THE INFLUENCE OF A LIQUID FLOW ON SOUND FIELDS CONFINED BY CONICAL WALLS

Sound propagation in conical waveguides is analyzed for the case where a background flow is maintained through the cone and points along the radial co-ordinate r only. A general expression for the acoustic pressure is derived and the perturbations of the acoustic field accommodated by the presence of a background flow are found by use of the Green function method. In the second part of this paper, flow measurement properties are discussed. The designation of propagation constants such as the wave number and phase speed lose much of their intuitive meaning in a conical waveguide. Instead, the so-called pseudo-guide wave number and pseudo-phase speed are introduced as they are well defined in the cone case and simplifies to the wave number and phase speed in the cylinder case respectively. It is shown that changes due to a background flow in pseudo-guide wave number, pseudo-phase speed, and zero-point crossing times all exhibit an oscillatory behavior as a function of the r co-ordinate. This is in contrast to the case of a cylinder where such changes become a linear function of the distance from the transmitter. The oscillatory behavior in the changes in zero-point crossing times as a function of r does not hamper flow measurement in the cone case since the only requirement to be fulfilled is, in principle, that a one-to-one correspondence between measured output (changes in zero-point crossing times) and actual flow (determined byv0 ) at a specific receiver location exists. It is shown that this requirement is fulfilled as changes in zero-point crossing times depend linearly on the flow coefficient v0at a given r co-ordinate. There are, however, certain discrete r co-ordinate values where this is not the case, namely those where changes in zero-point crossing times become zero for any value of v0. In other words, if the receiver is positioned near r co-ordinates where zero-point crossing times are at a maximum or a minimum for a given value of v0, the truncated cone flow meter sensor is able to measure flow unambiguiosly by detection of changes in zero-point crossing times induced by a background flow.