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 http://www.casde.iitb.ac.in/

Outline

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

Using CFD in Design

Simulation Time   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) FLUENT CFD Conference 2003 3

Methodology

Problem Specification Parametrization Optimization using Surrogate Models (RSM, DACE) New parameters Geometry Generation Grid Generation CFD problem setup Flow Solution 4 FLUENT CFD Conference 2003

Methodology

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

3-D Duct Design Problem

 Pressure Recovery • Distortion • Swirl Entry Exit Location and shape known FLUENT CFD Conference 2003 Geometry of duct from Entry to Exit ?

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Parametrization

Y Z A X Duct Centerline

Control / Design Variables

X X Cross Sectional Area

FLUENT CFD Conference 2003 • Y m , Z m • A L/3 , A 2L/3 7

Parametrization

(contd.)

Y Z A

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X Duct Centerline

Control / Design Variables

X

• Y m , Z m • A L/3 , A 2L/3 8

Typical 3D-Ducts

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Grid Generation

Clustering Parameters   Complete grid generation process is automated and does not require human intervention Generation of entry and exit sections using GAMBIT Mesh file Complete control over • Distance of the first cell from the wall • Clustering • Number of grid points Grid parameters Conversion of file format to CGNS using FLUENT Entry & Exit sections Generation of structured volume grid using parametrization Conversion of structured grid to unstructured format 10 FLUENT CFD Conference 2003

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 k      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.

realizable turbulence model Two equation model Study by Devaki Ravi Kumar & Sujata Bandyopadhyay (FLUENT Inc.) FLUENT CFD Conference 2003 11

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 12

Distortion Analysis

DC 60 = (PA 0 where, PA 0 – P60 min ) /q - average total pressure at the section, P60 q min - minimum total pressure in a 60 0 sector, - 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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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 FLUENT CFD Conference 2003 14

Results: Total Pressure Profile

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Results

(contd.) Mass imbalance: Energy imbalance: sections: 0.17% 0.06% Total pressure drop: 1.42% Various turbulence related quantities of interest at entry and exit Turbulent Kinetic Energy Turbulent Viscosity Ratio Entry 124.24

5201.54

Exit 45.65

3288.45

y + at the cell center of the cells adjacent to boundary throughout the domain is around 18. FLUENT CFD Conference 2003 16

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 (0.61 0.31 1 1) duct slapped on (0.1 0.31 0.1 0.1) Without slapping With slapping Percentage time saving 3-decade-fall 4996 1493 70% 6-decade-fall 9462 6588 30%

These are huge benefits as compared to the efforts involved.

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Conclusion

Time per CFD Run

Time for simulation has been reduced to around 20% using parallel computation and slapping.

Serial Run Parallel Run Slapping

0 20 40 60

Time (hrs)

80 100   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 FLUENT CFD Conference 2003 18

Future Work

Further exploration and improvement of slapping methodology Identification and assessment of optimum optimization algorithm FLUENT CFD Conference 2003 19

Thank You

http://www.casde.iitb.ac.in/mdo/3d-duct/

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Problem Statement

• A diffusing S-shaped duct • Ambient conditions: 11Km altitude • Inlet Boundary Conditions • Total Pressure: 34500 Pa • Total Temperature: 261.4o K • Hydraulic Diameter: 0.394m

• Turbulence Intensity: 5% • Outlet Boundary Conditions • Static Pressure: 31051 Pa (Calculated for the desired mass flow rate) • Hydraulic Diameter: 0.4702m

• Turbulence Intensity: 5% FLUENT CFD Conference 2003 22

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 FLUENT CFD Conference 2003 23

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 m /2) specified C merge y(x), z(x) y 2 , z 2 r y 1 , z 1 C entry 0 L m /2 L m L m : x-distance between the entry and merger section x y 1 , y 2 , z 1 , z 2 : cubic polynomials for y(x) and z(x) 24

MFL Design Variables - 2

• y 1 (x) = A 0 • z 1 (x) = C 0 + A 1 x + A 2 x + C 1 x + C 2 x 2 2 + A 3 x 3, y 2 (x) = B + C 3 x 3, z 2 (x) = D 0 0 + B 1 x + B 2 x 2 + D 1 x + D 2 x 2 + B 3 x 3 + D 3 x 3 • y 1 (L m ) = y 2 (L m ), y 1 ’(L m ) = y 2 ’(L m ), y 1 ” (L m ) = y 2 ” (L m ) • z 1 (L m ) = z 2 (L m ), z 1 ’(L m ) = z 2 ’(L m ), z 1 ” (L m ) = z 2 ” (L m ) • y 1 ’(C entry ) = y 2 ’(C merger ) = z 1 ’ (C entry ) = z 2 ’(C merger ) = 0 • The shape of the MFL is controlled by 2 parameters which control the y and z coordinate of centroid at L m /2 • y(L m /2) = y(0) + (y(L) – y(0)) α y 0 < α y < 1 • z(L m /2) = z(0) + (z(L) – z(0)) α z 0 < α z < 1 FLUENT CFD Conference 2003 25

Area Design Variables – 1

Cross-section area at any station is interpolated from the entry and exit cross sections •A(x) = A(0) + (A(L m ) – 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 • P section = P entry + (P exit - P entry ) * β FLUENT CFD Conference 2003 26

Area Design Variables - 2

β variation is given by piecewise cubic curve as function of x β(L m /3) and β(2L m /3) is specified β(x) β 2 β 1 0 0 L m /3 2L m /3 L m β = A 0 B C 0 0 + A 1 x + A 2 x 2 + B + C 1 1 x + B x + C 2 2 x x 2 2 + A 3 x 3 0  + B 3 x 3 β 1  β < β 1 β  β 2 + C 3 x 3 β 2 < β  1 FLUENT CFD Conference 2003 1 x 27