Reduction of State-to-State Kinetics to Macroscopic Models in Hypersonic Flows

Colonna, G.; Armenise, I.; Bruno, D.; Capitelli, M.

doi:10.2514/1.18377

Cited by 100 publications

(67 citation statements)

References 16 publications

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“…The most general thermodynamic nonequilibrium model is the state to state model where each internal state of a molecule is independent and considered as a separate species [28,29,30,31,32,33,34,35,36,37]. When there are partial equilibria between some of these states, species internal energy temperatures can be defined and the complexity of the model is correspondingly reduced [30,31,32,33,34,35,36,37].…”

Section: A Multi-temperature Kinetic Frameworkmentioning

confidence: 99%

Relaxation of internal temperature and volume viscosity

Bruno

Giovangigli

2011

Physics of Fluids

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We investigate the relaxation of internal temperature and the concept of volume viscosity in nonequilibrium gas models derived from the kinetic theory. We first investigate a nonequilibrium gas model with two temperatures-translational and internal-where the volume viscosity is absent. We establish that, in a relaxation regime, the temperature difference becomes proportional to the divergence of the velocity fields and define a nonequilibrium, multitemperature, volume viscosity coefficient. We next analyze the convergence of the two temperature model towards the one temperature model when the relaxation is fast. We then investigate a nonequilibrium two temperature gas model with a fast and a slow internal energy mode. We establish that, in a relaxation regime, there are four contributions to the volume viscosity, namely the fast internal mode volume viscosity, the slow internal mode volume viscosity, the relaxation pressure and the perturbed source term. In the thermodynamic equilibrium limit, the sum of these four terms converges toward the one-temperature two-mode volume viscosity. We finally perform Monte Carlo simulations of spontaneous fluctuations near thermodynamic equilibrium. The numerical results obtained from the Boltzmann equation are compared to the predictions of the one and two temperature fluid models and the agreement between theory and calculations is complete.

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Section: A Multi-temperature Kinetic Frameworkmentioning

confidence: 99%

Relaxation of internal temperature and volume viscosity

Bruno

Giovangigli

2011

Physics of Fluids

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“…The global rate coefficient is therefore the equivalent or effective rate coefficient reflecting the behaviour of the species X n [12,[28][29][30][31][32][33]. This rate coefficient is a measurement of the net variation rate of X n due to the complex behaviour of the excited states.…”

Section: Global Rate Coefficient Definitionmentioning

confidence: 99%

“…In this section, an innovative reduced kinetic model is presented and firstly applied to pure N 2 and O 2 system [12,44] and to NO formation in air in recombination conditions [45,46]. To build this model we have applied an inductive approach, starting from a detailed analysis of the STS time evolution of the vibrational distributions and gas composition in conditions similar to those met in different fluid dynamic systems.…”

Section: Two-level Distribution (Tld) Modelmentioning

confidence: 99%

“…In the last years, STS vibrational kinetics have been developed and applied to 1D high enthalpy flows, such as boundary layer [1,2], nozzle expansion [3][4][5][6] and shock wave [3][4][5][7][8][9][10][11]. These models give a very accurate insight of the behavior of chemical processes and predict, for example, in recombination regimes, the overpopulation of the tail of vibrational distributions due to preferential pumping of high-lying vibrational levels [12]. Unfortunately, the systematic implementation of STS is difficult due to both the lack of data for rate coefficients for each internal level and to long computational times, preventing the use of these models in higher (2D-3D) dimensional codes.…”

Section: Introductionmentioning

confidence: 99%

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Reduction of State-to-State to Macroscopic Models for Hypersonics

Bourdon¹,

Annaloro²,

Bultel³

et al. 2014

TOPPJ

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Four different types of macroscopic models developed for the vibration-chemistry coupling in nonequilibrium flows for re-entry applications are presented. First, using an approach based on nonequilibrium thermodynamics, global rate coefficients of dissociation of N 2 and O 2 under parent molecular or atomic impact and backward molecular recombination are determined. Then a Two-Level Distribution (TLD) model is developed, in which a relaxation equation for vibrational temperature is solved as in the case of multi-temperature models but with the simultaneous solution of a kinetic equation, as in the case of state-to-state models, but only for the last vibrational level. In a third approach, a multiinternal temperature model is presented to describe accurately the vibrational distribution function in using several groups of levels, within which the levels are assumed to follow a Boltzmann distribution at an internal temperature of the group. This multi-internal temperature model allows us to describe accurately the vibrational energy relaxation and dissociation processes behind a strong shock wave. Finally, a rovibrational collisional coarse-grain model is developed to reduce a detailed rovibrational mechanism for the internal energy excitation and dissociation processes behind a strong shock wave in a nitrogen flow.

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“…10 A first attempt to build new macroscopic models has been studied in Ref. 13, where chemical rates were considered as not dependant on the vibrational temperature, but on other parameters, such as the gas composition. The most difficult problem in state-to-state modelling is the lack of kinetic data (rates for selected states).…”

mentioning

confidence: 99%

Consistent Comparison of Macroscopic and State-to-State Kinetics in Hypersonic Flows

Colonna¹,

D’Ambrosio

Capitelli

2007

39th AIAA Thermophysics Conference

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We present a comparison of numerical results in strongly expanding hypersonic flows that have been obtained using state-to-state and macroscopic thermochemical models. The macroscopic model, which includes direct cross coupling between chemical and vibrational relaxation, has been derived directly from the state-to-state kinetic rates. This makes the comparison the most consistent possible, as differences cannot be ascribed to original discrepancies in the used rates. The comparison is conducted in a N2-N system using the test conditions of the EAST facility nozzle experiment, for which experimental data are available. Nomenclature

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Reduction of State-to-State Kinetics to Macroscopic Models in Hypersonic Flows

Cited by 100 publications

References 16 publications

Relaxation of internal temperature and volume viscosity

Relaxation of internal temperature and volume viscosity

Reduction of State-to-State to Macroscopic Models for Hypersonics

Consistent Comparison of Macroscopic and State-to-State Kinetics in Hypersonic Flows

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