On models for turbulence modulation in fluid–particle flows

Mathematical Modelling of the Motion of Dust-Laden Gases in the Freeboard of CFB Using the Two-Fluid Approach

“…In this work the RANS method is used for both coexisting phases, namely the gas-and solid phases with the closure equations. Two basic predictions were used for closure of the governing equations of gaseous and dispersed phases: i) the four-way coupling model (Crowe, 2000) by that captures one capture the particleturbulence interaction phenomena and ii) the inter-particle collision closure model (Kartushinsky & Michaelides 2004) to assess an the particles interaction. The both models are used for receiving an output of necessary data which are the axial and radial velocities, turbulent energy and the particle mass concentration.…”

“…The closure equations of gas-phase are performed by using turbulence time scale) have to be calculated in advance (in preliminary calculations) for completion modelling in the pipe gas-solid turbulent flow system. An advantage of the fourway coupling model of (Crowe, 2000) (with the inclusion of particle collision) is that it includes the turbulence enhancement by the presence of particles, expressed via the term (Kartushinsky & Michaelides, 2004). Due to the particle turbulent diffusion and particle collision the diffusion coefficient has two components:…”

“…This amount of an additional turbulent energy is proportional to the square of velocity slip between the gaseous and the solid phases following the model by Crowe (2000) and it is substantial because of large velocity slip between the phases owing to high inertia of large particle size. Following to the model of Crowe (2000), this generation term is balanced by the introduced dissipation rate of turbulent energy and calculated via the hybrid turbulence length scale (last term in the right-hand side of Eq. 5).…”

“…As a whole, the trend shows that the particles in all the observed regimes generate the turbulence, which stems from the vortex shedding phenomenon behind the particles which is input to the level of turbulence generated by the flow itself. This effect of turbulence modulation, namely, the turbulence enhancement due to the presence of coarse particles is explained and computed using the four-way coupling model by Crowe (2000). This amount of an additional turbulent energy is proportional to the square of velocity slip between the gaseous and the solid phases following the model by Crowe (2000) and it is substantial because of large velocity slip between the phases owing to high inertia of large particle size.…”

“…5). The given four-way coupling model by Crowe (2000) is based on the criteria of turbulence modulation by particles considering the ratio of particle size to the integral turbulence length scale. In accordance with this criterion for the considered cases of two-phase turbulent flow loaded by 500 and 1000µm particles, this scale ratio is far above 0.1 and therefore the particles enhanced the turbulence of the carrier gas-phase flow.…”