![Unknowns: Density (ρ), Velocity (u,v,w), Pressure (p)
Dynamics of fluids is then given by
Conservation of Mass (Continuity equation)
Algebraic summation of Rate of mass flow rate in
= Algebraic summation of rate of mass flow rate out
Conservation of Momentum (Navier-Stokes
equations) [Newton’s second law]
Mass*acceleration in i direction =sum of forces in i direction
Total three equations in x, y and z direction.
Conservation of Energy (Energy equation) [First law
of thermodynamics]
Heat added = change in internal energy + work done
CFD-equations to solve](https://image.slidesharecdn.com/cfd0-180117133811/85/Cfd-0-11-320.jpg)
![Dynamics of fluids is then given by
Conservation of Mass (Continuity equation)
Conservation of Momentum (Navier-Stokes
equations) [Newton’s second law]
CFD-equations to solve
0
z
w
y
v
x
u
t
](https://image.slidesharecdn.com/cfd0-180117133811/85/Cfd-0-12-320.jpg)
Cfd 0
- 1. Computational Fluid Dynamics 22nd May- 27th May, 2017 @ ICT, Mumbai Part-0 Introduction to CFD Dr. Sachin L. Borse Professor, Rajarshi Shahu College of Engineering , Pune, Maharashtra (Formerly Hydraulic Design Engineer, Klein Schanzline Becker Pumps, India)
- 2. i) Definition of CFD ii)How CFD helps in design? iii ) CFD Analysis- steps iv) CFD-Aim of analysis v) CFD-equations to solve vi)CFD-Input needed from user vii)CFD-Boundary conditions viii) CFD-Initial conditions ix)CFD-Turbulence modelling x)Numerical Solutions steps Content
- 3. i)Definition of CFD:- CFD is the simulation of fluid flow and heat transfer associated phenomenon(chemical reaction) using modeling (mathematical physical problem formulation) and numerical methods (discretization methods, solvers, numerical parameters, and grid generations, etc.) What is CFD?
- 4. ii) How CFD helps in design? 1)It helps to predict performance of hydraulic and thermal design 2) Plenty alternate options can be tried, which otherwise difficult in experimental work 3) CFD gives detail insight of flow which otherwise is difficult 4) Can be used to validate experimental and analytical results. 5) This helps to make design process more scientific.
- 5. iii) CFD Analysis :- steps 0)Decide your goal:- accuracy, time, 1)Identification of domain(geometry):- Determine the domain size and shape. Decide on possibility of geometry simplifications to save time eg. 2D, symmetry, periodicity 2)Identification of right approximation Viscous/Inviscid, Laminar/Turbulent, Incompressible / compressible, Single-phase/multi-phase) 3)Identification of right solution method Finite Element / Difference/Volume, Structured/Unstructured mesh, Order of accuracy
- 6. CFD Analysis :- steps 4)Pre-processing:- Generate computational grid, assign boundary conditions, set initial conditions, compile code, prepare input parameters Meshing Mesh generation consist in dividing the physical domain into a finite number of discrete regions, called control volumes or cells in which equations are solved to obtain solution.
- 7. Solution:-Run the code, monitor the solution Post-processing:-Collect and organize data, analyze results Verification:-Do the results make sense? Are the trends right? Does it agree with previous calculations on similar configurations? Validation:- Does the result agree with theory/ experiment? CFD Analysis :- steps At every step, good understanding of theoretical fluid dynamics and heat transfer is essential.
- 8. iv) CFD-Aim of analysis what we look from Engineering analysis: forces (pressure , viscous stress etc.) acting on surfaces (Example:1) In an airplane, we are interested in the lift, drag, power, pressure distribution etc
- 9. CFD-Aim of analysis what we look from Engineering analysis: 2)forces and torque acting on impeller blade) velocity field (Example: 1)In a race car, we are interested in the local flow streamlines, so that we can design for less drag. 2)we look for flow separation in turbomachinery which can be corrected in future design)
- 10. CFD-Aim of analysis what we look from Engineering analysis: temperature distribution (Example: 1)Heat transfer in the vicinity of a computer chip 2)hot spot in gas turbine blade) Ultimate aim is to predict the behaviour of systems, to design more efficient systems.
