Direct and Large Eddy Simulation of Turbulence: Proceedings of the EUROMECH Colloquium No. 199, München, FRG, September 30 to October 2, 1985 PDF
Preview Direct and Large Eddy Simulation of Turbulence: Proceedings of the EUROMECH Colloquium No. 199, München, FRG, September 30 to October 2, 1985
Ulrich Schumann Rainer Friedrich (Eds.) Direct and Large Eddy Simulation of Turbulence Notes on Numerical Fluid Mechanics Volume 15 Series Editors: Ernst Heinrich Hirschel, MUnchen Maurizio Pandolfi, Torino Arthur Rizzi, Stockholm Bernard Roux, Marseille Volume 1 Boundary Algorithms for Multidimensional Inviscid Hyperbolic Flows (Karl Forster, Ed.) Volume 2 Proceedings of the Third GAMM-Conference on Numerical Methods in Fluid Mechanics (Ernst Heinrich Hirschel, Ed.) (out of print) Volume 3 Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves (Arthur Rizzi I Henri Viviand, Eds.) Volume 4 Shear Flow in Surface-Oriented Coordinates (Ernst Heinrich Hirschel I Wilhelm Kordulla) Volume 5 Proceedings of the Fourth GAMM-Conference on Numerical Methods in Fluid Mechanics (Henri Viviand, Ed.) (out of print) Volume 6 Numerical Methods in Laminar Flame Propagation (Norbert Peters I Jurgen Warnatz, Eds.) Volume 7 Proceedings of the Fifth GAMM-Conference on Numerical Methods in Fluid Mechanics (Maurizio Pandolfi I Renzo Piva, Eds.) Volume 8 Vectorization of Computer Programs with Applications to Computational Fluid Dynamics (Wolfgang Gentzsch) Volume 9 Analysis of Laminar Flow over a Backward Facing Step (Ken Morgan I Jaques Periaux I FranC!ois Thomasset, Eds.) Volume 10 Efficient Solutions of Elliptic Systems (Wolfgang Hackbusch, Ed.) Volume 11 Advances in Multi-Grid Methods (Dietrich Braess I Wolfgang Hackbusch I Ulrich Trottenberg, Eds.) Volume 12 The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics (Willi Schonauer I Wolfgang Gentzsch, Eds.) Volume 13 Proceedings of the Sixth GAMM-Conference on Numerical Methods in Fluid Mechanics (Dietrich Rues I Wilhelm Kordulla, Eds.) Volume 14 Finite Approximations in Fluid Mechanics (Ernst Heinrich Hirschel, Ed.) Volume 15 Direct and Large Eddy Simulation of Turbulence (Ulrich Schumann I Rainer Friedrich, Eds.) Manuscripts should have well over 100 pages. As they will be reproduced photomechanically they should be typed with utmost care on special stationary which will be supplied on request. In print, the size will be reduced linearly to approximately 75 %. Figures and diagrams should be lettered accordingly so as to produce letters not smaller than 2 mm in print. The same is valid for handwritten formulae. Manuscripts (in English) or proposals should be sent to the general editor Prof. Dr. E. H. Hirschel, Herzog-Heinrich-Weg 6, D-8011 Zorneding. Ulrich Schumann Rainer Friedrich (Eds.) Direct and Large Eddy Simulation of Turbulence Proceedings of the EUROMECH Colloquium No. 199, MUnchen, FRG, September 30 to October 2, 1985 Springer Fachmedien Wiesbaden GmbH CIP-Kurztitelaufnahme der Deutschen Bibliothek Direct and large eddy simulation of turbulence: proceedings of the Euromech Colloquium No. 199, Miinchen, FRG, September 30-0ctober 2, 1985 I Ulrich Schumann; Rainer Friedrich (ed.l. Braunschweig; Wiesbaden: Vieweg, 1986. (Notes on numerical fluid mechanics; Vol. 15) NE: Schumann, Ulrich [Hrsg.]; Euromech Colloquium (199, 1985, Miinchen>; GT All rights reserved © Springer Fachmedien Wiesbaden 1986 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig in 1986 No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise, without prior permission of the copyright holder. Produced by Lengericher Handelsdruckerei, Lengerich ISSN 0179-9614 ISBN 978-3-663-00048-8 ISBN 978-3-663-00197-3 (eBook) DOI 10.1007/978-3-663-00197-3 PREFACE This volume contains papers presented to a EUROMECH-Colloquium held in Munich, September 30 to October 2, 1985. The Colloquium is number 199 in a series of colloquia inaugurated by the European Mechanics Committee. The meeting was jointly organized by the 'Lehrstuhl fur Stromungsmechanik' at the 'Technische Universitat Munchen' and the 'Institut fur Physik der Atmosphare' of the 'Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt' (DFVLR) in Oberpfaffenhofen. 