Optimization of viscoelastic compliant walls for transition delay

Abstract

The potential of wall compliance for delaying boundary-layer transition through the attenuation of TollmienSchlichting waves (TSW) has been recognized in many previous theoretical studies. The present paper seeks to determine the best transition-delaying performance possible using compliant walls made from viscoelastic materials for marine applications. The wall may take the form of either a homogeneous slab of material or a thin, stiff upper layer resting on a thick, soft substrate, the latter type holding the most promise in the practical use of compliant walls. To determine the growth rates of the TSW, a highly efficient means of solving the coupled Orr-Sommerfeld/compliant-wall eigenproblem is presented. Using spectral methods, the eigenproblem is cast in a matrix form which can then be solved using an SIMD parallel computer. What prevents the use of very soft compliant walls to suppress TSW completely is the existence of hydroelastic instabilities in the wall/flow system, namely traveling-wave flutter (TWF) and divergence. Efficient methods are also presented for the evaluation of these wall-based instabilities. A thorough investigation of the effects of the wall configuration and its material properties is carried out. Both single- and double-layer walls are optimized over the full range of wall parameters. It is shown that the best performance of single- and double-layer viscoelastic walls, respectively yield 2.5- and 5-fold delays of transition when compared with a rigid wall. These factors have been achieved using the conservative value of n = 1 in the en calculations.