Gambit and Fluent: Turbulent Flow and Heat Transfer in a Mixing Elbow 1. Abstract This exercise comprises of two sections A and B, where in the first section an analysis in creating initial vertices will be carried out along with the creation of edges and faces, and the setting of boundary types. The program used for this phase of the investigation will be Gambit. These will then be generated into a mesh using Fluent. Moreover, section B will focus on the sensitivity to the computational mesh, sensitivity to the residuals and the use of higher order numerical discretization schemes.

The structure of this report analyses the discretization of meshes, showing difference in results subject to variable changes. The general findings show that the different contours and iterations produced become increasingly accurate as the grid value increase or the order of discretization increases. 2. Altering the Residuals The following graphs show comparisons in residuals for different number of iterations, for a first order discretization 2. 1 Iteration for a triangular mesh {draw:frame} {draw:frame} Figure 2. 1: Original mesh Figure 2. 2:Mesh with reduced residuals 2. Iteration for a quadilateral mesh {draw:frame} {draw:frame} Figure 2. 3: Original mesh Figure 2. 4: Mesh with reduced residuals From the graphs above one can observe an increase in iteration when the residuals are reduced. However, the general shape of the curves remain exactly the same for both the triangular and quadrilateral mesh. From these findings it can be concluded that as the convergent rate decreases, the number of iterations becomes more important. When the convergence was set at a value less than 10e-04 the results were more accurate. *3.

Comparison For* First Order Discretization 3. 1 Velocity magnitude {draw:frame} {draw:frame} Figure 3. 1: Velocity variation for triangular mesh Figure 3. 2: Velocity Variation for quadrilateral mesh These graphs show that the diffusivity isn’t as well accounted for the quadrilateral mesh as it is for the triangular mesh. This is evident from the greater amount of uniformity and higher magnitude in the quadrilateral mesh than the triangular one. 3. 2 Static Temperature {draw:frame} {draw:frame} Figure 3. 3 Static temperature for triangularmesh Figure 3. Static temperature for quadrilateral mesh Likewise to the previous section, the quadrilateral mesh displays more uniform, refined lines than the triangular one, however in contrast the temperature scale is within the same limits. The triangular mesh shows a more gradual spread in temperature than the quadrilateral one. The limits can clearly be obtained here from using a mesh with fewer edges since there is less precise detail in the triangular mesh, i. e. it is more difficult to make out the colours separately. Velocity Vectors The 2 diagrams below show a similarity in the velocity vectors for both the meshes; however where the quadrilateral mesh presents a more definite, uniform profile, the triangular mesh shows a less organized and somewhat scattered group of lines. Again this only further proves the greater precision in having a larger number of edges. {draw:frame} {draw:frame} Figure 3. 5 Velocity vector for a triangular mesh Figure 3. 6: Velocity magnitude for a quadrilateral mesh 3. 4 Static Pressure {draw:frame} {draw:frame} Figure 3. 7 Static pressure contours for triangular mesh Figure 3. Static pressure contours for quadrilateral mesh For the static pressure variable, the quadrilateral mesh appears to have a greater sensitivity than the triangular mesh, displaying an area of high pressure on small inlet pipe and a greater contour profile on the area of high pressure. However what’s interesting to note is the area of low pressure detected at the top curve of the triangular mesh which is completely neglected in the quadrilateral mesh. Furthermore at the points of lowest pressure for both diagrams, there is a greater contour profile for the triangular mesh.

It can thus be concluded that the quadrilateral mesh is better at displaying areas of high pressure and the triangular mesh is better at displaying areas low pressure. 3. 5 Temperature vs. Position {draw:frame} {draw:frame} Figure 3. 9 Temperature dist. for triangular mesh Figure 3. 10 Temperature dist. for quadrilateral mesh Both the distributions present a positive correlation between the temperature and position with figure 3. 10 in particular showing the sudden sharp increase in gradient as it approaches the pipe corner.

This is more logically consistent since it is where the hotter second inlet lies. There is a distinct difference in the level of accuracy for temperature where the quadrilateral mesh clearly shows a very steady increase at the start followed by a linear distribution and then finally leveling off as opposed to an almost linear relationship in the triangular mesh. The superior accuracy for the quadrilateral mesh is particularly important to note in this case as one can mistakenly assume that the static temperature and position are linearly proportional and continue to be so from observing the triangular.

This makes a stronger case for the need to increase the number of edges and obtain a greater level of accuracy. 3. 6 Static Pressure vs. Position {draw:frame} {draw:frame} Figure 3. 11 Static pressure dist. for triangular mesh Figure 3. 12 Static pressure dist. for quadrilateral mesh Both the distributions are very similar for the meshes. However, the notable increase in plots for the quadrilateral mesh is due to the fact that presents data for the entire pipe while the triangular mesh only provides record from the second inlet onwards.

The drop in pressure can be explained by the flow from the second inlet. 4. Comparisons for Second Order of Discretization 4. 1 Iteration {draw:frame} {draw:frame} Figure 4. 1 Residuals for triangular mesh Figure 4. 2 Residuals for quadrilateral mesh The graphs indeed have a similar shape, but a greater level of accuracy is maintained for the quadrilateral mesh since it requires less iteration to converge and displays far greater discontinuities as should be the case. 4. 2 Grid {draw:frame} {draw:frame} Figure 4. 3 Grid for triangular mesh Figure 4. : Grid for quadrilateral mesh Clearly there is a finer, more uniform and detailed mesh for the quadrilateral than for the triangular, so it is clearer as to what is actually happening. For instance there are darker shades at the steeper curve of the “L” shape in the quadrilateral mesh which is not so apparent in the triangular mesh. 4. 3 Adapted Iteration {draw:frame} {draw:frame} Figure 4. 5 Scaled residuals for triangular mesh Figure 4. 6 Scaled Residuals for quadrilateral mesh Both the graphs show steps, caused by the second inlet where warmer flow originates.

Again the quadrilateral mesh has more precise, accurate graphs, evident from the less number of iterations required for convergence and from the more detailed features. The process of adaptation improves the flow features without increasing the computational load by modifying the meshes. 5. First Order Discretization* versus Second Order *Discretization 5. 1 Discretization of Triangular Mesh {draw:frame} {draw:frame} Figure 5. 1 Contours of static temperature for 1st order disc. Figure 5. 2 Contours of static temperature for 2nd order disc. . 2 Discretization of Quadrilateral Mesh {draw:frame} {draw:frame} Figure 5. 3 Contours of static temperature for 1storder disc. Figure 5. 4 Contours of static temperature 2nd order disc. Both the shapes show similar effects when increasing the order of discretization, however it is quite clear that it is less effective, the greater the number of edges used. This is because increasing the number of edges already makes the contours more accurate and definite and hence eventually the accuracy will “level off” 6.

Conclusion The results show sufficient evidence that the iterations and contours become more accurate as the order of discretization and order of the grid shapes increases. However, this is only upto a certain extent after which the increase in the order of accuracy is somewhat negligible. Also when the residuals are decreased, the solutions take longer to converge. 7. References Tutorial 1. Turbulent Flow and Heat Transfer in a mixing Transfer in a Mixing Elbow. Dr. Mark Cotton