Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Bisi, Marzia; Spiga, G.

doi:10.1515/caim-2017-0002

Cited by 3 publications

(5 citation statements)

References 31 publications

(58 reference statements)

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“…Nevertheless, at the end of the paper, we are able to derive the complete closure of the equations for number densities and also the explicit expression of first-order density corrections. The dependence of densities (and also of temperature, related to densities through the mass action law) on the divergence of macroscopic velocity is in agreement with other asymptotic closures of macroscopic equations obtained in different frames, as a single polyatomic gas with discrete energies or chemically reacting mixtures of monatomic gases, see for instance references [3,6].…”

Section: Conclusion and Final Remarkssupporting

confidence: 87%

“…where χ i and ξ i are defined in (6) and (19), respectively. Using constraints (42) and (43), from the above condition we get…”

Section: Bgk Model For the Reacting Mixturementioning

confidence: 99%

“…Recalling the definition of χ i given in (6), the integral of the distribution function f i appearing in (18) leads to…”

Section: • Auxiliary Number Densities N Imentioning

confidence: 99%

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A BGK model for reactive mixtures of polyatomic gases with continuous internal energy

Bisi¹,

Monaco²,

Soares³

2018

J. Phys. A: Math. Theor.

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In this paper we derive a BGK relaxation model for a mixture of polyatomic gases with a continuous structure of internal energies. The emphasis of the paper is on the case of a quaternary mixture undergoing a reversible chemically reaction of bimolecular type. For such a mixture we prove an Htheorem and characterize the equilibrium solutions with related mass action law of chemical kinetics. Further, a Chapman-Enskog asymptotic analysis is performed in view of computing the first-order non-equilibrium corrections to the distribution functions and investigating the transport properties of the reactive mixture. The chemical reaction rate is explicitly derived at the first order and the balance equations for the constituent number densities are derived at the Euler level.

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Section: Conclusion and Final Remarkssupporting

confidence: 87%

“…where χ i and ξ i are defined in (6) and (19), respectively. Using constraints (42) and (43), from the above condition we get…”

Section: Bgk Model For the Reacting Mixturementioning

confidence: 99%

See 1 more Smart Citation

A BGK model for reactive mixtures of polyatomic gases with continuous internal energy

Bisi¹,

Monaco²,

Soares³

2018

J. Phys. A: Math. Theor.

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“…if we assume (8). The parameter ν12 denotes a typical value for the collision frequency, t a typical time scale, x a typical length scale and N the typical number of particles in x3 .…”

Section: Dimensionless Formmentioning

confidence: 99%

“…In [15], with the proposed model there, they are able to fix the diffusion parameter and the Prandtl number but not the thermal diffusion parameter. There are also hydrodynamic limits for kinetic models dealing with reactive mixtures, and for mixtures related to the description of polyatomic molecules, see for example [8,7,22] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Using a kinetic BGK model to determine transport coefficients of gas mixtures

Klingenberg,

Pirner

2018

Preprint

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We consider a non reactive two component gas mixture. In a macroscopic description of a gas mixture we expect four physical coefficients characterizing the physical behaviour of the gases to appear. These are the diffusion coefficient, the viscosity coefficient, the heat conductivity and the thermal diffusion parameter in the Navier-Stokes equations. We present a Chapman-Enskog expansion of a kinetic model for gas mixtures by Klingenberg, Pirner and Puppo, 2017 that has three free parameters in order to capture three of these four physical coefficients. In addition, we propose several possible extensions to an ellipsoidal statistical model for gas mixtures in order to capture the fourth coefficient.

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Modeling of nitrogen and oxygen gas mixture with a novel diatomic kinetic model

2020

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Practical applications involve flows that often have more than one constituent. Therefore, the capability to model a gas mixture flow is important. Extending kinetic model equations of the Bhatnagar–Gross–Krook type from a single-species gas to multi-species gas mixtures presents a number of important challenges. This challenge is further pronounced when diatomic gas mixtures are considered due to the addition of internal energy modes. In this paper, a novel diatomic binary mixture model with separate translational, rotational, and vibrational temperatures is derived. The species drift-velocity and diffusion are considered by introducing separate species velocities and accounting for their relationship. The derivation is detailed as a logical build-up with a multi-step approach from a diatomic model for a single gas, known in the literature. Transport properties are obtained through the Chapman–Enskog type expansion. The diatomic mixture model is numerically evaluated for a gas mixture of nitrogen and oxygen. The model is validated against Monte Carlo results for normal shocks, showing good agreement for species density and temperature profiles. A parametric study demonstrates the variation in flow properties for different Mach numbers, vibrational collision numbers, and concentrations. Interesting results for the mixture properties are shown when the physics of the flow is discussed in greater detail. The effect of the different levels of vibrational excitation in the different species emphasizes the importance of modeling the flow as a mixture. The newly introduced diatomic gas mixture model demonstrates promising computational results for relevant applications.

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Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Cited by 3 publications

References 31 publications

A BGK model for reactive mixtures of polyatomic gases with continuous internal energy

A BGK model for reactive mixtures of polyatomic gases with continuous internal energy

Using a kinetic BGK model to determine transport coefficients of gas mixtures

Modeling of nitrogen and oxygen gas mixture with a novel diatomic kinetic model

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