Nonequilibrium Processes and Plasma Radiation in ...users.ba.cnr.it/imip/cscpal38/Erice/LECTURES/LinodaSilva.pdfNonequilibrium Processes and Plasma Radiation in Hyperbolic Atmospheric

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Nonequilibrium Processes and Plasma Radiation inHyperbolic Atmospheric Entry Flows

M. Lino da Silva, V. Guerra, J. Loureiro

(1) Centro de Fisica de Plasmas, Instituto Superior Tecnico, Lisboa, Portugal

3 August 2005

Mario Lino da Silva Nonequilibrium Processes & Plasma Radiation

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1 Physical-Chemical-Radiative Problems of HyperbolicAtmospheric Entries

2 Example for Radiative Calculations: Mars Atmospheric Entries

3 Nonequilibrium Excitation Processes in Shock-Heated EntryFlows

4 Concluding Remarks and Perspectives


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Hyperbolic Atmospheric EntriesMars Atmospheric Entries Radiation

Nonequilibrium Processes in Shock-Heated FlowsConclusions & Perspectives

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Spacecraft Atmospheric Entries from Outer Space

Hyperbolic entry trajectories at v > 10km/s (From Mars v = 11 km/s).Space-Shuttle entries from orbit(parabolic trajectory) at v < 7 km/s.Plasma radiation important for overallheat fluxes calculation at v > 5 km/sExtreme nonequilibrium conditionsbehind the strong shock-wave,Ttr � Tvib, Ttr > 10, 000 K














Estimation of the Spacecraft Aerodynamic and Thermal(Convective + Radiative) Loads

Gas radiative properties determined by thewavelength-dependent emission and absorption coefficients:

εul = NuAul∆Eul

αlu = NlBlu∆Eul

Besides the transition radiative properties (Aul ,Blu), the statepopulations need to be known (Nu,Nl), usually in astate-to-state approach

Dissociation (endothermic) and recombination (exotermic)chemical reactions affect convective heating loads and alsoneed to be treated in the state-to-state approach






εul = NuAul∆Eul

αlu = NlBlu∆Eul








εul = NuAul∆Eul

αlu = NlBlu∆Eul








εul = NuAul∆Eul

αlu = NlBlu∆Eul








εul = NuAul∆Eul

αlu = NlBlu∆Eul






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Simulation of Atmospheric Entry Radiation

Two different issues: calculation of transition probabilities(quantum mechanics models) and calculation of quantumstates populations (collisional-radiative models)

Calculation of transition probabilities can now be routinelycarried for most chemical species

No complete collisional-radiative model exists for thesimulation of atmospheric entry flows. Most simulationsassume Boltzmann equilibrium conditions

Additional issue (not discussed here): radiation transport →different numerical models available




























Atmospheric Entry Radiation Research Activities at IST

Line-by-Line numerical code SPARTAN: Simulation ofPlasmA Radiation in ThermodynAmic Nonequilibrium

63 atomic and molecular bound-bond, bound-free(Photodissociation, Photoionization, Photodetachment), andfree-free (Bremsstrahlung) transitions from C, N, and Ocontaining species (Earth & Mars)

Online Gas & Plasma Radiation Database (GPRD) athttp://cfp.ist.utl.pt/radiation for providing the scientificcommunity with a database for molecular radiation


















Radiative Transition Probabilities Calculation

Systematic calculation of thetransition probabilities Aul

by an ”ab-initio” method

Reconstruction of themolecular potentials usingthe RKR method andresolution of the Schrodingerequation

Example for the CN Violet System




Spectral Simulation of the Equilibrium Radiative Propertiesof a Martian-Type Plasma

High resolution calculation of emission and absorptioncoefficients for a 100A–100µm spectral range at 1000, 5000,and 10000 K using the full spectroscopic database (49transitions)

30 min calculation time on a laptop for a spectrum of∼ 105 − 106 points




Spectral Simulation of the Equilibrium Radiative Propertiesof a Martian-Type Plasma

High resolution calculation of emission and absorptioncoefficients for a 100A–100µm spectral range at 1000, 5000,and 10000 K using the full spectroscopic database (49transitions)

30 min calculation time on a laptop for a spectrum of∼ 105 − 106 points




Radiative properties at 1000 K

Emission coefficient Absorption coefficient














Equilibrium Radiation of a Martian-type Gas at 4300 Pafor the Temperature Range 200-10000 K

Selected pressure of 4300 Pa which corresponds to thepost-shock pressure in a aerocapture manoeuver in Marsatmosphere

