Model of drag reduction by compliant walls

Abstract

A numerical model of the effect of compliant walls on turbulent boundary layer flows, has been investigated. The model is based on Burton’s1 observation that turbulent bursts produce large pressure fluctuations that tend to produce low speed ’’streaks’’ near the wall. These streaks undergo space-time retardation and a new burst appears when the velocity profile becomes highly inflectional. The idea of the model is that the compliant wall motion interrupts this feedback loop of burst formation and that short wavelength wall motions can possibly delay burst formation long enough for the favorable gradient part of the pressure pulse caused by previous bursts to effect a decrease in the burst frequency. The numerical model involves solution of the two-dimensional time-dependent Navier–Stokes equations in a rectangular geometry. A typical calculation is performed using 257 grid points in the downstream direction with inflow-outflow boundary conditions applied. In the boundary layer direction 33 Chebyshev polynomials are used; linearized boundary conditions are applied at the compliant boundary and a match is made to a logarithmic velocity profile in the outer region. A large moving pressure pulse is applied in the outer region and it is assumed that the background turbulent Reynolds stress between bursts is a small fraction of the mean stress. This code is used to determine mean velocity profiles and has been checked thoroughly by comparison with the velocity profiles measured by Blackwelder. A stability analysis is then made of the resulting mean velocity profiles. The results of the stability analysis are not yet complete and will be reported in detail elsewhere.2 The results of our calculations to date indicate that only very small wavelength wall motions have a significant effect upon the stability of the turbulent boundary layer. This result suggests that novel structural dynamics will be an essential component of successful drag reduction by compliant walls. This work was supported by the National Aeronautics and Space Administration Langley Research Center under contract No. NAS1-14275.