'Direct' and 'large eddy simulation' are terms which denote two closely con nected methods of turbulence research. In a 'direct simulation' (DS), turbu lent motion is simulated by numerically integrating the Navier-Stokes equations in three-dimensional space and as a function of time. Besides ini tial and boundary conditions no physical simplifications are involved. Com puter resources limit the resolution in time and space, though simulations with an order of one million discrete points in space are feasible. The simu lated flow fields can be considered as true realizations of turbulent flow fields and analysed to answer questions on the basic behaviour of turbulence. Direct simulations are valid as long as all the excited scales remain within the band of resolved scales. This means that viscosity must be strong enough to damp out the not resolved scales or the simulation is restricted to a lim ited integration-time interval only. In summary, DS provides a tool to investigate turbulent motions from first principles at least for a finite band of scales. Large eddy simulation (LES) is a combination of direct simulation with sta tistical modelling. The large 'eddies' are the motion structures at scales which remain after a certain filter has been applied to the turbulent field. This filter is strongly related to the discrete numerical representation of the flow field employed in the simulation algorithm. For a finite difference simulation the large scales must be resolvable by the underlying grid. In contrast, the 'subgrid-scales' are those which are too small for the grid. In LES, these subgrid-scales are modelled by a subgrid-scale (SGS) model. The SGS-model mainly provides the correct damping of those resolved scales which lie at the border of resolution and- which are excited by the large scale motions. Also, the SGS-model has to describe turbulent fluxes not represented by the large scales. SGS-models are formally very similar to the models com monly used to describe time- or ensemble-averaged turbulent fields. Thus they have bas ically the same advantages and disadantages. Approximation er,rors in SGS-models are of less importance, however, because the SGS-motion v carries only a fraction of total turbulent kinetic energy and fluxes. If the grid (and the related filter) is fine enough, this fraction becomes very small. In summary, LES serves as a tool to construct the large scale portion of turbulent fields at high Reynolds numbers. Direct turbulence simulations were pioneered by Orszag and co-workers since 1969. The first convincing large eddy simulations were reported by Deardorff in 1970 for a turbulent channel flow and applied to atmospheric boundary lay ers thereafter. His SGS-model employed a proposal by Smagorinsky (1963) for parametrization of subgrid-scale motions in meteorology. Lilly (1966) showed that this SGS-model is consistent with Kolmogorov's inertial-subrange theory. The state of the art as of 1983 was reported by Rogallo & Moin (1984). The Colloquium was concerned with the discussion of new developments in the field of DS and LES and its applications. The presentations included new aspects on the numerical algorithms to integrate the basic equations, treat ments of filtering, boundary and initial conditions, and subgrid-scale mod els. Also new concepts based on fractals and helicity were outlined which possibly are capable of influencing SGS-modelling in the future. The applica tions included transition and established turbulence, homogeneous and inhomogeneous turbulence. They were related to basic research as well as to engineering problems and to atmospheric boundary layers. We were glad to receive much response to our invitation. About fifty scien tists attended the colloquium, among them we could welcome most of the active researchers in the field, in particular from the USA and Japan, and about thirty papers have been presented. This was the first meeting of experts from all over the world on this special subject. As no collection of papers exists, which summarizes the present