Unsteady Characteristics of Nonlinear Pressure Loss in a Flow through a Restrictor

To elucidate the unsteady characteristics of a nonlinear pressure loss generated in a restricted flow, pressure drops across and flow rates through an orifice were precisely measured in sinusoidally oscillating oil flows. It has turned out that the unsteady relationship between the nonlinear pressure loss and the flow rate describes a closed loop turning around along the characteristic curve of the steady-state one in the counter-clockwise direction, which indicates that the change of the nonlinear pressure loss is delayed behind that of the flow rate in an unsteady orifice flow. The phenomenon occurs probably because the structure of turbulence in an orifice jet flow, where a nonlinear pressure loss is generated by energy dissipation, has inertia against a change of the flow rate and cannot follow it without a time lag. A mathematical model incorporating a constant time lag into the steady-state nonlinear pressure loss was proposed to simulate the unsteady characteristics of the nonlinear pressure loss, successfully explaining the long-term question in acoustics why the reactive part of an acoustic orifice impedance decreases as the amplitude increases.