Theories of compliant coating drag reductions

Abstract

Approximately two decades ago, Kramer1–3 reported skin friction drag reductions of up to 60% for compliant-walled bodies towed in water. Since Kramer’s initial experiments, many other investigators have delved into this intriguing area. The results have been mixed. Some have reported drag reductions in water and air with compliant coatings while others found no decrease in drag. Most of those who found decreases have reported that these decreases were found when the compliant wall was immersed in a turbulent boundary layer. Kramer originally stated that he felt the drag reduction was perhaps due to retarding the transition from laminar to turbulent flow. Benjamin,4 Boggs and Tokita,5 Landahl,6 Kaplan,7 and Gyorgyfalvy8 were among the early theoreticians who examined the possibilities of retarding transition by compliant walls. Generally, their calculations showed that with the proper compliant wall properties it was theoretically possible to retard transition. A few years later most of the theoretical work was aimed at trying to explain how a compliant coating might respond to a turbulent boundary layer in such a manner so as to reduce the turbulent wall skin friction. Different theories were proposed by Ffowcs-Williams,9 Blick,10 Amfilokhiyev,11 Semenov,12 Grosskreutz,13 Ash,14 and Zimmerman.15 Most of the theories are somewhat incomplete, some had errors in them, and none have demonstrated that they adequately explain all, or even a sizeable portion of the body of experimental data. However, at the moment Semenov’s theory seems to hold the most promise.