Title: A thesis defense
1Solution Adaptive Meshing for Flows With Vortices
- A thesis defense
- Submitted in Partial Fulfillment of the
Requirements - For the Degree of Master of Science
- In Aerospace Engineering
Naser Talon Shamsi Kasmai June 27, 2008
2Graduate Committee
- David S. Thompson, Ph.D.
- Associate Professor of Aerospace Engineering
- Major Professor
- Edward Luke, Ph.D.
- Associate Professor of Computer Science and
Engineering - Committee Member
- Keith Koenig, Ph.D.
- Professor of Aerospace Engineering
- Committee Member
3Acknowledgements
- This work is supported by the NASA Constellation
Universities Project (CUIP, NCC3-994) - Great thanks goes out to Monika Jankun-Kelly for
her great software that makes this work possible - Thanks to Dr. Yasushi Ito for his cooperation and
work on this project
4Overview
- Introduction
- Vortices
- Solution Adaptive Meshing
- Related Work
- Thesis Statement
- Meshing Strategies
- Feature-based Adaptive Meshing
- Vortex Characterization
- Adaptive Mesh Refinement
- Adaptive Mesh Regeneration using Embedded
Surfaces - Results
- Wing in wind tunnel
- Spinning Missile
- Conclusion
5Vortices
- A vortex is a fluid flow characterized by spiral
streamlines - Caused by a pressure difference between the lower
and upper surface of the wing - Two important aspects
- Formation at the wingtip
- Convection downstream
6Vortices
7Solution Adaptive Meshing
- For meshing in general, desire to have a balance
of accuracy and computational efficiency - Refinement increases accuracy, but adds
computational cost - Solution adaptive meshing produces a mesh that
evolves in response to the solution - Allows refinement in places that need it the most
- Maximizes accuracy to cost balance
8Solution Adaptive Meshing Related Work
- Finite volume methods used in CFD do not provide
a direct mechanism for error estimation - Local error estimation techniques include
- Divided difference
- Solution and local solution reconstruction
difference - Eigenvalues of a symmetric Hessian matrix for a
field quantity - Gradient-based weight functions can be considered
as an error technique because the functions
approximate truncation error of the numerical
scheme used
9Solution Adaptive Meshing Related Work
- Dindar et al. and Kenwright Haimes applied
refinement at the core line of a vortex - Refinement was performed in a region defined by a
percentage of the cores vorticity - Found that feature-based refinement resolved
small-scale features while error-based refinement
did not - Murayama et al. also employed refinement at the
vortex core line - Found that solutions computed on meshes with
refinement along the core line showed improved
agreement with experimental data - Turnock et al. used a statistical vortex
detection method to identify core regions - Refinement was achieved by using a set mesh
density across the core surrounded by an annulus
of lower density cells. - Significant improvement was seen when compared to
computations on an unrefined mesh
10Thesis Statement
- Abstract feature descriptors can be employed
along with mesh refinement or mesh regeneration
with embedded surfaces to facilitate an effective
solution adaptive meshing strategy. Strategies
will be applied to different configurations to
evaluate the robustness of the strategy and to
verify the approach
11Feature-based Adaptive Meshing
- Vortex feature characteristics are used to locate
flow field regions that are near vortices - Regions near the vortices are marked for
enrichment - Assume that the quality of the solution will
improve if a mesh is enriched near flow features
i.e. vortices - Two mesh improvement techniques are used
- Mesh refinement
- Mesh regeneration using embedded surfaces
- Algorithm described by Jankun-Kelly is used to
produce a high-level description of vortices - Previous research shows that mesh improvement
needs to be performed around and in the region of
the vortex core - Can an initial solution computed on a coarse mesh
be used to initiate adaptive meshing?