Calculation of the gas optically thin radiative power

Calculation of the individual contribution of each system tothe overall radiative power


















Quantitative Radiative Properties of a Martian-type Gas at4300 Pa for the Temperature Range 200-10000 K

Optically thin radiative power of a Martian-type gas at4300 Pa, in the temperature range 200-10000 K

Contribution from each atomic and molecular system




Selection of an Appropriate Spectral Database

For equilibrium conditions, few atomic and molecular systemscontribute for overall radiative flux

Not to be extrapolated to nonequilibrium conditions! (evenfor Boltzmann equilibrium of the flow, e.g. C2 Swan Bands).Also for non-optically thin gas must account for absorbingtransitions, e. g. O2 Schumann–Runge

Must have the most reduced set without losing precision(lower number of calculated lines)

More difficult task in strong nonequilibrium conditions! (e. g.behind shock-waves)




























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Challenges Associated to the Development of aNonequilibrium Entry Flow Model

Definition of a self-consistent rate equations set valid inatmospheric entry conditions

Also computational issues! Must retain a reduced butaccurate set of rate equations




Challenges Associated to the Development of aNonequilibrium Entry Flow Model

Definition of a self-consistent rate equations set valid inatmospheric entry conditions

Also computational issues! Must retain a reduced butaccurate set of rate equations




Kinetic Scheme Features for Entry Flows

Different processes behind theshock-wave lead to the formationof an entry plasma

Dissociation, ionization processeswith Etr−rot � Evib,Eel

V–E Excitation of molecularelectronic levels will contribute forgas radiation and Penningionization(N2(A)+N2(a’)�N2(X)+N+

2 (X))

Maxwellian EEDF may be assumedas the electrons are thermalized








2 (X))









2 (X))









2 (X))





Reproduction of Inflight Flow Conditions in Ground-TestFacilities

Shock-tube facilities typical offorebody flows, closer to entryflow conditions (Etr > Eel) butshort test times (<1 ms) andtypically with v<10 km/sPlasma facilities typical ofafterbody flows and fartherfrom entry flow conditions(Etr < Eel) but virtuallyunlimited test times

Simulation of entry-like flows in different ground-testfacilities




Reproduction of Inflight Flow Conditions in Ground-TestFacilities

Shock-tube facilities typical offorebody flows, closer to entryflow conditions (Etr > Eel) butshort test times (<1 ms) andtypically with v<10 km/sPlasma facilities typical ofafterbody flows and fartherfrom entry flow conditions(Etr < Eel) but virtuallyunlimited test times

Simulation of entry-like flows in different ground-testfacilities




Simulation of Dissociation Processes Behind HyperbolicShock-Waves

Translational Temperatures up to 100,000 KV–T & V–V–T dissociation processes simulated by the FHOmodel

Model more accurate than FOPT models, and compares wellwith more complex mehods (QCT – Billing, Lagana)

Model developed in the 60’s (Rapp, Kerner, Treanor,Zelechow) and extended by Adamovich in the 90’s

























The Forced Harmonic Oscillator Model

V–T probabilities for collinear atom-diatom non-reactivecollisions (Kerner:1958) & (Treanor:1965)

P(i → f , ε) = i!f !εi+f exp (−ε)

∣∣∣∣∣n∑

r=0

(−1)r

r !(i − r)!(f − r)!εr

∣∣∣∣∣2

,

n = min(i, f ).

V–V–T probabilities for collinear diatom-diatom collisions(Zelechow:1968)

P(i1, i2 → f1, f2, ε, ρ) =

∣∣∣∣∣∣n∑

g=1

(−1)(i12−g+1) × Ci12g,i2+1C

f12g,f2+1

ε12

(i12+f12−2g+2)exp (−ε/2)

×√

(i12 − g + 1)!(f12 − g + 1)! exp [−i(f12 − g + 1)ρ] ×n−g∑l=0

(−1)l

(i12 − g + 1− l)!(f12 − g + 1− l)!l!εl

∣∣∣∣∣∣2

,

i12 = i1 + i2, f12 = f1 + f2,

n = min(i1 + i2 + 1, f1 + f2 + 1).




