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:

(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).