Numerical investigation of non-Newtonian power law flows using B-spline material point method

Abstract

• A weakly compressible BSMPM method for simulating non-Newtonian flow is proposed. • Complex free surface flow and fluid structure interaction problems for power law fluid are studied. • Shear thickening/thinning, jet buckling/splashing, and vortex whirling are well represented. • Results demonstrate the efficacy of the proposed method for non-Newtonian power law flow problems. Simulating the complex flow with free surface and large deformation of non-Newtonian fluid is a challenging problem and plays a significant role in many industrial areas. In this paper, a weakly compressible B-spline material point method (WC-BSMPM) is presented and extended to solve the complex free surface flow of non-Newtonian fluid with a power law rheology model. Numerical examples including two-dimensional problems of plane Poiseuille, dam break, and container filling flow as well as three-dimensional sphere water entry problems are adopted to demonstrate the effectiveness and capabilities of the proposed method. The simulated results show good agreements with analytical solutions or published experimental data. Moreover, significant flow features for non-Newtonian power law fluid, including shear thickening, shear thinning, jet buckling, jet splashing, vortex whirling, and fluid-structure interactions can be well captured. Meanwhile, the numerical noise of the traditional MPM can be eliminated by the proposed method, which confirms that the WC-BSMPM method is a promising alternative to simulate the complex free surface flow and fluid-structure interactions for the non-Newtonian power law fluid.