MSV:Multi-Scaler Viscosity Model of Turbulence

Kriventsev, V.

Multi-Scale Viscosity (MSV) model is proposed for estimation of the Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. We assume that flow in an "ideal" channel is always stable, i.e.laminar, but turbulence is developing process of external perturbations cased by wall roughness and other factors. We also assume that real flows are always affected by perturbations of any scale lower than the size of the channel. The turbulence can be modeled in form of internal or "turbulent" viscosity increase. The main idea of MSV can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of local turbulent Reynolds number below some critical value. Here, local turbulent Reynolds number can be defined in two different ways: (1)as a product of value of axial velocity deformation for a given scale and generic length of this scale divided by accumulated value of laminar and turbulent viscosity of lower scales (2)as a ratio of the difference between total kinetic energy and "flat-profile" kinetic energy to the work of friction forces In MSV, the only empirical parameter is the critical Reynolds number that is estimated to be around 100 in the former case and about 8.33 in the later. MSV model has been applied to the fully-developed turbulent flows in straight channels such as a circular tube and annular channel. Friction factor and velocity profiles predicted with MSV are in a good agreement with numerous experimental data. The MSV model can be classified as "zero-order" integral model of turbulence. Because of simplicity, MSV can be easily implemented for calculation of fuIly-developed turbulent flows in straight channels of arbitrary shapes including fuel assemblies of nuclear reactors. The intent of this report is to summarize the progress made in the development of the model of turbulence. Since the final ...