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Numerical Methods in CFD

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Numerical Methods in CFD

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  1. INTRODUCTION TO CFD ARVIND DESHPANDE

  2. Introduction  Computational Fluid Dynamics or CFD is the analysis of systems involving fluid flow, heat transfer and associated phenomena such as chemical reactions by means of computer based simulation.  A tool for solving PDE’s  3 fundamental principles: Mass is conserved (Continuity equation); Newton’s second law (Navier-Stokes Eqn); Energy is conserved (Bernoulli’s Equation) 3/7/2012 2 Arvind Deshpande (VJTI)

  3. Introduction  Governing equations - PDE’s or integral equations  Analytical and experimental approach (Old) “A theory is something nobody believes except the person proposing the theory and an experiment is something everybody believes except the person doing the experiment” --Albert Einstein Albert Einstein 3/7/2012 3 Arvind Deshpande (VJTI)

  4. Numerical Solutions (New)  Computers can only do the following:  Add, Subtract, Multiply and Divide  Perform simple logical operations  Display colours on the screen  What is Discretization?  Analytical Solution : Continuous  Numerical Solution : Discrete 3/7/2012 4 Arvind Deshpande (VJTI)

  5. Introduction  CFD - Science of determining a numerical solution to the governing equations of fluid flow whilst advancing the solution through space or time to obtain a numerical description of the complete flow field of interest.  It is very important to know velocity, pressure and temperature fields in a large no. of applications involving fluids i.e liquids performance of devices such as turbo machinery and heat exchangers is determined entirely by the pattern of fluid motion within them. and gases. The 3/7/2012 5 Arvind Deshpande (VJTI)

  6. Why CFD?  Growth in complexity of unsolved engineering problems  Need for quick solutions of moderate accuracy  Absence of analytical solutions  The prohibitive costs involved in performing even scaled laboratory experiments  Efficient solution algorithms  Developments in computers in terms of speed and storage  Serial/parallel/web computing  Sophisticated pre and post processing facilities 3/7/2012 6 Arvind Deshpande (VJTI)

  7. Procedure 1. Virtual model 2. The flow region or calculation domain is divided into a large number of finite volumes or cells 3. Partial differential equations are discretized using a wide range of techniques: finite difference, finite volume or finite element 4. Algebraic equations gathered into matrices which are solved by an iterative procedure 5. Numerical solution gives the values of the dependent variables at discrete locations 6. Chemical reaction, Multiphase flow, mixing, phase change, mechanical movement 3/7/2012 7 Arvind Deshpande (VJTI)

  8. 3/7/2012 8 Arvind Deshpande (VJTI)

  9. CFD - Third approach in fluid dynamics  CFD today is equal partner with pure theory and pure experiment in the analysis and solution of fluid dynamic problems.  It nicely and synergistically complements the other two approaches of pure theory and pure experiment, but it will never replace either of these approaches.  CFD carry out numerical experiments.  Numerical experiments carried out in parallel with physical experiments sometimes be used to help interpret physical experiment. in the laboratory can 3/7/2012 9 Arvind Deshpande (VJTI)

  10. Advantages of CFD  It complements experimental and theoretical fluid dynamics by providing an alternative cost effective means of simulating real flows.  Insight Better visualization and enhanced understanding of designs.  Foresight Testing many variations until you arrive at an optimal result before physical prototyping and testing. Practically unlimited level of detail of results at virtually no added expense.  Efficiency Compression of design and development cycle. 3/7/2012 10 Arvind Deshpande (VJTI)

  11. Advantages of CFD  The simulation results in prediction of the flow fields and engineering parameters, which are very useful in the Design and Optimization of processes and equipments.  Substantial reduction of lead times and costs of new designs  Ability to study systems where controlled experiments are difficult or impossible to perform (e.g. very large systems)  Ability to study systems under hazardous conditions at and beyond their normal performance limits (e.g. safety studies and accident scenarios)  CFD is slowly becoming part and parcel of Computer Aided Engineering (CAE) 3/7/2012 11 Arvind Deshpande (VJTI)

