Effect of nonsymmetric flow resistance upon orifice impedance

Abstract

Previous laboratory work has indicated that dc flow resistance of an orifice may be dependent upon the direction of flow, especially in the presence of a crossflow on one side of the hole. Here, an analytical study is presented which assumes a nonreactive orifice in an infinite baffle. An ambient pressure difference, Δp, exists across the orifice, and the pressure on one side varies sinusoidally with amplitude 1.0. The resultant flow is taken to be quasisteady. The orifice resistance, Δp/u, is discontinuous at zero velocity and exhibits the constant values R+ and R− for u > 0 and u < 0, respectively. An expression is found for the pressure difference, d = (Δp)ū=0, required for zero net flow as a function of the resistance ratio R+/R−. It is found that if 0.5 ⩽ R+/R− ⩽ 2.0, then |d| ⩽ 0.22 and a frequency analysis of the flow velocity (for δp = d) shows little energy in harmonics of the excitation frequency. Thus, for R+/R− near unit, an equivalent constant resistance, Re, which accounts for small energy loss to harmonics, may be an adequate expression for the acoustical impedance of the orifice for some purposes.