- 11. Unknowns: Density (ρ), Velocity (u,v,w), Pressure (p) Dynamics of fluids is then given by Conservation of Mass (Continuity equation) Algebraic summation of Rate of mass flow rate in = Algebraic summation of rate of mass flow rate out Conservation of Momentum (Navier-Stokes equations) [Newton’s second law] Mass*acceleration in i direction =sum of forces in i direction Total three equations in x, y and z direction. Conservation of Energy (Energy equation) [First law of thermodynamics] Heat added = change in internal energy + work done CFD-equations to solve
- 12. Dynamics of fluids is then given by Conservation of Mass (Continuity equation) Conservation of Momentum (Navier-Stokes equations) [Newton’s second law] CFD-equations to solve 0 z w y v x u t
- 13. Unknowns: Density (ρ), Velocity (u,v,w), Pressure (p) Dynamics of fluids is then given by 5 equations to determine 5 unknowns. All of fluid dynamics is contained in these equations. If turbulence is considered additional one or two or six equations are solved based on type of turbulence model. Mixing length- k-epsilon model 2-equation K-omega model 2-equation For k-epsilon turbulence model total 7 equations will be solved. CFD-equations to solve
- 14. vi)CFD-Input needed from user 1)Model/s selection:- Laminar/turbulent Single phase/multi phase Isothermal/heat transfer Pressure based/density based 2)Material properties:- material properties Fluid flow only Density, viscosity Fluid flow with heat transfer Density, viscosity, specific heat, thermal conductivity, If properties of particular material are not available, please visit http://www.matweb.com 3)Cell zone specification:-rotating or non rotating 4) Boundary conditions:-set by selecting patch and assigning required boundary condition with values.
- 15. CFD-Input needed from user 5)Initial conditions:- initial conditions are only enforced at the beginning of analysis 6)Stopping criteria:-input to decide stopping of calculations Steady state problem a)Number of iterations b)Maximum residual value permitted Unsteady state problem a)End time b)Maximum residual value permitted per time step 7)Solution control:-to control solution to get converged solution Steady state problem Relaxation parameters Unsteady state problem Time step
- 16. vii)CFD-Boundary conditions Boundary conditions, are enforced through out calculations. They are must. The boundary settings have strong effect on the convergence rate and on the accuracy of the results. Types of boundary conditions 1)Wall:-translational and rotational velocity can be assigned to wall. for fluid flow a)No slip b)free slip c)wall roughness for heat transfer a)constant heat flux b)zero gradient(adiabatic wall) c)constant wall temperature
- 17. CFD-Boundary conditions 2)Symmetry:- used to reduce computational effort Assumption-zero normal velocity and zero normal gradient . In above diagram only half domain divided by redline will be considered.
- 18. CFD-Boundary conditions 3)Periodic:- used when physical geometry and expected pattern of flow /thermal solutions have periodically repeating nature Benefit-reduces computational efforts
- 19. CFD-Boundary conditions 4)inlet:- Pressure inlet or Incompressible Velocity inlet Compressible flow Mass flow inlet
- 20. CFD-Boundary conditions 5)Outlet:- Pressure outlet Or Velocity outlet Outflow
- 21. CFD-Boundary conditions Recommended boundary condition configurations:- Most robust:- velocity /mass flow at an inlet; static pressure at outlet Robust:- Total pressure at inlet velocity /mass flow at an inlet; Sensitive to initial guess:- Total pressure at inlet static pressure at outlet Very unreliable:- static pressure at inlet static pressure at outlet
- 22. CFD-Boundary conditions Convergence is major issue in CFD. Ways to improve convergence 1)Extend the location of inlets and outlets so that outlet is far from recirculation area. 2)Use laminar solution to as initial condition.
- 23. viii) CFD-Initial conditions Unlike boundary conditions, initial conditions are only enforced at the beginning of analysis. They are primarily used for transient analyses, but sometimes they are useful for steady state analysis. Convergence problem can be improved by giving better initial condition.