12Vortex Characterization
- Output of the process is a set of high-level
descriptors, including geometric, kinematic, and
dynamic properties - Vortex core line
- Vortex extent surface (MTV)
- Two important attributes of the vortex
characterization and extraction process - Able to extract core lines from complex vortex
configuration - Extent surface is an unambiguous descriptor that
captures regions of high velocity curvature
13Vortex Characterization
(1) Aggregation of candidate cells
(2) Identification and classification of
aggregates
14Vortex Characterization
(3) Core line extraction
(4) Extent surface extraction
15Adaptive Mesh Refinement
- Uses geometric, feature-based descriptors to
identify regions that should be refined - Mesh independent set of descriptors
- UGSensor marks nodes in regions defined by the
vortex characterization process, UGVortex - User may choose which regions to mark
- Near core
- Near extent
- Inside extent
- Near extent and near core
16Adaptive Mesh Refinement
Near the core line Near the extent surface
17Adaptive Mesh Refinement
18Adaptive Mesh Refinement
(a) Prism (b) tetrahedron
(c) hexahedron
(d) Refined pyramid (e) refined/unrefined
cell neighbors
19Adaptive Mesh Regeneration Using Embedded Surfaces
- Strategy uses feature aligned embedded surface
meshes - Surface meshes are used as interior boundaries
for mesh regeneration - Strategy allows for more specific control over
the volume mesh compared to standard
redistribution methods - Strategy may improve feature resolution because
of alignment of faces with those features for
Riemann based flow solvers, like CHEM
20Adaptive Mesh Regeneration Using Embedded Surfaces
21Adaptive Mesh Regeneration Using Embedded Surfaces
22Results
- Two configurations
- Wing in a wind tunnel at 10º AoA
- Two mesh improvement techniques
- Missile spinning at 30Hz and 60Hz with canards
deflected to 15º - All flow solutions were computed using the HPCCs
Raptor cluster - Flow solver used in all cases was CHEM
23Results Wing in Wind Tunnel
- Low-speed turbulent flow past a rectangular
planform half-wing - Aspect ratio of 0.75, NACA 0012 cross-section
- 10º AoA, Re 4.6 x 106
- Experimental and additional CFD results reported
by Dacles-Mariani et al. - C-O topology structured grid, Baldwin-Barth
turbulence model (modified) - High-order (5th) CFD simulations were used,
yielding superior numerical results
24Results Wing in Wind Tunnel
25Results Wing in Wind Tunnel
- Turbulence model used is Spalart-Allmaras
- Modified to decrease the production of turbulence
in the vortex core - Inflow boundary conditions (fixed mass)
- Mass flow rate 81.2 kg/s
- Stagnation temp 290.4 K
- Outflow boundary (farfield)
- Pressure 1 atm
- Temperature 288.15 K
- Velocity 67.528 m/s
26Results Wing in Wind Tunnel
27Wing Adaptive Mesh Refinement
- Vortex computed on the baseline mesh is quite
diffuse and shorter in length compared to further
refinements - Due to artificial dissipation associated with
comparatively large elements - Unwise to perform multiple refinements using the
solution from the coarse baseline mesh - To alleviate this, only two levels of refinement
were performed on the baseline and the two
following adaption cycles - An additional refinement cycle was performed
using four levels of refinement using different
refinement strategies
28Wing Adaptive Mesh Refinement
Baseline solution CYCLE 0
After 1st refinement CYCLE 1
After 2nd Refinement CYCLE 2
29Wing Adaptive Mesh Refinement
30Wing Adaptive Mesh Refinement
31Wing Adaptive Mesh Refinement
- Cycle 3A Refinement in a region near the vortex
core line. The radius of refinement is limited to
25 of the local distance to the extent surface - Cycle 3B Refinement in a region near the extent
surface. The refinement is limited to 25 of the
local distance from the core line to the extent
surface on either side of the extent surface
32Wing Adaptive Mesh Refinement
- Cycle 3C Refine inside the extent surface.
Fairly conservative technique, but it ensures
that the vortex is fully captured in the
refinement section of the mesh. - Cycle 3D Refine inside and near the extent
surface. Provides the highest level of
refinement, near refinement is limited to 25 of
the local distance from the core line to the
extent, on either side
33Wing Adaptive Mesh Refinement
34Wing Adaptive Mesh Refinement
35Wing Adaptive Mesh Refinement
(a) Baseline
(b) Cycle 1
(c) Cycle 2
36Wing Adaptive Mesh Refinement
(a) Cycle 3A core refinement
(b) Cycle 3B refinement near extent
37Wing Adaptive Mesh Refinement
(a) Cycle 3C
(b) Cycle 3D
38Wing Adaptive Mesh Refinement
- Results suggest that refinement inside and near
the extent yields the best results in terms of
the solution achieved - Vortex was successfully captured within the
refinement region - Use of the local maximum tangential velocity
surface as a measure of vortex extent provides an
unambiguous and grid-independent geometrical
characteristic - The capability to initiate computation and
subsequent refinement from a very coarse baseline
mesh was fully demonstrated
39Wing Adaptive Mesh Refinement
40Wing Mesh Regeneration Using Embedded Surfaces
- Again, attaining a good enough initial solution
from a coarse baseline mesh remains as a hurdle. - Hurdle is overcome by being able to refine enough
in the general area of the vortex to achieve a
