Computation and Comparison of Efficient Turbulence Models for Aronautics - European Research Project ETMA Edited by Alain Dervieux Marianna Braza and Jean-Paul Dussauge Notes on Numerical Fluid Mechanics (NNF:NI) Volume 65 Series Editors: Ernst Heinrich Hirschel, MOnchen (General Editor) Kozo Fujii, Tokyo Bram van Leer, Ann Arbor Michael A. Leschziner, Manchester Maurizio Pandolfi, Torino Arth ur Rizzi, Stockholm Bernard Roux, Marseille Volume 65: Computation and Comparion of Efficient Turbulence Models for Aeronautics - ETMA project (A. Dervieux I M. Braza I J. P. Dussauge, EDS.) Volume 64: Computation and Visualization of Three-Dimensional Vortical and Turbulent Flows (R. Friedrich I P. Bontoux, Eds.) Volume 63: Vortil;es and Heat Transfer (M. Fiebig I Nimai K. Mitra, Eds.) Volume 62: Large-Scale Scientific Computations of Engineering and Environmental Problems (M. Griebel I O. P. I1iev IS. D. Margenov I P. S. Vassilevski, Eds.) Volume 61 Optimum Aerodynamic Design & Parallel Navier-Stokes Computations, ECARP-European Computational Aerodynamics Research Project (J. Periaux I G. Bugcda I P. Chaviaropoulos I K. Gianllokogloll I S. Lanteri I B. Mantel, Eds.) Volume 60 New Resull.s in Numerical and Experimental Fluid Mechallics. Contributions to the 10th AG STABIDGLR Symposium Braunschweig, Germany 1996 (H. Korner I R. Hilbig, Eds.) Volume 59 Modeling and Computations in Environmental Sciences. Proceedins of the First GAMM Seminar at ICA Stuttgart, October 12-13, 1995 (R. Helmig I W. Jager! W. Kinzelbach I P. Kllabner I G. Witturn, Eds.) Volume 58 ECARp .. · European Computational Aerodynamics Research Project: Validation of CFD Codes and Assessment of Turbulence Models (W. Haa,e I E. Chaput IE. Elsholz I M. A. LeschziJlcr I U. R. Mlill~r, Eds.) Volume 57 Euler and Nav;er-Stokes Solvers Using Multi-Dimensional Upwind Schemes and ~uJtigTid Acceleration. Results of the BRlTE/EURAM Projects AERO-CT89-0003 and AER2-CT92-00040.1989-1995 (H. Deconinck I B. Koren, Eds.) Volume 56 EUROSHOCK-Drag Reduktion by Passh;e Shock Control. R~slllts of the Project EUROSHOCK, AER2-Cf92-0049 Supported by the European Union, 1993-1995 (E. Stanewsky I J. Delery I 1. Fulker I W. GeiSler, Eds.) Volume 55 EUROPT .. A El.1ropean Initiati.ve on Optimum Design Methods in Aerodynamics. PrOl:eedings of the Brite/Euram Project Workshop .. Optimum Design in Aerodynamics", Barcelona, 1992 (J. Periaux I G. Bugeda I P. K. Chaviaropoulos I T. Labrujere I B. Stoufflet, Eds.) Volume 54 Boundary Elements: Implementation and Analysis of Advanced Algorithms. Proceedings of the Twelfth GAMM-Seminar, Kiel, January 19-21, 1996 (W. Hack-busch! G. Wittum, Eds.) Volume 53 Compl!tation of Three-Dimensional Complex Flows. Proceedin,gs of the IMACS-COST Conference on Computational Fluid Dynamics, Lausanne, September 13-15, 1995 (M. Deville I S. Gavrilakis I I. L. Ryhming, Eds.) Volume 52 Flow Simulation with High-Performance Computers II. DPG Priority Research Programme Results 1993-1995 (E. H. Hirschel. Ed.) Volumes 1 to 51 arc oct lIf print. The addresses of the Editors are listed at the end of the book. Computation and Comparison of Efficient Turbulence Models for Aeronautics - European Research Project ETMA Edited by Alain Dervieux Marianna Braza and Jean-Paul Dussauge I I VI.wag Die Deutsc.he Bibliothek - CIP-Einheitsaufnahme Compotation and comparison of emcient torbolence models for aeronaofics - Eoropean Researcb Project ETMA led. by Alain Dervieux ... - Braunschweig; Wiesbaden: Vieweg, 1998 (Notes on numerical fluid mechanics; VoI. 65) All rights reserved © Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 1998 Softcover reprint of the hardcover Ist edition 1998 Vieweg is a subsidiary company of the Bertelsmann Professional Information. No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise, without prior permis'lion of the copyright holdcr. http://www.vieweg.de Produced by Geronimo GmbH, Rosenheim Printed on acid-free paper ISSN 0179-9614 ISBN 978-3-322-89861-6 ISBN 978-3-322-89859-3 (eBook) DOI 10.1007/978-3-322-89859-3 FOREWORD AND INTRODUCTION The computation of complex turbulent flows by statistical modelling has already a long history. The most popular two-equation models today were introduced in the early sev enties. However these models have been generally tested in rather academic cases. The develope ment of computers has led to more and more acurate numerical methods. The interactions betwe~n numerical and modelling techniques are generally not well mastered. Moreover, computation of real life cases, including 3D effects, complex geometries and pressure gra dients based on two-equation models with low-Reynolds treatment at the proximity of walls are not really of common use. A large number of models has been proposed; this is perhaps the sign that none of them is really satisfactory, and then the assessment of their