BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSIS

1. BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSIS MEEN 5330 Presented By Chaitanya Vudutha Parimal Nilangekar Ravindranath Gouni Satish Kumar Boppana Albert Koether Pages-28

2. Overview • Introduction • History of CFD • Basic concepts • CFD Process • Derivation of Navier-Stokes Duhem Equation • Example Problem • Applications • Conclusion • References

3. Introduction Since 1940s analytical solution to most fluid dynamics problems was available for idealized solutions. Methods for solution of ODEs or PDEs were conceived only on paper due to absence of personal computer. Daimler Chrysler was the first company to use CFD in Automotive sector. Speedo was the first swimwear company to use CFD. There are number of companies and software's in CFD field in the world. Some software's by American companies are FLUENT, TIDAL, C-MOLD, GASP, FLOTRAN, SPLASH, Tetrex, ViGPLOT, VGRID, etc. What is CFD? Prediction fluid flow with the complications of simultaneous flow of heat, mass transfer, phase change, chemical reaction, etc using computers History ofCFD

4. BASIC CONCEPTS Fluid Mechanics Fluid Statics Fluid Dynamics Laminar Turbulent Newtonian Fluid Non-Newtonian Fluid Rheology Ideal Fluids Viscous Fluids Compressible Flow Incompressible Flow CFD Solutions for specific Regimes Components of Fluid Mechanics

5. volumes no smaller than say (1*10 m3) Molecular Particles of Fluid Basic fluid motion can be described as some combination of • Translation: [ motion of the center of mass ] 2) Dilatation: [ volume change] 3) Rotation: [About one, two or 3 axes ]. 4) Shear Strain

6. Compressible and Incompressible flow A fluid flow is said to be compressible when the pressure variation in the flow field is large enough to cause substantial changes in the density of fluid. Viscous and Inviscid Flow In a viscous flow the fluid friction has significant effects on the solution where the viscous forces are more significant than inertial forces

7. Steady and Unsteady Flow Whether a problem is steady or unsteady depends on the frame of reference Laminar and Turbulent Flow Newtonian Fluids and Non-Newtonian Fluids In Newtonian Fluids such as water, ethanol, benzene and air, the plot of shear stress versus shear rate at a given temperature is a straight line

8. Initial or Boundary Conditions • Initial condition involves knowing the state of pressure (p) and initial velocity (u) at all points in the flow. • Boundary conditions such as walls, inlets and outlets largely specify what the solution will be.

9. Discretization Methods • Where Q - vector of conserved variables • Finite volume method • Finite Element method • F - vector of fluxes • V - cell volume • A –Cell surface area Ri=Equation residual at an element vertex Q- Conservation equation expressed on element basis Wi= Weight Factor

10. Finite difference method • Boundary element method Q – Vector of conserved variables F,G,H – Fluxes in the x ,y, z directions The boundary occupied by the fluid is divided into surface mesh

11. CFD PROCESS • Geometry of problem is defined . • Volume occupied by fluid is divided into discrete cells.

12. CFD PROCESS cont.. • Physical modeling is defined. • Boundary conditions are defined which involves specifying of fluid behavior and properties at the boundaries. • Equations are solved iteratively as steady state or transient state. • Analysis and visualization of resulting solution. post processing

13. DERIVATION OF NAVIER-STOKES-DUHEM EQUATION The Navier-Stokes equations are the fundamental partial differentials equations that describe the flow of incompressible fluids. Two of the alternative forms of equations of motion, using the Eulerian description, were given as Equation (1) and Equation (2) respectively: (1) (2)

14. DERIVATION (Cont’d) If we assume that the fluid is isotropic , homogeneous , and Newtonian, then : (3) Substituting Equ(3) into Equ(2), and utilizing the Eulerian relationship for linear stress tensor we get : (4) ( for compressible fluids )

15. DERIVATION (Cont’d) For incompressible fluid flow the Navier-Stokes- Duhem equation is: If the fluid medium is a monatomic ideal gas, then :

16. DERIVATION (Cont’d) Navier stokes equation for compressible flow of monatomic ideal gas is :

17. EXAMPLE PROBLEM Neglecting the gravity field, describe the steady two- dimensional flow of an isotropic , homogeneous, Newtonian fluid due to a constant pressure gradient between two infinite, flat, parallel, plates. State the necessary assumptions. Assume that the fluid has a uniform density.

