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Meow
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Objectives
•
Understand what is CFD and why should we study CFD• Understand the importance of a high-quality, good
resolution mesh
• Apply appropriate boundary conditions to computational
domains
• Understand how to apply CFD to basic engineering
problems and how to determine whether the output is
physically meaningful
• Realize that you need much further study and practice
to use CFD successfully
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Motivation
Modern engineers apply both experimental and CFD analyses, and the two
complement each other. For example, engineers may obtain global properties,such as lift, drag, pressure drop, or power, experimentally, but use CFD to obtain
details about the flow field, such as shear stresses, velocity and pressure profiles,
and flow streamlines.
In addition, experimental data are often used to validate CFD solutions by matching
the computationally and experimentally determined global quantities.
CFD is then employed to shorten the design cycle through carefully controlled
parametric studies, thereby reducing the required amount of experimental testing.
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Equations of Motion
Continuity equation
Navier –Stokes equation
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1. A computational domain is chosen, and a grid (also called a mesh) is
generated; the domain is divided into many small elements called cells.
2. Boundary conditions are specified on each edge of the computational
domain (2-D flows) or on each face of the domain (3-D flows).
3. The type of fluid (water, air, gasoline, etc.) is specified, along with fluid
properties (temperature, density, viscosity, etc.).
4. Numerical parameters and solution algorithms are selected.
5. Starting values for all flow field variables are specified for each cell.
6. Beginning with the initial guesses, discretized forms of governing equations
are solved iteratively, usually at the center of each cell.
7. Once the solution has converged, flow field variables such as velocity andpressure are plotted and analyzed graphically.
8. Global properties of the flow field, such as pressure drop, and integral
properties, such as forces (lift and drag) and moments acting on a body, are
calculated from the converged solution
Solution Procedure
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A quality grid is
essential to a
quality CFD
simulation.
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Additional Equations of Motion
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Grid Generation and Grid Independence
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Boundary Conditions
Appropriate boundary conditions
are required in order to obtain an
accurate CFD solution.
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Wall Boundary Conditions
The simplest boundary condition is that of
a wall.
Since fluid cannot pass through a wall, the
normal component of velocity is set to zero
relative to the wall along a face on which
the wall boundary condition is prescribed.
In addition, because of the no-slip
condition, we usually set the tangential
component of velocity at a stationary wall
to zero as well.
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Inflow/Outflow Boundary Conditions
There are several options at the boundaries
through which fluid enters the computational
domain (inflow) or leaves the domain
(outflow).
They are generally categorized as either
velocity-specified conditions or pressurespecified conditions.
At a velocity inlet, we specify the velocity of
the incoming flow along the inlet face.
If energy and/or turbulence equations are
being solved, the temperature and/orturbulence properties of the incoming flow
need to be specified as well.
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Miscellaneous Boundary
Conditions
Some boundaries of a computational domain
are neither walls nor inlets or outlets, but
rather enforce some kind of symmetry or
periodicity.
For example, the periodic boundary
condition is useful when the geometry
involves repetition.
Periodic boundary conditions must be
specified as either translational (periodicityapplied to two parallel faces, or rotational
(periodicity applied to two radially oriented
faces).
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Internal Boundary Conditions
The final classification of boundary
conditions is imposed on faces or edges
that do not define a boundary of the
computational domain, but rather exist
inside the domain.
When an interior boundary condition is
specified on a face, flow crosses through
the face without any user-forced changes,
just as it would cross from one interior cell
to another.
This boundary condition is necessary forsituations in which the computational
domain is divided into separate blocks or
zones, and enables communication
between blocks.
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LAMINAR CFD CALCULATIONS
Computational fluid dynamics does an excellent job at computing
incompressible, steady or unsteady, laminar flow, provided that the
grid is well resolved and the boundary conditions are properlyspecified.
We show several simple examples of laminar flow solutions, paying
particular attention to grid resolution and appropriate application of
boundary conditions.
In all examples in this section, the flows are incompressible and
two-dimensional (or axisymmetric).
