Fluent Course Work MEC3028 Computational Heat and Fluid Flow Semester 1 - Academic Year 2024-25 Instructions The course work consists of two problems for a total of 100 marks. Please read the instructions below and within the questions carefully and thoroughly before doing the coursework. Failure to comply will result in a mark penalty. 1. The report should have a title page with your name, student number and module code. 2. The report should be typed and produced digitally. No hand written content is allowed. 3. Figures must have adequate resolution and their legend, labels and titles. 4. Use appropriate headings in boldface in the report when answering the questions. For instance, when answering the item “A” of problem 1, one can write: Answer to P1.A. Your answer consists of text, figures and tables where applicable. 5. Please comply with the words/lines limits given for the comments and analysis. 6. Use of any AI tools in any capacity is prohibited. MEC3028 - Semester 1 2024/25 Fluent Coursework Problem 1: Flow over a rotating cylinder [50 Marks] Consider a circular cylinder of diameter D = 1 (m) positioned in a stream of fluid. The fluid flows with the velocity of U∞ = 1 (m/s) towards positive x-direction (left to right in domain) as shown in Fig.1(a). The flow Reynolds number based on the cylinder diameter D and the free stream velocity U∞ is defined as Re = ρU∞D/µ = 200 where ρ (kg/m3) and µ (Pa.s) are density and viscosity of fluid respectively. The cylinder rotates in counter-clockwise (CCW) direction with the angular speed of ω (rad/s) as shown in Fig.1(a). Using the cylinder diameter D, free stream velocity U∞ and angular speed of the cylinder ω, the dimensionless angular speed can be defined as ω∗ = 0.5Dω/U∞. Refinement Region (b) 9D 8.5D 6D U ∞ D 25D ω Cylinder (a) 10D 20D Fluid domain x y U ∞ x y Figure 1: Schematic of (a) The computational domain and related dimensions. (b) The location of refined mesh. Note that the plot is not to the scale. GEOMETRY: To simulate this problem, set up the domain as shown in Fig.1(a) where the cylinder is positioned at the origin of coordinates at (xc, yc) = (0, 0) and has a diameter of D = 1 m. The fluid domain extends 10D upstream and 20D downstream of the cylinder in x-direction respectively. Domain sides are positioned ±12.5D from the cylinder in the y-direction. MESH: To tessellate the computational domain, divide the cylinder wall into 360 divisions and create a boundary layer inflation with the first layer thickness of 2.5× 10−3 m and 45 layers with expansion ratio of 1.2 over the cylinder wall. To balance the computational expense, set the mesh “global size” to 1 m in the domain. Moreover, to accurately capture the wake region, refine the mesh in the region shown in Fig.1(b) with the element size of 0.05. SIMULATIONS: Consider the flow Reynolds number of Re = 200 for the simulations. Conduct transient simulations for ω∗ = 0.25, 0.5, 1 using the Coupled Method with the time step size of ∆t = 0.1 s until Tfinal = 25 s. Set the relaxation factor for velocity and pressure to 1. Assume the flow is laminar. Page 2 MEC3028 - Semester 1 2024/25 Fluent Coursework A. Provide a figure of (i) the mesh in the entire domain (ii) A close-up view of the region near the cylinder. Provide these figures as a sub-figures of one single figure. [5 marks] B. What Transient formulation is used? [5 marks] C. Record the boundary conditions and their corresponding values in table 1. follow the example below. [5 marks] Example: For a stationary wall with no slip condition, the boundary condition should be recorded as: Type: wall, Wall motion: Stationary, Shear condition: no slip Table 1: Boundary conditions settings Boundary Boundary conditions Cylinder Wall Left Boundary Right Boundary Top Boundary Bottom Boundary D. Calculate the Lift Coefficient CL = FLift/ (0.5ρU 2 ∞D) over time for each case. Plot CL versus time for all cases as overlay in a single plot. Set an appropriate limit for y-axis and 0-25 for the x-axis. Label each clearly using their associated ω∗. [15 marks] F. Plot the contours of velocity magnitude for each case at T = 25. Use the same minimum and maximum for the velocity magnitude for all contour plots. Present the contour plots as subplots of a single figure. [15 marks] G. Analyse the flow dynamics based on the simulation results. Use CL plot you have already provided in your analysis and explain how the lift force changes with ω∗ and why.(max 5 lines) [5 marks] HINT: Set the fluid properties µ and ρ to produce the required Re number. I would recommend using ρ = 1 (kg/m3) and compute the µ to have Re = 200. HINT: Be advised not to confuse ω and ω∗. Page 3 MEC3028 - Semester 1 2024/25 Fluent Coursework Problem 2: Flow in a periodic channel [50 marks] Laminar fluid flows through a two-dimensional channel of height H = 2 m, and length L = 0.2 m in a periodic manner, which implies that the flow is between two infinitely long flat plates (see Fig.2) and is fully developed. Periodic boundary conditions ensure that the fluid which leaves the domain is reimposed at the inflow of the domain, thereby no inlet or outflow boundaries need to be imposed in this case. The fluid has a viscosity of µ = 1/64 kg/(ms), a density of ρ = 1 kg/m3. A constant pressure gradient ∂P/∂x = −1 Pa/m should be imposed in the axial flow direction. Details on how to apply the periodic boundary conditions as well as imposing