  12. Why do we use CFD ? Complements actual engineering testing  Reduces engineering testing costs  Provides comprehensive data not easily obtainable from experimental tests.  Reduces the product-to-market time and costs  Helps understand defects, problems and issues in product/process  3/7/2012 12 Arvind Deshpande (VJTI)

  13. Benefits of CFD Understand Problems Reduce System Cost Improve Performance Reduce Design Time & Cost 3/7/2012 13 Arvind Deshpande (VJTI)

  14. HOW IT DIFFERS FROM STRESS ANALYSIS?  Stress analysis is generally check for safe working of the design, Very rarely the performance of the system depends on the stress levels  The governing equations are linear  Ease of solution  Not much dependencies on the grid or mesh  Need of auxiliary physics and models for CFD  Turbulence  Reactions  Multiple phases their transformations  Confined domains  Conservation of only energy, against conservation of mass, forces and energy  CFD problems are, in general, more difficult to solve. Hence CFD was lagging behind structural mechanics. 3/7/2012 14 Arvind Deshpande (VJTI)

  15. Applications of CFD  Aerodynamics of aircraft : lift and drag  Automotive : External flow over the body of a vehicle or internal flow through the engine, combustion, Engine cooling  Turbo machinery: Turbines, pumps , compressors etc.  Flow and heat transfer in thermal power plants and nuclear power reactors  HVAC  Manufacturing – Casting simulation, injection moulding of plastics  Marine engineering: loads on off-shore structures  Hydrodynamics of ships, submarines, torpedo etc. 3/7/2012 15 Arvind Deshpande (VJTI)

  16. Applications of CFD  Electrical and electronic engineering: transformers, Computers, microcircuits, Semiconductor processing, Optical fibre manufacturing  Chemical process engineering: mixing and separation, chemical reactors, polymer molding  Transport of slurries in process industries  Environmental engineering: External and internal environment of buildings, wind loading, Investigating the effects of fire and smoke, distribution of pollutants and effluents in air or water,  Hydrology and oceanography: flows in rivers, oceans  Meteorology: weather prediction  Enhanced oil recovery from rock formations  Geophysical flows: atmospheric convection and ground water movement  Biomedical engineering: Flow heart, nasal cavity, Inhalers cooling of equipment like in arteries, blood vessels, 3/7/2012 16 Arvind Deshpande (VJTI)

  17. Pressure distribution on a pickup van with pathlines 3/7/2012 17 Arvind Deshpande (VJTI)

  18. Streamlines on a Submarine with the surface colored with Pressure 3/7/2012 18 Arvind Deshpande (VJTI)

  19. Aerospace applications 3/7/2012 19 Arvind Deshpande (VJTI)

  20. Aerospace applications 3/7/2012 20 Arvind Deshpande (VJTI)

  21. Automotive applications Evaporating diesel fuel inside an autothermal reformer mixing chamber 3/7/2012 21 Arvind Deshpande (VJTI)

  22. Temperature distribution in IC Engine 3/7/2012 22 Arvind Deshpande (VJTI)

  23. Surface pressure distribution in an automotive engine cooling jacket. 3/7/2012 23 Arvind Deshpande (VJTI)

  24. Cooling of transformers 3/7/2012 24 Arvind Deshpande (VJTI)

  25. Flow pathlines and temperature distribution in a fan-cooled computer cabinet. 3/7/2012 25 Arvind Deshpande (VJTI)

  26. FLOW IN LUNGS-Inhaling and exhaling of air 3/7/2012 26 Arvind Deshpande (VJTI)

  27. Applications in Chemical Engg. 3/7/2012 27 Arvind Deshpande (VJTI)

  28. Biomedical applications 3/7/2012 28 Arvind Deshpande (VJTI)

  29. Flow through the turbine distributor runner draft tube rotating blades 29

  30. Computed flow in the runner 30

  31. Computed flow in the draft tube 3/7/2012 31 Arvind Deshpande (VJTI)

  32. Some more applications 3/7/2012 32 Arvind Deshpande (VJTI)

  33. Some more applications 3/7/2012 33 Arvind Deshpande (VJTI)

  34. Some more applications Vortical structures generated by an aircraft landing gear Fluid flows around the spinnaker and main sail of a racing yacht design Temperatures on flame surface modeled using LES and state-of the- art combustion models Pressure distribution on an F1 car 3/7/2012 34 Arvind Deshpande (VJTI)

