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Grid Quality and Resolution Issues from the Drag Prediction Workshop Series. The DPW Committee Dimitri Mavriplis : University of Wyoming USA J. Vassberg, E. Tinoco, M. Mani : The Boeing Company USA O. Brodersen, B. Eisfeld: DLR Braunschweig, GERMANY - PowerPoint PPT Presentation
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Grid Quality and Resolution Issues from the Drag
Prediction Workshop Series
The DPW Committee
Dimitri Mavriplis : University of Wyoming USAJ. Vassberg, E. Tinoco, M. Mani : The Boeing Company USAO. Brodersen, B. Eisfeld: DLR Braunschweig, GERMANYR. Wahls, J. Morrison: NASA Langley Research Center , USAT. Zickhur, D. Levy: Cessna Aircraft Co. USAM. Murayama: Japan Aerospace Exploration Agency, JAPAN
Motivation
• DPW Series – Assess State-of-art for Transonic Cruise Drag
Prediction using RANS methods• DPW I: Anaheim CA, June 2001• DPW II: Orlando FL, June 2003• DPW III: San Francisco CA, June 2006• DPW IV: June 2009
– Considerable scatter in results particularly for cases with flow separation (off-design)
– Emerging Consensus• Discretization errors are (a) dominant source of error
Motivation
• DPW focused increasingly on assessing discretization/grid induced errors– DPW I: Single grid study– DPW II: Grid convergence study (3 grids)– DPW III: All results examined in context of grid
convergence study (3 or 4 grids)
• Implications– Dominant discretization errors preclude accurate
assessment of other errors• Turbulence/transition modeling
Motivation
• DPW demonstrated grid convergence for some codes mostly for attached flow cases
• Separated flow cases much more difficult to obtain grid independent results
• Scatter often does not decrease with increasing grid resolution
• Contradictory grid convergence results– Different grid families converge to different results
Overview
• Overview of DPW test cases
• DPW Gridding Guidelines
• Discussion of gridding issues– Grid Resolution– Grid Convergence– Grid Quality
• Possible improvements
• Conclusions
DLRF4-F6 Test Cases (DPW I,II,III)
• Wing-Body Configuration• Transonic Flow• Mach=0.75, Incidence = 0 degrees, Reynolds number=3,000,000
DPW III Series Cases
• Designed fairing to suppress flow separation (Vassberg et al. AIAA 2005-4730)
DPW III Series Cases
• 2 closely related simple wing geometries– Well behaved flow– Enhanced grid refinement study (4 grids)
General Gridding Guidelines• Grid Resolution Guidelines
– BL Region• Y+ < 1.0, 2/3, 4/9, 8/27 (Coarse,Med,Fine,VeryFine)• 2 cell layers constant spacing at wall• Growth rates < 1.25
– Far Field: 100 chords – Local Spacings (Medium grid)
• Chordwise: 0.1% chord at LE/TE• Spanwise spacing: 0.1% semispan at root/tip• Cell size on Fuselage nose, tail: 2.0% chord
– Trailing edge base:• 8,12,16,24 cells across TE Base (Coarse,Med,Fine,Veryfine)
• Grid Convergence Sequences– X3 increase in resolution per refinement– Maintain same family of grids in sequence
Overset Meshes (DPW III)
Overset Meshes (DPW III)
Structured Multi-Block Wing-Body GridsConstructed with Boeing Zeus/Advancing Front Method
Typical Wing Grid H-H Topology
Embedded Blunt Trailing Edge Grid Block
VGRID : Wing Body (~40M pts)
VGRID : Wing Alone (~30M pts)
DPW Submitted Grids
• Wide variety of grid types and constructions
• Grid topology and type affects local resolution
• Compliance with guidelines not evaluated precisely
• Large data-base of high-quality aero grids made available
DPW I RESULTS (circa 2001)
• Drag polar for single grid resolution
DPW II RESULTS (circa 2003)
• Drag vs number of grid points (Wing-body alone)
DPW III RESULTS (2006)
• Idealized drag vs grid index factor (N-2/3)– Wing-body and Wing-body+fairing
Grid Related Experiences from DPW
• Grid Resolution
• Grid Convergence
• Grid Quality
Grid Resolution
• Always need more– DPW I: ~ 3M pts– DPW III: ~ 40M pts– Interim/Follow-on studies/DPW4: > 100M pts– Grid convergence studies point to need for > 109 pts
• Wide range of scales present in aerodynamics– Highly variable:
• Far field ~100 MAC• Trailing edge ~.01 MAC
– Anisotropic:– Boundary Layer Y+=1: ~ 10-6 MAC
Grid Resolution
• Wide range of scales requires:– Intuition or rule-based grid generation– Anisotropic in Boundary Layer (and spanwise)– Codified in DPW guidelines
• Effect of Grid Resolution is Complex– Direct effect on surface profiles is small– Indirect effect can be large
• Location of separation• Integration of small differences Lift, Drag, Moment
W1 Grid Convergence Study
• CP at station 5:
W1 Grid Convergence Study
• CP at station 5:
W1 Grid Convergence Study
• CP at station 5:
W1 Grid Convergence Study
• CP at station 5:
Effect of Normal Spacing in BL
• Inadequate resolution under-predicts skin friction– Direct influence on drag prediction– Indirect influence: Wrong separation prediction
Effect of Normal Resolution for High-Lift
(c/o Anderson et. AIAA J. Aircraft, 1995)
• Indirect influence on drag prediction• Easily mistaken for poor flow physics modeling
Grid Resolution
• Separated flow cases more demanding and often contradictory experiences
Grid Resolution• Side-of-Body Separation increases with grid resolution
– Boeing: Overset– Boeing: Unstructured– DLR: Unstructured
• Side-of-Body Separation constant with grid resolution– Boeing: Block Structured– JAXA: Block Structured, Unstructured
• Trailing edge separation grows with grid res:– UW : Unstructured (NSU3D)
• Trailing edge separation constant with grid res:– JAXA: Structured, Unstructured– Boeing: Overset
• Experimentation with much finer grids required to understand behavior…
Grid Convergence
• Increased focus of DPW Series
• For second-order accurate method, error should decrease as O(h2)– Define average cell size h as: N-1/3
• N=number of grid pts
– Drag vs N-2/3 should plot as straight line– Project to y-axis to get continuum value
Importance of Grid Convergence
Agreement on initial grid (DPW I) gets worse (Lee-Rausch et al. AIAA-2003-3400)
Grid Convergence
• Grids must come from same “family”– Self-similar topologically– Same relative variations of resolution
• Achieved through IJK factors for structured grids• Requires global grid spacing factor for unst. grids• Boundary layer growth must be taken into account
• Not clear how well all grids meet these requirements– Most likely represents state-of-art
• Perform grid convergence at fixed Lift or fixed incidence conditions ?
