This document discusses experimental and analytical techniques in fluid mechanics, as well as computational fluid dynamics (CFD). It notes that full-scale experiments can be difficult or expensive, so analytical models using differential equations are commonly used, though assumptions limit their applicability. CFD solves these equations numerically on a grid using techniques like finite difference, finite element, and boundary element methods. It has applications in automotive and biomedical fields.

1. Fluid Mechanics II
Lecture 11
Muhammad Usman

2. Experimental Techniques
• In certain situation, an experimental
investigation involving full-scale equipment
can be used to predict how the equipment
would perform under given conditions.
However in most engineering applications,
such full scale tests or either difficult or
very expensive to perform or not possible
at all.

3. Analytical Techniques
• Analytical models work out the consequences of a
mathematical model which represents the behavior of a
system. The mathematical model representing the
physical process mainly consist of a set of differential
equations. If classical mathematics were used to solve
these equations, we call the approach as analytical
approach.
• In most engineering applications, various assumptions
and simlifications need to be made to enable the
analytical solution of the differential equations
representing the physical solution. This at one hand
limits the applicability of these methods to simple type
problems, or limits the validity of the solutions if too
many assumptions and simplifications are made.

4. Computational Fluid Dynamics
• It is used to calculate the approximate
solutions to wide variety of fluid mechanics
problems.
• Replacing partial differential equation with
discreted algebric equation. These
equations are then used to calculate the
solution at discrete points in space or in
time.

5. • The analytical solution for navier stokes
equation are available for only limited
number of simplified flow geometries.
• The CFD Simulation solves for the
relevent flow variables only at discrete
points. Interpolation are used to obtain the
values for non grid location.

6. Numerical Experiements Vs CFD
• Modeling • Formulation of the
• Measurement governing equation
• Analysis of results and development of
the numerical
algorithm.
• Running an algorithm
in the computer
• Analysis of results

7. Discretization Techniques for
Numerical Solution
• Finite Difference Method.
• Finite Element ( Volume ) Method.
• Boundary Element Method.

8. Finite Element Method
• Flow field is broken into a set of small fluid
elements.
• The conservation equations ( Conservation of
mass, momentum and energy ) are written for
each of the element.
• For flows with complex boundaries, the number
of algebric equations must be solved also
inceases.
• Commonly problems include the formation of 1
million gird cells.

9. Boundary Element Method
• Boundary of the flow field is broken into
discrete segments.
• It requires less time and space then finite
element method.

10. Finite Difference Method
• The method of using Taylor’s Series expansion
to obtain discrete algebric equations is called
finite difference method.
• Along with this approximation comes some
amount of error, this type of error is called
tuncation error, because in taylor’s series
expansion higher order terms are ignored.
• The tuncation error tends to zero as the grid is
refined by making Δx and Δy smaller.
• The larger the number of grid points used the
larger the number of equations that must be
solved.

11. Example

12. Example
• The equations can then be solved through
computational techniques and the
solutions between these six nodes can be
obtained through interpolation.

13. Grids
• The arrangment of the discrete points in the flow
domain is called grid.
• The grid must represent the geometry of the
correctly since an error in this representation can
have significant error.
• The grid must also have suffient grid resolution.
• It is usually necessary to increase the number of
grid points where large gradient are to be
expected as in the boundary layer of the solid
surfaces.

14. Type of Grids
• Structured
• Structured grid has some type of regular
coherent structure to the mesh layout that
can be defined mathematically.

15. Types Of Grids
• The grid spacing in the normal direction
increases as one moves away from the
surface.Such kind of variable grid spacing
is used where there is need to increase
the grid resolution
and is termed
as grid stretching.

16. Types of the Grids
• Unstructured
• The grid cell arrangment is irregular and
has no systamatic pattern.
• It consists of trianles for 2D patterns
• And tetrahedron for 3D patterns.
• Each grid cell and connection information
to the neighboring cell is defined
separatly.
• This can be applied to complicated
geometeries.

17. Types of Grids
• Finite difference method is restricted to
structured grids, whereas finite element
method is can be used either for
structured or unstructured grids.

18. Types Of Grids
• Hybrid,
Combination of rectangles and triangles
Moving
Used for flows having time dependent
geometry
Adaptive
This type of grid adapt itself during the
simulation.

19. Area of Applications

20. Automotives

21. Biomedical Applications
• CFD can be used to model the flow of
blood in heart and valves.
• The use of CFD reduces the need of the
tests on the human being.

22. Softwares Used In CFD
• Abaqus CAE,
• Matlab,
• Flowlab,
• Fluent.