3. MATERIAL AND METHODS
3.3. Design Of Air Channel By Means Of CFD
3.3.2. CFD Analysis Studies
3.3.2.3. Grid Generation and Independence Study
The arrangement of discrete points throughout the flow field is simply called a grid. The determination of a proper grid for the flow over or through a given geometric shape is a serious matter. The way that such a grid is determined is called grid generation. The matter of grid generation is a significant consideration in CFD;
the type of grid you choose for a given problem make or break the numerical solution. Because of this, grid generation has become an entity by self in CFD (Anderson, 1995).
The matter of grid independence is a serious consideration in CFD. In general when you solve a problem using CFD, you are employing a finite number of grid points distributed over the flow field. Assume that you are using N grid points. If everything goes well during your solution, you will get numbers out for the flow-field variables at these N grid points, and these numbers may look qualitatively good to you. However, assume that you rerun your solution, this time using twice as many grid points, 2N, distributed over the same domain. You may find that the values of your flow-field variables are quite different for this second calculation. If this is the case, then your solution is a function of the number of grid points you are using. You must increase the number of grid points until you reach a solution, which is no longer
sensitive to the number of points. When you reach this situation, then you have achieved grid independence (Anderson, 1995).
One way to perform a grid independence study is to increase the number of grids in the simulation till that accuracy is reached. The solution from two models of different grid densities is compared. One or several such comparisons can be done to ensure grid independency. If the solutions of the highest two grids densities are within a sufficiently small-predetermined tolerance, the original grid density is considered sufficiently accurate for engineering purposes (Moujaes and Gundavelli, 2012).
The effect of grid on the results for the current simulations was determined by performing a grid independency study. In the current study, grid density of each of the parts forming the flow domain was changed and the effect of change was examined. For this purpose 4 different meshes with different densities and number of elements were generated and analyzed under the same conditions.
For grid generation, GAMBIT® 2.4.6 software package was used. For each of the volumes forming the flow domain, following grid generation procedure was employed. Definition of boundary layer, surface grid generation to the surface perpendicular to the flow direction, edge grid generation along to the channel, finally by referencing the grids generated, volume mesh generation of flow domain part.
Some sample views of grids are showed in the following Figures.
(a) (b)
Figure 3.60. Grid generated for main channel (a): Section view, (b): A portion of side view
Figure 3.61. Side view of grid generated for inlet channel
(a) (b)
Figure 3.62. Grid generated for exit channels (a): Section view, (b): Side view Properties of Grid A, B, C, and D are listed in Table 3.36.
Table 3.36. Properties of grids
Element Hex/Wedge Hex/Wedge Hex/Wedge Hex/Wedge
Type Cooper Cooper Cooper Cooper
Element Hex/Wedge Hex/Wedge Hex/Wedge Hex/Wedge
Type Cooper Cooper Cooper Cooper
Resultant values of element numbers and worst element’s equisize skewness of main, inlet, exit channels and whole flow domain can be seen in Table 3.37.
Table 3.37. Number of element and equisize skewness of grids
Grid A Grid B Grid C Grid D Main Channel 1.156.000 1.783.980 2.210.850 3.598.560 Exit Channels 1.780.835 2.290.645 3.199.888 4.829.846 Inlet Channels 1.828.224 3.005.640 4.420.542 5.723.136 Total Element Number 4.765.059 7.080.265 9.831.280 14.151.542 Worst Element’s Equiskewness Value 0,430 0,429 0,441 0,442
As can be observed from Table 3.37, while Grid A, which is the coarsest grid, has approximately 5 millions of element, Grid D, which is the finest grid, has over 14 millions of elements. And all of the grids have an equisize skewness value of under 0,45, which indicates that we have a geometrically very good quality mesh.
Another aspect of the numerical solution is that of boundary conditions.
Because, without the physically proper implementation of boundary conditions and their numerically proper representation, we have no hope whatsoever in obtaining a proper numerical solution to our flow problem (Anderson, 1995).
After grid generation operations, boundary conditions to each of the surface of volumes forming flow domain were identified with GAMBIT® 2.4.6 package software. Here, the surfaces, where the evaporator fans blow the air to the inlet channel were defined as “Velocity Inlet”. Outlet surfaces of exit channels were defined as “Pressure Outlet”. Contact surfaces of each of 21 volumes, where fluid will flow through were defined as “Interface”. And rest of the surfaces are defines as
“Wall”. Finally since only flow domain was modeled, all member of the flow domain was defined as “Fluid”. Definition of boundary conditions of Inlet channels, Exit channels, main channels and volumes can be seen in Figure 3.63, 3.64, 3.65 and 3.66 respectively.
