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State to state kinetics in 3D fluid-dynamic solver for expanding flows

L. Cutrone

Dept. of Aerothermodynamics, CIRA Italian Aerospace Research Center, Italy.

l.cutrone@cira.it

61st Course Hypersonic Meteoroid Entry Physics of the International School of Quantum Electronics Ettore Majorana Foundation and Centre for Scientific

Culture・ERICE | ITALY ・October 3 – 8, 2017

INTRODUCTION

In supersonic and hypersonic flows, thermal and chemical non-

equilibrium is one of the fundamental aspect to be taken into account

for plasma characterization

Classical multi-temperature model based on Park’s approach

completely exclude the non-Boltzmann character of the vibrational

distributions that strongly influence the rates of chemical processes

A State-to-state model for kinetics has been implemented in a CFD

code for the 3D simulation of an high enthalpy flow

OUTLINE

State to state kinetics in 3D fluid-dynamic solver for expanding flows

Governing Equations

Macroscopic vs StS modeling

Numerical issues

3D flow in expanding nozzle

Conclusions

GOVERNING EQUATIONS

4

x x

inv vis

V S V V

SymWdV F ndS A A dV dV

t r

1 1. .sNW u v w E R R

Reynolds Averaged Navier-Stokes (RANS) Equations for 2D, 2D-axi and 3D

flows for a mixture of gases in thermal and chemical non- equilibrium reads:

density

momentum

energy

chemical-related vars

where the unknowns are:

The dimension of the RANS equation system is then:

CH5N N

5

MACROSCOPIC MODELS

• Solution of NS -1 species partial densities

• Solution of NV molecular vibrational energies

#SPECIES Ns NV NCH

N2-N 2 1 1+1(VIB)

AIR 5 3 4+3(VIB)

1. CHEMICAL SYSTEM

6

MACROSCOPIC MODELS

2. CHEMICAL SCHEME• Chemical schemes for dissociations (DR), (e.g., Park88, CAST, etc)

#REACTIONS PARK93 STS-MACRO

N2-N 2 2

AIR 18 17

r = 1, Nr (number of reactions)

7

MACROSCOPIC MODELS

3. VIBRATIONAL MODEL• Vibrational models for vibration-translation (VT) transfer (e.g., Landau-

Teller) and dissociation-vibration coupling (e.g. Marrone-Treanor, Park)

Strongly tuned on experiments !!

8

MISCOSCOPIC (StS) MODELS

• Solution of an equation for each vibrational level

1. CHEMICAL SYSTEM

i = 1, Ns (number of species) l = 1, Nlev(i) (number of levels for the i-th species)

corresponding to a chemical system of NSsts equivalent species

#SPECIES NSSTS

N2-N 69

AIR 116

9

NITR

OG

EN

# process type

01 N2(v) + N2 ↔ N2(v-1) + N2 VTm

02 N2(v) + N ↔ N2(v-Dv) + N VTa

03 N2(v) + N2(w-1) ↔ N2(v-1) + N2(w) VV

04 N2(v) + N ↔ 2N2 + NN2 dissociation

05 N2(v) + N2 ↔ 2N2 + N2

OX

YGEN

# process type

06 O2(v) + O2 ↔ O2(v-1) + O2 VTm

07 O2(v) + O2(w-1) ↔ O2(v-1) + O2(w) VTa

08 O2(v) + O ↔ O2(v-Dv) + O VV

09 O2(v) + O ↔ 2O2 + OO2 dissociation

10 O2(v) + O2 ↔ 2O2 + O2

MISCOSCOPIC (StS) MODELS

2. STATE-TO-STATE PROCESSES

• Kinetic schemes for internal processes (VV,VTm,VTa) and dissociations (DRm,DRa)

10

NITR

OG

EN O

XID

E

# process type

18 O2(v) + N ↔ NO + O ZELD

19 N2(v) + O ↔ NO + N ZELD

20 NO+ N ↔ N + O + N

NO dissociation

21 NO+ O ↔ N + O + O

22 NO+ NO ↔ N + O + NO

23 NO + O2 ↔ N + O + O2

24 NO + N2 ↔ N + O + N2

MIX

ED

# process type

11 N2(v) + O2 ↔ N2(v-1) + O2VTm

12 N2(v) + O ↔ N2(v-Dv) + O VTa

13 N2(v) + O ↔ 2N2 + O DRa

14 N2(v) + O2 ↔ 2N2 + O2DRm

15 O2(v) + N2 ↔ O2(v-1) + N2VTm

16 O2(v) + N2 ↔ 2O2 + N2DRm

17 O2(v) + N2(w-1) ↔ O2(v-2) + N2(w) VV

STATE-TO-STATE: PROCESSES

• Classical macroscopic models,

– ,

–

,

– ,

• State-to-state approach

11

#SPECIES NCH

N2-N 1+1(VIB)

