Summary of Flow Modulation and Fluid-Structure Interaction Findings (eBook)

Title Page 2
Preface 6
Contents 8
List of Contributors 10
Introduction 14
Vortex Sheets of Aircraft in Takeoff and Landing 18
Introduction 19
Experimental Facilities 20
Wind Tunnel 20
Water Tunnel 20
Towing Tank 21
Measurement Instrumentation 22
Hot-Wire Anemometry 22
Particle Image Velocimetry 22
Model 23
Results 24
Near Field 24
Extended Near Field 28
Far Field 32
Force Fluctuations 37
Conclusion 38
References 39
An Adaptive Implicit Finite Volume Scheme for Compressible Turbulent Flows about Elastic Configurations 41
Introduction 41
Physical Model 43
Governing Equations 43
Turbulence Models 44
Transition Modeling 46
Boundary Conditions 48
Numerical Methods 48
Finite Volume Scheme 48
Matrix-Free Newton-Krylov Method 52
Fluid Structure Interaction 53
Results 53
Fishtail 54
Laminar Flat Plate 55
Transitional Flow over a Flat Plate 56
High-Lift Configuration 57
BAC 3-11 Airfoil - Shock Buffet 60
FSI - HIRENASD 60
Performance of the Matrix-Free Newton-Krylov Method 63
Conclusion 65
References 65
Timestep Control for Weakly Instationary Flows 68
Introduction 68
Governing Equations and Finite Volume Scheme 70
Adjoint Error Control - Adaptation in Time 72
Variational Formulation 72
Adjoint Error Representation for Target Functionals 73
Space-Time Splitting 74
The Conservative Dual Problem 75
Adaptive Concept 76
Asymptotic Decay Rates 77
Setup of the Numerical Experiment 78
Computational Results 81
Numerical Strategies 81
Strategy I: Fully Implicit Computational Results 83
Strategy II: Explicit-Implicit Computational Results 86
Conclusion 88
References 89
Adaptive Multiscale Methods for Flow Problems: Recent Developments 91
Introduction 91
Governing Equations and Finite Volume Schemes 93
Multiscale Analysis 94
Multiscale-Based Spatial Grid Adaptation 97
Adaptive Multiresolution Finite Volume Schemes 98
Approximate Flux and Source Approximation Strategies 101
Multilevel Time Stepping 102
FAS-Like Multilevel Scheme 103
Numerical Results 107
Multilevel Time Stepping: Oscillating Plate 107
FAS-Like Multilevel Scheme: Bump 108
Local Versus Exact Flux and Source Reconstruction: Burger’s Equation 110
Interaction of Wing-Tip Vortices and Jets in the ExtendedWake 118
Introduction 118
Governing Equations and Numerical Method 120
New One-Equation Turbulence Model 122
Adaptive Mesh Refinement 124
Data Communication 125
Results 128
RANS Simulation of the Flow over a Rectangular Wing with Engine Jets 129
Measurements of the Flow over a Wing with Engine Jets 131
Large-Eddy Simulation of Wake Vortices 135
Conclusions 144
References 145
Experimental and Numerical Investigation of Unsteady Transonic Airfoil Flow 149
Introduction 149
Experimental Setup 150
Numerical Method 150
Results 153
Wave/Shock Interactions 156
Variation of the Angle of Attack 158
Mechanisms of Pressure Wave Generation 159
References 162
Enabling Technologies for Robust High-Performance Simulations in Computational Fluid Dynamics 164
Introduction 164
Automatic Differentiation and Parallel Computing 165
Automatic Differentiation of OpenMP Programs 166
Automatic Scoping 167
Automatically-Generated Sensitivities in TFS 168
Sensitivities with Respect to Geometric Parameters 168
Sensitivities with Respect to Angle of Attack and Yaw Angle 175
Automatically-Generated Sensitivities in QUADFLOW 180
Finite Volume Scheme Implemented in QUADFLOW 180
Increasing the Robustness of an Approximate Newton Method 180
Enabling an Exact Newton Method 182
Conclusions 186
References 187
Influencing Aircraft Wing Vortices 192
Introduction 192
Coordinate Systems 193
Test Facilities 194
Wind Tunnel 194
Water Towing Tank at the ILR 194
Water Towing Tank at the DST 194
Measurement Techniques and Instrumentation 195
Particle Image Velocimetry 195
Flow Visualization 195
Results 196
Investigations of Wing Wakes in the Near Field with Additional Fin Vortices 196
Investigations of Multi-vortex Systems in the Far Field 201
Conclusion 212
Development of a Modular Method for Computational Aero-structural Analysis of Aircraft 216
Introduction 216
General Concept and Applied Numerical Methods 217
Flow Solver 219
Structural Solver 219
Flow Grid Deformation Method 220
The Aeroelastic Coupling Module 222
Selected Results of Preceding Funding Periods 234
Static and Dynamic Validation for an Elastic Swept Wing in Subsonic Flow 235