Assumptions for Shock-Heated Flows

V–V–T reaction rates for the 59 levels of: N2: 594 ∼ 107

⇒ P(i1, all → f1, all, ε, ρ) = P(i1 → f1, ε). (Adamovich:1995)

Dissociation occurs for a transition to a vibrational levelv > 59 (quasibound level)

P(i →, ε) = P(i → vqbound , ε) · Pdecay ,

Pdecay ∼ 1




Assumptions for Shock-Heated Flows

V–V–T reaction rates for the 59 levels of: N2: 594 ∼ 107

⇒ P(i1, all → f1, all, ε, ρ) = P(i1 → f1, ε). (Adamovich:1995)

Dissociation occurs for a transition to a vibrational levelv > 59 (quasibound level)

P(i →, ε) = P(i → vqbound , ε) · Pdecay ,

Pdecay ∼ 1




Level Energies Calculations

Inaccurate determinations oflevels energy separationsnear and above thedissociation limit willprovide inaccurate transitionprobabilities

Polynomial expansionsprevent the calculation ofquasibound vibrational levelsvqbound > 81 Vibrational levels energies for N2




Level Energies Calculations

Inaccurate determinations oflevels energy separationsnear and above thedissociation limit willprovide inaccurate transitionprobabilities

Polynomial expansionsprevent the calculation ofquasibound vibrational levelsvqbound > 81 Vibrational levels energies for N2




Possible Simplifications

Asymptotical expressions by Adamovich simplify calculationsand allow for rotation effects

P(5 → 4)

P(i → f , ε) = J2s (2√

nsε)

P(15 → 30)

J2s (2√

nsε) ∼= (ns )s

(s!)2εs exp

(−2nsεs+1

)No approximations used here. Variable precision arithmetics inMATLAB (64 digits numbers) used in calculations




Possible Simplifications

Asymptotical expressions by Adamovich simplify calculationsand allow for rotation effects

P(5 → 4)

P(i → f , ε) = J2s (2√

nsε)

P(15 → 30)

J2s (2√

nsε) ∼= (ns )s

(s!)2εs exp

(−2nsεs+1

)No approximations used here. Variable precision arithmetics inMATLAB (64 digits numbers) used in calculations




Validation of the FHO model

Comparison with experimentaldata and QCT calculations byBilling show very goodagreement in general

Failure of the FHO model fornear-resonant transitions atlower temperatures (notimportant for shock-heatedflows)

Near 100,000K reaction ratesachieve a plateau

Single-quantum V–V rates for N2–N2 (0, 1→1, 0)and (0, 1→20, 19) transitions and O2–N2 (0, 1→1,

0) transitions. − and −−, FHO model. ×,calculations of Billing:1979 for N2–N2. �,

interpolation of experimental data for N2–O2 (1,0→0, 1), Taylor:1969
























Simulation of Simplified Shock Geometries for Nitrogenflows

V–T reaction rate database calculated up to Ttr = 100, 000Kfor 100 levels of N2

Simulation of a Shock at an altitude of 76 km and fixedtranslational temperatures of 1,000, 10,000 and 100,000 K.




Simulation of Simplified Shock Geometries for Nitrogenflows

V–T reaction rate database calculated up to Ttr = 100, 000Kfor 100 levels of N2

Simulation of a Shock at an altitude of 76 km and fixedtranslational temperatures of 1,000, 10,000 and 100,000 K.




Shock Simulation at 1000 K

Reaction Rates Database at 1000 K Time Evolution of the VDF














Evolution of the Molecular Dissociation at Different ShockTemperatures

Dissociation times range frommore than 1 s for T ≤ 5, 000Kto 1 ns for T = 100, 000KFor lower temperatures,“ladder-climbing” phenomenaenhance dissociation after acertain incubation time

At higher temperatures,(T ≥ 50, 000K) dissociationproceeds equiprobably from allthe vibrational levels

Time evolution of N2 dissociation at different shocktemperatures


















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Conclusions

Development of radiation databases is a straightforward task,but needs extensive validations

Developed state-to-state models need to be valid for the mostextreme hyperbolic shock-waves. Importance of multiquantumtransitions

Computation time issues remain determinant as they preventfull-use of line-by-line calculations and state-to-state models.The errors induced by the used approximations (Boltzmannequilibrium, band models) remain unknown




Conclusions







Conclusions







Perspectives

V–T dissociation models should include effects of molecularrotation

V–E processes need more theoretical developments. Onlyavailable experimental data obtained for gas-dischargeapplications with Ttr ∼ 300KRadiation re-absorption may be important for hyperbolic flows(see Park 2004 for Galileo probe entry simulations)




Perspectives






Perspectives




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Nonequilibrium Processes and Plasma Radiation in ...users.ba.cnr.it/imip/cscpal38/Erice/LECTURES/LinodaSilva.pdfNonequilibrium Processes and Plasma Radiation in Hyperbolic Atmospheric