Turbulence first-order closure models

The next category of turbulence closures, i.e., impl3ung to be more accurate than the very simple algebraic models, is a hierarchy of turbulent models based on the transport equation for the fluctuating momentum field. These are the first-order closure models, i.e., those that require parameterizations for the second moments and the second-order closure models, i.e., those that... 

The first-order closure models are all based on the Boussinesq hypothesis [19, 20] parameterizing the Reynolds stresses. Therefore, for fully developed turbulent bulk flow, i.e., flows far away from any solid boundaries, the turbulent kinetic energy production term is modeled based on the generalized eddy viscosity hypothesis , defined by (1.380). The modeled fc-equation is... 

The k,E-model is based on a first order turbulence model closure according to Boussinesq. In analogy to laminar flows, the Reynolds stresses are assumed to be proportional to the gradients of the mean velocities. Transport equations for the turbulent kinetic energy and the turbulent dissipation are developed from the Navier-Stokes equations assuming an isotropic turbulence. The implementation of this model and the parameters used can be found in [10],... 

It can thus be thought that the intensive turbulence within EPRs, i.e. canopies, reveals some features that are very distinguishing from the common unobstructed turbulence. Such kind of the turbulence attracted an increased attention of researchers in last years, [81, 155, 186, 187, 305, 318, 410, 462, 500, 522], Despite the simplified first-order turbulence closures (algebraic models) or second-order ones (with differential equations for vr) turned useful and lead to some plausible results in practical areas, many its phenomena remains unexplained. Further information about basic turbulence laws is provided in Chapters 2, 4 to 9 along with further practical applications. 

Due to their robustness and reasonable accuracy, the first-order two-equation models, such as the k-s closure originally proposed by Harlow and Nakayama [62, 63], have become very popular for reactor simulations. In this section the formal derivation of the k-s model equations are given and discussed. A transport equation for the turbulent kinetic energy, or actually the momentum variance, can be derived by multiplying the equation for the fluctuating component v[, (1.395), by 2v[, there-... 

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