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)

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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).

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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

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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.

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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

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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)

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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)