Multi-scale Modeling And Numerical Simulation Of Complex Flows Based On Immersed Boundary Method

Dynamical fluid-solid interactions with complex moving geometries are widely found in chemical engineering, such as flows in stirred tanks and fluid-solid two phase flows. Although rapid development has been gained in computational fluid dynamics (CFD), accurate and efficient description of complex moving boundaries in numerical simulations remains a great challenge. Based on a fixed Eulerian grid, immersed boundary method (IBM) has become one of the popular techniques for complex flows with moving boundaries. In the present study, IBM is improved in a finite difference/volume context. With the aid of high performance computing (HPC), numerical simulation of stirred tanks at laboratory or even at industrial scale is realized, together with heat transfer and particle suspension. The main novelties of this work are summarized as follows:In conventional IBM, no-slip boundary condition and divergence-free condition are usually not satisfied at the same time. To overcome this limitation, modifications and improvements have been made in the present study: the elliptic equation for pressure is solved before evaluating the body force, the body force is distributed only inside the immersed boundaries and the multidirect forcing technique is further applied for a better satisfaction of the no-slip boundary condition. The improved IBM is validated in several benchmark simulations, and proved to be more accurate in the vicinity of the boundaries, especially moving boundaries, than the conventional IBM.Stationary and moving boundaries are usually encountered in practical applications of IBM, however, most simulations use only one kind of IBM for both cases, which does not take full advantage of this method. To address this problem, we propose a hybrid IBM in which different geometries are handled respectively by different IB techniques. The hybrid IBM shows higher efficiency than previous implementations without losing accuracy.To cope with the high computation cost in simulating complex flows, CPU (central processing unit)-GPU (graphic processing unit) hybrid parallel computing is applied, and 7-20-fold speedup in the test problems is achieved on a GPU when compared with a single CPU core. The transfer of variables between Lagrangian and Eulerian locations is better parallelized by a partial velocity interpolation and force distribution strategy, which simplifies the implementation without increasing the communication cost. Based on the efforts mentioned above, large scale computation of complex fluid-solid interactions at moderately high Reynolds numbers can be achieved.For the application of the proposed method, large eddy simulation (LES) is coupled with this method for the simulation of turbulent flow in a Rushton stirred tank. The agreement with experimental and other numerical data is satisfactory. It is suggested that present IBM-LES method is a promising tool for the study of turbulent flow in stirred tanks. The present method is further applied to the computation of fluid flow and heat transfer in a stirred tank at industrial scale with internal helical coils, which provides useful information for optimization.As another application, the discrete element method (DEM) is coupled with the present method to carry out direct numerical simulation (DNS) of fluid-solid systems in stirred tanks with CPU-GPU supercomputing. It is demonstrated that the tank geometries, such as impellers and baffles structures, have significant effect on solids suspension.Enabled by this study, simulation with complex moving boundaries at industrial scale can be accomplished using IBM implemented on supercomputers, and the details of flow and transport process can be revealed. It will become a powerful tool for the optimal design of industrial reactors, such as stirred tanks, if the method can be further developed.