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Pipe Flow Entrance
Region at Re = 500
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Flow around a Circular Cylinder
at Re = 150
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TURBULENT CFD CALCULATIONSCFD simulations of turbulent flow are much more difficult than those of laminar
flow, even for cases in which the flow field is steady in the mean (statisticiansrefer to this condition as stationary).
The reason is that the finer features of the turbulent flow field are always
unsteady and threedimensional—random, swirling, vortical structures called
turbulent eddies of all orientations arise in a turbulent flow.
Some CFD calculations use a technique called direct numerical simulation (DNS), in which an attempt is made to resolve the unsteady motion of all the
scales of the turbulent flow.
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When using a turbulence model, the steady Navier –Stokes equation is
replaced by what is called the Reynolds-averaged Navier –Stokes (RANS)
equation, shown here for steady (stationary), incompressible, turbulent flow,
Specific Reynolds
stress tensor
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Flow around a Circular Cylinder
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Flow around a Circular Cylinder at Re = 107
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Design of the
Stator for a Vane-Axial Flow Fan
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CFD WITH HEAT TRANSFERBy coupling the differential form of the
energy equation with the equations of fluid
motion, we can use a computational fluiddynamics code to calculate properties
associated with heat transfer (e.g.,
temperature distributions or rate of heat
transfer from a solid surface to a fluid).
Since the energy equation is a scalar
equation, only one extra transport
equation (typically for either temperature
or enthalpy) is required, and the
computational expense (CPU time and
RAM requirements) is not increased
significantly.
Heat transfer capability is built into most
commercially available CFD codes, since
many practical problems in engineering
involve both fluid flow and heat transfer.
As mentioned previously, additional
boundary conditions related to heattransfer need to be s ecified.
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Temperature Rise through a Cross-Flow Heat Exchanger
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Cooling of an Array of Integrated Circuit Chips
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COMPRESSIBLE FLOW CFD CALCULATIONS
When the flow is compressible, density is no longer a constant, butbecomes an additional variable in the equation set.
We limit our discussion here to ideal gases.
When we apply the ideal-gas law, we introduce yet another unknown,
namely, temperature T .
Hence, the energy equation must be solved along with the compressible
forms of the equations of conservation of mass and conservation of
momentum.
In addition, fluid properties, such as viscosity and thermal conductivity, are
no longer necessarily treated as constants, since they are functions of
temperature; thus, they appear inside the derivative operators in the
differential equations of Fig. 15 –74.
While the equation set looks ominous, many commercially available CFD
codes are able to handle compressible flow problems, including shock
waves.
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Compressible Flow through a Converging –Diverging
Nozzle
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Oblique Shocks over a Wedge
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OPEN CHANNEL FLOW CFD CALCULATIONS
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OPEN-CHANNEL FLOW CFD CALCULATIONS
Flow over a Bump on the Bottom of a Channel
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Flow through a Sluice Gate (Hydraulic Jump)
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Summary
INTRODUCTION AND FUNDAMENTALS
Motivation
Equations of Motion
Solution Procedure
Additional Equations of Motion
Grid Generation and Grid Independence
Boundary Conditions
Practice Makes Perfect
LAMINAR CFD CALCULATIONS
Pipe Flow Entrance Region at Re = 500
Flow around a Circular Cylinder at Re = 150
TURBULENT CFD CALCULATIONS
Flow around a Circular Cylinder at Re = 10,000
Flow around a Circular Cylinder at Re = 107
Design of the Stator for a Vane-Axial Flow Fan
CFD WITH HEAT TRANSFER
Temperature Rise through a Cross-Flow Heat Exchanger
Cooling of an Array of Integrated Circuit Chips COMPRESSIBLE FLOW CFD CALCULATIONS
Compressible Flow through a Converging–Diverging Nozzle
Oblique Shocks over a Wedge
OPEN-CHANNEL FLOW CFD CALCULATIONS
Flow over a Bump on the Bottom of a Channel
Flow through a Sluice Gate (Hydraulic Jump)
Recommended