Rotary Flow Meter as Turbulence Transducer

Abstract

Two factors prevent the direct determination of the point spectrum of axial turbulence from a spectrum of the fluctuations in rpm values of the analog output of a rotary flow meter. The first of these is the effect of the finite size of the flow meter propeller, the second is the effect of its inertia. The finite size effect depends on the local turbulence structure and is characterized by an efficiency factor which in general can only be estimated. The effect of propeller inertia can be evaluated by linearizing the equation of motion of the propeller. From the resulting linear ordinary differential equation with constant coefficients, a transfer function for the linear system can be calculated. This transfer function makes it possible to calculate a spectrum of axial turbulence in which the velocity is averaged over the area of the propeller. Experiments in which propellers were oscillated sinusoidally while being towed through still water showed that the amplitude response function is approximately equal to that of a first-order system, while the phase function appeared to be independent of the natural frequency of the system.