Introduction to Computational Fluid Dynamics

1
CFD Fundamentals
Lecture by
Prof. Kartik Ajugia
Department of Mechanical Engineering, DJSCE

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Solving Engineering Problem
Preparing a Model of Problem
Investigate Given Problem
Approach: Experimental /Analytical
Result Analysis
Analytical Approach

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System Modeling and its Simulation
System Modeling is a process of simplifying a given problem by idealizations
and approximations to make a problem amenable to a solution.
A nice model of an actual system completely characterize the behavior of
the given system without losing any significant information of interest.
Modeling an Engineering Problem
Physical Models
Mathematical Models
Numerical Models

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System Modeling
A physical model is one that resembles the actual system and is generally used to
obtain experimental results on the behavior of the system.
Example: Scaled down model of a car or a heated body, which is positioned in a
wind tunnel to study the drag force acting on the body or the heat transfer from it.
Physical Models

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Mathematical Models
Physical Problem
PDE Equations
Problem Solution
Identify Important
Variables Make reasonable
assumption and
approximation
Apply relevant
Physical Laws
Apply Applicable
Solution Technique
Apply Boundary and
Initial Conditions
Representing complete behavior and characteristics of a system in the form
of mathematical equations by employing approximations, simplifications, and
idealizations.

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Mathematical Model:
Example: A thermal and flow system being represented by a set of
partial differential equations.
Mass Balance Equation
X-momentum Equation
Y-momentum Equation
Energy Balance Equation
Mathematical Models

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• Derived from mathematical models which can be handled by
computer.
• It consists of a numerical scheme, numerical treatment of boundary
and initial condition and other inputs to capture complete system
information.
• Numerical modeling also refers discretization of the governing
equations in order to solve them on a computer.
Numerical Models

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Validation ensure the reliability and quality of the model to
represent the actual system. It is done with suitable benchmark
result.
• It represents the level of accuracy expected.
• Results should be independent of the numerical scheme and its
implementation, numerical parameters, such as grid size, time
step, convergence criterion, initial conditions etc.
Validation of Model:
System Modeling

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The process of studying the behavior of the system design under
various variables and operating conditions by means of a model,
before fabricating a prototype, is known as SIMULATION.
System Simulation
Importance of Simulation
• Experimentation on the system or its prototype is generally very expensive
and time consuming,
• Evaluate different designs for selection of an acceptable design,
• Study system behavior under off-design conditions,
• Determine safety limits for the system,
• Determine effects of different design variables for optimization,
• Improve or modify existing systems,
• Investigate sensitivity of the design to different variables.
Simulation

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An engineering problem is solved either Experimentally or Analytically.
Approach Advantages Disadvantages
Experimental 1. Highly reliable and more realistic 1. Equipment are required
2. Scaling problems
3. Correction factors
4. Operation cost
5. Measurement limitations
Theoretical
(Analytical)
1. Clean, general information which is
usually in formula form
1. Restricted to simple
geometry and physics
2. Usually restricted to linear
problems
Numerical
(Analytical)
1. No restriction to linearity.
2. Complicated physics can be treated.
3. Transient evolution of flow can be
obtained
1. Truncation errors
2. Boundary condition problems
3. Computation cost
Experimental or Analytical Approach

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Numerical Approach
COMPUTAIONAL
FLUID DYNAMICS

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Computational Fluid Dynamics
CFD is the science of predicting fluid flow, heat transfer, mass
transfer, chemical reactions, and related phenomena by solving
the mathematical equations which govern these processes using a
numerical methodology.
Engineering
Mathematics Computer
Science

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 As a research tool
 As an educational tool to learn fundamentals
 As a designing tool
 Troubleshooting
 Redesign.
•Application extends to all field of Engineering and Technology
• CFD analysis complements testing and experimentation.
• Reduces the total effort required in the laboratory.
CFD – Application

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• Relatively Low Cost
• Quick Analysis Tool
• 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.
• Ability to simulate ideal conditions
– CFD allows great control over the physical process, and provides the ability
to isolate specific phenomena for study.
– Example: a heat transfer process can be idealized with adiabatic, constant
heat flux, or constant temperature boundaries.
CFD – Advantages

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• Comprehensive information
– Experiments only permit data to be extracted at a limited number of
locations in the system (e.g. pressure and temperature probes, heat flux
gauges, LDV, etc.).
– CFD allows the analyst to examine a large number of locations in the region
of interest, and yields a comprehensive set of flow parameters for
examination.
CFD – Advantages

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• Physical 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 models on which
they are based.
• Numerical errors
– Solving equations on a computer invariably introduces numerical errors.
– 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. Mesh refinement is
one way to deal with truncation error.
CFD – Limitations

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Poor Better
Fully
Developed Inlet
Profile
Computational Domain
Computational Domain
Uniform Inlet Profile
• Boundary conditions
– As with physical models, the accuracy of the CFD solution is only as good
as the initial/boundary conditions provided to the numerical model.
– Example: flow in a duct with sudden expansion. If flow is supplied to
domain by a pipe, you should use a fully-developed profile for velocity
rather than assume uniform conditions.
CFD – Limitations

