Evaluation of strong shear thinning non-Newtonian fluid flow using single domain DR-BEM

Abstract

The dual reciprocity method (DRM) has been successfully employed along with the boundary element method (BEM) to simulate non linear flow phenomena such as convective momentum transport and shear thinning fluids. In the latter however, domain partitioning has been necessary to achieve convergence when the power law index is below 0.8. This paper shows how a single domain DR-BEM formulation for non Newtonian low Reynolds number flows can be implemented in order to obtain accurate results for lower values of the power law index. Some of the characteristics of this implementation are the use of quadratic elements and an iterative solution of the non linear system of equations using a modified Newton-Raphson method. Along with the implementation, two radial inelastic non Newtonian flow: couette mixing and slit flow. Solutions obtained are also compared to results from a multi-domain dual reciprocity method (MD-DRM) for equal meshes. Results showed that using the above mentioned strategies, single domain DR-BEM can accurately predict the flow field in inelastic non Newtonian flow for values of the power law index as low as 0.5. It is also worth noting that the accuracy of the single domain strategy was shown to be higher than MD-DRM, although the latter clearly reduced computational resource consumption. Keywords: single domain DRM, power law fluids, higher order elements, iterative methods for non linear systems.Boundary Elements and Other Mesh Reduction Methods XXIX 111

Indirect boundary integral formulation for the solution of shear-thinning flow inside single rotor mixers

“…This function has shown to be an accurate and simple alternative for use within the DRM approach (see [12,26,27] [26,28]). …”

Mobility of shear thinning viscous drops in a shear Newtonian carrying flow using DR‐BEM

“…This function has shown to be an accurate and simple alternative for use within the DRM approach (see [27][28][29] [27,30]). …”

“…To transform the domain integral in (30) into an equivalent series of surface integrals, the DRM is employed. The basis of this method is the expansion of the non-homogeneous term in the governing equations using the interpolation approximation…”