1. Using FLUENT in Design & Optimization
Devendra Ghate, Amitay Isaacs,
K Sudhakar, A G Marathe, P M Mujumdar
Centre for Aerospace Systems Design and Engineering
Department of Aerospace Engineering, IIT Bombay

2. Outline CFD in design Problem statement Duct parametrization
Flow solution
Results
Conclusion
FLUENT CFD Conference 2003

3. Using CFD in Design Simulation Time Integration Automation
CFD is takes huge amounts of time for real life problems
Design requires repetitive runs of disciplinary analyses
Integration
With optimizer
With other disciplinary analyses (e.g. grid generator)
Automation
No user interaction should be required for simulation
Gradient Information
No commercial CFD solvers provide gradient information
Computationally expensive and problematic ( ) to get gradient information for CFD solvers (finite difference, automatic differentiation)
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4. Problem Specification
Methodology
Problem Specification
Parametrization
New parameters
Geometry Generation
Grid Generation
CFD problem setup
Flow Solution
Optimization using
Surrogate Models
(RSM, DACE)
FLUENT CFD Conference 2003

5. Problem Specification
Methodology
Problem Specification
Parametrization
New parameters
Geometry Generation
Optimization using
Surrogate Models
(RSM, DACE)
Grid Generation
CFD problem setup
Flow Solution
FLUENT
FLUENT CFD Conference 2003

6. 3-D Duct Design Problem Entry Exit Pressure Recovery Distortion Swirl
Location and shape known
Pressure Recovery
Distortion
Swirl
Geometry of duct from Entry to Exit ?
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7. Parametrization Control / Design Variables Ym, Zm AL/3, A2L/3X Z
Duct Centerline A
Control / Design Variables
Ym, Zm
AL/3, A2L/3
Cross Sectional Area
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8. Parametrization (contd.)Y X Z
Duct Centerline A
Control / Design Variables
Ym, Zm
AL/3, A2L/3
Cross Sectional Area
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9. Typical 3D-Ducts
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10. Grid Generation
Clustering Parameters
Complete grid generation process is automated and does not require human intervention
Complete control over
Distance of the first cell from the wall
Clustering
Number of grid points
Generation of entry and exit
sections using GAMBIT
Mesh file
Conversion of file format to
CGNS using FLUENT
Entry & Exit sections
Generation of structured volume
grid using parametrization
Grid parameters
Conversion of structured grid
to unstructured format
FLUENT CFD Conference 2003

11. Turbulence Modeling Relevance: Time per Solution
Following aspects of the flow were of interest:
Boundary layer development
Flow Separation (if any)
Turbulence Development
Literature Survey
Doyle Knight, Smith, Harloff, Loeffer
Circular cross-section
S-shaped duct
Baldwin-Lomax model (Algebraic model)
Computationally inexpensive than more sophisticated models
Known to give non-accurate results for boundary layer separation etc.
k- realizable turbulence model
Two equation model
Study by Devaki Ravi Kumar & Sujata Bandyopadhyay (FLUENT Inc.)
FLUENT CFD Conference 2003

12. Turbulence Modeling (contd.)
Standard k- model
Turbulence Viscosity Ratio exceeding 1,00,000 in 2/3 cells
Realizable k- model
Shih et. al. (1994)
Cμ is not assumed to be constant
A formulation suggested for calculating values of C1 & Cμ
Computationally little more expensive than the standard k- model
Total Pressure profile at the exit section (Standard k-  model)
FLUENT CFD Conference 2003

13. Distortion Analysis DC60 = (PA0 – P60min) /q where,
PA0 - average total pressure at the section,
P60min - minimum total pressure in a 600 sector, q - dynamic pressure at the cross section.
User Defined Functions (UDF) and scheme files were used to generate this information from the FLUENT case and data file.
Iterations may be stopped when the distortion values stabilize at the exit section with reasonable convergence levels.
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14. Parallel Execution Parallel mode of operation in FLUENT
16-noded Linux cluster
Portable Batch Systems for scheduling
Batch mode operation of FLUENT (-g)
Scale up depends on grid size
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15. Results: Total Pressure Profile
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16. Results (contd.) Mass imbalance: 0.17% Energy imbalance: 0.06%
Total pressure drop: 1.42%
Various turbulence related quantities of interest at entry and exit sections:
Entry
Exit
Turbulent Kinetic Energy
124.24
45.65
Turbulent Viscosity Ratio
y+ at the cell center of the cells adjacent to boundary throughout the domain is around 18.
FLUENT CFD Conference 2003

