radiative gas dynamics ii - cnrusers.ba.cnr.it/imip/cscpal38/erice/lectures/surzhikov-ii.pdf ·...

2 August 2005 41st Course: Molecular Physics and Plasma in Hypersonics

1

Radiative Gas Dynamics - II

Sergey T. SurzhikovInstitute for Problems in Mechanics

Russian Academy of Sciences


2

Radiative Gas Dynamics

Part ITheoretical basis and general definitions

Part IINumerical simulations of aerospace RGD

applications


3

Outline

1. MHD/RGD governing equations2. Laser Plasma Aerodynamics3. 3D MHD numerical simulation of Hall plasma thruster

plume4. Safety rescue systems for astronauts and payload5. Non-equilibrium radiation of shock waves6. Entry and Re-Entry hypersonics7. Modern challenging problems of RGD and on-going

efforts


4

Block-diagram of the Radiative Gas DynamicsRadiative Gas

Dynamics Radiation Heat Transfer

Optical model:Absorption coefficients, emission coefficients, scattering coefficients and scattering indicatrix

Cross-sections of the elementary radiative processes

Thermodynamics and Statistical Physics

Gas Dynamics Chemical Physics Radiative Model

Radiation Transfer Model

Methods for solving RHT

problems

Quantum mechanics and quantum chemistry

Physical kinetics


5

MHD/RGD: Governing equations

pRM

T= 0 ρ

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )4

,,

1, ; ; ,4

em

J s ts s J s t

s

J s t s p s J s t d

νν ν ν

ν ν νπ

∂κ σ

∂

σ νπ ′

′Ω =

+ + =⎡ ⎤⎣ ⎦

′ ′ ′= + Ω∫

ΩΩ

Ω Ω Ω

,,

, ,

0divt

∂ρ ρ∂

+ =V

( ) ( ) [ ]0

1ediv grad p

t τ∂ρ ρ ρ ρ∂ µ

+ ⋅ = − − × + + +⎡ ⎤⎣ ⎦V V V J B F g E

( ) ( ) ( )

2 2 2

02 2 2m

Rad

ppe div et

div gradT div Aτ

∂ ρρ ρ∂ µ ρ ρ

λ ρ

⎡ ⎤⎛ ⎞ ⎛ ⎞+ + + + + + =⎢ ⎥⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠ ⎣ ⎦= + + + ⋅ + ⋅

V B VV

W g V J E


6

Laser Plasma Aerodynamics


7

Objectives of the Laser Plasma Aerodynamics development

Study of steady-state and unsteady regimes of the Laser Supported Waves (basic physics)Laser supported rockets engines (LSRE, lightcrafts) Technological applications of laser plasma plumesUsing laser sparks and LSW for flow control in different aerophysic applications


8

Laser impulse duration t>1-5 ms

Physics of the Laser Supported Waves (LSW)


9


Initiation of the first electrons

Heating of electrons in the field of laser radiation

Collisional heating of neutral particles

Diffusion of electrons

Avalanche ionization of atoms and molecules

Thermo-conductive and radiative heating of cold gas

Gas movement


10

Parameters of the Laser Rocket Engines (LRE) and Laser Supported Plasma Generators (LSPG) are very close to

powerful arc plasma generators !



11

Approaches

• Unsteady Navier-Stokes equations for chemically reacting gases

• Radiation heat transfer equation for spectral, group and integral heat radiation

• Real thermophysic, transport and optical properties of gases (air, hydrogen, CO2+N2, Ar, etc.)

• The temperature region: Т = 300 – 30 000 К• The pressure region: р = 0.0001- 100 atm



12

Thermophysical properties (Capitelli’s sci. group)

10000 20000 30000Temperature, K

2

4

6

Cp, cal/(g K)

Air, p=1 atm

5000 10000 15000 20000T, K

50

100

150

200

250

Cp, J/(g*K)

H2, p=1 atm

Specific heat at constant pressure



13

10000 20000 30000Temperature , K

2

4

6

Cp, cal/(g K)

10000 20000 30000Temperature , K

2

4

6

Total thermal conductivity, W/(m*K)

10000 20000 30000Temperature , K

2

4

6

Cp, cal/(g K)

10000 20000 30000Temperature , K

5E-05

0.0001

0.00015

0.0002

0.00025

Vis cos ity coe fficient, kg/(m*s )

Air, p=1 atm




14

5000 10000 15000 20000T, K

2

4

6

8

10

12

14

16

18Thermal conductivity, W/(m*K)

H2, p=1 atm

5000 10000 15000 20000T, K

1E-05

2E-05

3E-05

4E-05

5E-05

6E-05

7E-05

8E-05

9E-05

0.0001Viscosity, kg/(m*sec)




15

Optical properties: spectral models

50000 100000 150000Wave numbe r 1/cm

10-5

10-4

10-3

10-2

10-1

100

101

102

103T= 6000. KP= 1.000 atmRo=.04436 kg/mN .15787O .32381E- .00020NO .00931N2 .50830O2 .00031N+ .00000O+ .00000N2+ .00000O2+ .00000NO+ .00020

Abs orption coe fficie nt, 1/cm

50000 100000 150000Wave numbe r 1/cm

10 -3

10 -2

10 -1

100

101

102 T=20000. KP= 1.000 atmRo=.00442 kg/mN .01604O .00683E- .49008NO .00000N2 .00000O2 .00000N+ .38168O+ .10537N2+ .00000O2+ .00000NO+ .00000

Abs orption coe fficie nt, 1/cm

Air, p=1 atm



16

Optical properties: spectral modelsH2, p=1 atm

25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-10

10-8

10-6

10-4

10-2

100

Absorption coefficient, 1/cm

T = .200E+04Te = .200E+04P = .100E+01ABp = .555E-10Nom = 10000H2 = .100E+01H = .174E-02


