Section A (Introduction) Computational fluid dynamics (CFD) is the study of how the fluid flows using computers. The governing mathematical equations that explains how fluids flow are too difficult to be solved using pen and paper, that is why the fluids flow can be solved using computers to reduce time consumption. Figure 1: Real experiment vs CFD Simulation CFD is a tool that involves different application in physics, mathematics and computational software. For example, ANSYS is a software with good qualitative and quantitative prediction. It is used widely to analyse flow field, thermal properties, heat transfer, mass transfer, chemical reaction and related phenomena of the model. For example, heat transfer of a building, interaction of various object with surrounding and combustion in automobile engine. CFD involves few equations in solving the velocity flow, pressure difference and fluid flow.
The first equation is conservation of mass which is the difference in mass flow entering the control system. The difference of inlet mass and outlet mass is equal to the rate of change of mass in volume.The Second equation is the conservation of momentum. Since momentum is vector quantity, there are 3 different equation in different axis(x,y,z) to control volume of the domain.(J.S. Shang,2004).
The Accuracy of simulation depends on the sizes of grid applied. Hence, the finite difference or finite volume grid should be sufficiently fine to analyze the flow. Actually, CFD is able to estimate the value of an object in few parameters. To estimate the value, meshing, which is the process of separating volume into smaller pieces so that an more accurate result can be obtained can be used. However, the smaller the mesh size, longer period of calculation required to solve the fluid flow,that is why we need to be flexible and make the right choice depending on the case. History of CFD People has been wanting to know how the fluid flows from the early days until now. Experiments have been done from time to time and a major disadvantage has been found out, experiments consumes too much time and money to accurately to find out the phenomena of the fluid flow.
In the 1910’s,CFD is based on the Navier-Stokes equation which is a equation that is able to solve all single phase fluid flow.(J.S. Shang 2004). By using Navier-Stokes equations, the values of the fluid direction for pressure, velocity, density and temperature can be estimated in CFD.(J.S.
Shang,2004). In numerical solution, there are few method to perform the calculation such as finite element method, fluid division mixing and finite volume method. The original design of CFD is used to simplify equation and reduce the model into 2 dimension.
Conformal map is one of the method in two-dimensional area which used to identify the flow of an object such as airfoil or formula one. Transformation of dimensional region from higher-dimension to lower-dimension can be done by using the conformal transformation. Figure 2: Design of ENIACElectrical Numerical Integrator and Computer(ENIAC) was conducted in the setting of basis CFD in 1940s.
ENIAC is the earliest and first electronic purpose computers made and installed at Aberdeen.(Trevor English,2017) The problem was initially solved by using partial differential equation at Los Alamos National Laboratory. The computer able to model the fluid flow and solve the practical problem led by Francis.H.Harlow. From 1957 till the late of 1960s, first functional CFD computer simulation model was developed by a team. This group also discovered variety of numerical methods in simulate the two-dimensional model.
For example, Marker-and-cell method, Lagrangian-Eulerian and vorticity steam function method.(Trevor English,2017) By 1967, Douglas Aircraft able to resolve in 3-dimensional CFD analysis method. This analysis was first developed for fluid flow over an aircraft. The first paper of 3-dimensional model was announced by A.M.
O Smith and John Hess. They were using the panel method which able to predict the aerodynamics properties of streamlined airfoil sections. Panel method can calculate the pressure distributed by the air flow even in an inviscid parallel flowing condition. Antony Jameson and David Caughey developed a three-dimensional Full Potential code FLO22. The interacting boundary solution method was firstly developed by a CFD frontiersmen. Davis was able to solve the multiple dimensional compressible boundary layer equation by using the combination of finite difference and implicit-explicit theory.(Mathematik.uni-dortmund.
de,2018) Starting from 1995s, the technology and computing skills had become advanced. CFD able to predict the fluid flow of automotive design. This software is very useful in the aircraft and automotive sector. Hence, CFD is one of the powerful software to model fluid flow in engineering sector.Application of CFD Figure 3 : Piping system CFD diagram The applications of CFD that are used in the industry is for example pipeline component interface, heat exchanger and separation systems.(Dynaflow.
com,2017). CFD can analyse the fluid flow of the valves, pump and filter under the interface of pipeline component system. To summarize , CFD is used in this sector to optimize the design and improve the performance of the component, it can also determine the causes of the problem. Figure 4 : Temperatures changes in greenhouse effects CFD diagram Figure 5 : Biological animal crop CFD diagram In the agricultural industry application, CFD can be used to solve the environmental of greenhouse effects.This software able model out the environment condition of the greenhouse effects. CFD also able to simulate the crop animal biological responses function under specific condition. The current status of greenhouse CFD modelling was found to be at a higher standard than that of animal housing.
