Establishment and application of sediment diffusion coefficient model based on influence of particle dynamic scale

Abstract: On the basis of eddy viscosity coefficient theory, the semi-empirical sediment diffusion coefficient models are used widely to calculate the volume concentration of solid phase in the Eulerian two-phase flow simulation. However, the diffusion coefficient models' accuracy is not enough because the particle dynamic scale influence on the fluid turbulence intensity is ignored when they are applied to suspended load sediment two-phase flow simulation. Thus the fluid turbulence intensity change rate function about particle dynamic scale and solid volume concentration was derived, and a new sediment diffusion coefficient model was established in the present study. The new model was called DC-PDPC model. The function derivation was based on the semi-empirical eddy viscosity coefficient model, the particle-eddy interaction theory about the influence of the particle dynamic scale and solid concentration on the fluid turbulence intensity, the equilibrium flow theory and the multivariate regression theory with data. The suspended load sediment two-phase flow simulations were conducted in a circular tube. The results showed that the maximum relative error of relative solid phase volume concentration between the experiment and the calculated values by NON-DC model was 90%-120% and the error was 10%-25% for Diffusion-in-VOF model under different flow conditions. The simulation precision was low, because change of the sediment diffusion coefficient was not considered due to ignoring the particle dynamic scale and solid phase volume concentration influence on the fluid turbulence intensity. In different cases, the relative error between the experiment and the calculation by the three type models (Diffusion-in-VOF, NON-DC and DC-PDPC) were all high near the wall of the tube. When the particle dynamic scale was less than or equal to 1, the maximum relative error of relative solid phase concentration between the experiment and the calculation by the new DC-PDPC model was less than 10%, which was much less than the value of the other models. When the particle dynamic scale was more than 1, the maximum relative error of relative solid phase concentration were all less than 10% for Diffusion-in-VOF model and DC-PDPC model, because the formula expressions of both models were the same under this condition. By comparison with the other models, the new sediment diffusion coefficient model could better reflect the influence of the particle dynamic scale on sediment diffusion coefficient under different flow conditions. Along with the change of the solid phase concentration distribution caused by DC-PDPC model, the solid phase velocity distribution and the liquid phase velocity distribution all changed. The changing trend of the solid and liquid phase velocity distribution were closely related to the changing trend of the solid phase concentration distribution, but the change in the solid phase velocity and liquid phase velocity was small compared with change in solid phase concentration. The new DC-PDPC model can be accurately applied to the suspended load sediment solid-liquid two-phase flow field with obviously improved accuracy of flow field.