  35. CFD USAGE & GROWTH 60 % 40 % Worldwide: 1 Billion USD 18 % 17 % 15 % 15 % India: Rs 50 Cr Projected Growth Rate Estimated annual expenditure on CFD analysis Extrapolation of Published estimates 3/7/2012 35 Arvind Deshpande (VJTI)

  36. National Scenario in CFD  Educational / Research Institutes – IIT’s, IISc, BARC  Industry – NAL, BHEL, SAIL, GTRE, Cummins, Mahindra, Birla group GE, TCS  The number of companies adopting CFD is increasing in a major way in India each year  CFD is the fastest growing sector of the CAD/CAM/CAE market with a projected 40-50% growth each year in CFD in India 3/7/2012 36 Arvind Deshpande (VJTI)

  37. National Scenario in CFD The demand for CFD is spurred by:  Indian companies wanting to improve quality and compete globally CFD is predominantly used in Automotive Industry, Power Generation Industry and Chemical & Petrochemical Industry  MNC Engineering centers located in India and bringing their design/analysis work here and serving overseas clients Working on all aspects of design, analysis and performance improvement using CFD  Indian Science and Defence Labs enhancing their CFD research Defense labs like DRDO, NAL - Application of CFD to high-speed propulsion systems etc. Non defence labs - Focusing on materials and chemicals areas Students knowledgeable in CFD are being produced by only a handful of Institutes in India today The mismatch between the demand and availability of students is growing each year at a large rate    3/7/2012 37 Arvind Deshpande (VJTI)

  38. Methodology in CFD  Pre processor  Geometry generation  Geometry cleanup  Meshing  Solver  Problem specification  Additional models  Numerical computation  Post Processor  Line and Contour data  Average Values  Report Generation Pre Processor Solver Post Processor 3/7/2012 38 Arvind Deshpande (VJTI)

  39. 1. Pre-processor Definition of the geometry of the region of interest: the computational domain Creating regions of fluid flow, solid regions and surface boundary names Grid generation – the sub-division of the domain into a number of smaller, non-overlapping sub-domains: a grid (or mesh) of cells (or control volumes or elements) Accuracy of a solution, calculation time and cost in terms of necessary computer hardware are dependent on the fineness of the grid. Over 50% of time spent in industry on a CFD project is devoted to the definition of domain geometry and grid generation. Selection of the physical and chemical phenomena that need to be modeled. Definition of fluid properties. Specification of appropriate boundary conditions at cells which coincide with or touch the domain boundary         3/7/2012 39 Arvind Deshpande (VJTI)

  40. 2. Solver • CFD is the art of replacing the differential equation governing the Fluid Flow, with a set of algebraic equations (the process is called discretization), which in turn can be solved with the aid of a digital computer to get an approximate solution. 3/7/2012 40 Arvind Deshpande (VJTI)

  41. Finite difference method  Domain including the boundary of the physical problem is covered by a grid or mesh  At each of the interior grid point the original Differential Equations are replaced by equivalent finite difference approximations  Truncated Taylor series expansions are often used to generate finite difference approximations of derivatives of  in terms of point samples of  at each grid point and its immediate neighbours  Most popular during the early days of CFD  FDM has the most formal foundation because, its inherent straightforwardness and simplicity. 3/7/2012 41 Arvind Deshpande (VJTI)