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-3

10-2

10-1

100

101

Absorption coefficient, 1/cm

T = .200E+05Te = .200E+05P = .100E+01ABp = .632E-01Nom = 10000E- = .485E+00H+ = .485E+00H2 = .298E-08H = .428E-01


17

Optical properties: group models

50000 100000 150000Wave numbe r 1/cm

10-5

10-4

10-3

10-2

10-1

10 0

10 1

T= 6000. KP= 1.000 atmRo=.04436 kg/mN .15787O .32381E- .00020NO .00931N2 .50830O2 .00031N+ .00000O+ .00000N2+ .00000O2+ .00000NO+ .00020

Group abs orption coe fficie nt, 1/cm

50000 100000 150000Wave numbe r 1/cm

10-3

10-2

10-1

T=20000. KP= 1.000 atmRo=.00442 kg/mN .01604O .00683E- .49008NO .00000N2 .00000O2 .00000N+ .38168O+ .10537N2+ .00000O2+ .00000NO+ .00000

Group abs orption coe fficie nt, 1/cm

Air, p=1 atm



18

Optical properties: group models

50000 100000 150000Wavenumber, 1/cm

10-13

10-11

10-9

10-7

10-5

10-3

10-1

101

103

105

T= 2000. KP= .100E+01 atmRo= .120E-01 kg/m3

H .14447E-02E- .10003E-14H2 .99855E+00H+ .10198E-14H2+ .10034E-14H- .10000E-14

Group absorption coefficient, 1/cm

H2, p=1 atm

50000 100000 150000Wavenumber, 1/cm

10-3

10-2

10-1

100 T=20000. KP= .100E+01 atmRo= .310E-03 kg/m3

H .34608E-01E- .48447E+00H2 .54179E-08H+ .48092E+00H2+ .32272E-06H- .35571E-06

Group absorption coefficient, 1/cm



19

Radiative gas dynamic model of theLSPG (the laminar flow)

( ) 1 ( ) 0u r vt x r r

∂ρ ∂ ρ ∂ ρ∂ ∂ ∂

+ + =

43

u u u p uut x r x x x

∂ ∂ ∂ ∂ ∂ ∂ρ µ∂ ∂ ∂ ∂ ∂ ∂

⎛ ⎞ ⎛ ⎞+ + = − + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

v

1 1 23

u rr rr r r r r x r x r∂ ∂ ∂ ∂ ∂ ∂µ µ µ∂ ∂ ∂ ∂ ∂ ∂

⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ + −⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

v v

put x r r

∂ ∂ ∂ ∂ρ∂ ∂ ∂ ∂

⎛ ⎞+ + = − +⎜ ⎟⎝ ⎠

v v vv

2

4 23

u rx r x x r r r r∂ ∂ ∂ ∂ ∂ ∂ µµ µ µ∂ ∂ ∂ ∂ ∂ ∂

⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ + + − −⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

v v v

2 1 2 1 2 1 ( )3 3 3 2

u u rrr r x r r r x r∂ ∂ ∂µ µ ∂ ∂µ∂ ∂ ∂ ∂ ∂

⎛ ⎞ ⎛ ⎞− − + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

v v



20

Radiative gas dynamic model of theLSPG (the laminar flow)

pT T Tc ut x r

∂ ∂ ∂ρ∂ ∂ ∂

⎛ ⎞+ + =⎜ ⎟⎝ ⎠

v1T Tr Q

x x r r r∂ ∂ ∂ ∂λ λ∂ ∂ ∂ ∂ Σ

⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

L HRQ Q QΣ = −

2

2 2expLL

b b

P rQR Rωµπ

⎛ ⎞= −⎜ ⎟

⎝ ⎠( , 0)L

LP x r Px ω

∂µ

∂= − =

,1

( )gN

HR g b g g gg

Q U Uκ ω=

= − ∆∑ ,1( ) ( )

3 g g b g gg

div gradU U Uκκ

= − − g=1,2,…,Ng



21

Laser Supported Plasma Generator

,0)(1)(=++

rvr

rxu

t ∂ρ∂

∂ρ∂

∂ρ∂

+−=++xp

ruv

xuu

tu

∂∂

∂∂

∂∂

∂∂ρ )( ++ )(1)(

34

rur

rrxu

x effeff ∂∂µ

∂∂

∂∂µ

∂∂

),(132)(1

rrv

xrxvr

rr effeff ∂∂µ

∂∂

∂∂µ

∂∂

−

+−=++rp

rvv

xvu

tv

∂∂

∂∂

∂∂

∂∂ρ )( ++ )()(

xv

xru

x effeff ∂∂µ

∂∂

∂∂µ

∂∂

−− 22)(134

r

vrvr

rreff

effµ

∂∂µ

∂∂

+−−r

vrx

urrr

effeff ∂

∂µ∂∂µ

∂∂ 1

32)(1

32 ),)(

21(

32

rrv

xu

reff

∂∂

∂∂µ

+

+=++ )()(xT

xrTv

xTu

tTc effp ∂

∂λ∂∂

∂∂

∂∂

∂∂ρ ,)(1

Σ+ QrTr

rr eff ∂∂λ

∂∂

Radiative gas dynamic model of the LSPG (the turbulent flow)


22

HRL QQQ −=Σ , )exp( 2

2

2LL

LRr

RPQ −=

πµω , ,)0,( Prx

xP

=−= ωµ∂∂

),()3

1( ,)( ,,1

kkbkkk

kkkb

N

kk UUgradUdivUUQ

k−−=∆−= ∑

=κ

κωκ

,)()]([1 ρε∂∂

σµρ

∂∂

∂∂

σµρ

∂∂

∂∂ρ

−=−+−+ Pxkkv

xrkkur

rrtk

k

t

k

t

+−+ )]([1r

vrrrt

t∂∂ε

σµ

ρε∂∂

∂∂ρε

ε kCPC

xu

xt ερε∂∂ε

σµρε

∂∂

ε)()( 21 −=−

⎭⎬⎫

⎩⎨⎧ ++−

⎭⎬⎫

⎩⎨⎧ ++++= ]1[

32)(])()()[(2 2222

rru

rxvk

rv

xu

ru

xv

ruP tt ∂

∂∂∂µρ

∂∂

∂∂

∂∂

∂∂µ

,2 ⎟⎠⎞

⎜⎝⎛ +−

xp

xrp

rt

∂∂

∂∂ρ

∂∂

∂∂ρ

ρλ

tpttt ckC Pr/,/2 µλερµ µ ==


Radiative gas dynamic model of the LSPG (the turbulent flow)


