Direct Numerical Simulation Of A Spatially Developing Turbulent Boundary Layer Separating Over A Curved Wall

Flow separation is encountered in many engineering devices, e.g., turbines, diffusers, wings and aftbodies of aircrafts. The physical mechanisms of separated turbulent boundary layers over curved walls are not yet well understood. The main objectives of the present study are to: (i) develop an efficient numerical methodology to perform direct numerical simulations (DNS) of spatially-developing turbulent boundary layers (SDTBLs) over curved walls, and (ii) enhance our knowledge on the dynamics of turbulence in SDTBLs separating over curved walls. To achieve these objectives, we have developed a new pressure-correction method, called FastRK3, for simulating incompressible flows over curved walls. FastRK3 solves the incompressible Navier-Stokes (NS) equations written in orthogonal curvilinear coordinates. The orthogonal formulation of the NS equations substantially reduces the computational cost of the flow solver and the numerical stencils of its second-order finite difference discretization mirror that of the Cartesian formulation. This property allows us to develop an FFT-based Poisson solver for pressure, called FastPoc, for those cases where the components of the metric tensor are independent of one spatial direction: surfaces of linear translation (e.g., curved ramps and bumps) and surfaces of revolution (e.g., axisymmetric shapes). Our results show that the new FFT-based Poisson solver, FastPoc, is thirty to sixty times faster than the multigrid-based linear solver, and the new flow solver, FastRK3, is overall four to seven times faster when using FastPoc rather than multigrid. FastRK3 is an explicit, three-stage, third-order Runge-Kutta based projection-method which requires solving the Poisson equation for pressure only once per time step. We show theoretically and numerically that (i) FastRK3 has the same temporal order of accuracy for pressure and velocity as the standard RK3 method for both free-shear and wall-bounded flows when the RK3 coefficients and the pressure extrapolation scheme satisfy specific conditions herein theoretically derived, (ii) FastRK3 is third-order accurate in time for velocity and second-order accurate in time for pressure for free-shear flows, and (iii) FastRK3 is second-order accurate in time for velocity and pressure for `stiff' wall-bounded flows. In summary, given that the computational mesh satisfies the property of orthogonality, FastRK3 simulates flows over curved walls with second-order accuracy in both space and time. Using FastRK3, we perform DNS of a SDTBL separating over a curved wall. We validate FastRK3 by comparing our numerical results with published experiments. For the first time, we derive the budget equations of the turbulence kinetic energy and of the Reynolds stresses in orthogonal coordinates, and report the results from our DNS. We study the dynamics of turbulence of the separated flow over the curved wall by analyzing these budget equations. Our analysis shows that, in the separated region over the curved ramp, the TKE production occurs through the production of (u2) as well as (v2) in contrast to a ZPG SDTBL where the TKE production is mostly through the production of (u2). In the curved ramp region, the viscous diffusion and dissipation of (v2) and (uv) are not zero at the wall, unlike that for both a ZPG SDTBL over a flat-plate as well as a pressure-gradient induced turbulent flow separation over a flat plate. And, the curved ramp region of the flow is characterized by enhanced transport of the Reynolds stresses compared to those of the upstream ZPG SDTBL due to the mixing layer created in the flow by the flow separation. Finally, our results have shown, for the first time, that the Reynolds stress profiles and budgets in the orthogonal curvilinear coordinates are very similar to those in the APG region of the 'pressure-gradient induced flow separation' in a flat-plate turbulent boundary layer. Such a comparison is only possible because (i) we employ a structured orthogonal grid over the curved ramp in our simulations, and (ii) FastRK3 solves the governing equations written in orthogonal curvilinear coordinates.

This volume provides a snapshot of the current and future trends in turbulence research across a range of disciplines. It provides an overview of the key challenges that face scientific and engineering communities in the context of huge databases of turbulence information currently being generated, yet poorly mined. These challenges include coherent structures and their control, wall turbulence and control, multi-scale turbulence, the impact of turbulence on energy generation and turbulence data manipulation strategies. The motivation for this volume is to assist the reader to make physical sense of these data deluges so as to inform both the research community as well as to advance practical outcomes from what is learned. Outcomes presented in this collection provide industry with information that impacts their activities, such as minimizing impact of wind farms, opportunities for understanding large scale wind events and large eddy simulation of the hydrodynamics of bays and lakes thereby increasing energy efficiencies, and minimizing emissions and noise from jet engines. Elucidates established, contemporary, and novel aspects of fluid turbulence - a ubiquitous yet poorly understood phenomena; Explores computer simulation of turbulence in the context of the emerging, unprecedented profusion of experimental data,which will need to be stewarded and archived; Examines a compendium of problems and issues that investigators can use to help formulate new promising research ideas; Makes the case for why funding agencies and scientists around the world need to lead a global effort to establish and steward large stores of turbulence data, rather than leaving them to individual researchers.

The fifth ERCOFfAC workshop 'Direct and Large-Eddy Simulation-5' (DLES-5) was held at the Munich University of Technology, August 27-29, 2003. It is part of a series of workshops that originated at the University of Surrey in 1994 with the intention to provide a forum for presentation and dis cussion of recent developments in the field of direct and large-eddy simula tion. Over the years the DLES-series has grown into a major international venue focussed on all aspects of DNS and LES, but also on hybrid methods like RANSILES coupling and detached-eddy simulation designed to provide reliable answers to technical flow problems at reasonable computational cost. DLES-5 was attended by 111 delegates from 15 countries. Its three-day pro gramme covered ten invited lectures and 63 original contributions partially pre sented in parallel sessions. The workshop was financially supported by the fol lowing companies, institutions and organizations: ANSYS Germany GmbH, AUDI AG, BMW Group, ERCOFfAC, FORTVER (Bavarian Research Asso ciation on Combustion), JM BURGERS CENTRE for Fluid Dynamics. Their help is gratefully acknowledged. The present Proceedings contain the written versions of nine invited lectures and fifty-nine selected and reviewed contributions which are organized in four parts: 1 Issues in LES modelling and numerics 2 Laminar-turbulent transition 3 Turbulent flows involving complex physical phenomena 4 Turbulent flows in complex geometries and in technical applications.

A good understanding of turbulent compressible flows is essential to the design and operation of high-speed vehicles. Such flows occur, for example, in the external flow over the surfaces of supersonic aircraft, and in the internal flow through the engines. Our ability to predict the aerodynamic lift, drag, propulsion and maneuverability of high-speed vehicles is crucially dependent on our knowledge of turbulent shear layers, and our understanding of their behavior in the presence of shock waves and regions of changing pressure. Turbulent Shear Layers in Supersonic Flow provides a comprehensive introduction to the field, and helps provide a basis for future work in this area. Wherever possible we use the available experimental work, and the results from numerical simulations to illustrate and develop a physical understanding of turbulent compressible flows.