- 24. IX)CFD-Turbulence modelling In real life most of fluid flow problem fall under turbulent category. Turbulent flow has fluctuations in field which small in magnitude but large frequency. Solving turbulent Navier stokes takes huge computation resource. Hence turbulence modeling is required. Flow becomes turbulent with following condition, Re>2300 for internal flow eg flow inside duct or pipe line Re>1*105 for external flow eg flow over aeroplane Ra>109 for natural convection heat transfer eg hot surface in stand still air
- 25. CFD-Turbulence modelling Reynolds Averaged Navier stokes equation(RANS or RAS):- solves time averaged Navier stokes Equation. All length scale are modeled. Most widely used for calculating industrial flows. Faster and requires less computer resources. Eg. Spalart Allmaras model (one equation ) k-epsilon model (two equation) K-omega(two equation) RSM( Six equation ) Large Eddy Simulation(LES):- Large eddies are solved, small eddies are modeled. More expensive than RANS. Less expensive than DNS Direct Numerical Simulation(DNS):-Turbulent NS is directly solved without modeling.
- 26. CFD-Turbulence modelling Reynolds Averaged Navier stokes equation(RANS or RAS):- RANS may use wall function (eg k-epsilon model) to avoid large number of elements at wall and thus reduces computation effort. In such case y+ of boundary element should be in 30 to 100. More preferred for industrial application. When not using wall function eg (k-omega model) near wall element should have y+ <2. Thus requires more number of elements. More computation effort needed.
- 27. X)Numerical Solutions steps Monitoring Solution:- It involves observation of residual and certain parameter like drag etc
- 28. xi)Components of Numerical Solution a)mathematical model:-set of partial differential equations or integro- differential equations. Choose appropriate model for given application. b)Discretization method:- method of approximation of differential equation by set of algebraic equations i) finite difference method:- • oldest method. • Taylor series expansion(TSE) is used to approximate partial derivative. • Commonly applied to structured grid as it requires a mesh having high • degree of regularity. • This method is simple to apply. • Main disadvantage of this method is conservation is not enforced unless care is taken.
- 29. xi)Components of Numerical Solution • Taylor series expansion(TSE) is used to approximate partial derivative.
- 30. xi)Components of Numerical Solution i) finite difference method:- Field variable at point (i, j) with forward difference can be given by TSE Field variable at point (i, j) with backward can be given by TSE
- 31. xi)Components of Numerical Solution i) finite difference method:- Field variable at point (i, j) with central difference can be given by TSE Second order derivative at point (i, j) can be given by TSE
- 32. xi)Components of Numerical Solution ii) finite volume method:- •It discretize the integral form of conservation equations in space. •The domain is divided into a finite number of connected control volumes. •At centroid of each of control volumes, variable values are calculated. •Interpolation is used to express variable values at control volume surface. •An algebraic equation for each of control volumes can be obtained, in which a number of neighbouring nodal values appear. •As it works with control volumes and not grid intersection points, it has the capacity to accommodate any type of grid. • Thus here unstructured grid can be used, thus complicated shape can be mapped. •This method ensures conservation.
- 33. xi)Components of Numerical Solution iii) Finite element method: - •it was developed for determining stress-strain displacement solution in structural analysis. •Both FEM and FVM can handle complex computation domain. •Governing equations are first approximated by multiplying with shape functions before they are integrated over entire computational domain. •Each method gives same solution if mesh is very fine. c)Numerical grid:- discrete locations at which variables are to be calculated are defined by numerical grid. It divides domain into finite number of subdomains(element, control volume).
- 34. xi)Components of Numerical Solution d) Solution method:- i)direct method:- •Gauss elimination method. –convert matrix to upper triangular matrix. Use backward substitution to obtain values of variables. •Thomas Algorithm used for 1-D steady state conduction. ii)Iterative method In iterative method, solution is guessed and uses equation to systematically improve the solution until it reaches some level of convergence. Cost of using direct method is quite high if large number of elements. Two methods Jacobi and Gauss Siedal Method. Gauss Siedal method twice faster than Jacobi method. Jacobi method requires more memory space. e)Convergence criteria:- It value of residual at which software should stop to calculate.
- 35. xi)Components of Numerical Solution e) Few terms:- i)consitency:- •With decrease in cell size or time step truncation error should tend to zero this is called consistency. ii)stability Numerical method is said to be stable if it does not magnify errors occuring during solution process. Stability criteria for unsteady problem Co Courant No< 1 Co= u*Δt/Δx This is also called CFL criteria.
- 36. Thank you!