(Kaushal, P. and HK, S. 2008) Besides,it helps in the designing of the ventilation system for agricultural production system. Figure 6 : Meso-Mixing CFD diagram Figure 7 : Stirred tank CFD diagram In the application of CFD in food industrial, CFD able to improve the cleaning of food processing tank. Tank is used to store the raw material or end product. By using CFD, the hygienic design of the tank can be improved as well. CFD simulate the tank design and find out which region of tank excess higher shear stress along the wall. The geometry of different junction is compared several times in CFD.
This comparison gave an acceptable qualitative agreement with finite volume-based calculations that involve both steady-state and transient operations (Dynaflow.com,2017). The scientist use CFD to prevent the microbiological contamination due to it might affect the hygienic of the food. Advantages of CFDComputational Fluid Dynamics getting more popular in this generation. This is because most of the industrial use CFD as a domain software to analyse fluid flow of the designs. The benefits of CFD in the industry is quick processing and analysis time. It is considered as low-cost method for design iteration which mean it can simulate repeatedly.
(CFD Modeling Services,2018) Engineers use CFD to determine causes and possible uncertainty. Hence, the design can be modified several times in this software without over-budget. Another advantage of CFD is this software provides comprehensive information. CFD model offers precise and detailed information about heating, ventilation, and air conditioning design parameters.(Mehul Patel ,2013) CFD can analyse velocity, chemical concentration location and pressure distribution which helps engineers and scientists a lot. They able to understand the current issues appropriately and discover the best selections among the practical ideas.Moreover, CFD enables the user to simulate under desired settings of their prototype.
For example.the pressure flows and velocity flows condition can be analysed out easily. (Mehul Patel ,2013).For example, for the automotive sector especially in Formula 1 (F1), The designer use CFD to predict how the laws of physics and racing conditions affect a race car’s performance. Figure 8: Dam break analysisLastly, CFD is able to forecast and prevent dangerous situations from happening. By simulation, we are able to detect where the product is at fault and can prevent it from happening by changing something. For example, flooding due to dam failure can be catastrophic.
However, by using cfd to model catastrophic conditions , we can prevent the catastrophe to happen.Methodology of CFD Figure 9: Flowchart of how CFD works CFD consists of three stages which are pre-processing, solving and post-processing.a) Pre-processingThe modelling goals must be identified clearly before running the first step of pre-processing.
The aim of pre-processing is to identify the problem statement and the computational domain, it also serves to define the boundary of the simulation. First, the data is prepared such as the coordinate axes, origin and connectivity for describing the geometry. (Dr. Ganesh Visavale, 2012) The computational domain of interest is identified to determine the flow parameters and material data of the domain. To construct a computational domain, it is necessary to create a sketch 2D on to any plane. Then, the meshing process is needed to subdivide the domain into small cells called as elements for computation purpose. The smaller the mesh size, longer period of calculation required to solve the fluid flow,that is why we need to be flexible and make the right choice depending on the case. To verify that the results are not affected by the grid resolution, several mesh of the same geometry must be done to find the mesh size of the mesh independent by examining the convergence of the iteration .
After that, the boundary condition is defined at the domain boundary zone so that the system can recognize the boundary condition when running the simulation. Versteeg HK, Malalasekera W (1995) Figure 10:Shape of element that has been meshed in two dimensional. b) SolvingSolving process solves the problems that set up in the pre-processing process with the software on the computer called ANSYS. Solving is the differential equation governing the fluid flow with a set of algebraic equation called as discretization process which can solve the problem with approximate solution. The inlet velocity must be identified during pre-processing so that the pressure at the desired section can be determined. Once the flow physics model has been sketched , the material properties, flow parameter, and boundary conditions are set, so that the system will start solving equation. Physical conditions are required on the boundaries of the flow domain since a finite flow domain is specified.(Mehul Patel,2013) The simulation generally starts from an initial solution and uses an iterative method to solve a final flow field solution.
The user can decide the solution scheme and convergence criteria to be used for numerical computation to run the simulation. There are three common types of solution scheme and each type has their own capabilities. Figure 11 : Flowchart of SIMPLE MethodSIMPLE algorithm is an estimation and correct procedure for the calculation of pressure.The SIMPLEC algorithm allows faster convergence for simple problem for example, laminar flow with no physical model. Figure 12 : Flow chart of PISO algorithm PISO algorithm is useful in transient flow problems and the meshing element is higher than average skew (Althea de Souza, 2005) .
PISO algorithm also adds an extra correction step to SIMPLE to enhance its performance. The convergence criteria are based on the residual values of each variable calculation during the simulation. The solution is more numerically accurate as the residual value is lower. Anon, 2015 The convergence criteria also can be criticised by the imbalance solution and the quantities of interest like force, drag, or average temperature. c) Post-processingThe post processing is the final step of CFD simulation where the quantitatively analysis can be retrieved after the simulation is converged.