AIR 4+3(VIB)

#REACTIONS PARK93 STS-MACRO

N2-N 2 2

AIR 18 17

#SPECIES NCH

N2-N 69

AIR 116

#REACTIONS VV VTm VTa DRm DRa TOT

N2-N 2211 67 2278 68 68 4692

AIR 4103 223 5546 229 183 10397

MACROSCOPIC vs MICROSCOPIC

• Finite volume approach

• Structured grids, complex multi-block 3D topologies

• Spatial integration: FDS, AUSM, with 2 order ENO

• Time integration: Euler explicit, with chemical-related source terms computed with an implicit procedure:

12

2

1 2

Ntt t jii i

j j

W t

W t

D

D

Jacobians are usually evaluated numerically, by calling the formula for the source

term N time per cell and iteration

Source calculation per cell and itz

MACRO STS

N2-N 14 4964

AIR 84 13800

CH5N N

STATE-TO-STATE: NUMERICS

13

2

1 2

Ntt t jii i

j j

W t

W t

D

D

CH

NS CH52

NS CH1 12 2

Ntt t j ji i

i i

j jj j

W WT t t

T W t W t

D

D D

Splitting the sum

Computed

analytically

once for

each cell

Computed analytically since

the temperature dependence

of the rates is known and

easily differentiable

The law of the mass action is a

simple function of the partial

densities: this Jacobian can be

analytically evaluated

CH5N N

prorea

CH CH

rea pro

fr br

1 1 1

ir irR N NN

k ki ir ir

r k kk k

k kM M

ANALYTICAL vs NUMERICAL

~100 times faster

STATE-TO-STATE: NUMERICS

14

Nitrogen expansion is studied in a Electric Arc Shock Tube at NASA Ames, having

a 10 cm diameter driven section and a 2D nozzle plug insert.

Optical measurements are available for:

Level population distributions

Vibrational temperature

h° (J/kg) p° (Pa) T° (K) (kg/m3) YN2

Case B 7.30E6 1.0335E7 5616 6.164 1

EAST Nozzle TEST CASE: conditions

15

CFD details

FULL 3D and 2D PLANAR configurations

o 270000 cell 3D grid (16blocks)

o 6500 cell 2D grid (3blocks)

Euler and Laminar Navier-Stokes

FDS 2nd order, multi-block

Chemical models:1. PARK’93 (only nitrogen path)

2 species 1 vibrational energies

2 reactions

Landau-Teller VT model

Harmonic oscillator hypothesis

2. CAST MACRO (only nitrogen path)2 species 1 vibrational energies

2 reactions

Based on STS data

An-harmonic oscillator hypothesis

3. FULL STS

EAST Nozzle TEST CASE: CFD details

16

3D FLOW FIELD

17

N-N2 LEVEL DISTRIBUTIONS

18

EFFECTS OF FLUID-DYNAMIC MODELS: 2D vs 3D

19

EFFECTS OF FLUID-DYNAMIC VISCOSITY

20

EFFECTS OF CHEMICAL MODEL: AXIAL PROFILE OF Tv

21

LEVEL POPULATION DISTRIBUTIONS

22

AXIAL DISTRIBUTION OF LEVELS

Determinevibrationaltemperature

Determineglobal rates

At the nozzle exit the tail of the vibrationaldistribution is populated by atom recombination.

23

RADIAL DISTRIBUTION OF LEVELS at exit

• The solution algorithm has been optimized so that full 3D state-to-state simulations begins to be feasible

• The chosen “programming” strategy and implementation allows for easy addition of further processes

• Although classical models (Park) provide a better agreement with experimental data, they are strongly tuned on the particular experiment, so

more effective test conditions have to be used to really highlight the real capabilities of such STS model

• Implement oxygen processes to perform a StS simulation with air

• Implement a fully implicit procedure for run acceleration

24

CONCLUSIONS AND FUTURE WORKS