A Numerical Study of Laminar and Intermittently Turbulent Flow Over a Flat Plate Using Pseudo-Compressibility Model

Abstract

A study was conducted to investigate the characteristics of incompressible unsteady boundary layer flows (laminar and intermittently turbulent), numerically and experimentally. The main objective of the study is to validate and verify (V&V) the accuracy of the proposed pseudo-compressibility model in solving the incompressible Navier-Stokes (NS) equations. This approach will enable one to use a second order accurate (temporally and spatially) implicit finite-difference (FD) technique to solve NS equations (including RANS equations). Here, the proposed pseudo-compressibility model is used for laminar and intermittent turbulent flow simulations. Flow over a flat plate is chosen as the benchmark case for the validation of the proposed pseudo-compressibility model. An in-house code is developed to solve the boundary layer equations using an Alternating-Direction Explicit (ADE) FD technique. The boundary layer equations are discretized using explicit FD techniques which are second order accurate. The velocity field predicted by this code is compared to the one given by Blasius’ analytical solution. A second in-house code is also developed which adopts the proposed model of pseudo-compressibility to solve the incompressible NS equations. The two dimensional, unsteady conservation of mass and momentum equations are discretized using explicit finite-difference techniques. A standard K-ε closure model is used along with RANS equation to simulate turbulent flows. The primitive variables (velocity and pressure) predicted by this code are compared to the ones predicted by a commercial CFD package (Fluent). Once the method of pseudo-compressibility is validated, it is then implemented into another in-house computer code which employs implicit FD technique and Coupled Modified Strongly Implicit Procedure (CMSIP) to solve for the unknowns of the problem under study. The predictions based on the pseudo-compressibility model for laminar flow are validated using the results of the experiments in which Particle Image Velocimetry (PIV) technique was employed. The verification; that is, the numerical uncertainty estimation of the pseudo-compressible code was accomplished by using the Grid Convergence Index (GCI) method. The results of the present study indicate that the proposed pseudo-compressibility model is capable of predicting experimentally observed characteristics of the external flows successfully, and deviations between the predicted velocity magnitudes and experimentally measured velocities are within an acceptable range for laminar and intermittently turbulent flows conditions.