23

Temperature distribution inside cylindrical chamber of hydrogen LSPG at Uo=40 m/s, P=100 kWatt

X, cm0 2 4 6 8 100

0.5

1

1.5

2

T: 1.89E+03 3.29E+03 4.68E+03 6.08E+03 7.47E+03 8.86E+03 1.03E+04 1.17E+04 1.30E+04 1.44E+04 1.58E+04 1.72E+04 1.86E+04 2.00E+04 2.14E+04

R, cm



24


Investigation of the laser plasma flows:

• Prediction of exit plasma flows• Instabilities of the plasmadynamic configurations• The instabilities supression


25

Plasma instabilities in LSPG at Uo=30 m/s, P=100 kWatt

Air



26

Prediction of Radiative Heating of Internal Surfaces of Hydrogen and Air Laser

Supported Plasma Generators



27

Motivation:• Plasma temperature achieves T~20,000 K• There is a high-temperature tail of the plasma behind

LSW front at presence of internal gas flow. • Prediction of radiative heating of LSPG internal surfaces.

X, cm0 2 4 6 8 100

0.5

1

1.5

2


R, cm



28

X, cm0 2 4 6 8 100

0.5

1

1.5

2


R, cm

Temperature distribution in LSPG at Uo=20 m/s, P=100 kWatt

Hydrogen



29

X, cm0 2 4 6 8 100

0.5

1

1.5

2


R, cm


Hydrogen



30

X, cm0 2 4 6 8 100

0.5

1

1.5

2


R, cm


Hydrogen



31

X, cm0 2 4 6 8 100

0.5

1

1.5

2


R, cm


Hydrogen



32

X, cm0 2 4 6 8 100

0.5

1

1.5

2


R, cm


Hydrogen



33


Air; Laminar flow

x, cm0 5 1000.30.60.91.2


r, cm



34


Air; Turbulent flow

x, cm0 5 1000.30.60.91.2


r, cm



35

Discrete Ordinates Method (DOM): Radiation heat flux, W/cm**2

Distribution of integral radiation heat flux along internal cylindrical surface of the LSPG, W/cm2, at entrance velocity 30 m/s

Dependence of the radiation heat flux upon on the flow regime (laminar/turbulent)

AirX, cm

2 4 6 8 100

200

400

600

Turbulent flow, Uo=30 m/sLaminar flow, Uo=30 m/s

Integral radiative flux, W/cm2



36

DOM: Radiation heat flux, W/cm**2

X,cm

Flux

onto

pw

all(

r=2

cm),

W/c

m2

0 5 100

100

200

300

400

500

600

700

800

900

1000

20 m/s30 m/s40 m/s50 m/s60 m/s70 m/s

Wavenumber, 1/cm50000 100000 15000010-4

10-2

100

102

104

106

Radiation flux distribution along cylindrical surface for different entrance velocities (DOM: S12)

Group Radiation flux distribution , Watt/cm2, at x=3 cm on the cylindrical surface

Hydrogen



37


Laser Supported Waves in Free Space


38


Laser Supported Waves in Free Space


39


Laser Plumes: Laser Impulse Interaction with Material


40


Laser Plumes: Schematic of the problem and numerical simulation


41


Laser Plumes: Schematic of the problem and numerical simulation


42

Laser Supported Waves as the Late Stage of Laser Impulse/Material Interaction



43

Laser Plasma AerodynamicsR Laser beam =0.1 cm, P = 15 kW


44



45



46



47



48

3D MHD of Plume of the Hall Plasma Thrusters at Ionospheric Conditions


49

Problem statement

• Prediction of plasmadynamic and electro-dynamic characteristics of the Hall Plasma Thruster (HPT) or Pulsed Plasma Thruster (PPT) plumes

• Analysis of the possibility to use MGD codes (ideal and non-ideal) for describing interaction of the HPT/PPT plasma plumes with partially ionized rarefied atmosphere

• Creation 3D MGD/CFD codes as alternative for PIC/DSMC codes


50

The governing equations

t∂∂ Σ+∇⋅ =U F Q

t x y z∂ ∂ ∂ ∂∂ ∂ ∂ ∂

+ + + =U f g h Q

Eu NS MGD VMGDΣ = + + +F F F F F i j kΣ = + +F f g h

Eu NS MGD VMGD= + + +f f f f f

Eu NS MGD VMGD= + + +g g g g g

Eu NS MGD VMGD= + + +h h h h h


51

Initial conditions

9 3 4* *2.0 10 / , 4.49 10kg m p Paρ − −= ⋅ = ⋅

5 00 ^5 10 , 30B YB T α−= ⋅ =

inf

0inf 6.0 / , 30VW km s ϑ= − =

7 325 / , 2.0 10 / ,

20 , 0.03plume plume

plume exit

W km s kg m

p Pa R m

ρ −= − = ⋅

= =

6 , 70HPT simulationT s T sµ µ= =


52

3D plasma plume: Numerical simulation results: t=3 µs


53



54



55



56



57



58



59



60



61



62



63

3D Plasma plumes: Conclusions

• At distances ~0.5 m from HPT its plasma plume begins to interact with ambient ionospheric flow and frozen magnetic field

• High efficiency of the 3D code based on the splitting method is illustrated: Calculation time < 1.0 hour (Pentium-IV, f=3.2 GHz, mesh 100x100x100)


64

Safety rescue systems for astronauts and payload

Radiative Gad Dynamics for Aerospace Applications


65

Fireball generated at Challenger Fireball generated at Challenger catastrophe, January 1986catastrophe, January 1986

Numerical simulation of fireballs generated at probable explosions:

