COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL DEVELOPMENT
4.2 Model Specification
4.2.5 Grid Independence and Adaptation
In order to insure that the correct solutions are calculated, a grid sensitivity study was necessary for each different model created. The idea was to demonstrate that the solution was insensitive to the size of the mesh. The grid insensitivity was determined by computing a solution for a specific model, refining the mesh in critical regions, and then comparing the results until changes could no longer be detected. When changes in the results no longer occur, it can be said that the model is grid independent. At such a time the simulation results can be compared to the experimental and should prove to be the same. This is the best way to judge the accuracy of a simulation. If the results differ to the experimental, then the correctness of the experimental results can be questioned or the CFD model must be redone from scratch.
Mesh generation is the first and foremost important step in creating an accurate CFD model.
A vast amount of time was spent in creating and modifying the mesh to suit the type of simulation being run. Once the mesh is created in GAMBIT and a simulation is performed then, by studying the results, the mesh can be adapted in certain areas. There are two ways in which to modify a mesh. Firstly, the mesh can be modified manually in GAMBIT once the areas for adaptation have been marked. Secondly, FLUENT allows for solution-based grid adaptation.Itprovides the ability to adapt the grid, based on specific values or gradients of important flow characteristics such as velocity, temperature, pressure or turbulence. It also allows adaptation based on a wide range of desired wall unit values, or on specific flow boundaries.
The second approach was attempted many times, however every attempt failed as FLUENT reported fatal errors and promptly closed down. The error was reported to the FLUENT technical support. The reason for the adaptation failing was that FLUENT version 6.1.18 was simply unable to perform adaptations on a model that consisted of periodic boundaries. The only draw back of this was that the grid would have to be modified manually, this meant that time was wasted. However, very little time was spent modifying local regions of the grid.
The main flow region, which can only be meshed manually, proved to be the most problematic task, and will be discussed later in the chapter.
4.3 The Aerodynamic Analysis
FLUENT 6.1 is designed to solve both unstructured and structured meshes. Anunstructured mesh can contain either triangular, quadrilateral or a hybrid combination of both cell types.
Quadrilateral (quad) cells are favoured to triangular (tri) cells. The FV method works on quad cells. If tri cells are employed in the model then the FV "transforms" the tri cells into quad cells for the formulation, this then leadstoround-off errors.
Figure 4-2 shows the highly curved model geometry. The majority of time spent on the development of the CFD model wasingenerating the most suitable mesh in GAMBIT. The turbulence models that were investigated in FLUENT were the Spalart-Allmaras,k -E and the k - co models, along with all the near-wall treatments available.
4.3.1 Unstructured Mesh Using Only Triangular Cells (Grid 1)
It was decided that the mesh for the geometric model would be constructed slowly by starting off with a simple unstructured mesh that consisted of only tri cells. Figures 4-3 and 4-4 show the unstructured mesh. The flow field was meshed with 10315 cells and the solid region (the blade) with 3894 cells.
Figure 4-3: Unstructured triangular mesh (Grid1)
High pressure, temperature and velocity gradients are expected near the blade wall, where as such gradients will not be present in the bulk flow. It follows that the grid would haveto be fine near the wall and coarser in the free stream. To ensure that the mesh gradually increases away from the blade wall, a Sizing Function was employed for main flow mesh. The blade surface was discretized with elements of size
=
0.1 (grid was created in cm) and the flow' boundaries with elements of size=
1. The Sizing Function then ensures that the cells will linearly increase in size from the blade surfacetothe flow boundaries. The mesh in the solid region had a constant element size= 0.1.Figure 4-4: Close up of theunstructuredtriangular mesh (Grid1)
Only the Spalart-Allmaras (SA) turbulence model was investigated for the unstructured mesh. The reason being that, unlike all the other turbulence models, the SA model is designedtowork for small y+ values as well as for 300>y+>30. The y+ values in the near- wall for the first cell were all in the order of300. The entire boundary layer around the blade surface was housed in the first cell. As a result, no clear aerodynamic features could be seen in the near wall region. Figure 4-5 shows the pressure distribution, the SA turbulence model shows excellent agreement with the data on both the pressure and suction side of the blade.
The temperature distribution (shown in Figure 4-6) however, varies significantly from the data. It is evident from figure 4-6, that the boundary layer has not been accurately modelled.
Asa result, a boundary layer mesh will have to be employed. Figures F-1 and F-2 show the pressure and temperature contours, respectively, for the Spalart-Allmaras turbulence model.
Pressure Distribution 1
0.8
0: en
0.6Q.
0.4
--CFD, Sohn
o Experimental, Sohn
- - Spalart-Allmaras
1 0.2 0.4 0.6 0.8
o
xlL
0.2 -1--..,..--...,.---,--...,...----,---.----,---,---,---1
-1 -0.8 -0.6 -0.4 -0.2
Figure 4-5: Pressure distribution from the aerodynamic analysis using the Spalart- Allmaras tuIbulence model for Grid 1
Temperature Distribution
0 . 9 . . . , - - - . ,
o Experimental, Sohn
0.8
e
to- 0.7
~
0.6
--CFD, Sohn - - Spalart-Allmaras
0.5 1
o
xlL -0.5
0.5 - t - - - , - - - , - - - , . . - - ----j
-1
Figure 4-6: Temperature distribution from the aerodynamic analysis using the Spalart-Allmaras tuIbulence model for Grid 1