Challenges in Boundary- Layer Stability Analysis Based On Unstructured Grid Solutions

Transcription

1 Challenges in Boundary- Layer Stability Analysis Based On Unstructured Grid Solutions Wei Liao National Institute of Aerospace, Hampton, Virginia Collaborators: Mujeeb R. Malik, Elizabeth M. Lee- Rausch, Fei Li, Eric J. Nielsen, Chau- Lyan Chang, and Meelan Choudhari NASA Langley Research Center, Hampton, VA NIA Computational Fluids Dynamics Seminar February 14, 2012

2 Background: Why Laminar Flow? Skin- friction is 50% of total drag BL transition delay will result in substantial reduction in fuel burn - fuel saving - reduced environmental impact Aircraft Drag Budget Laminar flow is an important element of Environmentally Responsible Aviation (ERA) Project s Technology Portfolio Natural Laminar Flow (NLF) and Discrete Roughness Elements (DRE) Original plan ( ) Gulfstream II (G- 2) Current plan (2010- ) Gulfstream III (G- 3) Washburn (2011) Transonic Mach number C L ~.5 Sweep Angle > 30 o 2

3 Laminar- Turbulent Transition On Swept- wing Laminar Flow Attachment Line Instability/Contamination Tollmien-Schlichting Instability Crossflow Instability Secondary Instability Breakdown.. Turbulence 3

4 Swept- Wing Boundary Layer Transition Tollmien- Schlichting (TS) Mode viscous mode responsible for transition in 2D BL for NLF, maximize (- dp/dx) Crossflow (CF) Mode inviscid instability of the crossflow velocity profile crossflow induced due to sweep and - dp/dx responsible for transition in 3D BL for NLF, minimize sweep and/or - dp/dx Transition correlated with the N factor method, which is based on integral growth (N factor) of one of these modes 4

5 Crossflow in Swept- Wing Boundary Layer Stationary crossflow Induced by surface roughness Higher receptivity coefficient DRE is effective Traveling crossflow Induced by free stream turbulence Lower receptivity coefficient DRE is not effective Only stationary crossflow disturbances are relevant in flight transition. (Saric, et al., Phil. Trans. R. Soc. A, v369, 2011, pp ) Factors affecting crossflow modes in NLF Sweep angle destabilizing Favourable streamwise pressure gradient - dp/dx destabilizing Convex surface curvature stabilizing non- parallel effects destabilizing 5

6 What do DREs do? Swept wing transition in quiet environment Transition dominated by stationary crossflow vortices Placing roughness array near leading edge Transition is delayed Roughness spacing Control mode has shorter wavelength than target mode (most unstable crossflow instability) Shown to work at low Re (8M) Will DRE work for higher Re and Ma under real transonic flight conditions? 6

7 Research Objectives Develop a flow stability analysis procedure based on the unstructured grid strategy and implement it to the NASA in- house code, FUN3D, and LASTRAC Couple it with adjoint method modules of FUN3D for laminar flow control, design and optimization of low- drag aircraft wings under realistic flight conditions Apply the developed tools to evaluate the effectiveness of the DRE technology at high Reynolds numbers of relevance to transport aircraft 7

8 NASA Langley CFD and Stability Analysis Packages Unstructured- grid Navier- Stokes solver: FUN3D Finite volume discretization for full Navier- Stokes equations Hybrid unstructured grids: tetrahedra, pyramids, prisms, and hexahedra Multiple turbulence models: SA, SST, k- ω and k- ε. Discrete adjoint capability on static and dynamic meshes for design optimization FUN3D not yet coupled with transition prediction modules Boundary- layer mean flow codes: BLSTA and WINBL2 Langley Stability and Transition Analysis Code: LASTRAC N factor Computations for 2D/3D boundary- layers PSE analysis for fully 3D BL effects (e.g., aeroelastic/twist) Nonlinear PSE/secondary instability analysis Stand alone code/not coupled with an airfoil design code 8

