

normal wall spacing of 1e-6 m. The farfield condition of

the nozzle is given in table 4.

FIGURE 5. AXI SYMMETRIC COMPUTATIONAL

DOMAIN FOR THE SIMULATION

FIGURE 6. MACH NUMBER CONTOUR

FIGURE 7. TEMPERATURE CONTOUR

.

FIGURE 8. SIMULATION RESULT SHOWING

HEAT FLUX COMPARISON WITH NUMERICAL AN

EXPERIMENTAL RESULT

A number of grid independent study has been carried

out on this model and finalized the employed mesh size for

the current problem. Fig 6 and fig 7 shows the mach

number as well as the temperature contour respectively

around the model. Fig 8 shows the cold wall heat flux

value for fully catalytic as well as non catalytic wall

boundary conditions . Here one can observe that non

catalytic heat flux value is 63% less than the fully catalytic

wall condition at stagnation point which is evident from the

validation case which is explained above. In the validation

case this reduction is around 50%, In fact this reduction

will depend on the free stream conditions. In the same

figure experimental results also plotted along with the

numerical values. From that one can see that experimental

values are lying below the fully catalytic wall heat flux

values except at the wake region of the model, which can

be because of non existence of favourable conditions for

full recombination reactions at the front face of the model.

CONCLUSION In the current work a theoretical methodology has

been developed to model chemically non-equilibrium and

thermally equilibrium flows for two dimensional/axi-

symmetric geometries for high enthalpy flows. The solver

with the current methodology is well validated with the re-

entry bodies as well as on PWT test condition simulations,

which is available in the literature. Whereas only PWT test

with ELECTRE model only explained as validation study

in the current paper.

Validated methodology has been used for

simulating the non equilibrium flow around scaled model

of HSP crew module under plasma wind tunnel conditions.

Since the model is made of metal, the conditions prevailing

on the surface of the body will be more closer to fully

catalytic nature. The heat flux distribution along the

surface of the body shows good agreement with the fully

catalytic wall heat flux. From this work it is clear that

special care should be taken in modeling flow under such

high temperature environment by taking into account of

reactive chemistry corresponds to the wall conditions

prevailing over the body.

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