• Grid convergence for attached flow cases• Inconsistent behavior for separated flow case
– Separation bubble grows with grid resolution
Grid Convergence (Overflow)
• More consistent grid convergence at fixed CL
Grid Convergence (Wing Alone)
W1-W2 Grid Convergence Study(NSU3D Unstructured)
•Apparently uniform grid convergence
W1-W2 Results
• Discrepancy between results on 2 different families of grids (both generated with VGRID)
W1-W2 Results
• Removing effect of lift-induced drag : Results on both grid families converge consistently
– Consistent grid convergence at fixed CL instead of alpha
Grid Quality
• Distinguish grid quality from grid resolution– Relative distribution of resolution– Topology– Element type/shape– Aspect ratio– Orthogonality (BL, hybrid)
• Grid quality is (should be) constant for self-similar family of grids used for grid convergence study
Two Unstructured Grid Topologies
65 million pt grid72 million pt grid
High Resolution grids for DLR-F6 (DPW II) using NSU3D solver
Grid Convergence on Topology #1
• Drag is grid converging• Sensitivity to dissipation decreases as expected
65M pt mesh Results
• 10% drop in CL at AoA=0o: closer to experiment• Drop in CD: further from experiment• Same trends at Mach=0.3• Little sensitivity to dissipation
Grid Convergence• Grid convergence apparent using self-similar family of grids
• Large discrepancies possible across grid families– Sensitive areas
• Separation, Trailing edge• Pathological cases ?
• Would grid families converge to same result limit of infinite resolution ?– i.e. Do we have consistency ?– Due to element types ?, Aspect ratio ?
• Possible ways forward:– Higher order discretizations– Adjoint-based error estimation
hp-adaptive DG Li Wang and Dimitri Mavriplis
Adjoint-Based Spatial Error Estimation + AMRAdjoint-Based Spatial Error Estimation + AMR
Adjoint Solution : Green’s Function for Objective (Lift)
Change in Lift for Point sources of Mass/Momentum
Error in objective ~ Adjoint . Residual (approx. solution)
Predicts objective value for new solution (on finer mesh)
Cell-wise indicator of error in objective (only)
hp-adaptive DG Li Wang and Dimitri Mavriplis
hh-refinement for target functional of lift-refinement for target functional of lift
Fixed discretization order of p = 1
Final h-adapted mesh (8387 elements) Close-up view of the final h-adapted mesh
hp-adaptive DG Li Wang and Dimitri Mavriplis
Comparison between h-refinement and uniform mesh refinement
Error convergence history vs. degrees of freedom
Functional Values and Corrected Values
hh-refinement for target functional of lift-refinement for target functional of lift
Complex Geometry: Vehicle Stage Separation(CART3D/inviscid)
Top View
Side View
• Initial mesh contains only 13k cells
• Final meshes contain between 8M to 20M cells
Initial Mesh
Pressure Contours
M∞=4.5, α=0°
• Minimal refinement of inter-stage region
• Gap is highly refined
• Overall, excellent convergence of functional and error estimate
Cutaway view of inter-stage
Unsteady Problems
Total error in solution
Temporal error
(discretization/resolution)
Spatial error
(discretization/resolution)
Flow
Algebraic error
Mesh Other Flow Mesh Other Flow Mesh Other
•Solution of time-dependent adjoint: backwards integration in time•Disciplinary adjoint inner product with disciplinary residual
•Interaction of isentropic vortex with slowly pitching NACA0012
•Mach number = 0.4225
•Reduced frequency = 0.001
•Center of pitch is quarter chord
•Functional is
Time-integrated functional
8,600 elements
Unsteady Adjoint Error Estimation
Density contours of initial condition
Comparison of adapted temporal domain
Temporal Error Adaptation
Algebraic Error Adaptation
Adapted Flow/Mesh convergence tolerances:
Adjoint-Based Refinement Results
•Error in Lift versus CPU TimeUniform cost is only finest solution costAdaptive cost is all solutions (+ adjoint cost)Corrected value provides further improvement
Conclusions• Grid related issues are dominant error source in drag
prediction
• Grid and solver interaction is complex
• Drive toward much higher resolution
• Grid quality difficult to assess
• Inconsistent grid convergence results point to possible inconsistent errors : O(1)
• All these issues much more prevalent for separated flows
Conclusions• A posteriori error estimation
– Criteria for adaptive meshing– Gradient based– Adjoint based for specific outputs
• Looks promising– Extends to temporal, algebraic error from different disciplines– Combine spatial, temporal, algebraic…– Still a linearization about current solution– Slow to production– Inconsistent errors not resolvable with AMR
• A priori error estimation– Grid quality metrics– Approximation error of test functions