The reduction of pressure losses using in-plane contraction/relaxation waves

This paper examines how in-plane contraction/relaxation waves applied to the walls affect a two-dimensional laminar flow in a channel. Of primary interest is how the application of such waves alters the pressure gradient required to drive a prescribed flow rate. It is shown that the waves generate a pumping effect that acts in the direction opposite to wave propagation. Depending on the exact configuration at hand, this pumping can enhance or reduce the pressure losses in the flow. Waves that propagate against the flow always reduce the pressure losses, while waves that propagate with the flow can only reduce the losses if they are sufficiently slower than the flow. It is demonstrated that a significant increase in pressure losses can be achieved when the properties of the waves align with the natural frequencies of the flow. Finally, it is shown that the pumping effect generates propulsion if one of the walls is allowed to move.