  42. Finite Element Method The solution domain is discretized into number of small sub regions (i.e. Finite Elements). Select an approximating function known as interpolation polynomial to represent the variation of the dependent variable over the elements. The piecewise approximating functions for  are substituted into the equation it will not hold exactly and a residual is defined to measure the errors. The integration of the governing differential equation (often PDEs) with suitable weighting Function, over each elements to produce a set of algebraic equations-one equation for each element. The set of algebraic equations are then solved to get the approximate solution of the problem. Structural Design, Vibration Analysis, Fluid Dynamics, Heat Transfer and Magnetohydrodynamics       3/7/2012 42 Arvind Deshpande (VJTI)

  43. Finite volume method  FLUENT, PHOENICS, and STAR-CD  Integration of the governing equations of fluid flow over all the (finite) control volumes of the solution domain. This is equivalent to applying a basic conservation law (e.g. for mass or momentum) to each control volume.  Discretisation involves the substitution of a variety of finite – difference – type approximations for the terms in the integrated equation representing flow process such as convection, diffusion and sources. This converts the integral equations into a system of algebraic equations.  Solution of the algebraic equations by an iterative method. 3/7/2012 43 Arvind Deshpande (VJTI)

  44. Rate of change of  in the control volume with respect to time Net flux of  due to convection into the control volume + = Net flux of  due to diffusion into the control volume + Net rate of creation of  inside the control volume 3/7/2012 44 Arvind Deshpande (VJTI)

  45. 3.Post-processor Versatile data visualization tools.  Domain geometry and grid display  Vector plots showing the direction and magnitude of the flow.  Line and shaded contour plots  2D and 3D surface plots  Particle tracking  View manipulation (translation, rotation, scaling etc.)  Visualization of the variation of scalar variables (variables which have only magnitude, not direction, such as temperature, pressure and speed) through the domain.  Quantitative numerical calculations.  Charts showing graphical plots of variables  Hardcopy output  Animation for dynamic result display  Data export facilities for further manipulation external to the code 3/7/2012 45 Arvind Deshpande (VJTI)

  46. 3/7/2012 46 Arvind Deshpande (VJTI)

  47. Problem solving with CFD  Convergence – The property of a numerical method to produce a solution which approaches the exact solution as the grid spacing, is reduced to zero.  Consistency - The property of a numerical method to produce system of algebraic equations solution which are equivalent to original governing equations as the grid spacing, is reduced to zero.  Stability - associated with damping of errors as the numerical method proceeds. If a technique is not stable, even round off errors in the initial data can cause wild oscillations or divergence. 3/7/2012 47 Arvind Deshpande (VJTI)

  48. Problem solving with CFD  Conservativeness – Local conservation of fluid property for each control volume. It also ensures global conservation of fluid property for the entire domain.  Boundedness – In a linear problem, without sources the solution is bounded by the maximum and minimum boundary values of the flow variables. Similar to stability.  Transportiveness – Numerical account for the directionality of influencing in terms of the relative strength of diffusion to convection. schemes must 3/7/2012 48 Arvind Deshpande (VJTI)

  49. Problem solving with CFD  Convergence (measure properties) are very small.  Good initial grid design relies largely on an insight into the expected properties of the flow.  Background in the fluid dynamics of the problem and experience of meshing similar problems helps.  Grid independence study successive refinement of initially coarse grid until certain key results do not change. of overall iterative process Residuals the – of of conservation flow - A procedure of 3/7/2012 49 Arvind Deshpande (VJTI)

  50. Problem solving with CFD CFD is no substitute for experimental work, but a very powerful problem solving tool. Comparison with experimental test work High end – Velocity measurements by hot wire or laser Doppler anemometer Static pressure or temperature measurements with static pitot tube traverse can also be useful. Comparison with previous experience Comparison with analytical solutions of similar but simpler flows. Comparison with closely related problems reported in the literature e.g ASME Main outcome of any CFD exercise is improved understanding of the behaviour of the system. Main ingredients for success in CFD are experience and a thorough understanding of the physics of the fluid flows and fundamentals of the numerical algorithms.        3/7/2012 50 Arvind Deshpande (VJTI)

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