To validate the simulation results, actual experimental results are used to be compared with them so that we can know the percentage error of the simulation . The data is visualized and the accuracy of the result is estimated. The results of the modelling can be shown with different methods like contour plots, vector plot, streamlines, graphics and animations. (Dr. Ganesh Visavale, 2012) For example, colour may be used to indicate the value of some component of stress on the surface of the component. By using the results of the simulation, it can generate a graph and the solution should be validated. If solution is invalid, change the meshing size of model and re-simulate to optimise the model.
According from the article written by Scott H. Woodward (2006), the CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. (Hoi, 2006) Figure 13: results of the modelling with different methods. (Joung et al., 2014)Part B (Simulation)Simulation Setup For this simulation test, Fluid Flow(Fluent) was used as solvers in order to analyse the flow behaviour of the sudden contraction with different Lextend at the domain downstream of the contraction.A. Geometry Setup 1) The geometry of the sudden contraction was sketched out. Note that the sketched geometry is only half of the actual model due to the assumption of the flow is asymmetric and steady.
2) The default dimension of the sketched geometry was set as follow: LineLength (mm)H710H60.4V14V51 3) The surface was generated from the sketch by selecting “Surface From Sketches” and followed by “Generate”. A surface is necessary to be generated to run the 2D simulation.4) B. Mesh Setup 1) All the edges was named as shown in diagram below by right click on each edge and select “Create Named Selection”.
This step is necessary in order to define the boundary in the model. Figure B.1: Naming of edges 2) The inflation was added to all the edges named as “wall” and the maximum inflation layer was set to 20. Addition of inflation layer on the wall is necessary to ensure a more accurate result; without the layer the condition at the wall (e.g wall shear stress) was unable to be analyse.3) The mesh size generated to run this simulation test is as follow: Other Sizing setting in this simulation test was remained as program default.Note that the mesh size stated above is verified to be grid independent.
Verification of grid independent is important and necessary to be done in all type of simulation. Figure B.2: Mesh size and inflation layer generatedC.
Calculation Setup Summary of setting applied in the simulation Note: Other setting which does not mentioned above was not subjected to change and remained as program defaultRemarks :1. Pressure-based option was selected due to the assumption of the flow in this study is incompressible. 2. Steady option was selected due to the assumption of the velocity is not vary in time throughout the flow field. 3. Models setting: a) Multiphase was off as there is no other phases (e.g solid and liquid) involved in the flow.
b) Standard K-? model was selected instead of Standard k-? model as viscous model due to k-? model have been found to work favourably well for a wide range of wall-bounded. c) Energy model, Radiation model, Heat Exchanger model, Special model, Discrete Phase model, and Solidification & Melting model was off due to no thermodynamics work was done to and done by the system. d) Acoustics model was off as sound pressure is totally out of analysis in this study. 4. SIMPLE was chosen due to a few reason as belowa) SIMPLEC can obtain a converged result faster than SIMPLE with the aid of pressure-correction under-relaxation. However, the high mesh skewness in the grip lead to instability and therefore was not an option b) The models used in this simulation test included a turbulence model (Standard K-? model), which usually requires small time steps, using PISO may cause an increased computational expense, therefore SIMPLEC or SIMPLE should be considered instead.
c) Section B Problem Statement 2i. Table 1 Table 2 Based on the table 2, the number of the elements is higher as the meshing size is lower. Since the number of element is increased, the time consumed for calculating the solution is increased. The value for the minimum size, maximum face size and maximum size are increased 10% each time to determine the best meshing size.
Table 3: Data from simulation Graph 1: Graph of static pressure against the length Table 4 Graph 2 By using the data in table 4 and graph 2, the grid independent resolution for different mesh sizes is determined. The line that circled by red from graph 2 is stabilizes, therefore the mesh size at that section is selected to determine the pressure at sudden contraction area for the following ratios. This is due to the results that obtain is more accurate compare to other mesh size as the number of element is higher. Leap CFD Team says that the best way to check for a grid independent is to plot a graph of the resultant monitor value against the number of cells in your simulation by modifying the mesh in the model. (Team, L. 2012) Comparison of the flow fieldNo2712Min size(mm)0.
00660000.01062940.0171187Max face size(mm) 0.0132000 0.
0212587 0.0342374Max size(mm)0.01320000.02125870.0342374Element25153610081441952 Mesh Velocity Vectors Table 5 Based on the table 5, it indicates that the smaller mesh size has a better resolution for the velocity vector compare to the bigger mesh size due to the smaller mesh size has smaller grid which has higher number of element.
Therefore, the simulation results for the smaller mesh size has high accuracy, however, it affects the time required to achieve converged solution. Steven. Williams mentions that the larger the mesh numbers, the smaller the openings in the mesh.
