Response of a pliable coating to turbulent pressure pulsations

Abstract

The duration of the portions of coherence of turbulent pressure pulsations is determined experimentally. Based on this the dimensionless rate of deformation of the surface of a pliable coating is calculated with allowance for its inertial properties.Interest in studying pliable coatings was provoked by a series experiments of Kramer [1]. His coatings imitated the skin of dolphins, which can swim at an abnormally high speed. Kramer assumed that the coating damps Tollmin-Schlichting waves and thereby delays the transition to turbulence.Benjamin [2] assumed that a pliable coating can reduce friction in turbulent flow, modifying its boundary layer, but the character of the flow itself remains turbulent. Indeed, in Kramer's experiments, too, the turbulent friction was, apparently, reduced since there was a turbulizer in the forepart of his model. Many schemes of pliable coatings, a classification of which is proposed in [3], have been put forward and tested in the ensuing years. The greatest attention was paid to passive coatings deformed by turbulent pressure pulsations.To explain the friction reduction in a developed turbulent flow, two hypotheses have currently been developed. The first considers the propagation of deformation waves over the coating surface that are caused by the pressure pulsations on the wall. The friction reduction is associated with energy dissipation inside the wall. In the most developed theory [4], one predicts parameters of the coating material for which unstable deformations of the surface do not occur.The second theory [5] assumes that the coating is locally deformable. This means that running waves do not propagate from the site of application of the periodic deformation. The friction reduction is related to a change in the pattern of generation of Reynolds stresses (puv) in the wall region. Such a change is quite possible, since the component of the pulsating velocity v that is normal to the wall can change in both magnitude and phase because of deformation of the wall by the turbulent pressure pulsations. So far, neither theory can calculate the friction reduction; they are capable only of predicting the region of the parameters of the coating material where friction reduction is possible.In [6], a material whose properties are calculated according to the Duncan theory is used and a decrease in the turbulence intensity, coefficient of friction, and Reynolds stresses is obtained. Coatings calculated according to the Semenov theory turned out to be much more rigid but showed a decrease of up to ---17% in the friction and the level of pressure pulsations [7]. Tests of these coatings in a cavitation tunnel at the University of Newcastle carried out by independent researchers [8] using more sophisticated measuring equipment conf'umed the validity of the previous neasurements.Thus, there are two alternatives at present: "soft" coatings with running waves and locally deformable "rigid" coatings. To describe the operation of both coatings, we must know the manner in which the coating surface i...