A Numerical Study of Laminar and Intermittently Turbulent Boundary Layer on an Oscillating Flat Plate Using Pseudo-Compressible RANS Model

A numerical study was conducted to study the unsteady characteristics of incompressible boundary layer flows over an oscillating flat plate under laminar and intermittently turbulent flow conditions using pseudo-compressible Reynolds Averaged Navier-Stokes (RANS) model. The plate is assumed to be of infinite in length, smooth and is oscillated in the stream-wise direction with sinusoidal velocity variations. The numerical study is carried out using an in-house code and a commercial CFD package (Fluent). In the in-house code, the two-dimensional, unsteady conservation of mass and momentum equations are discretized using finite difference techniques which employs second order accurate (based on Taylor series) central differencing for spatial derivatives and first order accurate differencing for temporal derivatives. Two equation (k-ε) turbulence closure model, modified near the wall, is used along with RANS equations to simulate intermittently turbulent flows. The in-house code employs Fully Explicit-Finite Difference technique (FEFD) to solve the governing differential equations of the mathematical model. The computational domain in wall normal direction is sufficiently large enough to ensure no obstruction to boundary layer growth and the mesh is stretched near to the wall. The stream-wise extent of the domain was chosen to keep aspect ratio of the mesh below five for computational stability. Time and mesh independence studies were conducted using the in-house code to verify the pseudo-compressibility model. The simulations were performed for sufficient number of oscillation cycles to ensure the initial transient effects are eliminated from final set of results. For validation purposes, the velocity fields predicted by the in-house code and commercial CFD package are compared to the one given by analytical solution to Stokes’ second problem for an oscillating flat plate. Using the proposed pseudo-compressible NS and RANS models, numerical experiments were conducted for unsteady cases for Reynolds number (based on Stokes’ thickness) corresponding to laminar and intermittently turbulent flows, respectively. Time dependent velocity profiles, shear stress distribution, turbulence properties during the accelerating and decelerating stages of oscillations, and time lag between maximum fluid velocity and maximum shear stress is predicted. Phase lag between maximum fluid velocity and maximum turbulent kinetic energy, production and dissipation, are also predicted by the in-house code. The above predictions are then compared to ones predicted by commercial CFD code. The sudden rise in shear stress, during the acceleration phase of the oscillation, indicating the onset of intermittence is observed and discussed. Comparison of the results show that the observed deviations between the velocity magnitudes predicted by the in-house code and commercial CFD code are within acceptable range for laminar and intermittently turbulent flow conditions. Based on the results of the present study, one can conclude that the proposed pseudo-compressible RANS model is capable of predicting the characteristics of unsteady external flows successfully.