18. SOLUTION (Cont’d) The Navier – stokes equations for incompressible flow is: Since the flow is steady and the body forces are neglected, the Navier-stokes equation becomes:

19. SOLUTION (Cont’d) The no slip boundary conditions for viscous flow are: at Using the boundary conditions ( q2= 0 at y2=+/- a ) Thus, the first Navier-stokes equations becomes

20. SOLUTION (Cont’d) Integrating twice, we obtain The results, assumptions and boundary conditions of this problem in terms of, mathematical symbols are as follows: Constant

21. HOMEWORK PROBLEM • Using the Navier-Stokes equations investigate the flow (qi) between two stationary, infinite, parallel plates a distance h apart. Assuming that you have laminar flow of a constant-density, Newtonian fluid and the pressure gradient is constant (partial derivative of P with respect to 1).

22. Types of Errors and Problems Types of Errors: • Modeling Error. • Discretization Error. • Convergence Error. • Reasons due to which Errors occur: • Stability. • Consistency. • Conservedness and Boundedness.

23. Applications of CFD 1. Industrial Applications: CFD is used in wide variety of disciplines and industries, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, petroleum exploration, pulp and paper operation, medical research, meteorology, and astrophysics. Example: Analysis of Airplane CFD allows one to simulate the reactor without making any assumptions about the macroscopic flow pattern and thus to design the vessel properly the first time.

24. Application (Contd..) • Two Dimensional Transfer Chute Analyses Using a Continuum Method: • Fluent is used in chute designing tasks like predicting flow shape, stream velocity, wear index and location of flow recirculation zones. • Bio-Medical Engineering: The following figure shows pressure contours and a cutaway view that reveals velocity vectors in a blood pump that assumes the role of heart in open-heart surgery. Pressure Contours in Blood Pump

25. Application (Contd..) 4. Blast Interaction with a Generic Ship Hull The figure shows the interaction of an explosion with a generic ship hull. The structure was modeled with quadrilateral shell elements and the fluid as a mixture of high explosives and air.The structural elements were assumed to fail once the average strain in an element exceeded 60 percent Results in a cut plane for the interaction of an explosion with a generic ship hull: (a) Surface at 20msec (b) Pressure at 20msec (c) Surface at 50msec and (d) Pressure at 50msec

26. Application (Contd..) 5. Automotive Applications: Streamlines in a vehicle without (left) and with rear center and B-pillar ventilation (right) In above figure, influence of the rear center and B-pillar ventilation on the rear passenger comfort is assessed. The streamlines marking the rear center and B-pillar ventilation jets are colored in red. With the rear center and B-pillar ventilation, the rear passengers are passed by more cool air. In the system without rear center and B-pillar ventilation, the upper part of the body, in particular chest and belly is too warm.

27. Conclusion • Nearer the conditions of the experiment to those which concern the user, more closely the predictions agree with those data, the greater is the reliance which can be prudently placed on the predictions. • CFD iterative Methods like Jacobi and Gauss-Seidel Method are used because the cost of direct methods is too high and discretization error is larger than the accuracy of the computer arithmetic. • Many software’s offer the possibility of solving fully nonlinear coupled equations in a production environment. • In the future we can have a multidisciplinary, database linked framework accessed from anywhere on demand simulations with unprecedented detail and realism carried out in fast succession so that designers and engineers anywhere in the world can discuss and analyze new ideas and first principles driven virtual reality

28. References • Hoffmann, Klaus A, and Chiang, Steve.T “Computational fluid dynamics for engineer’s” vol. I and vol. II • Rajesh Bhaskaran, Lance Collins “Introduction to CFD Basics” • http://www.cham.co.uk/website/new/cfdintro.htm accessed on 11/10/06. • Adapted from notes by: Tao Xing and Fred Stern, The University of Iowa. • http://www.cfd-online.com/Wiki/Historical_perspective accessed on 11/12/06. • Frederick and Chang,T.S.,”Continuum Mechanics” • http://navier-stokes-equations.search.ipupdate.com/ • http://en.wikipedia.org/wiki/Computational_fluid_dynamics#Discretization_method s, ”Discretization Methods” • McIlvenna P and Mossad R “Two Dimensional Transfer Chute Analysis Using a Continuum Method”, Third International Conference on CFD in the Minerals and Process Industries, Dec 2003. • Subramanian R.S. “Non-Newtonian Flows”. • Lohner R., Cebral J., Yand C., “Large Scale Fluid Structure Interaction Simulations, IEEE June 2004”. • http://www.cd-adapco.com/press_room/dynamics/23/behr.html,“Predicting Passenger Comfort • http://www.adl.gatech.edu/classes/lowspdaero/lospd2/lospd2.html, “Types of Fluid Motion”

29. Thank You Questions are Welcome