HW3_Solution(2)

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Dec 6, 2023

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Homework 3: ANSYS Tube Banks In this assignment you will compare empirical relations for calculating heat transfer from tube banks against solutions using ANSYS Fluent. The tube bank has the following relevant dimensions and configuration: Inlet conditions are u = 3 m/s, and T i = 290 K with air as the fluid. The tube surface temperature is held constant at 350 K. 1 Pre-analysis Mathematical model The actual mathematical model used by ANSYS Fluent to solve the given problem is not something we’ve covered in detail because it is very difficult/not possible to solve by hand and thus we’ve focused on empirical correlations. It is still good practice to identify the mathematical model, including boundary conditions and assumptions, since that will inform your interpretation of results. The equations solved are called the Reynolds Averaged Navier-Stokes (RANS) equations, including the energy equation, with the k-omega SST turbulence model and the intermittency transition model. Assumptions include steady state, 2D planar geometry with an infinite (i.e., very large) number of tubes in each row (remembering rows are normal to the incoming fluid direction), and that air properties are constant with the following values: Density ( ρ ) 1.225 kg/m 3 Specific Heat ( c P ) 1006.43 J/kg-K Thermal Conductivity ( k ) 0.0242 W/m-K Dynamic Viscosity ( µ ) 1 . 7894 × 10 5 kg/m-s The boundary conditions are: uniform velocity inlet at 3 m/s, inlet temperature of 290 K, pressure outlet at 0 gauge, constant pipe surface temperatures at 350 K. Symmetric boundary conditions on the top and bottom surfaces allow us to approximate an infinite number of tubes in each row. Hand Calculations 1. What is the Reynolds Number for this tube bank? 2. Select the appropriate Nusselt Number correlation from Table 7-2 and 7-3 in your text. Write down which correlation you choose and how many rows the current tube bank has. 3. Calculate the Nusselt Number (please use the same (constant) air properties as defined in the Mathe- matical Model) and average convective heat transfer coefficient. 4. What is the outlet (a.k.a. exit) temperature of the fluid from the tube bank? 1
5. What is the total rate of heat transfer for the given tube bank? You should calculate your heat transfer rate for the same geometry as given in the ANSYS Fluent mesh, i.e. your surface area will be for a single tube per row and to get the true overall rate of heat transfer you would need to multiple your answer by however many tubes per row you actually had in the real system. Geometry, Mesh, Mathematical model setup, Numerical solution A mesh file is provided to you. You will need to import this mesh file by creating a new Fluent project in workbench, and then importing the mesh. After importing the mesh, double-click on Setup to load Fluent (accept the default launch parameters), and then follow the directions in the following YouTube video link to set up and solve the given problem in ANSYS Fluent: https://www.youtube.com/watch?v=ebiIkOdZtHU . The video was recorded using an older version of ANSYS Fluent and the intermittency model options have changed from a check box to a drop- down menu. Select the gamma-transport-eqn model from the drop down, and make sure that Production Kato-Launder is checked if it isn’t automatically selected. 2
2 Post-processing 1. Create contour plots of the temperature and velocity (2 different plots) in the fluid both using the cyan-yellow color map. 2. What is the mass-weighted average fluid temperature at the outlet in the simulation? 3. What is the total rate of heat transfer summed over all rows in the tube bundle. 4. Using the total rate of heat transfer and temperatures from the ANSYS simulation it is possible to reverse out an average convective heat transfer coefficient and Nusselt Number. What are the average convective heat transfer coefficient and Nusselt Number based on the ANSYS predicted temperatures and overall rate of heat transfer? 3 V&V 1. The original source for the correlations listed in the textbook gives their accuracy as ± 15%. Using the values derived from the correlation as the baseline values, are the Nusselt Numbers calculated with the correlation and the CFD results consistent to within the stated correlation accuracy (i.e. is their relative difference less than ± 15%)? 2. List 2 changes to the mathematical model you would make to improve the accuracy of the CFD simulations and explain why you think they would improve the simulation accuracy. 3
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