Resonance Frequencies of Ventilated Wind Tunnels

Abstract

EXPERIMENTS suggest that the theory widely used to predict the transverse resonance frequencies in slotted tunnels is in error in the 0-0.5 Mach number range. One reason for the error is that the theory is based on an unrepresentative wall boundary condition. Moreover, the theory implies that the plenum chamber depth is generally less than twice the tunnel height. An improved theory is developed which shows that the resonance frequencies of ventilated tunnels are influenced by the depth of the plenum chamber for Mach numbers up to about M=0.6. Although the theory is approximate, it agrees well with experiments for slotted and perforated walls (with both normal and 60 deg inclined holes) in a small pilot wind tunnel (100 x 100 mm). The earlier theory was only valid for slotted working sections. The results are consistent with other experiments, which show that plenum chamber design can influence the flow unsteadiness within the working section of a ventilated tunnel. Contents The previous theory for the resonance frequencies1 assumed that the oscillatory pressure difference across the equivalent homogeneous wall (which replaced the slotted wall) was independent of the plenum chamber size and proportional to the streamline curvature. The new theory2 includes a plenum chamber and uses the notation shown in Fig. 1. The two-dimensional working section extends from x= — oo to + 00 and has a uniform flow velocity U at a Mach number M. It is surrounded by two plenum chambers, each of depth dH/2, with zero mean flow. The working section is separated from the plenum chambers by homogeneous ventilated walls, which are thin, rigid, and have no boundary layers. For simplicity, we assume that the mean pressure and static temperature are the same in the working section and plenum chambers. Hence, the densities in the freestream and plenum chambers are the same. We know from the measurements of Smith and Shaw,3 however, that the static temperature within a cavity is close to the freestream total temperature, not the freestream static temperature; but the error in density is trivial at Mach numbers up to M= 1.0. For the oscillatory flow we seek compatible solutions for the velocity potentials c/> and \l/ in the freestream and plenum chambers. The boundary condition on the outer walls of the plenum chamber is simply that the normal velocity should be zero. Thus, plenum chamber, so that