9 Development of NLF Design Tools Unstructured Flow Solver (FUN3D) Adjoint Solver for Optimization Design Direct Extraction Procedure Transition Prediction Module Cp Cp Boundary Layer Codes (BLSTA/WINGBL2) Mean Flow ProEiles Gradient Calculation Shape deformation & Grid ModiEication Stability & Transition Prediction Using LASTRAC 9

10 G- 3 & G- 2 Aircraft and Swept Wing/Glove G- 3: Laminar Flow Glove designed by Texas A&M University Mach number:.75 Sweep Angle = o Re c : 22 x10 6 G- 2: Design also from Texas A&M University [AIAA ] Mach number:.75 Sweep Angle = 30 o Re c : 17 x

11 11 Unstructured Grid and Solutions for G3 aircraft

12 12 Cp distributions

13 LST N- factors for G- 3 Airfoil Using N = 14 (polished surface, Ref: Saric), x/c =.52,.58 and.56 for inboard, mid- span and outboard locations, respectively Using N = 9 (operational surface, Ref: Saric), x/c =.14,.44 and.44 for inboard, mid- span and outboard locations, respectively Inboard (y =204 ) Mid-span (y =234 ) Outboard (y =264 ) Stationary crossflow disturbances, fixed spanwise wavelengths 13

14 PSE N- factors for G- 3 Airfoil PSE N factors are lower by about 6, compared to LST PSE includes nonparallel and surface curvature effects Re c = Re c = Re c = Stationary crossflow disturbances, fixed spanwise wavelengths 14

15 Nonparallel and Surface Curvature Effects Nonparallel effect destabilizing, surface curvature stabilizing Common understanding: Two effects essentially negate each other OK to use LST in NLF design Holds for G- 2 airfoil For G- 3, stabilizing effect of surface curvature much larger than destabilizing effect of nonparallel mean flow Use of LST too conservative for NLF design (based on stationary crossflow) Nonparallel Curvature Nonparallel Curvature 15 G-2 N factors [Re c = 17 x 10 6 ] G-3 N factors [Re c = 22 x 10 6 ]

16 N factors for Traveling Crossflow Disturbances LST and PSE results for traveling (f = 1000 Hz) disturbances of fixed spanwise wavelengths, for the G- 3 airfoil Maximum N factors about the same (LST = 16.5, PSE = 15.5) PSE N factors for traveling disturbances higher by 11 as compared to results for stationary disturbances Could this large difference make traveling disturbances relevant in swept wing transition? 16 LST PSE

17 Remarks Observations: Large spanwise Cp variations on glove surface Amplitude of stationary crossflow disturbance is significantly influenced by surface curvature Traveling crossflow disturbance is much less influenced by surface curvature Consequently, traveling crossflow N factor higher by 11 as compared to stationary disturbances Large difference due to disparate effect of surface curvature Is the difference large enough to overcome much higher receptivity of stationary disturbances? Conclusions: Glove needs to be redesigned Surface curvature should be used as a control parameter for NLF design Important to investigate the receptivity of stationary and traveling disturbances 17 Malik M, Liao W, Lee- Rausch E, Li F, Choudhari M, Chang C- L. Computational Analysis of the G- III Laminar Flow Glove. AIAA

18 Direct Extraction Procedure From Unstructured Grid Solutions 1. User defines a 2D Cartesian grid 2. FUN3D projects the 2D Cartesian grid onto the wing surfaces to obtain seed points there 3. Profile points are distributed along normal vectors computed at each seed point according to user input 4. Single- plane structured grid established at each spanwise location 5. FUN3D identifies the unstructured grid elements containing the profile points 6. Unstructured solutions are interpolated to all profile points by interpolations 7. Structured stability grids and interpolated solutions are output in the PLOT3D format 18

19 Features for Extraction Procedure Definition of the 2D Cartesian grid for seed points The wing leading edge (LE) is detected by an iteration program automatically, which forms one edge of the 2D grid Users specify the domain extent in streamwise and spanwise direction A stretching function is used to distribute the grid points along streamwise direction, which make grid clustered near LE Projection of the 2D Cartesian grid onto the wing surfaces Optional constraint: Can only project to certain boundary patches Optional constraint: Masking on coordinate values (e.g., z<0) 19

