Flow and Heat Transfer in a Mixing Elbow

Transcription

1 Flow and Heat Transfer in a Mixing Elbow Objectives The main objectives of the project are to learn (i) how to set up and perform flow simulations with heat transfer and mixing, (ii) post-processing and interpretation of the numerical solutions, (iii) creation of flow geometry and meshing, (iv) grid refinement and grid convergence. For this purpose, we will study fluid flow and heat transfer in a mixing elbow taken from ANSYS- FLUENT tutorial. The original problem is 3D but we will perform simulations only for a 2D (planar) case for simplicity. Problem description The flow to be simulated is shown schematically in Figure 1. The problem is to predict the flow and temperature fields in a mixing elbow". This is a common pipe structure used in process plants and process industries, where fluids of different temperatures and velocities are mixed. The aim is to compute the temperature and velocity profiles at the outflow part of the upper right corner. As seen in Fig. 1, a cold fluid at K (20 o C) flows into the pipe through a large inlet and mixes with a warmer fluid at K (40 o C) that enters through a smaller inlet located at the elbow. The mixing elbow configuration is encountered in piping systems in power plants and process industries. For simplicity, here we consider only a two-dimensional planar geometry instead of the actual three-dimensional pipes. It is often important to predict the flow field and temperature field in the area of the mixing region in order to properly design the junction. Figure 1: Flow geometry and boundary conditions for Task 1.

2 Your Tasks: You have two tasks labeled as Task 1 and Task 2. Task 1 is required and will be performed by everybody. Task 2 is optional and you will get bonus for it. I strongly recommend you do both Task 1 and Task 2. We assume that flow is incompressible. Task 1: In this part, you need to import the geometry and mesh directly from OpenFOAM tutorial repository. The main job is to include heat transfer, i.e., solve energy conservation equation together with the mass and momentum conservation (Navier-Stokes) equations. For this purpose, do the following steps. 1. Go to OpenFOAM tutorial folder and find the example: /incompressible/icofoam/elbow. In this example, geometry and mesh (unstructured) are created in ANSYS-Fluent and then imported to OpenFOAM. You can use the "fluentmeshtofoam elbow.msh" command instead of "blockmesh" in order to create the geometry and mesh. Use the default geometric dimensions and boundary conditions, for which the flow is fully laminar. Since it is fully laminar flow, you can use "icofoam" solver to solve the flow field as discussed in tutorial sessions. The geometry and mesh are shown in Fig Modify icofoam solver such that the energy conservation equation is also solved to determine the temperature field. You can refer to the manual. Solve the "elbow" problem using the OpenFOAM solver with the default "elbow" initial and boundary conditions for pressure, velocity and temperature fields. Velocity BC: Large inlet: A uniform velocity at 1 m/s Small inlet: A uniform velocity at 3 m/s (except for Step 4 for which you need to use different values). Outlet: The zero-gradient boundary condition is applied for velocity. Pressure BC: Large and small inlets: The zero-gradient boundary condition is applied for pressure. Outlet: Pressure is constant at the exit. Since flow is incompressible, exact value of the pressure at the exit is not important and you can simply set it to zero. Temperature BC: Wall_4 and Wall_8 (lateral surfaces): Zero-gradient. Velocity_inlet_5 (large inlet): 290 K Velocity _inlet_6 (small inlet): 310 K Pressure_outlet_7 (outlet): Zero-gradient 3. Post process and visualize the flow and temperature fields: After you solve the problem with the modified solver, the temperature field should look something like that shown in Fig Repeat simulations for larger velocity in the smaller inlet, i.e., repeat simulations for v = 2 m/s, v = 4 m/s and v = 6 m/s while keeping the velocity in the larger inlet the same. For this, you need to modify velocity BCs for the small inlet. Compare results for all three cases and discuss about effects of jet velocity on mixing.

3 Figure 2: The channel geometry and unstructured computational grid as imported from the repository /incompressible/icofoam/elbow. Figure 3: Typical temperature distribution obtained from the simulation. As you can see, a cool and a hot flow enter from two different inlets, get mixed and then exit from the outlet. In this problem, the inlet flows have constant temperature and the walls are considered to be adiabatic.

4 Task 2 (Optional with 50% bonus): This part is optional but you are strongly recommended to do it. You can get 50% more points when you complete Task 2 properly. The main task is to create the computational geometry, generate a structured computational grid, perform grid refinement and perform simulations for the laminar flow case. Specifically, perform the following steps: 1. Consider the flow shown in Fig. 4. For this case, create the geometry and generate a structured mesh using the blockmesh utility. For this step, among many such tutorial that are available online, you are recommended to watch the tutorial posted on YouTube : 2. Generate at least two sets of computational grids: (i) The first one must contain as many grid cells as the unstructured grid you used in Task 1. (ii) The second grid must be at least twice as fine as the first one, i.e., it must contain at least 4 times more grid points than the first grid. 3. Perform simulations for three jet velocities in the small inlet, i.e., for v = 0.8 m/s, v = 1.6 m/s and v = 2.4 m/s. 4. Discuss about the effects of grid refinement on solution quality. 5. Discuss about the effects of jet velocity on mixing. 6. Compare your results with the results of Task1. Figure 4: Flow geometry and boundary conditions for Task 2. Format of the Report Your report should contain the following sections: 1. Introduction: This section contains a general introduction to the project addressing questions such as what is the problem you studied?, why is this problem important,

5 what are the previous studies if there is any, which tools are used? and what have you done in your work?. You can also give an outline of your report in the last paragraph. 2. Description of the physical problem: In this section, describe the physical problem that you have studied (some sketches might help), the initial and boundary conditions, material properties, etc. Discuss the mathematical model (equations), numerical method and also the software you use. 3. Results and Discussions: This section is the most important part of your report. In this section, report your findings and discuss about them. You may organize this section as follows: a. Describe the computational domain and present a sample grid used in computations including a close-up view. b. Show some qualitative results such as contour plots for the temperature and pressure fields, vector plots of the velocity fields for selected cases, and interpret the results. You may also include blown out plots showing important regions such as the vicinity of the smaller inlet where mixing occurs. c. Show some quantitative results such as velocity and temperature profiles in selected cross-sections, particularly between the smaller inlet and exit sections. d. Discuss about the effects of jet velocity on mixing. e. Discuss about the effects of grid refinement on quality of computational results. Is grid convergence achieved? What is the grid needed to achieve grid convergence? f. Compare your results with the results you obtained for Task1. You can use temperature and velocity fields for this purpose and the grid size you determine in part e. g. Anything that you think it is interesting to report. Deadline: 5:00pm, Friday, December 29, 2017