Static Deformation Effects in Wind Tunnel Experiments of Transport Aircraft 237
Selected Results of the Final Funding Period – Validation for the HIRENASD Experiments 239
Dependence of the Lift Coefficient on the Angle of Attack 240
Lift Divergence Behaviour 242
Prescribed Motion According to the Second Flap-Bending-Dominated Mode Shape 242
Conclusion 247
References 248
A Unified Approach to the Modeling of Airplane Wings and Numerical Grid Generation Using B-Spline Representations 250
Introduction and Overview 250
Parametric Grids 251
B-Spline Grid Generation 252
Generation of Wing Models 253
Outline of Paper 254
Notation 254
Geometry Description and Outline of the Modeling Process 255
Cross Sections and Wing Construction 255
Mounting Unit 257
The Wing Tip 259
Winglet Construction 260
Elliptic Grid Generation 262
Spekreijse’s Grid Generation System 262
B-Spline Collocation 262
Application Example 263
Boundary Orthogonality 264
Complete Boundary Control 266
Deforming Grids 268
Deforming the Framework 269
Example: High Lift Configuration 270
Conclusion 273
References 273
Parallel and Adaptive Methods for Fluid-Structure-Interactions 275
Introduction 276
Fluid-Structure Coupling 277
Multiscale Decompositions–Basic Ingredients 282
Multiscale Analysis and Grid Adaptation 283
Algorithms 285
Data Structures 287
Parallelisation 288
Load-Balancing via Space-Filling Curves 288
Parallel Grid Adaptation and Data Transfer 293
Embedding of Parallel Multiscale Library into the Quadflow Solver 295
Numerical Results 297
Performance Study for Multiscale Transformation 297
Application 300
References 303
Iterative Solvers for Discretized Stationary Euler Equations 305
Introduction 305
The Euler Equations 306
Test Problems 307
Homogeneous Stationary Flow on the Unit Square 307
Stationary Flow around NACA-0012 Airfoil 307
Point-Block Preconditioners 308
Methods 309
Numerical Experiments 310
Concluding Remarks 312
Renumbering Techniques 312
Methods 313
Numerical Experiments 317
Concluding Remarks 320
Time Integration 320
CFL Evolution Strategies 320
Numerical Experiments 322
Locally Optimal CFL Numbers 323
Concluding Remarks 326
Matrix-Free Methods for Second Order Jacobians 327
Numerical Experiments 327
Concluding Remarks 330
Outlook 330
References 332
Unsteady Transonic Fluid – Structure – Interaction at the BAC 3-11 High Aspect Ratio Swept Wing 334
Introduction 334
Experimental Setup 336
Wind Tunnel Facility 336
Swept Wing Model 337
Videogrammetric Model Deformation Measurement Setup 341
Time-Resolved Pressure-Sensitive Paint Visualization Setup 342
Steady Wing Flow Properties 344
Time-Averaged Flow Topology 344
Dynamic Shock-Boundary Layer Interaction 349
Wing Model Deformation 354
Forced Harmonic Wing Oscillation Experiments 355
Bending Degree of Freedom 356
Torsional Degree of Freedom 359
Fluid-Structure Energy Exchange 363
Conclusion 366
References 367
Structural Idealization of Flexible Generic Wings in Computational Aeroelasticity 371
Introduction 371
Structural Design ofWing Box 373
Geometry Configuration 373
Rib Arrangements 374
Stringer Arrangements 374
Sweep and Taper Effects 375
Warping Effects 375
Material Anisotropy 375
Structural Idealization 377
One-Dimensional Idealization 377
Three-Dimensional Idealization 379
Structural Dynamics 384
Numerical Results 386
Sweep Effects 386
Warping Effects 386
FE-Validation of Stress 388
Modal Analysis 388
Static Tailoring 391
Vibration Tailoring 391
Conclusions 393
References 394
Aero-structural Dynamics Experiments at High Reynolds Numbers 396
Introduction 397
Experimental Setup andWindtunnel Conditions 398
Wind Tunnel Model in the European Transonic Windtunnel 398
Measuring Equipment of the Wing Model 400
Internal Forced Vibration Excitation 403
Wind Tunnel Conditions 404
Selected Experimental Results from Static Tests 405
Wave Processes during the Tests for Steady Polars 410
Upstream Travelling Waves 410
Stochastic Processes during the Tests 414
Frequency and Damping Analysis 414
Analysis of Normal Force Caused by Stochastic Aerodynamic Disturbances 415
Selected Experimental Results from Dynamic Tests 417
Processing of Measured Data as for Dynamic Tests 417
Unsteady Polars with Defined Vibration Excitation 419
Influence of Parameters in Dynamic Tests on Chord-Wise Pressure Distribution 424
Conclusions 428
References 429
Author Index 432

