The momentum equation, energy equation, turbulent energy equation, dissipation equation are all in convection diffusion type. However, the continuity equation is not in convection diffusion type.

In this model, the dissipation of the turbulent kinetic energy of gas bubbles is governed by the dissipation equations of the gas bubbles. The convection, diffusion, production and dissipation of the turbulent kinetic energy of bubbles, and the coupling interaction between the mass, momentum, and energy of two fluids are taken into account.

The Reynolds Stress Model (RSM) for turbulence is described together with the kε model with and without the buoyancy term. This article describes the RSM of 11 Equation which was developed from RSM of 7 Equation for heated flows by solving additional transport equations for the turbulent heat fluxes and for the variance of the temperature fluctuations.

The characteristic length scale of subgrid turbulence is no longer given by the spatial discretization step size, but by the use of a dissipation equation.

Fallacies include the mixing-length concept; the effect of pressure gradient on Reynolds shear stress; the separability of time and space derivatives; models of the dissipation equation; and chaos.

Fluctuation-dissipation equation of asymmetric simple exclusion processes

We prove that the fluctuation-dissipation equation w=Lu+D?η has a solution for some function u and some constant D identified to be the diffusion coefficient.

It is shown that this behavior is very much dependent on the gravitational production term in the turbulent dissipation equation, about which there is insufficient understanding in the literature.

Based on the standard single phase turbulent flow model, a new turbulence model is put forward to model the gas-liquid two-phase bubbly flow in a general non-orthogonal curvilinear co-ordinate system. In this model, the dissipation of the turbulent kinetic energy of gas bubbles is governed by the dissipation equations of the gas bubbles. The convection, diffusion, production and dissipation of the turbulent kinetic energy of bubbles, and the coupling interaction between the mass, momentum, and energy of two...

Based on the standard single phase turbulent flow model, a new turbulence model is put forward to model the gas-liquid two-phase bubbly flow in a general non-orthogonal curvilinear co-ordinate system. In this model, the dissipation of the turbulent kinetic energy of gas bubbles is governed by the dissipation equations of the gas bubbles. The convection, diffusion, production and dissipation of the turbulent kinetic energy of bubbles, and the coupling interaction between the mass, momentum, and energy of two fluids are taken into account. Theroretically it is a more perfect model k*.ε and k*.ε*.k p. The predicted results by this model for the gas-liquid two-phase flow in a straight duct are in satisfactory agreement with the experimental data in the literature, with a maximum relative deviation of less than 20% within the investigated range.

The Reynolds Stress Model (RSM) for turbulence is described together with the kε model with and without the buoyancy term. This article describes the RSM of 11 Equation which was developed from RSM of 7 Equation for heated flows by solving additional transport equations for the turbulent heat fluxes and for the variance of the temperature fluctuations. These two models are verified by comparison to unheated turbulent pipe flow data and then applied to two problems having thermal stratification and mixing....

The Reynolds Stress Model (RSM) for turbulence is described together with the kε model with and without the buoyancy term. This article describes the RSM of 11 Equation which was developed from RSM of 7 Equation for heated flows by solving additional transport equations for the turbulent heat fluxes and for the variance of the temperature fluctuations. These two models are verified by comparison to unheated turbulent pipe flow data and then applied to two problems having thermal stratification and mixing. The first application had unstable thermally stratified flow between two horizontal plates. The second had thermal mixing between a forced convection flow and a thermal cavity which simulates the plenum above the core of a pool type fast reactor. The computational results were compared with various experimental data and show that RSM of 11 Equation is the most suitable model for simulating anisotropic turbulence in thermally stratified flows.

The momentum equation, energy equation, turbulent energy equation, dissipation equation are all in convection diffusion type. However, the continuity equation is not in convection diffusion type. By rational mathematic deduction, the continuity equation is transformed into convection diffusion type without any assumption or simplification for compressible flow. This effort makes all the fluid dynamic equations take on the unified convection diffusion type. A finite analytic scheme for solving such equations...

The momentum equation, energy equation, turbulent energy equation, dissipation equation are all in convection diffusion type. However, the continuity equation is not in convection diffusion type. By rational mathematic deduction, the continuity equation is transformed into convection diffusion type without any assumption or simplification for compressible flow. This effort makes all the fluid dynamic equations take on the unified convection diffusion type. A finite analytic scheme for solving such equations are given in this paper.