state of the art in DS and LES, it was decided to collect the contributions for the present volume. Each paper has been revised after being reviewed by at least one reviewer. A few contrib utions have the form of extended abstracts; they summarize results, which were presented at the Colloquium and which are described in more detail in papers under publication. Some contributions are not included because their content has been published just recently. However, we include the contrib ution of Dr. McComb who was not able to participate in the colloquium. The papers are grouped into sections of related subjects: 1. Transition to turbu lence, 2. Subgrid-scale models and basic concepts, 3. Large eddy simulations of wall-bounded shear flows, 4. Direct and large eddy simulations of mixed shear and buoyant flows, 5. Convective or stable atmospheric boundary layers. The volume ends up with summarizing statements on results, trends and recommendations. VI We are very grateful to all who supported the Colloquium and the resultant proceedings. We thank the Volkswagen Foundation, the companies Cray Research, Munich and Messerschmitt-Bolkow-Blohm, Munich for financial sup port of the meeting. Last, but not least we are indebted to all colleagues who contributed to the proceedings or took part in the reviewing process. Ulrich Schumann Rainer Friedrich April 1986 Oberpfaffenhofen Mlinchen VII CONTENTS Page 1. TRANSITION TO TURBULENCE N. GILBERT, L. KLEISER: Subcritical Transition to Turbulence in Channel Flow ................................. . T. HERBERT: Vortical Mechanisms in Shear Flow Transition. . . . . . .. 19 2. SUBGRID-SCALE MODELS AND BASIC CONCEPTS B. AUPOIX: Subgrid Scale Models for Homogeneous Anisotropic Turbulence 37 W. D. McCOMB: Application of Renormalization Group eRG) Methods to the Subgrid Modelling Problem. . 67 E. LEVICH~ Helical Fluctuations, Fractal Dimensions and Path Integral in the Theory of Turbulence . . . . . . . . . . . . . . . 82 3. LARGE EDDY SIMULATIONS OF WALL-BOUNDED SHEAR FLOWS S. GAVRILAKIS, H. M. TSAI, P. R. VOKE, D. C. LESLIE: Large-Eddy Simulation of Low Reynolds Number Channel Flow by Spectral and Finite Difference Methods . . . . . 105 K. HORIUTI, A. YOSHIZAWA: Large Eddy Simulation of Turbulent Channel Flow by 1-Equation Model .... . . 119 T. KOBAYASHI, M. KANO: Numerical Prediction of Turbulent Plane Couette Flow by Large Eddy Simulation . 135 D. LAURENCE: Advective Formulation of Large Eddy Simulation for Engineering Type Flows . . . . 147 L. SCHMITT, K. RICHTER, R. FRIEDRICH: Large-Eddy Simulation of Turbulent Boundary Layer and Channel Flow at High Reynolds Number 161 Short Contributions: J. KIM: Numerical Investigation of a Vortical Structure in a Wall- Bounded Shear Flow . . . . . . .. ........... . .. 177 VIII Page P. MOIN: Recent Results on the Structure of Turbulent Shear Flows using Simulation Databases 181 4. DIRECT AND LARGE EDDY SIMULATIONS OF MIXED SHEAR AND BUOYANT FLOWS T. M. EIDSON, M. Y. HUSSAINI, T. A. ZANG: Simulation of the Turbulent Rayleigh-Benard Problem using a Spectral/Finite Difference Technique. 188 G. GROTZBACH: Application of the TURBIT-3 Subgrid Scale Model to Scales Between Large Eddy and Direct Simulations 210 K. KUWAHARA, S. SHIRAYAMA: Direct Simulation of High-Reynolds-Number Flows by Finite-Difference Methods . . . . . . 227 U. SCHUMANN, S. E. ELGHOBASHI, T. GERZ: Direct Simulation of Stably Stratified Turbulent Homogeneous Shear Flows . . . 245 Short Contribution: R. W. METCALFE, S. MENON, J.J. RILEY: The Effect of Coherent Modes on the Evolution of a Turbulent Mixing Layer . 265 5. CONVECTIVE OR STABLE ATMOSPHERIC BOUNDARY LAYERS D. J. CARRUTHERS, J. C. R. HUNT, C. J. TURFUS: Turbulent Flow near Density Inversion Layers . . . . 271 C.-H. MOENG: A Large Eddy Simulation Model for the Stratus-Topped Boundary Layer . . . 291 F. T. M. NIEUWSTADT, R. A. BROST, T. L. van STIJN: Decay of Convective Turbulence, a Large Eddy Simulation . 304 6. SUMMARIZING STATEMENTS ON RESULTS, TRENDS AND RECOMMENDATIONS 318 List of Participants 336 List of Authors 340 IX
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