Feathered Valve Closures

(Smyth, Abel, & Smith)

$$\frac{dU}{dt} = \frac{\sqrt{2}A(t_0)^{\frac{1}{2}}}{\rho}(p_0(t_0) - p_1(t_0)) - \frac{U(t_0)^2}{\sqrt{2}A(t_0)^\frac{3}{2}}$$

• The volume-flow Bernoulli term behaves differently depending on whether the channel area $A(t)$ is small or large.

• When $A(t)$ is small and the volume flow $U(t)$ changes direction, the volume flow is truncated to zero.

• Problem: Truncation is inaccurate, causing aliasing.