Numerical simulation of minor losses due to a sudden contraction and expansion in high amplitude acoustic resonators

A time-accurate high-order numerical simulation is used to study the minor losses due to an abrupt change in a resonator's cross-sectional area. A finite amplitude standing wave is established in the resonator using two different types of driver. In one case the entire resonator is shaken and in the other a line source is used to simulate the effect of a piston. It is found that a net pressure difference is generated across the change in cross-sectional area. It is due to the minor loss coefficients being different in one half cycle than the other in an oscillatory flow. This net pressure difference is almost a constant along the resonator. The results of the numerical simulation are in a very good agreement with the results of a complementary experiment for a wide variety of the operating conditions. It is found that a quasi-steady approach underpredicts the minor losses. An empirical relationship is defined for the minor losses based on the results of the numerical simulation. An approach based on the second law of thermodynamics is also used to examine the loss of availability due to the net minor loss.