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**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

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**Outline CFD in design Problem statement Duct parametrization**

Flow solution Results Conclusion FLUENT CFD Conference 2003

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**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) FLUENT CFD Conference 2003

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**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

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**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

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**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 ? FLUENT CFD Conference 2003

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**Parametrization Control / Design Variables Ym, Zm AL/3, A2L/3**

X Z Duct Centerline A Control / Design Variables Ym, Zm AL/3, A2L/3 Cross Sectional Area FLUENT CFD Conference 2003

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**Parametrization (contd.)**

Y X Z Duct Centerline A Control / Design Variables Ym, Zm AL/3, A2L/3 Cross Sectional Area FLUENT CFD Conference 2003

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Typical 3D-Ducts FLUENT CFD Conference 2003

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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

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**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

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**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

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**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. FLUENT CFD Conference 2003

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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

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**Results: Total Pressure Profile**

FLUENT CFD Conference 2003

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**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

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**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

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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 FLUENT CFD Conference 2003

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

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Thank You

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FLUENT CFD Conference 2003

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**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

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**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

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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) FLUENT CFD Conference 2003

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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 FLUENT CFD Conference 2003

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**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 FLUENT CFD Conference 2003

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**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 = FLUENT CFD Conference 2003

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