Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows

Munafò, Alessandro; Panesi, Marco; Magin, Thierry

doi:10.1103/physreve.89.023001

Cited by 93 publications

(54 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The use of a spherical coordinate system in the integrals over u, u , ω and ω in Eqs. (37)- (39) gives, after some algebra, the thesis. As an example, the integral over u in Eq.…”

Section: ) Of the Partial Elastic And Inelastic Collision Operators (mentioning

confidence: 99%

“…Since in the definition provided by Eqs. (37)- (39) no assumption is made on the differential cross-section, anisotropic interactions can also be taken into account.…”

Section: Remarkmentioning

confidence: 99%

“…To the authors' knowledge, the proposed numerical method is the first deterministic spectral method for the full non-linear Boltzmann equation for a multi-energy level gas. This work is part of a broad effort that aims at developing new models based on Kinetic Theory and applying them to macroscopic scale for aerospace applications [36][37][38][39].…”

mentioning

confidence: 99%

See 2 more Smart Citations

A spectral-Lagrangian Boltzmann solver for a multi-energy level gas

Munafò

Haack

Gamba

et al. 2014

Journal of Computational Physics

View full text Add to dashboard Cite

In this paper a spectral-Lagrangian method is proposed for the full, non-linear Boltzmann equation for a multi-energy level gas typical of a hypersonic re-entry flow. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and relaxation) are accounted for. The formulation developed can also be used for the case of a gas mixture made of monatomic gases without internal energy (where only elastic collisions occur). The advantage of the spectral-Lagrangian method lies in the generality of the algorithm in use for the evaluation of the elastic and inelastic collision operators, as well as the conservation of mass, momentum and energy during collisions. The latter is realized through the solution of constrained optimization problems. The computational procedure is based on the Fourier transform of the partial elastic and inelastic collision operators and exploits the fact that these can be written as weighted convolutions in Fourier space with no restriction on the cross-section model. The feasibility of the proposed approach is demonstrated through numerical examples for both space homogeneous and in-homogeneous problems. Computational results are compared with those obtained by means of the DSMC method in order to assess the accuracy of the proposed spectral-Lagrangian method.

show abstract

“…The use of a spherical coordinate system in the integrals over u, u , ω and ω in Eqs. (37)- (39) gives, after some algebra, the thesis. As an example, the integral over u in Eq.…”

Section: ) Of the Partial Elastic And Inelastic Collision Operators (mentioning

confidence: 99%

“…Since in the definition provided by Eqs. (37)- (39) no assumption is made on the differential cross-section, anisotropic interactions can also be taken into account.…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

A spectral-Lagrangian Boltzmann solver for a multi-energy level gas

Munafò

Haack

Gamba

et al. 2014

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…[27][28][29][30][31][32] However the applicability of such approaches to CFD is restricted due to the large number of equations to be solved and to the huge number of kinetic processes to be modeled.…”

Section: Vibration-chemistry-vibration Couplingmentioning

confidence: 99%

Modeling of Non-equilibrium Plasmas in an Inductively Coupled Plasma Facility

Zhang

Lani

Chew³

et al. 2014

45th AIAA Plasmadynamics and Lasers Conference

View full text Add to dashboard Cite

This paper presents the results of the numerical simulation of plasma flows inside the torch of the VKI inductively coupled plasma facility. The main purpose of this work is the parametric investigation of thermo-chemical non-equilibrium effects on the plasma jet at different operating pressures ranging from 3 to 15 kPa. The test gas is an ionized air mixture including eleven species. While the induced electric field inside the torch is computed by solving Helmholtz induction equation, a standard two-temperature formulation is used to account for non-equilibrium effects. In particular, the present analysis assesses the impact of different models for chemical kinetics and for vibration-chemistry-vibration coupling on the resulting plasma field. Solutions previously computed assuming LTE conditions are used as a reference for our benchmarks. Considerable differences on both the induced electric and temperature field are highlighted for the lower pressure cases.

show abstract

“…In recent time a substantial advancement in the numerical solution of these equations has been reached including calculations of collisional cross sections and roto-vibrational transition probabilities [4][5][6][7][8][9][10][11]. The interesting coarse grain model has very recently been derived from detailed ro-vibrational state-to-state models in [12]. However, the use of the accurate data obtained within this approach for aerodynamic problems is hardly possible because it requires to consider tens of thousands of state-to-state energy transitions and chemical reactions.…”

Section: Introductionmentioning

confidence: 99%