Section CFD plays an important role in designing

Section A

Computational
Fluid Dynamics(CFD) is a software used of combination of physics and applied
mathematics to visualize the flow of fluids (Kuzmin, 2017) . ItIn other
words it analyses the fluid flow in qualitative or quantitative in some cases
by mathematically modelling and numerical method through the software. Figure
below shows the CFD simulation of an experiment:

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(Kuzmin,2017)

Figure 1.1

From the
diagram above, it shows that the CFD simulation has produced quite accurate
data as compared to the reality.

 

Computational fluid dynamics can be
related to transport of mass, momentum and energy. In early 1960s, CFD starts
to emerge as computer was popularized. Nowadays, CFD plays an important role in
designing engineering equipment and simulating the environmental phenomena.
Since the early 1970s, computer codes become available, making CFD an important
component of engineering practice in industrial, and environmental
organizations. (Google Books, 2005)

 

When designing a vehicle that
requires to be aerodynamically accurate and precise, or investigating the flow
of supernova, or even when it comes to smaller objects like golf balls, things
becomes complicated due to the high cost of setting up a wind tunnel or the
situation is too complex for an experiment to be set up. Thus, the
understanding of the three dimensional flow over a body is extremely important.
The research work for situations mentioned can be less tedious with CFD. CFD
functions by using proven theoretical equations to calculate the flow in a
simulated environment, it can used to gain greater physical insights into
problems of interest. Therefore, CFD is a beneficial tool in most of the cases
as it can simulate the real flow over the body.  (Dongwook, 2015)

 

There
was an effort to study the motion of fluids in 18th and 19th centuries.
Bernoulli’s equation was invented by Daniel Bernoulli (1700-1782), and Euler
equations was derived by Leonhard Euler (1707-1783). Euler equation describe
how the velocity, pressure
and density
of a moving fluid are related (Hall, 2017) while Bernoulli equation is about the principle of conservation of
energy for ideal fluids in steady, or in other words, streamline flow. It
involved the movement of a fluid through a region with pressure difference.
Claude Louis Marie Henry Navier (1785-1836) from French and George Gabriel
Stokes (1819-1903) from Irish, are the significant contributors that enhanced
Euler equations. Their hard work paid off when Navier-Stokes equation was
invented.

 

The
basis of the nowadays’ computational fluid dynamics (CFD) industry are these
differential mathematical equations that they proposed nearly 200 years ago.
Indeed, those equations are difficult to solve until the invention of computers
in the 1960s and 1970s which real flow can be predicted within reasonable
range. Jean Le Rond d’Alembert, Jean Louis Marie Poiseuille, John William
Rayleigh, M. Maurice Couette, Osborne Reynolds, Joseph Louis Lagrange, and
Pierre Simon de Laplace were the other contributors who developed theories
related to fluid flow in 19th century. Ludwig Prandtl (1875-1953) proposed a
boundary layer theory,compressible flows, the Prandtl number in the early 20th
Century while Theodore von Karman (1881-1963) analyzed the von Karman vortex
street (Chang-Ming,
2008)

 

Patankar
and Spaldingin devised the SIMPLE (Semi-Implicit Method for Pressure-Linked
Equations) algorithms. SIMPLE is one of the few algorithm in solving CFD
solutions. SIMPLE can perform very well on coarse grids, but it shows low
convergence rates. Hence, rough solutions can be calculated effectively even
for very complex problems. However when the grid is fine, the effectiveness
decreases drastically. Numerous modifications were made from years to years to
the basic SIMPLE procedure such as removed some of assumptions made previously,
improving the solutions for time dependent problems when the grid is spacious.
When the grid is spacious, it will lead to inefficient of SIMPLE to be used in
this case. (J. M., 2007)

 

SIMPLE can be used in order to
calculate the pressure, in which in the equation, pressure is denoted
by p*, while its velocity are denoted by u*,v*,w*.