ARIANE-V, Zenith, Proton, Aurora



66

0 1000 2000 3000R, m

0

1000

2000

3000

P1.7661.7121.6581.6041.5501.4961.4421.3881.3341.2801.2261.1721.1181.0641.0100.9560.9020.8480.7940.7400.6860.6320.5780.5240.470

X, m

0 1000 2000 3000R, m

0

1000

2000

3000

X, m

ShockShock--wave structure at ARIANEwave structure at ARIANE--V explosion at altitudeV explosion at altitude 55 55 ккmmand at flight velocity V=2 and at flight velocity V=2 ккm/sm/s



67

PROTONPROTONRadiative Fireball above Radiative Fireball above launch padlaunch padFireball dynamics Fireball dynamics without without RHTRHT



68

PROTONPROTONRadiative Fireball above Radiative Fireball above launch padlaunch padFireball: Fireball: fullfull RGD modelRGD model



69


PROTONPROTONRadiative Fireball above Radiative Fireball above launch padlaunch padFireball: Fireball: volume emission volume emission modelmodel (no (no reabsorbtionreabsorbtion))


70

Numerical simulations of aerospace RGD applications

Non-equilibrium radiation of shock waves for entry and re-entry velocities


71

Motivation• Creation of closed hierarchy theory of non-equilibrium

kinetic processes behind shock waves

• Prediction of real shock waves (air, CO2-N2) at velocities V=3-12 km/s and pressures ~0.1-1000 torr

• Comparison of numerical simulations (spectral radiation emissivity !) with experimental data and calculations of other authors

Prediction of Nonequilibrium Radiation From CO2-N2 and Air Shock Waves


72

Physical-chemical processes included in the developed model

• Chemical reactions (thermal dissociation, neutral exchange reactions)

• Reactions involving charged particles (dissociative recombination reactions, associative ionization, electron-impact ionization, charge-exchange reactions, ion-molecule reactions)

• Excitation of CO2, N2, CO vibration modes during translational-vibrational (VT), and vibrational-vibrational (VV) energy exchange

• Nonequilibrium dissociation • Nonequilibrium radiation



73

Gas dynamic model:

0 0u uρ ρ= , 2 20 0 0p u p uρ ρ+ = + ,

2 20

02 2u uh h+ = + ,

where:

0

1, ,

N

i i i i Ai

R Tp nkT M x m NMρ µ µΣ

=Σ

= = = =∑ ,

,2 3,0

,,1 exp( ) 1

V iNL Li j

p i i ji ji j

Rh C T x qM

T

θθ

+

=Σ

= +−

∑ ∑ ,

320

1 1

5 32 2

LL

p l il i

RC x xM= = Σ

⎛ ⎞= + +⎜ ⎟⎝ ⎠

∑ ∑



74

( ) ( ), , , ,1 1 1

+ , 1,2,...,R

ij ijN N N

a bf rkk j k j j i k j k j j i

j i i

dX b a k X a b k X k Ndt = = =

⎡ ⎤= − − =⎢ ⎥

⎣ ⎦∑ ∏ ∏

[ ] [ ], ,1 1

, 1,2, ,fj

rj

kN N

i j i i j i Rki i

a X b X j N= =

⇔ =∑ ∑ …

expnj

Ek A TkT

±± ±±

⎡ ⎤= −⎢ ⎥⎣ ⎦

, ,1000lg j eq j eq jK A B

T= + ,

,i jni

ij w

e j

pK

p p=∏

Model of chemical kinetics



75

m m mmvT vv cv

de Q Q Qdt

= + + ,

10

1 ,

,N

m m m ivT m

im m i

e e xQ ττ τ

−

=

⎛ ⎞−= = ⎜ ⎟⎜ ⎟

⎝ ⎠∑ , , ,

VNmvv m n m n

nQ k F=∑ ,

( ) ( ), 1 exp 1r qq rn mm n n m m n

m

r q rF e e e eg T T

θ θ⎡ ⎤⎛ ⎞= + − − +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦,

, ,( )cn

m n l m n ll

k x k=∑ , ( )1

1 RNm mcv mj m

j ji

dXQ e eX dt=

⎛ ⎞= − ⎜ ⎟⎝ ⎠

∑ ,

,

1

exp 1m

m

v m

e

Tθ

=⎛ ⎞

−⎜ ⎟⎝ ⎠

Model of vibrational kinetics



76

21 , (50000 / )8 ( )VT V V

t V m

TN kT M

τ τ σ σσ π

′= + =

1/ 3exp ( ) 18.42VT VT VTp A T Bτ −⎡ ⎤= − −⎣ ⎦

1 1/ 3, 1/ 3 2 / 3

1 1, expm n VV VV VV VV VV VVk p A B C D TT T

τ τ− ⎛ ⎞= = + + +⎜ ⎟⎝ ⎠




77


1 /

exp 1 exp 1

m mmj

m m

F F

DeD

T T

θθ

= −⎛ ⎞ ⎛ ⎞

− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

,

1 1 1 , 3Fm n

T U TT T U

= − − =

( ) ( ) ( )0, ,v vk T T k T Z T T=

( ) ( ) ( )( ) ( )

, Fv

v

Q T Q TZ T T

Q T Q U=

−, ( ) ( )

( )01 exp

1 expD T

Q TT

αα

αθ− −

=− −

, , , ;v F vT T T T U T Tα = − <



78

The electronic energy conservation model: 3

32

erg cm= ,sec

e e e e

ei ea ai ion ev

d duT n u T ndz dz

Q Q Q Q Q

⎛ ⎞ + =⎜ ⎟⎝ ⎠

⋅+ + + +

203 21,21 10 lne

ei e ie

T TQ X XT−

= ⋅ Λ

( )1

103,378 10 1 1 eea e a e e

a

TQ X X T T TT

−

∗

⎡ ⎤⎛ ⎞⎢ ⎥= ⋅ − − +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

( )1 1q q

q q

f rai q q a b e q q e a b

q qQ T k X X T k X Xα β +

= =

= −∑ ∑N, N O, O C, Cf f f

ion e e e e e eQ Tk X X Tk X X Tk X Xγ δ θ= − − −

16V , 1,0,V2 10ev e e V

VQ n n Pω−= ⋅ ⋅∑

, ,

2 2

,

1,44 1,44exp exp

1,44 1,441 exp 1 exp

e V e V

e v

e V e

e v

T T

T T

ω ω

ω ω

⎧ ⎫⎛ ⎞ ⎛ ⎞⎪ ⎪− −⎜ ⎟ ⎜ ⎟⎪ ⎪⎝ ⎠ ⎝ ⎠⋅ −⎨ ⎬⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎪ ⎪− − − −⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎪ ⎪

⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦⎩ ⎭



79

Model of spectral radiation emissivity

10 ' "6

' "3.202 10 exp ( ')eel v v

eelv vvr v v

N S hcj E vQ B kTλ λ

− ⎡ ⎤= ⋅ − ⋅⎢ ⎥∆ ⎣ ⎦

∑∑

'' " 'exp ( )v

v v vr v

hc B BkT B

ω ω⎡ ⎤

⋅ − − +⎢ ⎥∆⎣ ⎦, W/(cm3⋅µm⋅sr)



80

Validation of the model

• Comparative analysis of calculated spectral radiation intensities with experimental data and theoretical predictions of other authors

– G.Thomas and W.Menard (AIAA Journal, 1966, Vol.4, No.2) – Calculations of C.Park, J.Howe, R.Jaffe, and G.Candler (J. of

Thermophysics and Heat Transfer, 1994, Vol.8. No.1)– the Kozlov-Losev-Ponomarenko experiments, Moscow State

University, 1998-1999



81

0.4 0.6 0.8W avelength, micron

10-1

100

101

102

103

104J, W /(cm**2*micron*sr)

Non-equilibrium radiation behind the shock wave for the Thomas-Menard experiments: p0=0.25 torr and Us=7620 m/s (9%CO2-90%N2-1%Ar). The radiative-collisional model for excited electronic levels is presumed. Comparison of the calculations (solid line)with the experimental data (diamonds)

0 .4 0 .6 0 .8W avelength, m icron

1 0 -2

1 0 -1

1 0 0

1 0 1

1 0 2

1 0 3

1 0 4J, W /(cm **2 *m icron*sr)

Non-equilibrium radiation behind the shock wave for the Thomas-Menard experiments: p0=0.25 torr and Us=7620 m/s(9%CO2-90%N2-1%Ar). The Boltzmann distribution of excited electronic levels is presumed.



82

0.4 0 .6 0.8W avelength, micron

10 -1

100

101

102

103


Non-equilibrium radiation behind the shock wave for the Thomas-Menardexperiments: p0=0.25 torr and Us=7620 m/s (30%CO2-70%N2). Theradiative-collisional model for excited electronic levels is presumed.Comparison of the calculations (solid line) with the experimental data(diamonds)



83

10-8 10-6 10-4 10-2 100

X, cm

103

104

TT(CO21)T(CO22)T(CO23)T(CO)T(N2)Te

Temperature, K

Temperature distributions behind the shock wave for the Thomas-Menardexperiments: p0=0.25 torr and Us=7620 m/s (30%CO2-70%N2). Theradiative-collisional model for excited electronic levels is presumed



84

0.2 0 .4 0 .6 0 .8W avelength, micron

10 -3

10 -2

10 -1

10 0

10 1

10 2

10 3J, W /(cm**2*micron*sr)

0.2 0.4 0.6 0.8W avelength, micron

10-3

10-2

10-1

100

101

102


Non-equilibrium radiation behind the shock wave for conditions of the Kozlov-Losev-Romanenko experiments:

p0=0.5 torr and Us=3750 m/s (4.8%CO2-0.15%N2-95.05%Ar).

The Boltzmann distribution of excited electronic levels is presumed.

The radiative-collisional model for excited electronic levels is presumed.

Comparison of the present calculations (solid line) with the experimental data (dotted line)



85

Resume (CO2+N2):

1. Two models of excitation of the electronic energy levels of diatomic molecules have been studied for conditions of the Thomas-Menard experiments, the Kozlov-Losev_Ponomarenko experiments, and for the Park-Howe-Jaffe-Candler calculations. The first model presumes the Boltzmann distribution of the excited levels, and the second one demands integration of equations of the radiative-collisional kinetic model.

2. Comparison of the present calculations with experimental and theoretical data permits to make a conclusion about acceptability of the model for prediction of the non-equilibrium radiation for spacecraft entering the Martian atmosphere at velocities between 3÷8 km/s. However, there is a need to develop and validate such theoretical models in comparisons with new experimental data.



86

Air:

V=12 km/s

H=70 km

10-4 10-3 10-2 10-1 100 101 102

X, cm10-10

10-8

10-6

10-4

10-2

100

NOE-N2O2NON2+O2+NO+N+O+

p /pi a

10-4 10-3 10-2 10-1 100 101 102

X, cm107

109

1011

1013

1015

1017

NOE-N2O2NON2+O2+NO+N+O+

n , 1/cm**3 b



87

Air:

V=12 km/s

H=70 km

10-4 10-3 10-2 10-1 100 101 102

X, cm102

103

104

105

TTv(N2)Tv(O2)Te

eTemperatures

10-4 10-3 10-2 10-1 100 101 102

X, cm

10-3

10-2

10-1

100

101

102 e-Ve-Ione-Atome-Ass/IonIonizationLaser

Heating of the electronic gasc



88

Air:

V=12 km/s

H=70 km

10-4 10-3 10-2 10-1 100 101 102

X, cm

10-3

10-2

10-1

100

101

102

e-Ve-Ione-Atome-Ass/IonIonizationLaser

Energy Losses

dT0 = .217D+03P0 = .520D+02U0 = .120D+07Ro0 = .839D-07H0 = .217D+10TEMPE = .217D+03Plaser = .100D+01-------------------------T1 = .703D+05P1 = .101D+06U1 = .201D+06Ro1 = .502D-06H1 = .702D+12



89

All test data and preliminary calculations show that the local thermodynamic equilibrium (LTE) is not realized in spatial zone (~3 cm) behind shock wave at shock wave velocity more than 9 km/s and P1=0.05-0.2 torr .

