Code Verification of Non-Newtonian Fluid Solvers for Single- and Two-Phase Laminar Flows

Abstract

The presence of complex fluids in nature and industrial applications combined with the rapid growth of computer power over the past decades has led to an increasing number of numerical studies on non-Newtonian flows. In most cases, non-Newtonian models can be implemented in existing Newtonian solvers by relatively simple modification of the viscosity. However, due to scarcity of analytical solutions for non-Newtonian fluid flows and widespread use of regularisation methods, performing Code Verification to ensure that the code is free of mistakes is a challenging task. The Method of Manufactured Solutions (MMS) is a powerful tool to generate analytical solutions for Code Verification. In this article, we present and discuss results of three verification exercises based on MMS: (i) steady single-phase flow; (ii) unsteady two-phase flow with smooth interface; (iii) two-phase flow with free surface. We show that, with the first and second exercise, rigorous verification of non-Newtonian fluid solver is possible both on single and two-phase flows. The third test case revealed that `spurious velocities' typical of free-surface calculations with the Volume-of-Fluid (VoF) model lead to `spurious viscosities' in the non-Newtonian fluid. The procedure is illustrated herein on a second-order finite-volume CFD code using the Herschel-Bulkley fluid model as an example. Nonetheless, the same methodology is applicable to any CFD code and it can be easily extended to all rheological models falling under the class of Generalised Newtonian Fluid (GNF) models.

Application of a maritime CFD code to a benchmark problem for non-Newtonian fluids: the flow around a sphere

“…Combining the evidence of our previous code verification exercises [30,31] and the results of this work, it is concluded that the power-law, Bingham and Herschel-Bulkley models are implemented correctly and that the code is capable of reproducing literature data with good accuracy despite the high non-linearity introduced by the non-Newtonian viscosity. This provides confidence to employ REFRESCO for more complex applications such as a ship sailing through fluid mud.…”

“…The two schemes have the same computational cost, thus, in principle, there is no reason to prefer one scheme to the other. Furthermore, when we performed a code verification exercise (not shown here) similar to that in [30], the two schemes exhibited the same accuracy and rate of convergence of the residuals. However, on the present problem, the first scheme (Eq.…”

“…Our previous code verifications [30,31] ensured that the Herschel-Bulkley model was correctly implemented. However, even if the code is correct, fully-converged solutions for realistic non-Newtonian problems may still be difficult to obtain.…”

Code-verification techniques for the method-of-moments implementation of the electric-field integral equation

“…By eliminating the presence of the basis functions in (31) and (32), we have eliminated the solutiondiscretization error.…”

“…Code verification has been performed on computational physics codes associated with several physics disciplines, including aerodynamics [20], fluid dynamics [21][22][23][24][25][26][27], solid mechanics [28], fluid-structure interaction [29], heat transfer in fluid-solid interaction [30], multiphase flows [31,32], radiation hydrodynamics [33], electrostatics [34], electrodynamics [35], and ablation [36][37][38][39][40]. For surface integral equations in computational electromagnetics, code-verification activities that employ manufactured solutions have been limited to the EFIE [41][42][43][44].…”