Couette-Poiseuille flow based non-linear flow over a square cylinder near plane wall

A numerical study on the flow over a square cylinder in the vicinity of a wall is conducted for different Couette-Poiseuille-based non-uniform flow with the non-dimensional pressure gradient P varying from 0 to 5. The non-dimensional gap ratio L (=$H^{\ast}/a^{\ast}$) is changed from 0.1 to 2, where $H^{\ast}$ is gap height between the cylinder and wall, and $a^{\ast}$ is the cylinder width. The governing equations are solved numerically through finite volume method based on SIMPLE algorithm on a staggered grid system. Both P and L have a substantial influence on the flow structure, time-mean drag coefficient ${\bar{C}}_D$, fluctuating (rms) lift coefficient ($C_L{^{\prime}}$), and Strouhal number St. The changes in P and L leads to four distinct flow regimes (I, II, III and IV). Following the flow structure change, the ${\bar{C}}_D$, $C_L{^{\prime}}$, and St all vary greatly with the change in L and/or P. The ${\bar{C}}_D$ and $C_L{^{\prime}}$ both grow with increasing P and/or L. The St increases with P for a given L, being less sensitive to L for a smaller P (< 2) and more sensitive to L for a larger P (> 2). A strong relationship is observed between the flow regimes and the values of ${\bar{C}}_D$, $C_L{^{\prime}}$ and St. An increase in P affects the pressure distribution more on the top surface than on bottom surface while an increase in L does the opposite.