Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

The initial flow past an impulsively started translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier-Stokes equations. The asymptotic solution obtained shows that the tangential and normal slip velocities on the cylinder surface are of the order of 1/root lambda and 1/lambda, respectively, within the second approximation of the present asymptotic analysis, where lambda is the penalization parameter. This result agrees with the estimation of Carbou & Fabrie (Adv. Diff. Equ., vol. 8, 2003, pp. 1453-1480). Based on the asymptotic solution, the influence of the penalization parameter lambda is discussed on the drag coefficient that is calculated using the adopted three formulae. It can then be found that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625-647) as lambda ->infinity.