Figure 3.63. Boundary condition definitions of inlet channels
Figure 3.64. Boundary condition definitions of exit channels
Figure 3.65. Boundary condition definitions of main channels
Figure 3.66. Continuum definitions of flow domain
Also interface surface connections were defined by using FLUENT® 6.3.26 package software.
In order to determine the numerical value of velocity inlet boundary condition, 3 fans, fitted to the experimental setup, were run. And the exit velocities of each of the exits were measured 3 times by anemometer as shown in Figure 3.67 and average of the values are noted to Table 3.38.
Figure 3.67. Exit velocity measurement
Table 3.38. Measured and average exit velocity values taken from experimental setup
Exit Number Measurement 1 Measurement 2 Measurement 3 Average Velocity (m/s)
Exit 1 19,00 19,19 16,11 18,10
Exit 2 17,21 16,87 17,55 17,21
Exit 3 15,70 17,36 16,53 16,53
Exit 4 15,90 16,54 15,26 15,90
Exit 5 15,45 14,68 16,22 15,45
Exit 6 20,42 17,08 18,19 18,56
Exit 7 15,41 16,63 19,92 17,32
Exit 8 14,22 13,64 15,22 14,36
Exit 9 14,90 15,05 13,89 14,61
Exit 10 15,24 14,94 15,54 15,24
Exit 11 16,71 15,11 15,91 15,91
Exit 12 17,46 15,18 16,32 16,32
Exit 13 15,20 16,19 18,17 16,52
Exit 14 16,08 17,42 16,75 16,75
Average Exit
Velocity (m/s) 16,35 16,13 16,54 16,34
As can be seen from Table 3.38, mean velocity of an exit is 16,34 m/s. So by considering flow as continuous and incompressible and employing the simple formula Q=V.A. Inlet velocity boundary condition can be calculated as follows;
Cross-section area of an exit channel (d:45 mm): 3,14*(22,5*10-3)2 =1,59*10-3 m2 Volume flow rate for 14 exits=(1,59*10-3)*14*16,34=363,6*10-3 m3/s
By assuming this amount of air must be supplied from the fans having 2 inlets with dimensions of 60X104 mm. The inlet velocity was determined as follows;
Area of each inlet:0,060*0,104=6,24*10-3 m2 Area of each fan having 2 inlets: 12,48*10-3 m2 Total cross-section area of 3 fans: 37,44*10-3 m2 Inlet Velocity: 363,6*10-3/37,44*10-3=9,7 m/s
So, the inlet velocity magnitude, which will be used in analyses, was determined as 9,7 m/s.
Mesh generated with GAMBIT® was transferred to FLUENT® and solved with k- Standard turbulence model under indicated conditions.
Before starting iterations in FLUENT®, grid checked by using “Check”
feature under “Grid” menu and by using the “Scale” option under “Grid” menu, grid was scaled by defining that grid was generated in mm.
Analyses were run under conditions (Table 3.39) for each of the grids having different number of elements and resultant average exit velocity magnitudes were compared with each other.
Table 3.39. Grid Independency study analysis conditions
Solver : Pressure Based, Implicit, Steady, 3D Turbulence Model : k- , Standard
Near-Wall Treatment
: Standard Wall Functions Discretization : First Order Upwind Boundary
Resultant average exit velocity magnitudes of each of the analyses are tabulated in Table 3.40.
Table 3.40. Resultant average exit velocity magnitudes of each of the analyses
Exit
In order to investigate in detail and see clearly the results, exit velocity values obtained from each of the grids were graphed as in Figure 3.68.
Figure 3.68. Graph of grid independency analyses result
When we investigate the result table and graph in Figure 3.68, it is seen that in transition from GRID A, which is the coarsest, to GRID B, which is finer than GRID A, some results has big changes respectively. Similar situation can also be observed in transition from GRID B to GRID C. However, the amount of changes in transition from GRID C to GRID D, which is the finest grid, is very small.
In order to convert these observations into numerical values, a deviation value was calculated by taking square root of the average of square of differences of exit velocity results obtained from different grids. The formula employed can be seen as follows;
n
i XGRIDB XGRIDA
n 1
. 2
. )
1 (
Deviations calculated by using the above formula was tabulated in Table 3.41.
Table 3.41. Values of deviations between the grids
Grid Transition Deviation Grid A- Grid B 0,28 Grid B- Grid C 0,27 Grid C- Grid D 0,07
By evaluating the tables, graphics, and calculations mentioned above, it is clearly seen that the GRID D, which is the finest grid with 14.151.542 elements, gives the most suitable results and the solution is independent from the grid. So, for the following analyses, grid will be generated by employing the properties of GRID D in Table 3.36.
3.3.2.4. Analyses For Determining Suitable Turbulence Model