 

The flow variable can be expressed
as

 

u = u* + u ?  v = v* +
v ? and p = p* + p ?  (J. M., 2007)

 

Where ” * ” denotes an initial
estimate, and ” ? ” represents a correction and it is a function of space and
time. These can then be substituted into the Navier– Stokes equations and
further derived. (J. M., 2007)

 

There are two types of corrections
in SIMPLE which is velocity correction and pressure correction.(Sharma, 2008)
SIMPLER,stands for SIMPLE-Revised. The pressure corrections used in SIMPLE
seems to have sufficient corrections for velocity components, but were always
quite inaccurate when pressure was required to calculate. So ,Patankar invent
another algorithmic formula that would retain the part of SIMPLE associated
with velocity calculations, but replace the method used to obtain pressure
which is SIMPLER.(J. M., 2007).

 

Computational Fluid Dynamics
basically includes three activity stages which are pre-processing, processing
and post processing.

Figure 1.2

In
pre-processing, the preparation of data is done by setting up the simulation.
The flow parameters then determined and then material data soon after. However,
there are some precautions during the modification of the mathematical model.
Firstly, the right plane must be chosen with the corresponding relevant flow
model; also, the fluid flow direction must be determined. After the
computational domain is defined, the computational effort can then be simplified,
for example, by checking for symmetries and flow directions on whether it is a
2D or 3D flow so elements that has no influence on the flow can be completely
neglected. Then the initial conditions and the boundary conditions are
specified.

The discretization process divides
the geometry into finite elements to prepare for analysis purpose. The mesh
generation process is to break down the domain into small elements in a
triangular or quadrilateral shape. This process might be different depending on
the software used.

Iterative
solution strategy is an incremental formulation which is frequently used to
solve non-linear flow equations. There are two types of iterations which are
the outer iteration and the inner iteration. For the outer iteration, to avoid
from the non-linearity, the equation is solved by a restricted pattern; the
coefficients for the discrete problem are then updated using the values of the
previous iteration. For inner iteration, the linear sub-problem sequence is
solved by the iterative method. Through the iteration solution, a converging
result is needed. There are some criteria for the convergence which is the
necessity to check for the remaining, the changes of the corresponding solution
and also the signal to make sure the iterations converge.

 

In CFD simulation, the computing
times are depends on few criteria(Kuzmin,2017):

1.      The
numerical algorithms and also the data structure.

2.      The
stopping principle for the iterative solvers

3.      The
discretize parameters for example the mesh size used

4.      The
hardware used to run the simulation for example the parallel setting used, the
number of cores used and so on

 

On the other hand, the quality of
the simulation results will depends on the

1.      The
mathematical model used and the hidden assumptions made

2.      The
form of the approximation used

3.      The
mesh size setting again

4.      The
simulation setting and the indicators for the error

 

 

Last step of the CFD simulation is
post-processing(Kuzmin,2017). Post-processing process involves the analysis of
the result obtained earlier. It includes the step of conceiving the data and
appraisal of the accuracy. In the post-processing process, the forces needed on
the particular surface are computed and so is any other quantity that is
needed. In other words, post-processing of the results allows information to be
extracted from the flow field that had computed earlier. The calculation can be
either for the derived quantities like vorticity, wall shear stress or integral
parameters like lift and drag. It can also perform visualization of result.

 

CFD visualizes the results in 1D, 2D
or 3D. 1D is the function values which are connected by straight lines. 2D is
the color diagrams, the streamlines and the contour levels. 3D refers to the
cut-planes, cut-lines and so on. CFD also displays the result simulated in
animated form. CFD performs the systematic data analysis
by the usage of the statistical tools. It then follows by debugging of the CFD
codes. Lastly, it ends up with the verification and validation of the CFD
model.

Figure 1.3 Colour diagram for the 2D
data

 

(Lstm.uni-erlangen.de, 2017)

Figure 1.4

Diagram above shows the animation
presentation of the CFD result which flow pass through a circular cylinder.

 

There are 3 measurements for qualities of a mesh, that is
skewness, smoothness and aspect ratio. Skewness, defined as difference between
the shape of the cell and the shape of an equilateral cell of equivalent
volume.

 

 

 

 

 

 

 

 

 

 

Figure 1.5

 

Next is smoothness and aspect ratio, smoothness indicates
the change in cell size in terms of constant change is smooth and a large
disparity in cell size means low smoothness.