generality is not an easy task: it requires a lot of understanding of the physics and a lot of work for testing the large number of relevant cases in order to assess their limits of validity which is a condition for an improved confidence in engineering applications. This is probably why workshops and working groups are frequent and the ETMA consor tium has choosen to build a state of the art in theoretical and numerical statistical turbu lence modelling for real life computations by taking some marks with respect to previous workshops such as the Stanford meetings (1980,1981); some problems are kept or updated by new experiments, some problems are discarded, some new problems are introduced; the focus is kept on flows with 2D geometries. The ETMA Project The project on Efficient Turbulence Models for Aeronautics (ETMA) was established to study the statistical turbulence models, from the points of view of building new models, making new experiments, deriving new numerical methods, computing new cases or better computing existing cases. The aims of ETMA involved also knowledge dissemination through a data base involving experimental and numerical results together with numerical kernels. The ETMA project was co-financed by the Industrial and Materials Technology Pro gramme Area 3 Aeronautics under the Third Research Framework Programme of the Euro pean Union (EU). The ETMA Consortium Participants to the consortium were twenty research organisations and universities from eleven European countries and five industrial endorsers: ETMA Partners INRIA, Sophia-Antipolis/Rocquencourt (F) LSTM, Erlangen (D) 1ST, Lisbon (P) Ecole Centrale de Paris (F) Imperial College, London (UK) AFM, Lyngby (DK) Aero-Delft (NL) LAT, Patras (OR) NTUA-LTT, Athens (OR) NTUA-LA, Athens, (OR) University of Sevilla (E) UMIST, Manchester (UK) VUB, Brussels (B) Politecnico, Torino (I) IMF, Toulouse (F) INSA, Rouen (F) Ecole Centrale de Lyon (F) IMST, Marseille (F) FFA, Bromma (8) KTH, Stockholm (S) Industrial Endorsers Daimler-Benz Aerospace Airbus (D) Alenia, Torino (I) Dussault Aviation, Saint-Cloud (F) Hispano-Suiza, Le Havre (F) SNECMA, Villaroche (F) Coordination The responsibility for the coordination of ETMA was placed on A. Dervieux (lNRIA, So phia-Antipolis), F. Durst and I. Lekakis (LSTM, Erlangen) ETMA Project Overview The ETMA project involved the foHowing activities: Model Testing and Computations Such as testing of different second moment models (wall treatment: wall functions or in tegration to the wall) in a large range of incompressible flows: homogeneous flows, free turbulent flows, plane channel flow, boundary layers, sink flows(including laminarization), oscillating boundary layers and channel flows, 3-D turbulent boundary layers, round im pinging jets, backward facing step, tube bundle. There were also studied second-order closure predictions of separated flows with and with out combustion, flow around a disk with central orifice, the prediction ofa turbulent pre mixed V-shape flame stabilized behind a cylindrical rod by Ihe k-E and k-A models for turbulence and the coherent flame model for combustion, the prediction of incompressible sudden expansion, including near-wall effects, heat and particle transport, using the k-E and Reynolds stress models. Furthermore, k-E, k-'t and RSM predictions were also investigated for a wall mounted ob stacle in duct (2-D) and fence-on-wall, bump-on-wall flow geometries. The prediction of incompressible turbulent wake flow behind a flat plate and a boundary layer both under adverse pressure gradient was studied by using the k-E, k-A. and Reynolds-stress models and k-E, k-'t and RSM predictions were applied to low and transonic Mach numbers flows over airfoil&. At last, spatial DNS was performed on a zero-pressure gradient boundary layer and com putations of the two-point correlations needed for model developments at LSTM-Erlangen (k-A etc.). A special focus was put on compressible models of industrial interest; new models, vari ants, and assessments have been considered for the improvements for zero-and two-equa tion and RSM steady models. Four important aspects of this domain have been specially addressed, the effects of com pressibility, the introduction of anisotropy in two-equation models, the low-Reynolds treat ment of compressible boundary layers, the application of statistical models to unsteady flows by phase averaging and hOlTlogenisation. Compressibility effects are important on free shear flows; from the Stanford meeting, errors in mixing layers have been pointed out; shock-boundary-Iayer interactions result in separa tion difficult to predict. The anisotropic and nonlinear two-equation models constitute a compromise between basic two-equation models and second moment models. Low-Reynolds boundary treatment (without multi-layer models) was an important issue because