"Development of a Modular Method for Computational Aero-structural Analysis of Aircraft (S. 205-206)

Lars Reimer, Carsten Braun, GeorgWellmer, Marek Behr, and Josef Ballmann

Abstract. This paper outlines the development of the aero-structural dynamics method SOFIA over the duration of the Collaborative Research Center SFB 401. The algorithms SOFIA applies for the spatial and the temporal aero-structural dynamics coupling are presented. It is described in particular how SOFIA’s load and deformation transfer algorithms suitable for non-matching grids at the coupling interface were enhanced towards the application to complete aircraft configurations. The application of SOFIA to various subsonic and transonic aeroelastic test cases is discussed.

1 Introduction

The design of high-performance wings for large commercial aircraft requires the inclusion of their aeroelastic properties into the aerodynamic and structural design process. During preliminary design, the geometry of the wing is defined as a compromise between good flight performance during take-off, landing and cruise flight on the one hand and load capacity and weight of the structure on the other hand. In an iterative fashion, the aerodynamic shape, the loads, the construction of the wing assembly and the deformation are studied sequentially and more or less independently. Aerodynamic wind tunnel testing with rigid or nearly-rigid reduced-scale models plays a key role.

But in those tests, similarity with the full scale body can only be achieved in a very limited manner, primarily with respect to the aerodynamic parameter Mach number and to a certain extent also with respect to the Reynolds number. Aeroelastic similarity is usually not achieved. Based on the aerodynamic analysis, wing loads, deformations and particularly the aerodynamic twist are determined. Then the wing geometry and construction of the wing assembly are modi- fied a posteriori so that after taking into account the static aeroelastic deformation in cruise flight sufficient lift and minimum drag are ensured.

The described design and construction procedure requires several iterations because in every step the aeroelastic coupling and the nonlinearity of the problem cannot be captured completely. Besides that, nonlinear flutter possibly occuring in the transonic flow regime cannot be predicted with such a procedure. Therefore it is necessary to develop numerical methods, which reliably predict the interaction between aerodynamic, structural and inertial forces. Such a numerical method has been progressively developed in the past four funding periods of the Collaborative Research Center SFB 401 Flow Modulation and Fluid-Structure Interaction at Airplane Wings at RWTH Aachen University. This paper gives an overview about this numerical method named SOFIA and its past and present development stages. The organization of the subsequent sections of this paper is as follows."