better solution for the next iteration - Each mesh is generated using the vortex extent
surface extracted from the previous mesh in
sequence - The extracted extent surface is then used as an
internal boundary on which the surface mesh was
generated
41Wing Mesh Regeneration Using Embedded Surfaces
42Wing Mesh Regeneration Using Embedded Surfaces
43Wing Mesh Regeneration Using Embedded Surfaces
44Wing Mesh Regeneration Using Embedded Surfaces
45Wing Mesh Regeneration Using Embedded Surfaces
(a) baseline
(b) Cycle 1
46Wing Mesh Regeneration Using Embedded Surfaces
(a) Cycle 2
(b) Cycle 3
47Wing Mesh Regeneration Using Embedded Surfaces
Mesh spacing for the embedded surface meshes
Mesh statistics for the wing in wind tunnel using
mesh regeneration using embedded surfaces
48Wing Mesh Regeneration Using Embedded Surfaces
- Results reiterate the need to refine in all
critical areas, i.e. core and extent, especially
over the wingtip - As more iterations are performed, the location of
the extent surface becomes, for the most part,
stationary - For the most part, the vortex location has been
accurately predicted - For further solution improvement, the nodal
density of the mesh has to be increased in other
critical regions, namely along the vortex core
line over the wingtip
49Results Spinning Missile
- Missile spinning with forward canards deflected
15 - Two cases
- 30Hz spin
- 60Hz spin
- M 1.6
- Re 41.3 x 106
50Results Spinning Missile
- Rotation occurs about the missiles long axis
with the rotation vector (right-handed) pointing
out of the nose of the missile - Both rotation rates display significant vortex
asymmetry and curvature - For the 60Hz case, the inboard, port side vortex,
shed from the forward canard, impinges on the
missile body, causing it to terminate prematurely - CHEM used to compute the flow solution
- Menters SST k-? turbulence model was used
51Results Spinning Missile
(a) Baseline mesh at 30Hz
(b) Baseline mesh at 60Hz
52Results Spinning Missile
- Based on results from the wing case, the mesh was
refined inside and near the extent surface - Baseline mesh used is roughly equivalent to the
cycle 2 mesh used for the wing case - Mesh improvement between cycles consisted of 3
levels of refinement
53Results Spinning Missile
30Hz Case
54Results Spinning Missile
60Hz Case
55Results Spinning Missile
- As shown, the refinements made for both cases
show improved resolution of the stagnation
pressure contours - For the 30Hz case, the resolution of the vortices
is noticeably improved, especially the outermost
two - The innermost vortices are only slightly improved
because they lie close to the missile body, a
naturally more refined region - The 60Hz case contains highly asymmetric vortex
structure, including a vortex that wraps around
the missile body (outboard, port) - The two starboard vortices can be seen
interacting, and are in the process of merging - Significant improvement can be seen in all
vortices - For the port vortex, improvement can be seen
along the entire missile body - For the starboard vortex, improvement can be seen
over ¾ of the body
56Conclusions
- Overall, the effectiveness of vortex-based
solution adaptive meshing has been demonstrated
for two different configurations. - Two strategies were employed to achieve adaptive
meshing - Adaptive mesh refinement
- Adaptive mesh regeneration using embedded
surfaces
57Conclusions Wing in Wind Tunnel
- For mesh refinement, through comparison to
experimental data, the most effective method was
determined refinement in and near the vortex
extent - Results obtained were noticeably improved across
the board when compared to any previous iteration - Mesh regeneration using embedded surfaces was
able to effectively improve the flow solution
through adaptive mesh improvement - Through comparison to experimental results, it
was determined that full solution correlation
could not be had - Adequate mesh resolution in the core over the
wingtip region could not be obtained
58Conclusions Wing in Wind Tunnel
- Through the application of both adaptive meshing
strategies, refinement performed near and inside
the vortex extent surface was determined to be
the highest performer - Method was seen to have superior definition in
crossflow velocity contours - Method was determined to have the closest
agreement with experimental data (tangential
velocity vs. local vortex extent radius)
59Conclusions Wing in Wind Tunnel
(a) Mesh refinement near and inside extent
(b) Mesh regeneration final refinement
60Conclusion Spinning Missile
- Baseline mesh used was somewhat refined in the
region near the missile body - Comparable to the cycle 2 mesh used for the wing
refinement - In one refinement cycle, the solution was greatly
improved for both the 30Hz and 60 Hz scenario - Based on overall observed vortex resolution and
coherence of the vortex core line - The vortical asymmetry caused by missile rotation
highlights the need for solution based adaptive
meshing
61Conclusion
- The study presented demonstrates that abstract
feature descriptors can be used along with mesh
refinement or regeneration to facilitate
effective solution adaptive meshing - Verification of the strategies was achieved
through application to various configurations,
including more complex flows, showing the
robustness and plausibility of each.
62Thank You