Numerical Studies Of Transitiion From Laminar To Turbulent Flow Over A Flat Plate

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).

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).

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.

The 24 papers presented at the international concluding colloquium of the German priority programme (DFG-Verbundschwerpunktprogramm) "Transition", held in April 2002 in Stuttgart. The unique and successful programme ran six years, starting April 1996, and was sponsored mainly by the Deutsche Forschungsgemeinschaft, DFG, but also by the Deutsches Zentrum für Luft-und Raumfahrt, DLR, the Physikalisch-Technische Bundesanstalt Braunschweig, PTB, and Airbus Deutschland. The papers summarise the results of the programme and cover transition mechanisms, transition prediction, transition control, natural transition and measurement techniques, transition - turbulence - separation, and visualisation issues. Three invited papers are devoted to mechanisms of turbulence production, to a general framework of stability, receptivity and control, and a forcing model for receptivity analysis. Almost every transition topic arising in subsonic and transonic flow is covered.

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 any number of applications for information regarding transition location and the details of the subsequent turbulent flow. The JUT AM Symposium on Laminar-Turbulent Transition, co-hosted by Arizona State University and the University of Arizona, was held in Sedona, Arizona. Although four previous JUT AM Symposia bear the same appellation (Stuttgart 1979, Novosibirsk 1984, Toulouse 1989, and Sendai 1994) the topics that were emphasized at each were different and reflect the evolving nature of our understanding of the transition process. The major contributions of Stuttgart 1979 centered on nonlinear behavior and later stages of transition in two-dimensional boundary layers. Stability of closed systems was also included with Taylor vortices in different geometries. The topics of Novosibirsk 1984 shifted to resonant wave interactions and secondary instabilities in boundary layers. Pipe- and channel-flow transition were discussed as model problems for the boundary layer. Investigations of free shear layers were presented and a heavy dose of supersonic papers appeared for the first time. The character of Toulouse 1989 was also different in that 3-D boundary layers, numerical simulations, streamwise vortices, and foundation papers on receptivity were presented. Sendai 1994 saw a number of papers on swept wings and 3-D boundary layers. Numerical simulations attacked a broader range of problems.

Research has resulted in the derivation of a numerical scheme for the solution of the complete Navier-Stokes equations for two-dimensional time-dimensional time-independent viscous incompressible flow, as applied to the problem of the development of turbulence in the laminar boundary layer on a flat plate. The basic equations are reduced to a single quasi-linear vorticity-transport equation plus a Poisson equation; these are then written in finite-difference form. The solution of the difference system comprises a semi-implicit scheme for the quasi-linear equation together with an extrapolated line-Liebmann iteration method for the linear Poisson analog. Solutions for the two cases investigated (very low amplitude linear and very high amplitude nonlinear) are presented and discussed. The numerical scheme is demonstrated to be stable and capable of generating solutions which exhibit major theoretical and/or experimentally-observable features for each of the two cases. (Author).

A number of aspects of transition from laminar to turbulent flow were investigated on a flat plate with free stream water velocities between .75 feet per second and 1.2 feet per second. The study was primarily visual, using dye techniques, although some measurements were made using a hot film anemometer. Also investigated were the later stages of natural transition. Dye patterns associated with the chain of events leading from laminar to turbulent flow in natural transition were analyzed. (Author).

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.