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Flow Cases (flow + case)
Selected AbstractsNumerical approximation of generalized Newtonian fluids using Powell,Sabin,Heindl elements: I. theoretical estimatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003S.-S. Chow Abstract In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell,Sabin,Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd. [source] Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier,Stokes compressible flows on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001N. P. C. Marques Abstract This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier,Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6,17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier,Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd. [source] Mobility of shear thinning viscous drops in a shear Newtonian carrying flow using DR-BEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009M. Giraldo Abstract The study of drop behaviour has attracted great interest in the last years due to its importance in different industrial and biological systems. Most available works focus on Newtonian drops, excluding some very important applications such as polymer mixing. Simulations of non-Newtonian drops have had only limited study, mostly in time-dependent rheologies or simple flow cases. This work presents a boundary-only formulation based on the dual reciprocity method to model the motion and deformation of non-Newtonian shear thinning drops due to a shear Newtonian unbounded carrying flow. Pair-wise interactions at low Reynolds number between two viscous shear thinning non-Newtonian drops are numerically simulated in order to obtain mobility magnitudes under linear shear flow of different strengths. Separation of the drops in the direction perpendicular to the imposed flow field at high capillary number (small surface tension) and low viscosity ratio was favoured by shear thinning, increasing in magnitude as the capillary number increases and the viscous ratio decreases. Higher values of this separation occur at higher values of the viscosity ratio when compared with the case of Newtonian drops. In order to obtain a good physical description of the non-Newtonian drop behaviour, while maintaining good computational performance, the non-Newtonian viscosity is made to obey the truncated power law model. Copyright © 2008 John Wiley & Sons, Ltd. [source] A simplified v2,f model for near-wall turbulenceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2007M. M. Rahman Abstract A simplified version of the v2,f model is proposed that accounts for the distinct effects of low-Reynolds number and near-wall turbulence. It incorporates modified C,(1,2) coefficients to amplify the level of dissipation in non-equilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. Unlike the conventional v2,f, it requires one additional equation (i.e. the elliptic equation for the elliptic relaxation parameter fµ) to be solved in conjunction with the k,, model. The scaling is evaluated from k in collaboration with an anisotropic coefficient Cv and fµ. Consequently, the model needs no boundary condition on and avoids free stream sensitivity. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Copyright © 2007 John Wiley & Sons, Ltd. [source] An eddy viscosity model with near-wall modificationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2005M. M. Rahman Abstract An extended version of the isotropic k,, model is proposed that accounts for the distinct effects of low-Reynolds number (LRN) and wall proximity. It incorporates a near-wall correction term to amplify the level of dissipation in nonequilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz' inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate that the present model is a significant improvement over the standard eddy viscosity formulation. Copyright © 2005 John Wiley & Sons, Ltd. [source] Low Reynolds number k,, model for near-wall flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005M. M. Rahman Abstract A wall-distance free k,, turbulence model is developed that accounts for the near-wall and low Reynolds number effects emanating from the physical requirements. The model coefficients/functions depend non-linearly on both the strain rate and vorticity invariants. Included diffusion terms and modified C,(1,2) coefficients amplify the level of dissipation in non-equilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] Modified method of characteristics for solving population balance equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003Laurent Pilon Abstract This paper presents a new numerical method for solving the population balance equation using the modified method of characteristics. Aggregation and break-up are neglected but the density function variations in the three-dimensional space and its dependence on the external fields are accounted for. The method is an interpretation of the Lagrangian approach. Based on a pre-specified grid, it follows the particles backward in time as opposed to forward in the case of traditional method of characteristics. Unlike the direct marching method, the inverse marching method uses a fixed grid thus, making it compatible with other numerical schemes (e.g. finite-volume, finite elements) that may be used to solve other coupled equations such as the mass, momentum, and energy conservation equations. The numerical solutions are compared with the exact analytical solutions for simple one-dimensional flow cases. Very good agreement between the numerical and the theoretical solutions has been obtained confirming the validity of the numerical procedure and the associated computer program. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||