(Steven.Williams, 2008) ii. Table 6: Best mesh size The best grid is recorded in table 6 and it is used to generate solution for (. In order to avoid reverse flow at the pressure outlet, different ratios are tested by using the best grid selected and the results for reverse flow at the pressure outlet is recorded in table 7. Table 7 Figure 1: Velocity vector diagram for the 0.4 ratio with reserve flow Figure 2: Velocity vector diagram for the 0.
5 ratio Figure 3: Velocity vector diagram for the 0.6 ratio without reserve flow By referring the figure above and table 7, the reserve flow is occurred at the pressure outlet at 0.2, 0.3 and 0.4 ratios.
For the 0.5 ratio, the reserve flow at the pressure outlet is gone but if zoom in at the wall boundary above intermediate that shown as the figure 2, the eddy flow is occurred. However, the 0.6 ratio shows the reserve flow is no longer occurred at the pressure outlet and same going for the following ratios. Figure 4: Pressure diagram for the 0.2 ratio Figure 5: Pressure diagram for the 0.5 ratio Figure 6: Pressure diagram for the 2.0 ratio By observing the figure 1, 2 and 3, when the ratio is small, the eddy flow will forms at pressure outlet easily.
When the ratio is long, there are no backflow forms at the pressure outlet. There is always an eddy flow condition at the sudden contraction region due to the sharp edge that can separate the flow direction. According from the Barry Azzopardi, the sudden contraction will cause the pressure converts to kinetic energy. Hence, the eddy is formed to start consuming the kinetic energy of flow and causes the velocity decrease. However, the eddy flow will disappear when the pressure in increased until there is no more pressure gradient. (Azzopardi Barry J., 2011).
By increasing the ratio, the low pressure will only occur at the contraction area which the eddy flow will formed and the pressure outlet will higher. 3) Figure 3.1: Graph of ?P against Lextend / D2Data Analysis :1. According to Graph 3.1, it can be observed that the line of the graph started to become steady at Lextend / D2 = 0.
9 and the value of ?P is maintained at around 49000 Pa. This indicated that the Lextend / D2 is no longer affecting the pressure difference, ?P. 2. According to Table 3.1, the value of ?P stabilized at Lextend / D2 = 0.9. It can be observed that stating at Lextend / D2 = 0.
9, the value of ?P remained at around 49300 Pa with very small percentage changes, which is at the range of 0.1% to 0.4%. 3.
Based on the data from the table and the trend shown in the graph, a conclusion can be made. The pressure difference from the inlet to the axial location of the sudden contraction, ?P becomes independent of Lextend only when Lextend / D2 ? 0.9.4) Figure 4.1: Graph of Pin against Lextend / D2 Data Analysis :1.
Based on Figure 4.1, the graph started to become steady at Lextend / D2 = 0.9 and the value of inlet gauge pressure, Pin is maintained at around 48000 Pa. The steady line graph indicated that the pressure is no longer affected by Lextend / D2 ratio. 2. Based on Table 4.1, the value of the inlet gauge pressure, Pin stabilized at Lextend / D2 = 0.
7. The percentage difference of Pin achieved around 1%, which indicated the pressure is no longer affected by Lextend / D2 ratio. 3. The inlet gauge pressure, Pin becomes independent of Lextend only when the ratio of Lextend / D2 ? 0.7. This ratio is selected instead of 0.9 is because the ratio of Lextend / D2 = 0.
9 is obtained from the graph by observation. On the other hand the ratio of Lextend / D2 = 0.7 is obtained by analysis based on the percentage difference of Pin and therefore is more reliable. 4.
Conclusion : The objective of this simulation is to figure out the Lextend / D2 ratio needed to extend the domain downstream of the contraction in order for the flow field to be simulated accurately at upstream of the contraction. From the simulation results, the Lextend / D2 ratio must be ? 0.5 in order to prevent backflow at the downstream. In order for the Pin to become independent of Lextend, the the Lextend / D2 ratio must be ? 0.7. Lastly, in order for the pressure difference, ?P to become independent of Lextend , Lextend / D2 ratio must be ? 0.
9. In conclusion, 0.9 is the suitable Lextend / D2 to use in the simulation to predict the pressure difference from the inlet to the axial location of the sudden contraction. Recommendations :1.
The sharp corner of the models change to round corner due to the occurrence of eddy flow at the shape corner of the sudden contraction pipe. The velocity and the head loss of the round corner is lower than sharp corner. This is because the sharp corner give direct impact when water flows through. The velocity’s region after the contraction for sharp corner is lower than round corner.
This show that the pressure after contraction for round corner is small than sharp corner. 2. Laminar model should be used instead of k-? mode since the flow condition in this case study is laminar flow. The derivation of the k-? model, flow is assumed to be fully turbulent, and the molecular viscosity effect are negligible. The standard k-? model is therefore only suitable for fully turbulent flows.