Averaging formulation of governing equations

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Many multiphase-flow problems encountered in engineering – such as those with dispersed and mixed phases – have extremely complicated and deformable interfaces. It is not always possible to solve the local instance fluid flow, because the difficulty associated with interface tracking exceeds present computational capability. Fortunately, information about the discontinuity of properties at the interfaces and the exact locations of the interfaces are not always of interest to practical engineers. The macroscopic aspects of multiphase flow are more important to the design and operation of a multiphase system. Appropriate averaging can obtain the mean values of flow and thermal properties and eliminate the need to explicitly track interfaces and/or the local instance fluctuations of properties.

Volume averaging, Lagrangian averaging, and Boltzmann statistical averaging.
Continuity equation, momentum equation, energy equation,and conservation of species.
Continuity equation, momentum equation, energy equation, and conservation of species.
Basics, continuity equation, momentum equation, energy equation, and conservation of species.
Boltzmann Equation, Lattice Boltzmann Model (LBM), and LBM for multiphase flows.


Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

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