of the impact of accurate modelling in separation predictions. Experimental Test Cases A series of experimental test cases has been conducted. They are classified in three sub groups: internal and external separated flows (sudden pipe expansion, wall-mounted pris matic obstacle, sudden expansion with transport across streamline, PTV- studies of sudden expansion with water, fence-on-wall and bump-on-wall), 2-D and 3-D boundary layers (2-D boundary layer under pressure gradient, pipe flow and near-wall measurements, 3-D boundary layer, swept concave/convex surface, premixed propane/air flame in rectangular duct), free shear flows and wakelboundary layer interactions (mixing layerlboundary layer interaction, two-point correlations in round free jets, effects of pressure gradient on wakes, compressible/supersonic free shear layers). New Numerical Methods The project has contributed to the building, validation, and assessment of new numerical methods involving both approximation and solution aspects. For approximation, new schemes applying unstructured triangulations were built and ap plied to most of the compressible flows cases considered, as will be observed by the reader of this book. The solution of high speed turbulent flows necessitate the application of sophisticated algo rithms; crucial issues are robustness and efficiency. The ETMA consortium proposed three families of algorithms, fast explicit algorithms, implicit ones, multigrid ones. Conclusive comments on these numerical aspects will be found in the global synthesis in the last chapter of this book. The ETMA Workshop The ETMA Workshop on turbulent modeling for compressible flow arising in aeronautics was held at UMIST, Manchester, U.K. in November 14-16, 1994. The workshop was open to any people proposing a contribution. About 60 contributions were selected from extended abstracts from criteria related to the novelty of models or of numerical methods, the accuracy of the results (authors were strongly encouraged to per form mesh convergence). For each test case, one or two partners of ETMA took the responsibility not only of test case and output formats definition but also of meshes availability, assistance to contribu tors, synthesis of the contributions, and pre-edition of finally written contributions. They are mentioned in the following short description of test cases. Test Cases for Analysis Test Case 1: Supersonic mixing layer (Resp. M. Braza (IMF-Toulouse), T. Chacon (U. of Sevilla». Steady evolution from supersonic boundary layer to a mixing layer (Experiment : Barre, Quine, Dussauge 1994, Mc=0.62) unsteady; in the same flow infonnation on the frequency of the energetic turbulent structures and their convection velocity. Test Case 2: Supersonic rearward facing step (Resp. K. Giannakoglou (NTU-Athens» The experiments refer to axisymmetric configurations (Roshko, Thomke 1966, 2>M>4) to avoid three dimensional perturbations due to side walls. Test Case 2C: Incompressible flows with separation (Resp. P. Larsen (AFM, Lyngby» This involves a series of cases for which the ETMA project has obtained new measure ments. Test Case 3: Turbulelll boundary layers (Resp. Ch. Hirsch, E. Shang, (VU-Brussels» It was proposed to compute several cases: the reference cases of the subsonic zero pressure gradient flat plate boundary layer (Klebanoff 1954), an accelerated boundary layer (sink flow direct simulation, Spalart 1986), and a boundary-layer in an adverse pressure gradi ent (Samuel et Joubert 1974). The calculations were extended to supersonic zero-pressure gradient boundary layers on adiabatic wall (M<4). Test Case TC4: Compression ramp flow (Resp K. Giannakoglou (NTU-Athens» In the retained experiment (Princeton data), the Mach number is 2.84; several ramp angles from 8 to 24 degrees are explored, which cover the range of non-separated interactions, incipient separation, and full separation. Test Case TC5: Two dimensional transonic bump (Resp. A. Loyau, D. Vandromme (INSA-Rouen» This flow is one of the classical cases for shock/turbulent boundary layer interactions as described by the experiments conducted at ONERA by Delery anJ his group. Test Case TC6: Shock reflection on a flat plate (Resp. R. Arina (Poli-Torino» In this flow at Mach 2 (Delery 1992), the incident shock wave is imposed from the external flow, and hence it does not depend on the incoming turbulence. Test Case TC8: Flow around airfoil (steady) (Resp. LJ. Johnston (UMIST, Manchester» The selected experiments are those performed by Cook, Mc Donald and Firmin (1979) for the RAE 2822 aerofoil, and by Bucciantini, Oggiano, Onorato (1979) for a MBB-A3 aero foil at Mach numbers around 0.75. Test case TC8 his: Flow around airfoil (unsteady) (Resp. M. Braza (IMF-Toulouse), S. Tsangaris (NTU-Athens)) In a limited range of Reynolds and Mach numbers in the transonic regime, there is a com