Second Order Effects Of Oscillating Gas In Tubes Of Small Diameter

Abstract

The subject of this paper is the oscillations in a viscous and heat-conducting gas contained in a tube of small diameter, induced by harmonic pressure variations at the tube inlet. The amplitude of the inlet pressure variations is assumed to be significantly higher than that characteristic for acoustic oscillations. The maximum values of the amplitude are constrained by the laminar-turbulent transition criteria, and the limiting amplitudes of the laminar state of the motion are low enough so that only weakly non-linear effects are caused for which the perturbation method can be used. The second order complex amplitudes of the oscillating gas parameters, are determined in this paper. The most interesting results concern the pressure and velocity perturbations and they are presented as functions of the non-dimensional frequency and damping numbers. The thus determined second order terms are then compared with the known first order ones. Several examples of such comparisons for the pressure lead to the conclusion that the second order terms may add significant contributions to the solution of the problem. The problem is important in connection with pressure measuring technique in an unsteady gas stream, in which the pressure signal is transmitted pneumatically from the port of a pitot tube or a hole to the point at which it is sensed. The relation between the oscillating pressure at the tube inlet and at the transducer face can be significantly changed by the second order terms presented here.