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CFD activities started first through academic, research and in-house
codes. When one wanted to perform a CFD calculation, one had to write
a program.
Development of commercial code started in eighties and nineties that
are available today:
– Fluent (UK and US).
– CFX (UK and Canada).
– Fidap (US).
– Polyflow (Belgium).
– Phoenix (UK).
– Star CD (UK).
– Flow 3d (US).
– ESI/CFDRC (US).
– SCRYU (Japan).
– and more, see www.cfdreview.com.
Development of Commercial CFD Software

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Execution Methodology of CFD Simulation

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Domain for bottle filling problem
Filling Nozzle
Bottle
Execution of CFD
• Anticipating the under laying physics and
preparing its mathematical model to capture
hidden physics.
• Mathematical model emerges from basic
conservation of matter, momentum, and
energy applicable to region of interest.
• Fluid properties are modeled empirically.
• Simplifying assumptions are made in order to
make the problem executable (e.g., steady-
state, incompressible, inviscid, two-
dimensional).
• Provide appropriate initial and boundary
conditions for the problem.

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Problem Definition
Develop Mathematical Model
Decide Computational Domain
Discretize Computational Domain
Discretization of Governing Equation
Simple Algebraic Equation
Solve the Equations
Velocity, Pressure and
Temperature Distribution
Execution of CFD
Mesh for bottle filling problem.
The solution is post-processed to extract quantities
of interest (e.g. lift, drag, torque, heat transfer,
separation, pressure loss, etc.).

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• Domain is discretized into a finite set of control volumes or cells. The discretized
domain is called the “grid” or the “mesh”.
• General conservation (transport) equations for mass, momentum, energy, etc.,
are discretized into algebraic equations.
• All equations are solved to render flow field.
V A A V
dV d d S dV
t

  

     
    
V A A
unsteady convection diffusion generation
Fluid region of pipe
flow discretized into
finite set of control
volumes (mesh).
Control
volume
Execution of CFD : Discretization
General Transport Equation:

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• Should you use a quad/hex grid, a tri/tet grid, a hybrid grid, or a
non-conformal grid?
• What degree of grid resolution is required in each region of the
domain?
• How many cells are required for the problem?
• Will you use adaption to add resolution?
• Do you have sufficient computer memory?
triangle
quadrilateral
tetrahedron pyramid
prism or wedge
hexahedron
Execution of CFD : Selecting mesh
3d-mesh Elements 2d-mesh
Elements

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Tri / Tet vs. Quad / Hex Meshes:
For complex geometries, quad/hex
meshes show no numerical advantage,
and you can save meshing effort by
using a tri/tet mesh.
For simple geometries, quad/hex meshes
can provide high-quality solutions with
fewer cells than a comparable tri/tet mesh.

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Hybrid mesh example -
Hybrid mesh for an IC engine valve
port
Tet Mesh
Hex Mesh
Wedge Mesh
• Specific regions can be meshed
with different cell types.
• Both efficiency and accuracy are
enhanced relative to a hexahedral
or tetrahedral mesh alone.

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Dinosaur mesh example

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• For a given problem, you will need to:
– Select appropriate physical models.
– Turbulence, combustion, multiphase, etc.
– Define material properties.
• Fluid.
• Solid.
• Mixture.
– Prescribe operating conditions.
– Prescribe boundary conditions at all boundary zones.
– Provide an initial solution.
– Set up solver controls.
– Set up convergence monitors.
CFD : Numerical model setup

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• The discretized conservation equations are solved iteratively. A
number of iterations are usually required to reach a converged
solution.
• Convergence is reached when:
– Changes in solution variables from one iteration to the next are
negligible.
– Residuals provide a mechanism to help monitor this trend.
– Overall property conservation is achieved.
• The accuracy of a converged solution is dependent upon:
– Appropriateness and accuracy of the physical models.
– Grid resolution and independence.
– Problem setup.
CFD: Checking the Convergence

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• Visualization can be used to answer such questions as:
– What is the overall flow pattern?
– Is there separation?
– Where do shocks, shear layers, etc. form?
– Are key flow features being resolved?
– Are physical models and boundary conditions appropriate?
– Numerical reporting tools can be used to calculate
quantitative results, e.g:
• Lift, drag, and torque.
• Average heat transfer coefficients.
• Surface-averaged quantities.
CFD : Examine the Result

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• Graphical tools:
– Grid, Contour, and Vector plots.
– Pathline and Particle trajectory plots.
– XY plots.
– Animations.
• Numerical reporting tools:
– Flux balances.
– Surface and volume integrals and averages.
– Forces and moments.
CFD : Presenting Result

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Velocity vectors around a dinosaur

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Velocity magnitude (0-6 m/s) on a dinosaur

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Pressure field on a dinosaur

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Consider revisions to the model
• Are physical models appropriate?
– Is flow turbulent?
– Is flow unsteady?
– Are there compressibility effects?
– Are there 3D effects?
– Are boundary conditions correct?
• Is the computational domain large enough?
– Are boundary conditions appropriate?
– Are boundary values reasonable?
• Is grid adequate?
– Can grid be adapted to improve results?
– Does solution change significantly with adaption, or is the solution grid
independent?
– Does boundary resolution need to be improved?
CFD : Updating Models

Introduction to Computational Fluid Dynamics

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