This effect should be studied and taken into account at determination of the ionization and radiation characteristics ofsuper-orbital shock layer.

Resume (air)



90

Numerical simulations of aerospace RGD applications

Entry and Re-Entry Hypersonics


91

Radiative Gas Dynamics Radiation Heat Transfer

Optical model:Absorption coefficients, emission coefficients, scattering coefficients and scattering indicatrix

Cross-sections of the elementary radiative processes

Thermodynamics and Statistical Physics

Gas Dynamics Chemical Physics Radiative Model

Radiation Transfer Model

Methods for solving RHT

problems

Quantum mechanics and quantum chemistry

Physical kinetics



92

Code Verification

CFD codes Chemical kinetics

Physical kinetics

RHT codes

Opticalmodels

LTEapproach

Non LTEapproach

Grids &Calc. Domains

Laminar &Turbulent

1D, 2D, 3D problems

Data BaseOf

Chem. React. Velocities

Gas Phase

Surface Kinetics

Thermo destructionkinetics

Vibrational & Electronic

Kinetics

TransportProperties

Averaged on Rotational Structure Spectrum

Line-by-line models



93

General objective: Verification of gasdynamic, kinetic, radiative models for space vehicle aerothermodynamics

prediction

Model of Mars Sampler Return Orbiter (MSRO), postulated as the base model for TC3



94

TC3: MSRO Trajectory parameters

No. Time,s

Density, g/cm3

Pressure, erg/cm3

Velocity, m/s

Temperature,K

1 70 3.14·10-8 8.4 5687 140

2 115 2.93·10-7 78.7 5223 140

3 175 3.07·10-7 82.3 3998 140

4 270 2.82·10-7 7.6 3536 140



95

t x y∂ ∂ ∂

+ + =∂ ∂ ∂U E F G

1

2

...

N

uve

ρρρρρρ

ρ

=U1 1,

2 2,

,

( )

...

xx

xy

x

x

x

N N x

uuu pv

pu e q

u Ju J

u J

ρρ τρ τ

ρρ

ρρ

ρ

+ ++

+ +=

+

+

+

E

1 1,

2 2,

,

( )

...

yx

yy

y

y

y

N N y

vvu

vv p

pv e q

v J

v J

v J

ρρ τ

ρ τ

ρρ

ρ

ρ

ρ

+

+ +

+ +=

+

+

+

F1

2

000

...

N

Qϖϖ

ϖ

Σ=G

RadQ Q pdiv QαΣ = Φ + − +VN

i ii

q gradT hλ= − +∑ J , 1,2,...,i i iD grad i Nρ= − =J

Governing equations



96

0

, ,0

T

i p i iT

h c dT h= +∫0

, ,0

T

i v i iT

e c dT e= +∫N

i ii

p pe h hYρ ρ

= − = −∑

( )2 2 2 2

2223

v u v u v divr x r r x

µ⎧ ⎫⎡ ⎤∂ ∂ ∂ ∂⎪ ⎪⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞Φ = + + + + −⎢ ⎥⎨ ⎬⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭

V

223xx

u divx

τ µ µ∂= −

∂V

223yy

v divy

τ µ µ∂= −

∂V xy

u vy x

τ µ⎛ ⎞∂ ∂

= +⎜ ⎟∂ ∂⎝ ⎠

, ,, , , ,

1 1

( ') [ ] [ ]j l j lN N

i i i l i l f l j r l jl j j

M k X k Xν νϖ ν ν ′ ′′

= =

⎛ ⎞′′ ′= − −⎜ ⎟

⎝ ⎠∑ ∏ ∏ [ ]j j

j

X YMρ

= iiY ρ

ρ=

Rad RadQ div= W

Governing equations



97

( )grad div grad gradp pT pc c T T pt t

ρ ρ λ∂ ∂+ = + + +

∂ ∂V V

( ),1

grad gradsN

vib p i i ii

Q c D Y Tµ ρ=

+Φ + + ⋅∑1

divsN

R i ii

hϖ=

− −∑q

2 2 2

2 2 2r r xµ µ

⎡ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞Φ = + +⎢ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢⎣

v v u 2 223

u ux r x r r

⎤∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞+ + − + + ⎥⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎥⎦

v v v

Governing equations: Energy conservation equation



98

div div , 1, 2, ,ii i i si N

tρ

ρ ϖ∂

+ = − + =∂

V J …

( ),, ,div , 1, 2, ,mm m V

ee e m N

tρ

ρ∂

+ = =∂

V …vv v

( ) ( ) ( ) ( ),

,J

J jωω ω ωκ

∂+ =

∂r

r r rrΩ

Ω Ω

0, ,

, ( ) , ( )m m

m i m m i mm

e ee e wρ

τ−

= −v vv v ( )

0 ( ),

( ) ,exp 1m i m

mi m m V m

Re

M T

θ ρ

θ=

⎡ ⎤−⎣ ⎦v

( ) ( )4

d , dtot

R R Jωπ ω∆

= = Ω Ω∫ ∫q q z r Ω Ω

Governing equations



99

, ,1 1

, 1, 2, , ,s sN N

j n j j n j rj j

a X b X n N= =

⎡ ⎤ ⎡ ⎤= =⎣ ⎦ ⎣ ⎦∑ ∑ …

( ) ,, , ,

1

dd

ci n

Nj a

j f n j n j n jin

XW k b a X

t =

⎛ ⎞= = − −⎜ ⎟⎝ ⎠

∏( ) ,

, , , , ,1

ci n

Nb

r n j n j n i f j r ji

k a b X S S=

− − = −∏

( ), ( ),( ), ( ), expf r nn f r n

f r n f r nE

k A TkT

⎛ ⎞= −⎜ ⎟

⎝ ⎠

, ,n f n r nK k k=

Governing equations



100

Chemical Kinetics

Thermodynamic and transport properties

Radiation Heat Transfer (RHT)

