Three-dimensional finite difference saturated-unsaturated flow modeling with nonorthogonal grids using a coordinate transformation method

Study of the saturated-unsaturated flow in porous media is of interest in many branches of science and engineering. Among the various numerical simulation methods available, the finite difference method is advantageous because it offers simplicity of discretization. This method has been widely used for simulating saturated-unsaturated flows. However, the simulation of geometrically complex flow domains requires the use of high-resolution grids in conventional finite difference models because conventional finite difference discretization assumes an orthogonal coordinate system. This makes a finite difference model computationally less efficient than other numerical models that can treat nonorthogonal grids, such as the finite element model and finite volume model. To overcome this disadvantage, we use a coordinate transformation method and develop a multidimensional finite difference model for simulating saturated-unsaturated flows; this model can treat nonorthogonal grids. The cross-derivative terms derived by the coordinate transformation method are evaluated explicitly for ease of coding. Therefore, a 7 point stencil is used for implicit terms in the iterative calculation, as in the case of conventional finite difference models with an orthogonal grid. We assess the performance of the proposed model by carrying out test simulations. We then compare the simulation results with dense grid solutions in order to evaluate the numerical accuracy of the proposed model. To examine the performance of the proposed model, we draw a comparison between the simulation results obtained using the proposed model and the results obtained by using (1) a model in which all terms are considered fully implicitly, (2) a finite element model, and (3) a conventional finite difference model with a high-resolution orthogonal grid

Analysis of non-dimensional numbers of fluid flowing inside tubes of flat plate solar collector

The aim of this paper is to discuss the non-dimensional numbers of fluid flowing through inside the tubes of flat plate solar collectors. Empirically, to abate the cost and energy consumption or to boost up the performance and efficiency of solar collectors; computational simulation plays a vital role. In this study, CFD numerical simulation of aqueous ethylene glycol (60% water + 40%) ethylene glycol fluid flow has been done with ANSYS 15.0. Non-dimensional numbers such as surface Nusselt number, Skin friction coefficient and Prandtl number of fluids have been observed based on empirical and experimental properties. The geometry of design has been prepared using Solidworks software in accordance with the actual experimental model. The analysis revealed that the Nusselt number showed effective convection behavior, the skin friction coefficient was positive while the Prandtl number was large for both properties of aqueous ethylene glycol