the pressure gradient are provided in the Appendix at the end of this document. wall H L x y Figure 2: Schematic of the Taylor-Couette flow. (a) 3D view (b) top view (c) side view A. Generate a series of computational meshes for this problem with the specifications for each mesh given in the table 2. Please provide the plot of meshes in the report and clearly label them. Assemble these plots of meshes as a sub-figures of a single figure [5 marks] Note1: The domain geometry is fixed, but the mesh spacing is changed in different meshes. Note2: Note that you should make the geometry for each mesh separately as Fluent might causes problems with periodic conditions when duplicating the case setup. Table 2: Mesh Specifications for Problem 2 No. X direction Y direction 1 2 equidistant divisions 4 equidistant divisions 2 2 equidistant divisions 6 equidistant divisions 3 2 equidistant divisions 20 equidistant divisions 4 2 equidistant divisions 100 equidistant divisions 5 2 equidistant divisions 40 divisions with a bias factor of 8 towards both walls B. Conduct simulations using Fluent with different meshes given in table 2 using SIMPLE algorithm. For each case (mesh) run the simulation for two different discretisation: 1st order upwind and 2nd order upwind for the momentum equation. Record values of ∂u/∂y at the Page 4 MEC3028 - Semester 1 2024/25 Fluent Coursework bottom wall (H=0) for all the meshes and both discretisation schemes in table below (table 3). Use convergence criterion of 10−6 and at least 40,000 iterations for each simulation. The values for ∂u/∂y can be obtained by the derivative function under Plots, x-y plot option. [20 marks] Table 3: Computed Velocity Gradient ∂u/∂y Mesh 1st order 2nd order 4 equidistant divisions 6 equidistant divisions 20 equidistant divisions 100 equidistant divisions 40 divisions with a bias Note 1: Export the data using write to file option and use exact numbers rather than reading them from the plot Note 2: Report the numbers to the 4th decimal place for ∂u/∂y C. Do the 1st order and 2nc order discretisation for ∂u/∂y give the same outcome? For either yes or no, please comment and prove why. [10 marks] D. Wall friction velocity uτ is one of the most important quantity to evaluate the shear stress in wall bounded flows and it is defined as: uτ = ( |τw| ρ ) 1 2 (1) where τw is the wall shear stress and ρ is the fluid density. Evaluate uτ for all the meshes and all the numerical schemes used. Consequently compute the non-dimensional velocity u+ = u/uτ where u is the velocity of the flow in the x-direction. The dimensionless distance from the wall can be defined as y+ = (ρuτy/µ) where y is the dimensional distance from the wall in the y-direction. Additionally, an analytical solution to this problem can be obtained by using Eq.(2) u+ = u/uτ = (−H2/2µ)[(y/H)2 − (y/H)] (2) Plot u+ against y+ using the data obtained from Fluent simulations. Include the analytical solution (Eq.(2)) in the plot as well. [15 marks] Note 1: Please use different line colours for each line and label them appropriately. Note 2: u+ should be on the ordinate (vertical axis) and y+ on the abscissa (horizontal axis) Note 3: Use normal scale on for the ordinate and log scale for the abscissa Note 4: Plot the data from the bottom wall to the middle of the channel Page 5 MEC3028 - Semester 1 2024/25 Fluent Coursework APPENDIX: Imposing periodic boundary conditions and pressure drop Assume that the domain faces in question 2 at along the y-axis at x = 0 m and x = 0.2 m are x-left and x-right respectively. In the case of question 2 both x-left and x-right should be assigned interface boundary conditions under the boundary conditions tab as shown in Fig.3(a) and Fig.3(b) below. This can be done by double clicking the Boundary Conditions tab and then selecting the appropriate options. (a) Interface BC for x-left (b) Interlace BC for x-right Figure 3: Setting Interface boundary condition for the x-left and x-right Once both x-left and x-right have been assigned as interface boundaries then expand the Boundary Conditions tab on the left window in Fluent and then expand the Interface tab. Select both x-left and x-right while pressing the Ctrl button on the keyboard. Then right click and select Periodic as shown in Fig.4(a) below. A new window will appear as shown in Fig.4(b) where the Auto Compute Offset box needs to be unchecked and the value for Offset needs to be entered for X [m], which is 0.2m in this case. Once all the appropriate options have been selected then click the Create button. This will create a new boundary condition which will have the name as specified in the Zone name box as shown in Fig.5(a). Once the new zone has been created, select the new zone, and then click on the Periodic conditions button and a new window will appear as shown in Fig.5(b). Under the Pressure Gradient option specify the pressure gradient as -1 Pa/m, and this will specify the constant pressure drop condition Fig.5(b). Once all of these steps have been followed, you can continue for the rest of required settings and conducting your simulations. ‘ Page 6 MEC3028 - Semester 1 2024/25 Fluent Coursework (a) (b) Figure 4: Setting Interface boundary condition for the x-left and x-right (a) (b) Figure 5: Setting Interface boundary condition for the x-left and x-right Page 7 MEC3028 - Semester 1 2024/25 Fluent Coursework End of the coursework Good Luck Page 8 51作业君版权所有