Spectral Optical Properties Physical Kinetics


Databases

Databases

DatabasesDatabases



101

Numerical simulation methods

• Time relaxation method• Flux-corrected methods for the Navier-Stokes equations • Implicit method with using SOR on lines for mass

conservation equations (for chemical species) • Implicit method with using SOR on lines for energy

conservation equation• P1-approximation of the spherical harmonics method

(SHM) for radiation heat transfer equation• Discreet Ordination Methods for radiation heat transfer

equation• Ray-tracing method was used for prediction of radiation

heating of MSRO surface• Monte-Carlo method was used for calculation of spectral

signature of MSRO



102

Validation of the RGD/CFD Model

z, cm

r,cm

0 1 2 3 4 5 6 7 8 9 10 11 120

1

2

3

4

5

6

7

8

9Vx

9.67E-019.32E-018.98E-018.63E-018.29E-017.94E-017.60E-017.25E-016.91E-016.56E-016.22E-015.87E-015.53E-015.18E-014.84E-014.49E-014.15E-013.80E-013.46E-013.11E-012.77E-012.42E-012.08E-011.73E-011.39E-011.04E-016.97E-023.52E-026.69E-04

-3.38E-02

Reduced model of Pathfinder studied in experiments, and numerically predicted flowfield.

Hollis B.R., and Perkins J.N., High-Enthalpy Aero-thermodynamics of a Mars Entry Vehicle. Part 2: Experimental Results, Journal of Spacecraft and Rockets, Vol.34, No.4, pp.449-456, 1997



103


Hollis B.R., and Perkins J.N., High-Enthalpy Aero-thermodynamics of a Mars Entry Vehicle. Part 2: Experimental Results, Journal of Spacecraft and Rockets, Vol.34, No.4, pp.449-456, 1997

S/Rb

Qw

,W/c

m2

0 0.5 10

100

200

300

400

500

600

700

800

900

1000

Measured and numerically predicted (solid line) convective

heat flux



104


Pathfinder:t=66 s

Numerically predicted flowfield

z, cm

r,cm

0 100 200 300 400 500 600 7000

100

200

300Vx

9.25E-018.70E-018.15E-017.60E-017.05E-016.50E-015.95E-015.40E-014.85E-014.30E-013.75E-013.20E-012.65E-012.10E-011.55E-011.00E-014.55E-02

-9.50E-03-6.45E-02-1.20E-01



105


Milos F.S. and Chen Y.-K., et.al. Mars Pathfinder Entry Temperature Data,

Aerothermal Heating, and Heatshield Material Response, Journal of Spacecraft and Rockets.

Vol.36, No.3, 1999

Paterna D., Monti R., et.al. Experimental and Numerical Investigation of

Martian Atmosphere Entry, Journal of Spacecraftand Rockets. Vol.39, No.2, 2002

S, cm

Qw

,W/c

m**

2

0 25 50 75 1000

25

50

75

100

125

150

Present computation - Fully CatalyticPaterna et al. - Fully CatalyticMilos et al. - Fully CatalyticMilos et al. - Non CatalyticPaterna et al. - Non CatalyticPresent computation - Non Catalytic

Comparison of numerical results on convective heat

fluxes along the Mars Pathfinder forebody at

t = 66 s



106

Initial grid: MSRO

Z, cm

R,c

m

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600



107

Intermediate grid: MSRO

z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

200

400

600



108

Final grid: MSRO

z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

200

400

600



109

Numerical simulation results: MSRO, Point No.1

z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800 T7.00E+036.80E+036.61E+036.41E+036.21E+036.01E+035.82E+035.62E+035.42E+035.23E+035.03E+034.83E+034.64E+034.44E+034.24E+034.04E+033.85E+033.65E+033.45E+033.26E+033.06E+032.86E+032.66E+032.47E+032.27E+032.07E+031.88E+031.68E+031.48E+031.29E+031.09E+038.91E+026.94E+024.97E+023.00E+02

Temperature distribution. Trajectory point No.1.Pseudo-catalytic surface

z, cmr,

cm0 100 200 300 400 500 600 700 800 900 1000

0

100

200

300

400

500

600

700

800 Pres1.00E+008.73E-017.63E-016.66E-015.82E-015.08E-014.44E-013.87E-013.38E-012.96E-012.58E-012.25E-011.97E-011.72E-011.50E-011.31E-011.15E-011.00E-018.73E-027.63E-026.66E-025.82E-025.08E-024.44E-023.87E-023.38E-022.96E-022.58E-022.25E-021.97E-021.72E-021.50E-021.31E-021.15E-021.00E-02

Pressure distribution. Trajectory point No.1.Pseudo-catalytic surface



110


Temperature distribution. Trajectory point No.2. Pseudo-catalytic surface

Pressure distribution. Trajectory point No.2. Pseudo-catalytic surface

z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700


z, cmr,

cm0 100 200 300 400 500 600 700 800 900 1000

0

100

200

300

400

500

600

700




111




z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700


z, cmr,

cm0 100 200 300 400 500 600 700 800 900 1000

0

100

200

300

400

500

600

700




112




z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700


z, cm

r,cm

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700




113

Mass fraction of species

Non-catalytic surface Pseudo-catalytic surface



114

Numerical simulation results: MSRO, Point No.1, CO2 mass fraction

Non-catalytic surface

z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2

9.66E-019.32E-018.99E-018.65E-018.31E-017.97E-017.63E-017.30E-016.96E-016.62E-016.28E-015.94E-015.61E-015.27E-014.93E-014.59E-014.25E-013.91E-013.58E-013.24E-012.90E-012.56E-012.22E-011.89E-011.55E-01

Mass fraction of CO2. Trajectory point No.1. Non-catalytic surface

z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2


Mass fraction of CO2. Trajectory point No.1. Pseudo-catalytic surface



115





z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2


z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2




116





z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2


z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2




117





z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2


z, cm

r,cm

0 250 500 750 10000

100

200

300

400

500

600CO2




118

Numerical simulation results: convective heating

S, cm

Qw

,W/c

m**

2

0 100 200 300 40010-3

10-2

10-1

100

101

102

Convective heat flux along the MSRO surface for the 2nd trajectory point (non-catalytic surface); the

first mixture

S, cm

Qw

,W/c

m**

2

0 100 200 300 40010-3

10-2

10-1

100

101

102

Convective heat flux along the MSRO surface for the 2nd trajectory point (pseudo-catalytic surface); the first mixture


X, cm

Y,c

m

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

1

2

3

4

5


119

Numerical simulation results: radiative heating

Point number

Qra

d,W

/cm

2

20 40 60 80 100 120 140 1600

0.5

1

1.5

2

2.5

3

1234

Point numberQ

rad,

W/c

m2

20 40 60 80 100 120 140 1600

0.5

1

1.5

2

2.5

3

1234

Total radiation flux on the MSRO surface. Trajectory point No.1-4. Non-catalytic (left) and pseudo-catalytic (right) surface.

