The importance of random galilean transformation invariance in modelling dispersed particle flows

TL;DR

This paper emphasizes the significance of Random Galilean Transformation invariance in modeling dispersed particle flows, deriving a kinetic equation for particle phase space transport that respects this invariance, with applications to nuclear reactor aerosol behavior.

Contribution

It introduces a RGT-invariant kinetic equation for particle transport in turbulent flows, providing a new closure relation for phase space dispersion currents.

Findings

Derived a RGT-invariant kinetic equation for particle phase space transport.

Established a closure relation for the phase space dispersion current.

Applied the model to radioactive aerosol behavior in nuclear reactors.

Abstract

The principle of Random Galilean Transformation (RGT) Invariance is applied to the random motion of particles in a turbulent gas to construct a kinetic equation for the transport of the particle phase space probability <W(\mathbf{v},\mathbf{x},t)> where \mathbf{v} and \mathbf{x} are the velocity and position of a particle at time t. The essential problem is to find closed expressions for the phase space dispersion current \left\langle \boldsymbol{f}W\right\rangle , where \boldsymbol{f} is the fluctuating aerodynamic force at \mathbf{v} and \mathbf{x} at time t. The simplest form consistent with RGT invariance, the correct equation of state ancl form for the inter-phase momentum transfer tern is shown to be \left\langle \boldsymbol{f}W\right\rangle =-\left(\boldsymbol{\mu}\cdot\frac{\partial}{\partial\mathbf{v}}+\boldsymbol{\lambda}\cdot\frac{\partial}{\partial\mathbf{x}}\right)\left\langle W\right\rangle in which \text{\textbf{\ensuremath{\boldsymbol{\,\mu}}}\ensuremath{=<\boldsymbol{f}(t)\mathbf{v}(t)>}} and \boldsymbol{\lambda}=<\boldsymbol{f}(t)\boldsymbol{\mathbf{x}}(t)>.This approach to modeling gas-solid flows is currently being used to investigate the behavior of radioactive aerosols inside gas-cooled nuclear reactors.