 

 

 

 

 

 

 

Figure
1.6

Aspect ratio is the ratio of longest
edge length to the shortest edge length where the ratio closer to one is the
sign of a good mesh.

 

 

 

 

 

 

 

 

 

Figure
1.7

One of the few errors that affect the accuracy of the
simulation includes the high coarseness of the mesh, high skewness, drastic
fluctuations of volume of cells in the mesh and large aspect ratios.

 

When discussing the generation of
mesh, one of the most important factor is mesh density where the accuracy of
the results is dependent. On paper, it is logical to assume that a high density
mesh will yield a result with a higher degree of accuracy, but that requires a
high amount of computational power to generate a dense mesh, therefore it is
not economically and time-wise viable to generate that sort of mesh. Therefore
the independence of the grid must be found in order to save time and
computational power. Mesh independent is the situation where the results are no
longer influenced by the mesh density, the process of obtaining mesh
independent includes comparing the simulated results with the theoretical
values, but more often theoretical values are not available due to complex
calculation needed, therefore by conducting multiple simulations, mesh
independence can be deduced by comparing the results of each simulation until a
constant or convergence is achieved. Once the initial mesh has been solved, the
simulation must be repeated with a finer mesh in order to verify the accuracy
of the result, because a mesh too coarse will not have the necessary details to
provide accurate results, until the results are consistent regardless of a
finer mesh on subsequent simulations. Thus mesh independence is said to be
achieved.

 

Figure 1.8

For example, the static pressure at
region X can be assumed to be a constant from 1.25 million number of elements
and beyond, therefore the independence of mesh can be said to be achieved at
1.25 million number of elements.

Finding the mesh independent sizing is imperative as it
represents sufficient accuracy of the results along with the the benefits of
using minimal computational power and time

 

 

Advantages
and Disadvantages of Using CFD:

            The
advantages of using CFD is it allows observing and measure the flow without
disturbing the flow itself, compared to using a manometer to measure air
pressure, the system has to be modified, therefore the results are slightly
inaccurate compared to CFD where the system is virtually perfect. Moreover, CFD
also allows the observation of the flow in dangerous situations such as, flow
of high temperature fluids or the flow of air around high rpm turbine blades
and thus avoiding dangerous situations. Besides that, CFD can also be used to
make decisions regarding multiple system designs, the system can be tested in
the software to show results and flaws and thus less money are spent for
building multiple prototypes.(Airflowsciences.com, 2017)Lastly, CFD can also be
used to foresee the results or output of the design layout which is most
crucial and can improving the performance without building a real prototype.
(Pretechnologies.com, 2017)

 

        The disadvantages of using CFD is the
state of CFD today still requires a certain level of knowledge in order to
operate in case of wrong solutions. Besides that, CFD still requires a high
amount of computational power and it is unable to display results in real time.(Airflowsciences.com,
2017)Lastly, CFD can be expensive in terms of computational power and time
consumption for simulations that are complex. (Ifes-koeln.de, 2017)

 

Applications of CFD

        Architects use CFD as the application
of indoor and outdoor air simulation around the building, environmental
suitability, natural or low energy ventilation to design comfortable and safe
living environments. In the automotive industrial, CFD can be used to study the
external car aerodynamics, combustion in engines, exhaust flow and thus
improving the efficiency of a car. In the semiconductor industry, CFD can help
to get finer details easier compare with experiment, for example, the
deposition rate, temperature distribution over the surface and the rate of
desorption of a semiconductor. In the steel industry, CFD are used as the
trials of steel are usually carried out in very high temperature and the visual
opacity of the liquid steel is high so it is difficult to perform with real
prototypes. In the area of water and wastewater, CFD are used as it allows to
test the validity of the flow pattern designs and thus to improve the unit
process such as location of connections, the shape of basins and more, moreover
it can be used to check for possible short-circuits of inlets and
outlets.(Cfd-online.com, 2017) In the sterilization food preservation process,
CFD can be used to figure out the  both
temperature distribution and flow pattern of food in the sterilization process
and thus to preserve the quality of food. In the refrigeration process, CFD can
be used to calculate the heat and mass transfer in foods during refrigeration
as to preserve the quality of food.(Pdfs.semanticscholar.org, 2017).