Rarefied gas dynamics, which has been explored for more than a century, studies device being considered Traditionally, it has been used to study high-speed highaltitude flow applications, such as space re-entry vehicles, and flows under ultra-low pressure (vacuum) conditions, where ??has a large value However, recent technological developments have enabled major advances in fabricating miniaturized devices such as micro-electro-mechanical systems (MEMS) Gas flow in micro-scale devices can suffer from rarefaction effects because the characteristic length of the device is so small that it is comparable to the mean free path of the gas, even under atmospheric conditions

Macroscopic Transport Equations for Rarefied Gas Flows

New approaches to modeling rarefied gas flow in the slip and transition regime

For any study of microflows it is crucial to understand the collision dynamics of the molecules involved. In the present work we will discuss the collision dynamics of chemically reacting hard spheres(CRHS). The inability of the classical smooth inelastic hard spheres, which have been extensively used in the past to study granular gases, to describe the collision dynamics of chemically reacting hard spheres has been discussed. Using the model of rough inelastic hard spheres as a motivation, a new model has been proposed for chemically reacting hard spheres which has been further used to derive certain useful velocity transformations. A methodology to compute the moments of the Boltzmann’s collision operator arising from chemical reactions, using Grad’s distribution function, has been discussed in detail. Finally explicit expressions for the rates of the reaction have been obtained which contain contributions from higher order moment and thus can be used for non-equilibrium chemically reacting flows.

On the moments of the Boltzmann’s collision operator arising from chemical reactions

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Numerical Investigations of Slip Effects on Rarefied Gas Flows by First and Second-Order Slip Boundaries

Gas-particle flows are used in many industrial applications in the energy, oil and gas fields, such as coal gasification, production of light hydrocarbons by fluid catalytic cracking, catalytic combustion and different treatments aiming to reduce or eliminate pollutants. The particle phase of a gas-particle flow is described by analogy to a granular gas, by finding an approximate solution of the kinetic equation in the velocity-based number density function. In the recent past, many studies have been published on the mathematical modeling of gas-particle flows using hydrodynamic models (e.g. Enwald et al. 1996), where Navier-Stokes-type equations are solved to describe the particle phase as a continuum, computing its stress tensor using moment closures from kinetic theory (Gidaspow 1994). These closures, however, are obtained assuming that the flow is dominated by collisions and near equilibrium, which corresponds to considering a very small particle-phase Knudsen number. This assumption leads to inconsistencies and erroneous predictions of physical phenomena when these models are applied to dilute fluid-particle flows, where rarefaction effects are not negligible. In these flows, the wall Knudsen layers extend inside the bulk of the fluid, and cannot be accounted for with the simple addition of partial-slip boundary conditions. Recently Desjardin et al. (2008) showed that two-fluid models are unable to correctly capture particle trajectory crossing, seriously compromising their ability to correctly describe any velocity moment for finite Stokes numbers. These authors clarified that the particle segregation captured by two-fluid models for finite Knudsen numbers is artificially high due to their mathematical formulation, which leads to the formation of delta-shocks. In order to overcome these shortcomings, Fox (2008) developed a third-order quadrature-based moment method for dilute gas-particle flows, which has been successfully coupled to a fluid solver to compute dilute and moderately dilute gas-particle flows by Passalacqua et al. (2010) in two dimensions. These authors validated their model against Euler-Lagrange and two-fluid simulations. In this work, the fully coupled quadrature-based fluid-particle code described in Passalacqua et al. (2010) is applied to simulate turbulent gas-particle flow in the riser described by He et al. (2009), using a three-dimensional configuration. This application shows the predictive capabilities and the robustness of the quadrature-based moment method to predict the behavior of gas-particle flows in accordance with experiments (He et al. 2009).

background or methods

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1009&context=cbe_conf

Numerical simulation of turbulent gas-particle flow in a riser using a quadrature-based moment method

The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterise dissipation and best interpreted as effective diffusivities, or, in case of heat conduction, as effective heat conductivities of the material.

Spectral properties of dissipation

/pdf/macroscopic-transport-equations-for-rarefied-gas-flows-36pljxyd8k.pdf

Macroscopic Transport Equations for Rarefied Gas Flows

Citations

New approaches to modeling rarefied gas flow in the slip and transition regime

On the moments of the Boltzmann’s collision operator arising from chemical reactions

Numerical Investigations of Slip Effects on Rarefied Gas Flows by First and Second-Order Slip Boundaries

Numerical simulation of turbulent gas-particle flow in a riser using a quadrature-based moment method

Spectral properties of dissipation

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