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.
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*[[Averaging approaches]]
*[[Averaging approaches]]
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:[[Volume averaging|Volume averaging]], [[Lagrangian Averaging|Lagrangian averaging]], and [[Boltzmann statistical averaging]].
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:[[Volume averaging|Volume averaging]], [[Lagrangian Averaging|Lagrangian averaging]], and [[Basics of Boltzmann statistical averaging|Boltzmann statistical averaging]].
*[[Multi-fluid model]]
*[[Multi-fluid model]]
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:[[Multi-fluid model: continuity equation|Continuity equation]], [[Multi-fluid model: momentum equation|Momentum equation]], [[Multi-fluid model: energy equation|energy equation]],and [[Multi-fluid model: conservation of species|conservation of species]].
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:[[Multi-fluid_model#Continuity_Equation|Continuity equation]], [[Multi-fluid_model#Momentum_Equation|momentum equation]], [[Multi-fluid_model#Energy_Equation|energy equation]],and [[Multi-fluid_model#Species|conservation of species]].
*[[Homogeneous model]]
*[[Homogeneous model]]
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:[[Homogeneous Model: continuity equation|Continuity equation]], [[Homogeneous Model: momentum equation|Momentum equation]], [[Homogeneous Model: energy equation|energy equation]], and [[Homogeneous Model: conservation of species|conservation of species]].
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:[[Homogeneous_model#Continuity_Equation|Continuity equation]], [[Homogeneous_model#Momentum_Equation|momentum equation]], [[Homogeneous_model#Energy_Equation|energy equation]], and [[Homogeneous_model#Species|conservation of species]].
*'''[[Governing Equations for Porous Media|Porous media]]'''
*'''[[Governing Equations for Porous Media|Porous media]]'''
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:[[Basics of porous media|Basics]], [[Porous media: continuity equation|Continuity equation]], [[Porous media: momentum equation|Momentum equation]], [[Porous media: energy equation|energy equation]], and [[Porous media: conservation of species|conservation of species]].
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:[[Basics of porous media|Basics]], [[Governing_Equations_for_Porous_Media#Conservation_of_Mass|continuity equation]], [[Governing_Equations_for_Porous_Media#Conservation_of_Momentum|momentum equation]], [[Governing_Equations_for_Porous_Media#Energy_Equation|energy equation]], and [[Governing_Equations_for_Porous_Media#Species|conservation of species]].
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*[[Boltzmann statistical averaging]]
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:[[Boltzmann Equation]], [[Lattice Boltzmann Model (LBM)]], and [[LBM for multiphase flows]].
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==References==
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Faghri, A., Zhang, Y., and Howell, J. R., 2010, ''Advanced Heat and Mass Transfer'', Global Digital Press, Columbia, MO.
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==Further Reading==
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==External Links==

Current revision as of 13:43, 5 August 2010

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.

References

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

Further Reading

External Links