petition between the trailing edge and the shock induced separation, leading to periodic flow oscillations. The present case, based on the experiments of Mc Devitt, Levy Jr. and Deiwert (1976), was proposed to test the ability of numerical methods to predict this un steadiness. Finally discarded from the ETMA workshop were two extra test cases relying on (1) a curved mixing layer experimented by Castro I.P., and Bradshaw P., and (2) a compressible circular jet. General Organisation of the Book The book is organised with respect to test cases, a test case being either one single flow or a set of similar flows. For each test case, a set of contributions was proposed. For each contribution a short scope of the model and numerics is given; emphasis is then put on discussing the computation conditions and results. Besides the different contributions, an accurate description of each test case is given, with some motivation for its choice, and the outputs expected from con tributors are specified, in order to allow to use this book for the validation of new codes. Also, a synthesis yields to the reader the main keys for the interpretation of results and the identification of the best ones. Acknowledgements The scientific editors wish to express their warmest thanks to: Catherine Juncker and Moni que Simonetti, Bureau des Relations Exterieures de l'INRIA for their vigourous and effi cient organisation of the workshop and Leslie L. Johnston for his contribution to the local organisation at UMIST. Our thanks also go to Franr;oise Trucas-Martin for taking care of the assembling of this book, and to Christian Olivier who was responsible of the ETMA Data Base. The test cases responsibles and in particular P. Larsen for the set of incompressible test cases, made important pre-edition work and we express our gratitude to them. Peter Bradshaw and Jean Delery brought important help in test case definition and informa tion. The work of the ETMA project was supported by EU through the Industrial and Materials Technology Programme. Particular thanks go to Dietrich Knoerzer, who was a very open minded and helpful partner at the European Commission and contributed to the success of the ETMA program and workshop. The workshop meeting was also supported by the EU programme COMETT II through UETP ERCOFTAC, which is gratefully acknowledged. Sophia-Antipolis, November 1997 Alain DERVIEUX Marianna BRAZA Jean-Paul DUSSAUGE CONTENTS Page CHAPTER 1: MIXING LAYERS ............................................. 1 Test Case 1: supersonic mixing layers. J.-P. Dussauge .................... 3 Numerical simulation and modeling of an unsteady supersonic mixing-layer flow. M. Braza. F. Hanine ............................... 11 A modified k-e model derived by homogenization techniques. T. Chacon. D. Franco. F. Orteg6n. I. Sanchez . . . . . . . . . . . . . . . . . . . . . . . . .. 20 Compressibility models applied to supersonic mixing layers. D. Gu6zengar. H. Guillard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28 Numerical simulation of supersonic mixing layers at different convective Mach numbers with a k-e model. C. Le Ribault ............. 37 Supersonic mixing layer, S. Tsangaris. A. Pentaris. M. Thomadakis ....... 45 Synthesis on compressible mixing layers, J.-P. Dussauge ................ 52 CHAPTER 2: COMPRESSIBLE BACK-STEP FLOW .......................... 59 The supersonic flow over an axisymmetric rearward facing step. Synthesis of results. K. C. Giannakoglou ............................. 61 Computation of an axisymmetric supersonic back-step flow using a pointwise k-k2/e turbulence model. V.C. Goldberg ..................... 68 Supersonic rearward-facing step calculations using an explicit fractional-step method and a two-equation turbulence model, C. Vassilopoulos, K.C.Giannakoglou, K.D. Papailiou ................... 76 CHAPTER 3: INCOMPRESSIBLE WALL FLOWS WITH SEPARATION .......... 87 Presentation of test cases TC-2A, TC-2B, TC-2C. TC-2D. two-dimensional. incompressible. wall flows with separation. P.S. Larsen.. 89 Incompressible recirculating flows, TC2-A low-Re backward-facing step, TC2-B high-Re backward-facing step, R.D. Harper, M.M. Gibson ... 95 Computational results on test cases TC-2C and TC-2D two dimensional. incompressible flows with recirculation. J.1. Schmidt. P.S. Larsen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 103 Incompressible recirculating flows, TC-2C fence-on-a-wall. TC-2D obstacle-in-channel. R.D. Harper. M.M. Gibson ......................................... 111 Numerical solution of the turbulent flow over a fence using two equation models, J.C.F. Pereira, M.H. Kobayashi, N.P.C. Marques ........ 119 Computations of separating and reattaching flows with high-and low-Reynolds-number second moment closure. S. Jakirlic. K. Hanjalic. I. Hadzic ............................................ 127