Numerical Studies On Laminar Turbulent Transition In Boundary Layers

Methodic investigations of laminar-turbulent transition in wall-bounded she ar flows under controlled conditions are essential for untangling the various complex phenomena of the transition process occurring in flows at practical conditions. They allow understanding of the instability processes of the la minar flow, and thus enable the development of tools for flow control. On the one hand the laminar flow regime can be extended by delaying transition to reduce viscous drag, and on the other hand large-scale flow disturbances or transition can be forced in order to enhance momentum and mass ex change. Thus flow separation can be prevented, or mixing of fuel and air in combustion engines enhanced, for instance. The "DFG Verbund-Schwerpunktprogramm Transition" - a cooperative priority research program of universities, research establishments and indu stry in Germany - has been launched in April 1996 with the aim to explore transition by a coordinated use, development and validation of advanced experimental techniques and theoretical/numerical simulation methods, bin ding together all the appropriate resources available in Germany. At the very beginning of the six-year research period specifically selected test problems were to be investigated by various theoretical and experimental methods to identify and possibly rule out inadequate numerical or experimental methods. With respect to experiments it was planned to use multi-sensor-surface measuring techniques, the infrared measuring technique, and particle image velocimetry (PlV) in addition to hot-wire techniques to get instantaneous images of flows in sections, on surfaces, or within the complete flow field.

A finite-difference technique is developed for analyzing the time-dependent two-dimensional flow of an incompressible viscous fluid over a semi-infinite flat plate. The complete (nonlinear) equations of motion for perturbed Blasius flow are numerically integrated with respect to time, and the propagation of disturbances in the boundary layer is determined. An analysis of the theoretical convergence and stability properties of the difference scheme is carried out. The method developed has been employed in two test calculations, in which slightly unstable oscillatory disturbances have been introduced at some upstream point. The numerical solutions exhibit many of the major theoretical and experimentally observed features associated with transition from laminar to turbulent boundary-layer flow. (Author).

The workshop concentrated on the following turbulence test cases: T1 Boundary layer in an S-shaped duct; T2 Periodic array of cylinders in a channel; T3 Transition in a boundary layer under the influence of free-stream turbulence; T4 & T5: Axisymmetric confined jet flows.

The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are many practical applications for information regarding transition location and the details of the subsequent turbulent flow. This proceedings volume contains the papers of two keynote lectures as well as of 104 technical presentations and posters that were presented at the IUTAM Symposium on Laminar-Turbulent Transition in Sedona, Arizona, September 13-17, 1999. The papers published in the present volume document the state of the art in transition research, and therefore, increased emphasis on the various topics covered in this meeting can be expected in the future.

Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculating two-dimensional and axisymmetric laminar and turbulent boundary layers. This book will be useful to readers who have advanced knowledge in fluid mechanics, especially to engineers who study the important problems of design.

A finite-difference technique is developed for analyzing the time-dependent two-dimensional flow of an incompressible viscous fluid over a semi-infinite flat plate. The complete (nonlinear) equations of motion for perturbed Blasius flow are numerically integrated with respect to time, and the propagation of disturbances in the boundary layer is determined. An analysis of the theoretical convergence and stability properties of the difference scheme is carried out. The method developed has been employed in two test calculations, in which slightly unstable oscillatory disturbances have been introduced at some upstream point. The numerical solutions exhibit many of the major theoretical and experimentally observed features associated with transition from laminar to turbulent boundary-layer flow.

A numerical method for solving the equations for laminar, transitional, and turbulent compressible boundary layers for either planar or axisymmetric flows is presented. The fully developed turbulent region is treated by replacing the Reynolds stress terms with an eddy viscosity model. The mean properties of the transitional boundary layer are calculated by multiplying the eddy viscosity by an intermittency function based on the statistical production and growth of the turbulent spots. A specifiable turbulent Prandtl number relates the turbulent flux of heat to the eddy viscosity. A three-point implicit finite-difference scheme is used to solve the system of equations. The momentum and energy equations are solved simultaneously without iteration. Numerous test cases are compared with experimental data for supersonic and hypersonic flows; these cases include flows with both favorable and mildly unfavorable pressure gradient histories, mass flux at the wall, and traverse curvature.

Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at late stages of transition. These include secondary instabilities and nonlinear features of boundary-layer perturbations that lead to the final breakdown to turbulence. Thus, the reader is provided with a step-by-step approach that covers the milestones and recent advances in the laminar-turbulent transition. Special aspects of instability and transition are discussed through the book and are intended for research scientists, while the main target of the book is the student in the fundamentals of fluid mechanics. Computational guides, recommended exercises, and PowerPoint multimedia notes based on results of real scientific experiments supplement the monograph. These are especially helpful for the neophyte to obtain a solid foundation in hydrodynamic stability. To access the supplementary material go to extras.springer.com and type in the ISBN for this volume.