Numerical Modelling of Heat Transfer in Fine Dispersive Slurry Flow

Abstract

Slurry flows commonly appear in the transport of minerals from a mine to the processing site or from the deep ocean to the surface level. The process of heat transfer in solid–liquid flow is especially important for the long pipeline distance. The paper is focused on the numerical modelling and simulation of heat transfer in a fine dispersive slurry, which exhibits yield stress and damping of turbulence. The Bingham rheological model and the apparent viscosity concept were applied. The physical model was formulated and then the mathematical model, which constitutes conservative equations based on the time average approach for mass, momentum, and internal energy. The slurry flow in a pipeline is turbulent and fully developed hydrodynamically and thermally. The closure problem was solved by taking into account the Boussinesque hypothesis and a suitable turbulence model, which includes the influence of the yield shear stress on the wall damping function. The objective of the paper is to develop a new correlation of the Nusselt number for turbulent flow of fine dispersive slurry that exhibits yield stress and damping of turbulence. Simulations were performed for turbulent slurry flow, for solid volume concentrations 10%, 20%, 30%, and for water. The mathematical model for heat transfer of the carrier liquid flow has been validated. The study confirmed that the slurry velocity profiles are substantially different from those of the carrier liquid and have a significant effect on the heat transfer process. The highest rate of decrease in the Nusselt number is for low solid concentrations, while for C > 10% the decrease in the Nusselt number is gradual. A new correlation for the Nusselt number is proposed, which includes the Reynolds and Prandtl numbers, the dimensionless yield shear stress, and solid concentration. The new Nusselt number is in good agreement with the numerical predictions and the highest relative error was obtained for C = 10% and Nu = 44.3 and is equal to −12%. Results of the simulations are discussed. Conclusions and recommendations for further research are formulated.

Numerical Heat Transfer and Fluid Flow: A Review of Contributions to the Special Issue

“…The author concluded that for the same bulk velocity of the slurry, the Nusselt number decreases with an increase in solid volume concentration, and the highest rate of decrease in the Nusselt number is for a solid concentration below 10% by volume. The author noticed that more work needs to be done on examining the new Nusselt number for solid volume concentrations below 10% and greater than 30%, for different heat fluxes and pipe diameters [41].…”

“…Passive methods, such as increasing heat transfer area and/or temperature difference, shaping an insert with dedicated perforation, or mechanically deformed pipes, have been studied for several years and have become commercial solutions [4][5][6][7][8][9]. Active methods, such as air injection, bubble or vortex generation, or proper pulsation, can lead to increased heat transfer coefficient, and, finally, can produce increased heat transfer process [10][11][12][13]. Some of such methods have been demonstrated by contributors to the Special Issue.…”

Determination of the Critical Reynolds Number in a Transitional Flow of Lime Slurry with the Addition of Deflocculant

“…The phenomenon of increasing the viscosity at the wall was indirectly confirmed by Squires and Eaton (1990), who used direct numerical simulation of isotropic turbulence to investigate the effect of turbulence on the solid concentration of heavy particles. Some other researchers reasoned that a laminarisation effect in fine dispersive slurries exists (Wilson and Thomas, 1985), (Bartosik, 2008). In conclusion, slurry flow with fine solid particles is very complex, and it remains a challenge to perform experiments on the influence of the solid particles on the transition to turbulence.…”