Numerical Study of Unsteady Viscous Flow past a Lifting Plate

Numerical predictions are made for the unsteady two-dimensional viscous flow past a finite flat plate at angle of attack. The flow is analyzed from the standpoint of vorticity production and transport using the complete vorticity transport equation. The entire fluid motion is ultimately calculated through application of the velocity induction law (Law of Biot-Savart). Fundamental to the approach is the specification of bound and sheet vortex distributions at the plate location. These are so constituted that the surface adherence condition appropriate to the viscous flow is satisfied. The analysis shows how the vortex distributions arise, their interrelationship, and their effect on the developing rotational flow about the plate. Results are first presented for a low Reynolds number flow (Re = 4) at zero angle of attack. These are followed by results for the plate at 30° angle of attack for Reynolds numbers of 4 and 400. The flow simulation is found to be very good, and to whatever extent possible, the results are compared with those from earlier works based on conventional approaches involving the stream function. The comparisons are quite satisfactory. Nomenclature Bp = series coefficients in expression for y, Eq. (5) K = time-function of integration in expression for y L = cord length of the plate m = summation index in Eq. (13) n = number of time increments Re = Reynolds number, UL/v