Transducer resolution and the turbulent wall pressure spectrum

The size of a pressure transducer will affect the accuracy of measurements of the wall pressure beneath a turbulent boundary layer because of spatial averaging over the sensing area of the transducer. The effect of transducer size on the wall pressure spectrum was investigated by numerically applying wave-number filters corresponding to various size and shape transducers to a database of wall pressure generated from a direct numerical simulation of turbulent channel flow. Circular transducers with piston-type and deflection-type sensitivities were modeled along with square transducers having piston-type sensitivity. The rms wall pressure is attenuated less for a deflection-type transducer than for a piston-type transducer of the same area. The wave-number spectrum of the wall pressure measured using a large transducer has lobes and zeros corresponding to those in the wave-number response function of the transducer. These lobes and zeros in the wave-number spectrum are also evident in the frequency spectrum, although they are smeared. Using Taylor's frozen field hypothesis, an approximate upper bound on the frequency of wall pressure fluctuations that can be measured before the zeros in the wave-number response function is o>d/Uc<C, where co is the frequency, d the dimension of the transducer, Uc the convection velocity, and C 6.3, 7.7, and 11.0 for square piston, circular piston, and circular deflection transducers, respectively. The Corcos correction to the wall pressure spectrum recovers the true spectrum within this bound.