Slide 1
Introduction to Computational Fluid Dynamics Course
NotesVenkatesh Ramakrishnan, M.E,Assistant Professor-Thermal,
Fluids & Energy Science Stream,Department of Mechanical
Engineering Sandwich,PSG College Of
Technology,Peelamedu,Coimbatore-641004.Tamilnadu, India.1What is
CFD/FD ?CFD is a branch of Fluid dynamicsSo what really is
Engineering Fluid Dynamics in the first place? Lets look at some
examples: We are interested in the forces (pressure , viscous
stress etc.) acting on surfaces (Example: In an airplane, we are
interested in the lift, drag, power, pressure distribution etc) We
would like to determine the velocity field (Example: In a race car,
we are interested in the local flow streamlines, so that we can
design for less drag) We are interested in knowing the temperature
distribution (Example: Heat transfer in the vicinity of a computer
chip)Roughly put, in Engineering fluid dynamics, we would like to
determine certain flow properties in a certain region of interest,
so that the information can be used to predict the behaviour of
systems, to design more efficient systems etc..
2Fluid DynamicsTheoretical Most important branch of fluid
dynamics. Crucial in understanding concepts (Example: L = U),
Usually good in predicting trends (Example: ~ Re-1/2) Can obtain a
lot of information using simplifying assumptions, sometimes enough
for detailed design (Example: the SR-71 Blackbird was designed
completely using theoretical ideas) However, doesnt always provide
sufficient informationExperimental Only way to obtain reliable data
in many situations. However, costly, difficult to achieve exact
conditions, difficult to isolate effects, sometimes difficult to
assess error, sometimes not repeatableComputational (CFD) Becoming
important as computers are getting faster and cheaper. Potential to
provide tremendous amount of data at a fraction of the cost of
experiments. But sometimes unreliable because of
numerical/modeling/human errors. Sometimes more expensive than
experiments Very important to validate with theory/experiments
3Sample Application 1 [Simulation to understand physics]
Flow over F-16 at 45o angle of attackSurface Pressure contours
and streamtraces
Courtesy: Kyle Squires, ASU4Sample Application -2[Validation
with Experiment] ExperimentComputation
Flow over fixed wing Expt. vs CFD of velocity contours5Sample
Application -3[Simulation to aid theoretical understanding]
Merger of co-rotating vortices due toElliptical
instability(Movie)Courtesy: CERFACS6Procedures in CFDIdentification
of right approximation (Viscous/Inviscid, Laminar/Turbulent,
Incompressible / compressible,
Single-phase/multi-phase)Identification of right solution method
(Finite Element / Difference/Volume, Structured/Unstructured mesh,
Order of accuracy)Pre-processing (Generate computational grid,
assign boundary conditions, set initial conditions, compile code,
prepare input parameters)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 (or an aspect of the
result)) agree with theory/experiment?)At every step, good
understanding of theoretical fluid dynamics is essential!!!
7Example: Flow over a pitching airfoilProblem: Predict the loads
acting on an airfoil pitching in a wind tunnel under the following
conditions: =10o + 10o sin(w t), Re = 3.8x106, M = 0.3, w =
0.06
Identification of right approximation : Viscous, Turbulent,
compressible, Single-phaseIdentification of right solution method
(Finite Volume, Structured mesh, second order accurate)
8Governing Equations of fluid dynamicsAssumptions: Continuum
flow, Newtonian fluidLets restrict ourselves to single phase,
single species, perfect gases (this way, incompressible flow is a
special case)Ignore body forcesUnknowns: Density (), Velocity
(u,v,w), Pressure (p)Dynamics of fluids is then given by
Conservation of Mass (Continuity equation) [Law of common sense]
Conservation of Momentum (Navier-Stokes equations) [Newtons second
law] Conservation of Energy (Energy equation) [First law of
thermodynamics]5 equations to determine 5 unknowns.All of fluid
dynamics is contained in these equations
9All of fluid dynamics is contained in these three
equationsGoverning equationsHow to derive these equations? Integral
form Differential formReynolds transport theorem:Rate of change of
stuff inside a control volume = Net flux of stuff entering/leaving
the boundaries + generation of stuff destruction of stuffIn
addition, need some more info (such as stress-strain relation,
temperature-heat flux relation etc.)
