Stability of Shear Layers over Rough Surfaces

Presence of surface imperfections may have significant impact on the stability of the adjacent shear layer and on the laminar-turbulent transition process in this layer. The main objective of the present study is the quantitative assessment of such effects in the case of distributed surface roughness. The analysis is focused on the linear stability theory and considers asymptotic as well as transient growth of flow perturbations. The explicit calculations are carried out in the context of channel flow. 1.0 INTRODUCTION Understanding of the transition process in flows over rough surfaces is one of fundamental questions in fluid dynamics. This question is of practical interest in aerospace applications including the classical problem of the design of laminar airfoils as well as in the more current problem of the design of surface modifications for flow control. The latter application area involves development of strategies for improvement of mixing for better control/manipulation of the separations process in boundary layers and has significant potential for creation of means for active/passive manipulation of heat transfer in engines. Flows over rough walls have been studied since the early works of Hagen [Hagen 1854] and Darcy [Darcy 1857], which were focused on turbulent regimes. Reynolds [Reynolds1883] was the first to pose the problem in the context of laminar-turbulent transition. In spite of many attempts [Schlichting 1979] the resolution of this problem is still uncertain. The original investigations involved measurements of flows in open channels and in pipes. Various possible roughness forms were classified using the concept of “equivalent roughness”. Jimenez [Jimenez 2004] gives a nice description of the history and the current state-of-the-art of this concept. The phenomenological effects of the “equivalent roughness” are summarized in the form of friction coefficient [Nikuradse 1933], [Colebrook 1939], [Moody 1944]. These and other similar investigations show that surface roughness contributes directly to the dynamics of flow only if the wall is hydraulically rough. The concept of hydraulic smoothness is conceptually very appealing, however no precise criterion exists that would allow to predict if a given surface can be considered as being hydraulically smooth for flow conditions of interest. While the modelling concepts of this type have been continuously re-evaluated [Bradshaw 2000] and improved [Waigh 1998], they failed so far to uncover the mechanisms that govern the complex, flowcondition-dependent interaction between the roughness geometry and the moving fluid. There were a number of concepts pursued in the attempt to link distributed surface roughness with the transition process. Singh [Sigh 1972], Lessen [Lessen 1976] and Kendall [Kendall 1981] considered roughness -distorted average velocity profile, but linear stability analysis of this profile proved inconclusive. Paper presented at the RTO AVT Specialists’ Meeting on “Enhancement of NATO Military Flight Vehicle Performance by Management of Interacting Boundary Layer Transition and Separation”, held in Prague, Czech Republic, 4-7 October 2004, and published in RTO-MP-AVT-111. RTO-MP-AVT-111 16 1 UNCLASSIFIED/UNLIMITED UNCLASSIFIED/UNLIMITED Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 01 OCT 2004 2. REPORT TYPE N/A 3. DATES COVERED 4. TITLE AND SUBTITLE Stability of Shear Layers over Rough Surfaces 5a. CONTRACT NUMBER