Analysis of the aerodynamic interaction between two plunging plates in tandem at low Reynolds number for maximum propulsive efficiency

The thrust generated by two heaving plates in tandem is analyzed computationally by solving the Navier–Stokes equations for an incompressible and two-dimensional flow at low Reynolds numbers. We consider with detail two particular sets of configurations of interest in forward flight in a wide range of heaving amplitudes and frequencies: a plunging leading plate with the trailing plate at rest, and the two plates heaving with the same frequency and amplitude, but varying the phase difference. In almost all cases the thrust efficiency of the leading plate is augmented in relation to a single plate heaving with the same frequency and amplitude. In the first configuration with a trailing plate at rest, we characterize the range of nondimensional heaving frequencies and amplitudes of the leading plate for which the stationary trailing plate contributes positively to the global thrust. The maximum global thrust efficiency of this configuration, reached for an advance ratio slightly less than unity and a reduced frequency close to 5, is about the same as the maximum efficiency for an isolated plate, reached for slightly smaller frequencies. But for low frequencies the tandem configuration with the trailing plate at rest is more thrust efficient than the isolated plate. We also characterize the nondimensional frequency and amplitude regions for which the flow becomes chaotic. In the second configuration, the maximum of the total thrust efficiency is reached for a phase lag of 180° (counterstroking), particularly for an advance ratio unity and a reduced frequency 4.4. It is almost the same as the maximum thrust efficiency in the other configuration with the trailing plate at rest and that of a single plate. We discuss the flow structures and the aerodynamic interaction between plates responsible for the optimal thrust configuration in both cases.