20 Features for Extraction Procedure Profile points distributed along normal vectors at each seed point The extent in normal direction is determined by boundary thickness, which was estimated by A stretching function is used to the grid points in normal distribution Interpolating unstructured solutions to all profile points All types of cells have been considered: tetrahedra, hexahedra, pyramid and prism Interpolation is done based on tetrahedral with the volume as the weight. The extraction process has been parallelized and integrated to solver 20

21 Boundary layer transition location specification Stability analysis must be conducted based on laminar mean flow profiles Turning off the turbulence production terms in laminar regions (see AIAA- 2004_0554) FUN3D original 2D transition setup Can only specify a 2D transition with x- location=constant Only work for a single patch FUN3D new 3D transition setup Can use polylines to define the shape of laminar flow region Allow multiple patches to be set along with polyline setup Upper and lower surface setup 21

22 22 Boundary Profiles Obtained by Direct Extraction

23 Significant Difference Between BL Codes and Direct Extraction Reasons for the discrepancy: 1) Infinite swept wing assumption breaks down due to strong 3D effects of the glove? 2) Errors in Extraction procedure? 3) Poor grid resolutions inside the boundary layer? LST N- factors for mean flows obtained by BLSTA and Direct Extraction 23

24 24 Strong 3D effects?

25 Accuracy of Extraction Procedure? Flat plate on unstructured grid with pure tetrahedra Infinite swept wing with structured grid and converted unstructured grid with tetrahedral cells Compare stability analysis results for the mean flows obtained by both direct extraction and sample flow field output by FUN3D 25

26 Validation of Extraction Procedure Flat Plate (1) Tetrahedral grid in X- Y plane and X- Z plane 26

27 Validation of Extraction Procedure Flat Plate (2) Profiles of the velocity and its 1 st - order and 2 nd - order gradients For stability analysis, not only must mean flow profiles themselves be accurate, but also must their 1 st and 2 nd order gradients in the direction normal to wall. 27

28 Validation of Extraction Procedure Flat Plate (3) Growth rate vs. disturbance frequency at two locations 28

29 Validation of Extraction Procedure Infinite Swept Wing (formed by the midspan of G3 glove) Cp distribution N- factors CFL3D: on a structured grid FUN3D: on a converted pure tetrahedral grid 29

30 Validation: N- factor Comparison Based On Mean Flows By FUN3D Output and Direct Extraction 30 Using Tecplot to project a 2D stability grid to a surface output by FUN3D and then obtain flow solutions on the given stability grid

31 31 Reexamine What Affected Mean Flow Accuracy?

32 Grid Resolutions Not Enough In Boundary Layers? Grid Resolution around inflection point of crossflow profiles Grid Resolution near the leading edge 32

33 Grid Resolutions Not Enough In Boundary Layers? Grid Requirements for Mean Flow Computations: Enough points in the streamwise direction at the leading edge (30-50 points in one radius of curvature). More than 100 grid points inside the boundary layer Enough resolution near the inflection points of the crossflow profiles With a stretching ratio as small as possible to ensure good resolution at different areas in boundary layers Grid is smooth in and near the boundary layers 33

34 Challenges for Grid Generation VGRID: For full G3 aircraft, even with points inside the boundary layers, variable stretching ratio led to strong grid discontinuity and skewness; For wing- only case, the universal stretching ratio results in a grid having 87M nodes with only 70~80 points in the boundary layers; GRIDPRO: No meanings to use a small and variable stretching ratio for the grid in the boundary layer after more than half a year exploration. 34

35 Grid Discontinuity and Skewness Grid at the midspan of the glove 35

36 What We Are Trying Now? GeoLab: (fine and coarse) unstructured grids by VGRID and (very fine) structured grids by GRIDGEN for wing- glove only without fuselage, engine and winglet; Only for validation purpose Difficulty in unstructured grid generation for full G3 aircraft Overflow computations on overset structured grid for full G3 aircraft; CFL3D computations on Gridpro structured grid with new features of stretching ratio setup. 36

37 Any comments and suggestions? Thank you! 37