The stuff U is nothing but mass, momentum and energy10Derive
continuity equation here.AerospaceAutomobile and Engine
ApplicationsAppliancesBoatsComputersApplications
5/14/201411CFD codes are structured around the numerical
algorithms that can tackle fluid flow problems
Three main elements:Pre ProcessorSolverPost Processor How Does a
CFD Code Work?5/14/201412Consists of the input of a flow problem to
CFDUser Activities:define geometry & generate grid (50%
time)selection of phenomena to be modeleddefinition of fluid
propertiesspecification of boundary and initial conditions 1)
Pre-Processor
5/14/201413Three primary numerical solution techniquesfinite
difference, finite element, finite control volumeThe numerical
method performs the following:Approximates the unknown variables by
simple functionsDiscretization by substitution of the
approx-imations into the governing flow equations and subsequent
mathematical manipulationsSolution of the algebraic equations2)
Solver5/14/201414Finite difference methods describe the unknowns f
of the flow problems by means of point samples at the node points
of a grid co-ordinate linesSolver - Finite Difference Method
Truncated Taylor series expan-sions are used to generate finite
difference approximations of the derivatives of f in terms of point
samples of f at each grid point and its immediate neighbors
5/14/201415Based on control volume formulation of analytical
fluidsThe domain is divided into a number of control volumes (aka
cells, elements) - the variable of interest is located at the
centroid of the control volume. The differential form of the
governing equations are integrated over each control volume. Finite
difference approximations are substituted for the terms in the
integrated equations (discretization) converts the integral
equations into a system of algebraic equations.Set of algebraic
equations are solved by an iterative method.
Solver - Finite Volume Method5/14/201416Provides a user friendly
(??) way to look at the results of a simulationDomain geometry and
grid displayVector PlotsContour PlotsParticle Tracking
3) Post Processor
5/14/201417Results of CFD are at best as good as the physics
embedded in it as at worst as good a its operatorTHESE PROBLEMS ARE
COMPLEXPrior to running a simulation there is a stage of
identification and formulation of the flow problem in terms of the
physical and chemical phenomena that need to be considered.A
successful simulation hasconverged solutiongrid independenceProblem
Solving With CFD5/14/201418Applications of CFD
Applications of CFD are numerous! Flow and heat transfer in
industrial processes (boilers, heatexchangers, combustion
equipment, pumps, blowers, piping, etc.). Aerodynamics of ground
vehicles, aircraft, missiles. Film coating, thermoforming in
material processing applications. Flow and heat transfer in
propulsion and power generation systems. Ventilation, heating, and
cooling flows in buildings. Chemical vapor deposition (CVD) for
integrated circuitmanufacturing. Heat transfer for electronics
packaging applications. And many, many more!Relatively low cost.
Using physical experiments and tests to get essential
engineeringdata for design can be expensive. CFD simulations are
relatively inexpensive, and costs are likely todecrease as
computers become more powerful.
Advantages of CFD
Advantages of CFDSpeed. CFD simulations can be executed in a
short period of time. Quick turnaround means engineering data can
be introduced early inthe design process.Ability to simulate real
conditions. Many flow and heat transfer processes can not be
(easily) tested,e.g. hypersonic flow. CFD provides the ability to
theoretically simulate any physical condition.
Advantages of CFDAbility to simulate ideal conditions. CFD
allows great control over the physical process, and provides
theability to isolate specific phenomena for study. Example: a heat
transfer process can be idealized with adiabatic,constant heat
flux, or constant temperature boundaries. region of interest, and
yields a comprehensive set of flow parameters for
examination.Advantages of CFDComprehensive information. Experiments
only permit data to be extracted at a limited number oflocations in
the system (e.g. pressure and temperature probes, heatflux gauges,
LDV, etc.). CFD allows the analyst to examine a large number of
locations in the
Limitations of CFDPhysical models. CFD solutions rely upon
physical models of real world processes(e.g. turbulence,
compressibility, chemistry, multiphase flow, etc.). The CFD
solutions can only be as accurate as the physical modelson which
they are based.Numerical errors. Solving equations on a computer
invariably introduces numericalLimitations of CFDERRORS. Round-off
error: due to finite word size available on the computer.Round-off
errors will always exist (though they can be small in most cases).
Truncation error: due to approximations in the numerical
models.Truncation errors will go to zero as the grid is refined.
Meshrefinement is one way to deal with truncation error.
Limitations of CFDBoundary conditions. As with physical models,
the accuracy of the CFD solution is only asgood as the
initial/boundary conditions provided to the numerical model.
Example: flow in a duct with sudden expansion. If flow is supplied
todomain by a pipe, you should use a fully-developed profile
forvelocity rather than assume uniform conditions.