Ng=91, Nm=100, Nθ=91, Nϕ=100



120

Numerical simulation results: MSRO Group radiation fluxes

Pseudo-catalytic surface

Wavenumber, 1/cm103 104 10510-7

10-6

10-5

10-4

10-3

10-2

12345

Spectral radiation flux, W*cm/cm**2

1: R1surf= 0.114E+02 Z1surf= 0.107E+022: R2surf= 0.235E+02 Z2surf= 0.128E+023: R3surf= 0.452E+02 Z3surf= 0.208E+024: R4surf= 0.122E+03 Z4surf= 0.647E+025: R5surf= 0.569E+01 Z5surf= 0.201E+03

Spectral radiation fluxes at some points of the MSRO surface. Trajectory point No.1. Pseudo-catalytic surface. Ng=91, Nm=100

Wavenumber, 1/cm103 104 10510-7

10-6

10-5

10-4

10-3

10-2

12345



Spectral radiation fluxes at some point on the MSRO surface. Trajectory point No.2. Pseudo-catalytic surface. Ng=91, Nm=100



121

Numerical simulation results: MSRO Group radiation fluxes

Pseudo-catalytic surface

Spectral radiation fluxes at some points of the MSRO surface. Trajectory point No.3. Pseudo-catalytic surface. Ng=91, Nm=100

Spectral radiation fluxes at some point on the MSRO surface. Trajectory point No.4. Pseudo-catalytic surface. Ng=91, Nm=100

Wavenumber, 1/cm103 104 10510-7

10-6

10-5

10-4

10-3

10-2

12345



Wavenumber, 1/cm103 104 10510-7

10-6

10-5

10-4

10-3

10-2

12345





122

• Numerical simulation results on radiative heating of a surface of space vehicle MSRO at four trajectory points for opposite assumptions concerning surface catalicity are presented

• It is shown that radiation heat flux to back surface of enteringspace vehicle MSRO reaches value of ~ 1 W/cm2

• The radiation fluxes are formed generally by emissivity of CO2and CO molecules.



123

Aerothermodynamics of re-entry space vehicleH=59 km, V=10.6 km/s

X

Y

0 100 200 3000

100



124

Wavenumber, 1/cm

Spe

ctra

lrad

iatio

nflu

x,W

*cm

/cm

**2

50000 100000 15000010-5

10-4

10-3

10-2

10-1

100

101

500 000 spectral points

Line-by-line calculation of radiating heating:H=59 km, V=10.6 km/s



125

CFD-MODEL VERIFICATION BY DATA OF FLIGHT EXPERIMENT FIRE –II

FIRE II trajectory conditions

Time(sec)

Altitude(km)

Velocity(km/s)

Density(kg/m3)

T∞ (K)

1634 76.42 11.36 3.72 10-5 195

1637.5 67.05 11.25 1.47 10-4 228

1640.5 59.26 10.97 3.86 10-4 254

1643. 53.04 10.48 7.8 10-4 276

1645 48.37 9.83 1.32 10-3 285



126


6.00 8.00 10.00 12.00Vs,km/s

40.00

50.00

60.00

70.00

80.00

H,k

m

Time(sec)

Altitude(km)

Velocity(km/s)

Density(kg/m3)

T∞(K)

1634 76.42 11.36 3.72 10-5 195

1637.5 67.05 11.25 1.47 10-4 228

1640.5 59.26 10.97 3.86 10-4 254

1643. 53.04 10.48 7.8 10-4 276

1645 48.37 9.83 1.32 10-3 285

The boundary of LTE disturbance on ionization for flight conditions (H-V coordinates).



127


x, cm

T,K

1 2 3 4 50

5000

10000

15000

20000

25000

Wavenumber, 1/cm

Spe

ctra

labs

orpt

ion

coef

ficie

nt,1

/cm

103 104 10510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

1

2

Spectral absorption coefficient (with atomic lines) in the point of maximal

temperature (1), and near to surface (2)



128


x, cm

T,K

1 2 3 4 50

5000

10000

15000

20000

25000

Wavenumber, 1/cm

Spe

ctra

lrad

iatio

nhe

atflu

x,W

cm/c

m**

2

103 104 10510-4

10-3

10-2

10-1

100

101

Spectral radiation flux (with radiation of atomic lines) incident upon the streamlined surface



129

On-going efforts

• Development of numerical simulation methods for radiation heat transfer problems for 3D curvilinear geometry

• Development of quantum-mechanics and quasi-classical models for prediction of radiative properties of hot gases in non-equilibrium conditions

• Development of quantum-mechanics models for calculation parameters of atomic lines

• Development of RGDSV-2 model for prediction of radiative and convective heating of space vehicles at different assumptions concerning catalytic and ablative properties of SV heat protection material

• Further verification of all calculation data (TC1, TC2, TC3,TC4)



130

Acknowledgments

The author thanks my friends and colleagues M. Capitelliand D.Giordano for invitation to take part in thelecture course and for many useful discussions


131


Part ITheoretical basis and general definitions

Part IINumerical simulations of aerospace RGD

applications

radiative gas dynamics ii - cnrusers.ba.cnr.it/imip/cscpal38/erice/lectures/surzhikov-ii.pdf ·...

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