The flow-induced pressures generated by turbulent boundary layers cause vibration and, ultimately, sound. The convected nature of the pressures has led to considerable sophistication in the mathematical modeling of boundary-layer-induced vibration and sound. The work in this general area has been applied, and is of direct importance, to the prediction and reduction of cabin noise in aircraft fuselages and automobile interiors, the vibration of reentry vehicles, sound in sonar domes, and vibrations and sound generated in pipes and ducts. This chapter will develop various ways of describing the forcing function, discussing the nature of the cross-spectral and wave vector properties of surface pressures generated by turbulent flow over smooth or rough surfaces that relate to the production of sound and vibration.

Essentials of Turbulent Wall Pressure Fluctuations

The present paper is concerned with the experimental study of the influence of Toms' phenomenon on the convective part of the hydrodynamic turbulent wall-pressure field. The experiments were carried out in a water tunnel, at flow velocities of 2.3, 3.3 and 4.3 m/s, where amounts of drag reduction up to 40% were obtained by injecting dilute polymer solutions. An investigation of the spectral feature of the wall-pressure frequency spectrum and the wall-pressure frequency cross-spectrum was achieved from data taken using pinhole transducers. The scaling laws for the mid- and high-frequency regions of the spectrum were examined both for the water flow and the drag-reducing flow. The use of a noise cancellation procedure allowed observation of the maximum of the spectrum in the mid-frequency range at an approximately reduced frequency ωδ u τ of 80 for the water flow. This maximum is shifted towards a higher value of the reduced frequency in the presence of Toms' effect. From cross-spectral data obtained over separation distances ranging from 0.4 δ to 2.8 δ, the effect of drag reduction was estimated on the coherence functions as well as the convection velocity. These data show a correlated shift of the threshold which delineates the low wave number group identified as the large-scale turbulence contributor in the outer region of the flow and the high wave number group associated with turbulent sources in the log-region. The effect of drag reduction on the convection velocity data supports the fact that the contributions to the different wave number groups should be attributable to activity in the outer and inner regions, respectively. In addition, a computation of the root mean square pressure was achieved from the wall-pressure frequency spectrum. When expressed as functions of the percentage of drag reduction, the rms pressures related to the wall shear stress are found to increase monotonicaly. The equivalent ratio obtained by scaling the rms pressures using the dynamic pressure is found to decrease in the drag-reducing flow. Finally, an estimation of the probability density distribution showed that the skin friction reduction affects predominantly the occurrence of higher pressure amplitudes as well as very low pressure amplitudes. This confirms the important contribution of the large pressure peak events to the overall features of the wall-pressure.

The effect of drag-reducing polymer additives on wall-pressure fluctuations in turbulent channel flows

Small amounts of high molecular weight polymers (a few parts per million by weight) dissolved in a solvent can reduce the turbulent flow frictional resistance from that of the pure solvent by as much as 90 percent. Since the viscosity of a polymer/solvent mix is slightly increased over that of the solvent alone, the fact that viscous drag is decreased is somewhat surprising. The study of these drag-reducing, non-Newtonian fluid flows received initial impetus from the study of Toms (1948). Since this work, the examination of the turbulent flow properties of dilute solutions of long chain high-molecular weight polymers has generated many hundreds of publications, of which a majority are experimental investigations. This preponderance of experimental studies is no doubt due to the difficult theoretical nature of the problem which must address not only the turbulent kinematics but also the interaction of a viscoelastic fluid with the turbulence. Several excellent reviews of the available experiments and possible explanations of this phenomenon have been published since Toms original work: Lumley (1969) & (1973), Hoyt (1972), Virk (1975), Little et al. (1975), and Berman (1978). Theoretical discussions of the drag reduction phenomenon can be found in Lumley (1973), Berman (1978) and a recent work by Ryskin (1987a). The text that follows includes a review of experimental methods utilized by both rheologists and fluid dynamicists in the examination of turbulent flows of drag-reducing polymer solutions. In addition, we review some of the major experimental findings and make recommendations for future research. Finally, we present some new measurements of wall pressure in a turbulent non-Newtonian channel flow.

E. M. Greshilov

Papers

Hydrodynamic noise and the Toms effect