Numerical study of non-newtonian fluid flow and heat transfer in a lid-driven skewed cavity using generalized curvilinear co-ordinates

Abstract

Numerical study of laminar fluid flow and heat transfer characteristics inside a lid-driven skewed cavity with non-Newtonian working fluid is done in this dissertation.Isothermal flows (lid-driven skewed cavity flow) as well as non-isothermal flows (natural convection in a skewed enclosure and mixed convection in a lid-driven cavity) are investigated. Two viscosity models,viz, power-law and Bingham models are considered in this study to represent the time-independent non-Newtonian fluid behavior. The considered physical model is a two-dimensional cavity where the bottom wall is considered to bealong the x-axis and the side walls make an angle with x-axis whereas the top wall is moving with a constant velocity from left to right. The flow is induced by the sliding motion of the top wall in conjunction with shear properties of fluid and governed by the equations of continuity, momentum as well as the constitutive equation of the respective viscosity model. In the case of non-isothermal flow, these equations are coupled with energy equation. The governing equations are initially transformed into non-dimensional form for each particular case using appropriate transformation. To use body-fitted non-orthogonal grid, these equations are transformed from Cartesian to curvilinear co-ordinates. Using this transformation the flow domain in physical space is mapped onto a rectangular domain in computational space. Finite volume numerical scheme with colocated grid arrangement is used to discretize the governing equations. An in-house FORTRAN code is employed to solve the governing equations. The code is designed using a revised form of a very well- known algorithm known as Semi-Implicit Pressure Linked Equation (SIMPLE) algorithm of Patankar and Spalding for laminar incompressible flow. In this algorithm a pressure correction field is formed with the help of the continuity equation. The iteration process starts with an initial approximation for flow variables and then the velocity and pressure fields are updated. This process is repeated until the convergence criteria is satisfied. To update the pressure field incomplete Cholesky-conjugate (ICCGS) algorithm is considered and to remove pressure-velocity decoupling arising from colocated grid arrangement, a non-linear momentum interpolation scheme known as Rhie and Chow interpolation is used for the evaluation of cell-face values from the nodal values. The resulting quasi-linear system is solved using BI-CGSTAB (Bi-Conjugate Gradient Stabilized method) solver.