4. Computational Fluid Dynamics is the science of predicting fluid flow, heat transfer,
mass transfer, chemical reaction and related phenomena by solving mathematical
equations which govern these processes using numerical methods (i.e. on a computer).
Why CFD…??
Growth in complexity of unsolved engineeringproblem.
Need for quick solutionsof moderate accuracy.
Absence of analytical solutions.
The prohibitive cost involvedin performing evenscaled laboratoryexperiments.
Efficient solutionalgorithms.
Developments in computersin terms of speed and storage.
Serial/parallel/web computing.
Sophisticated pre and post processing facilities.
5. Inside the CFD Process :CFD Process Flow :
Pre-processing
Geometry Creation
Geometry Clean-up
Mesh Generation
Boundary conditions
Solver
Problem Specification
Additional Models
Numerical Computations
Post-processing
Understanding flow with color,
contour etc. plots.
Line and Contour Data
Average Values (Drag, lift, heat
transfer coefficient)
Report Generation
Pre-processing
Solver
Post-processing
6. Inside the CFD process
…
Analysis Begins with the mathematical model of
a physical problem.
• Conservation of Mass, momentum and energy
conservation must be satisfied throughout the region of
interest.
• Simplifying assumptions are made to make the problem
more tractable (e.g. steady state, incompressible, inviscid,
two-dimensional etc.)
• Provide appropriate boundary and initial conditions for
the problem.
Domain of interest :
Area between two fins
Half thickness of fin
First Thing First…
Commercial Fin-tube Heat Exchanger
CFD applies Numerical methods (called
discretization) to develop algebraic equations to
approximate the governing differential equations of
fluid mechanics in the domain to be studied.
Entire domain should be divided into small cells or
volume.
The collection of cells is called the grid or mesh.
Meshing your way into it …
Inside the CFD process
…
Mesh Generation
7. Inside the CFD process …
Solver …
Inside the CFD process …
System of algebraic equations are
solved numerically (on a computer) for
the flow field variables at each node or
cell.
The final solution is post-processed to extract
quantities of interest (e.g. lift, drag, heat
transfer, separation points, pressure loss, etc.)
What will I do with all this data …?
Temperature
Contours
Discretization
8. Governing Equations:
Conservation Of Mass
Momentum Conservation
Energy Conservation
Two different forms of equations:
Conservation form
Non-Conservation form
Inviscid & Viscid Equations
Navier-Stokes Equation
Euler Equations
9. Advantages of
CFD:
Low Cost:
- Using physical experiments and tests to get essential
engineering data for design can be expensive.
- Computational simulations are relatively inexpensive,
and costs are likely to decrease as computers
become more powerful.
Speed :
- CFD simulations can be executed in short period of
time.
- Quick turnaround means engineering data be
introduced early in design process.
Ability to Simulate Real Conditions:
- Many flow and heat transfer processes can not be
(easily) tested. E.g. hypersonic flow at Mach 20.
- 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.
Comprehensive Information:
- Experiments only permit data to 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.
10. Limitations of CFD:
Physical Models:
- CFD solutions rely upon physical models of real
processes (e.g. turbulence, compressibility,
chemistry, multiphase flow etc.)
- The solutions that are obtained through CFD 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 - errors due to finite word size available on the
computer.
Truncation error - error due to approximates in the numerical
models.
- Round-off errors will always exist( though they
should be small in most cases).
- Truncation errors will go to zero as the grid is refined
– so mesh refinement is one way to deal with
truncation error.
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