Introduction to Computational Fluid Dynamics by 28w075I


									Introduction to Computational
      Fluid Dynamics
           Course Notes (CFD 4)

Karthik Duraisamy
Department of Aerospace Engineering
University of Glasgow
        Course organization
• Homeworks – 25 %
• Report     -- 15 %
• Final exam -- 60 %

Interaction is extremely important
                  Learning Objectives
• Make the student understand the role of C in FD, its applicability,
  potential and limitations
• Give a basic foundation in numerical analysis, by teaching the relevance
  of accuracy and stability
• Give a working idea of the various choices of numerical methods and
  discretization schemes by applying them to simple model equations. In
  doing this, always remind them of the connection with the big picture.
• Make the student knowledgeable about the various terminologies in
  practical CFD (Grids, BCs, Approximations, Schemes etc)
• Ingrain the basics of good CFD practice (be aware of the
  applicability/feasibility of a particular model, its limitations, choose the
  right boundary conditions, ascertain grid/time independence,
• By the end of the class, the student should be in a position to set up
  simple aerodynamic problems and analyze them
• Introduction (1.5)
• Classification of PDE, Model equations (1.5)
• Finite difference methods:
   Spatial discretization (2.5)
   Temporal discretization (1.5)
   Convergence, Consistency, Stability (1)
• Grids/Boundary conditions (1)
• Euler equations (0.5)
• DNS/LES (1)
• RANS Equations and Turbulence modeling (1)
• Case studies & Best practices in CFD (1.5)
• Hands-on CFD/Lab sessions (8)

                      (.) – Approximate number of lectures
               What is CFD/FD ?
• CFD is a branch of Fluid dynamics
• So 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..
• Theoretical
                  Fluid Dynamics
         Most important branch of fluid dynamics. Crucial in
  understanding concepts (Example: L = ρUΓ), Usually good in
  predicting trends (Example: δ ~ 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, doesn’t always provide sufficient information
• Experimental
         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
• Computational (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
                  Words of wisdom
      (To be taken with a huge helping of salt :)
• Theoretical Fluid dynamics: Most important. Everyone HAS to learn

• Experimental Fluid dynamics: Important. Usually, everyone believes
  it except the person that conducted the experiment.

• Computational Fluid dynamics: Also important. Usually, no one
  believes it except the person that performed the calculations.

• A good engineer understands the pro’s and con’s of all three
  methods, and should be in a position to assess which one is best
  under the circumstances
• More importantly, should not be prejudiced against any of the three
Courtesy: CFD society of Canada
Courtesy: CFD society of Canada
Sample Application – 1
[Simulation to understand physics]

                         Flow over F-16 at
                         45o angle of
                         Surface Pressure
                         contours and

                         Courtesy: Kyle
                         Squires, ASU
             Sample Application -2
               [Validation with Experiment]

      Experiment                       Computation

Flow over fixed wing – Expt. vs CFD of velocity contours
      Sample Application -3
[Simulation to aid theoretical understanding]

                          Merger of co-rotating
                          vortices due to
                          Elliptical instability
                          Courtesy: CERFACS
              Procedures in CFD
• Identification of right approximation (Viscous/Inviscid,
  Laminar/Turbulent, Incompressible / compressible, Single-phase/multi-
• 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
• 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
• At every step, good understanding of theoretical fluid dynamics is
     Example: Flow over a pitching
• Problem: Predict the loads acting on an airfoil pitching in a wind
  tunnel under the following conditions: α =10o + 10o sin(w t), Re =
  3.8x106, M = 0.3, w = 0.06

•  Identification of right approximation : Viscous, Turbulent,
  compressible, Single-phase
• Identification of right solution method (Finite Volume, Structured
  mesh, second order accurate)
    Example: Flow over a pitching
• Preprocessing:
     Example: Flow over a pitching
• Solution:
     Example: Flow over a pitching
• Post processing: Flow visualization (movie)
     Example: Flow over a pitching
• Post processing: Loads comparison
       Governing Equations of fluid
• Assumptions: Continuum flow, Newtonian fluid
• Lets restrict ourselves to single phase, single species, perfect gases
  (this way, incompressible flow is a special case)
• Ignore body forces
• Unknowns: Density (ρ), 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)
  [Newton’s second law]
         Conservation of Energy (Energy equation) [First law of
• 5 equations to determine 5 unknowns.
• All of fluid dynamics is contained in these equations
             Governing equations
• How to derive these equations?
         Integral form
         Differential form
• Reynolds transport theorem:
  Rate of change of “stuff” inside a control volume = Net flux of “stuff”
  entering/leaving the boundaries + generation of “stuff” – destruction
  of “stuff”
• In addition, need some more info (such as stress-strain relation,
  temperature-heat flux relation etc.)

                                      The “stuff” U is nothing but mass,
                                      momentum and energy
Governing equations for
compressible perfect gas
Governing equations for
compressible perfect gas
Example: One dimensional steady
          inviscid flow

                   Sound familiar?

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