Drag reduction at a plane wall

By D. C. Hill1. Motivation and objectivesThe reduction of the turbulent drag arising from flow over a wall is a majortechnological issue. Over the years, many schemes have been proposed to reduceturbulent drag (large eddy break-up devices, compliant walls, polymer addition,riblets etc.), with varied rates of success. The use of riblets, for example, canlead to about a 7% reduction in drag. The use of computational and theoreticalmethods has emerged recently as an effective tool for understanding new aspects ofthe physics of drag reduction.Abergel & Temam (1990) describe how theoretical optimal control schemes canbe developed for turbulent flow fields. The formulations are highly idealized andcannot be implemented even computationaUy due to a requirement for prohibitivelylarge data storage and computations. The problem lies in the need to have perfectknowledge of the flow field and its history in order to achieve the best drag reductionpossible.The so-called sub-optimal scheme (Choiet al. 1993) has more modest objectives.A distribution of control forces is derived based on the instantaneous state of thesystem, thereby eliminating the need to retain and investigate the entire history.The procedure has been shown to work well for the one-dimensional Burgers equa-tion, with both distributed and boundary control. Encouraged by the success of thisapproach, Bewley et al. have pursued the application of the sub-optimal scheme forchannel flow. A detailed description of the method and their results is reported inthis volume of the annual research briefs.The objective of the present work is to determine by analytical means how drag ona plane wall may be modified favorably using a minimal amount of flow information- preferably only information at the wall. What quantities should be measured?How should that information be assimilated in order to arrive at effective control?As a prototypical problem, we consider incompressible, viscous flow, governed bythe Navier-Stokes equations, past a plane wall at which the no-slip condition hasbeen modified. The streamwise and spanwise velocity components are required tobe zero, but the normal component is to be specified according to some controllaw. The challenge is to choose the wall-normal velocity component based on flowconditions at the wall so that the mean drag is as small as possible. There can be nonet mass flux through the wall, and the total available control energy is constrained.A turbulent flow is highly unsteady and has detailed spatial structure. The meandrag on the wall is the integral over the wall of the local shear forces exerted by thefluid, which is then averaged in time; it is a "macroscopic" property of the flow. Itis not obvious how unsteady boundary control is to be applied in order to modifythe mean flow most effectively, especially in view of the non- self-axijoint nature ofhttps://ntrs.nasa.gov/search.jsp?R=19940019667 2020-05-29T05:37:36+00:00Z