17. These are huge benefits as compared to the efforts involved.
Slapping
Methodology
Store the solution in case & data files
Open the new case (new grid) with the old data file
Setup the problem
Solution of ( ) duct slapped on ( )
3-decade-fall
6-decade-fall
Without slapping
4996
9462
With slapping
1493
6588
Percentage time saving
70%
30%
These are huge benefits as compared to the efforts involved.
FLUENT CFD Conference 2003

18. Conclusion
Time for simulation has been reduced to around 20% using parallel computation and slapping.
Process of geometry & grid generation has been automated requiring no interactive user input
FLUENT has been customized for easy integration into an optimization cycle
CFD analysis module ready for inclusion in optimization for a real life problem
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19. Future Work
Further exploration and improvement of slapping methodology
Identification and assessment of optimum optimization algorithm
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20. Thank You

21. FLUENT CFD Conference 2003

22. Problem Statement A diffusing S-shaped duct
Ambient conditions: 11Km altitude
Inlet Boundary Conditions
Total Pressure: Pa
Total Temperature: o K
Hydraulic Diameter: m
Turbulence Intensity: 5%
Outlet Boundary Conditions
Static Pressure: Pa (Calculated for the desired mass flow rate)
Hydraulic Diameter: m
FLUENT CFD Conference 2003

23. Duct Parameterization
Geometry of the duct is derived from the Mean Flow Line (MFL)
MFL is the line joining centroids of cross-sections along the duct
Any cross-section along length of the duct is normal to MFL
Cross-section area is varied parametrically
Cross-section shape in merging area is same as the exit section
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24. MFL Design Variables - 1
Mean flow line (MFL) is considered as a piecewise cubic curve along the length of the duct between the entry section and merging section x
y(x), z(x) Lm
Lm/2
y(Lm/2), z(Lm/2) specified
Centry
Cmerger
y1, z1
y2, z2
Lm : x-distance between the entry and merger section
y1, y2, z1, z2 : cubic polynomials for y(x) and z(x)
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25. MFL Design Variables - 2
y1(x) = A0 + A1x + A2x2 + A3x3, y2(x) = B0 + B1x + B2x2 + B3x3
z1(x) = C0 + C1x + C2x2 + C3x3, z2(x) = D0 + D1x + D2x2 + D3x3
y1(Lm) = y2 (Lm), y1’ (Lm) = y2’ (Lm), y1” (Lm) = y2” (Lm)
z1(Lm) = z2 (Lm), z1’ (Lm) = z2’ (Lm), z1” (Lm) = z2” (Lm)
y1’ (Centry) = y2’ (Cmerger) = z1’ (Centry) = z2’ (Cmerger) = 0
The shape of the MFL is controlled by 2 parameters which control the y and z coordinate of centroid at Lm/2
y(Lm/2) = y(0) + (y(L) – y(0)) αy < αy < 1
z(Lm/2) = z(0) + (z(L) – z(0)) αz < αz < 1
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26. Area Design Variables – 1
Cross-section area at any station is interpolated from the entry and exit cross-sections
A(x) = A(0) + (A(Lm) – A(0)) * β(x)
corresponding points on entry and exit sections are linearly interpolated to obtain the shape of the intermediate sections and scaled appropriately
Psection = Pentry + (Pexit - Pentry) * β
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27. Area Design Variables - 2
β variation is given by piecewise cubic curve as function of x x
β(x) Lm
Lm/3 1
2Lm/3 β1 β2
β(Lm/3) and β(2Lm/3) is specified
A0 + A1x + A2x2 + A3x  β < β1
B0 + B1x + B2x2 + B3x β1  β  β2
C0 + C1x + C2x2 + C3x β2< β  1
β =
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