Mechanical Engineering Question

Engineering

computational fluid dynamics cfd

University of New Hampshire

Question Description

I'm working on a mechanical engineering project and need a sample draft to help me study.

Hi, Please complete the posted assignment from Task 1 to Task 5. Task 1 to 4 needs to be done by hand and the simulation on Matlab, please send both the hand-written work and the code after you completed. Best if you can finish it by Tuesday, thank you very much.

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ME 709/809 Final [20 points] You will have 72 hours to complete this assignment. You will be simulating a 2D, fully developed channel flow using the k –  model. • TASK 1 [2 points]: Without using index notation, show the governing equations for a 2D, time averaged k –  model. – Show the time averaged continuity equation. – Show each of the components of the averaged Naveir-Stokes equations. Use the Boussinesq assumption as listed in section 6 of the notes. You can ignore the term in blue from the assumption. – Start from the modeled k and  equations (equations 11.97 and 11.98 in http://www.tfd.chalmers.se/~lada/postscript_files/solids-and-fluids_turbulent-flow_ turbulence-modelling.pdf) and show the modeled k and  equations for a 2D, timeaveraged flow. • TASK 2 [2 points]: Simplify the equations from TASK1 for a 2D fully developed channel flow. Clearly indicate what terms you are setting to 0 and why. Prove that the governing equations reduceh to: i ∂ ∂U + (ν + ν ) 0 = − ρ1 ∂P t ∂x ∂y ∂y ; 0= ∂ ∂y h ν+ νt σk  ∂k ∂y i + Pk − ;  i h ∂ ∂ 0 = ∂y ν + σνt ∂y + where   2 Pk = νt ∂U ; and ∂y  k (c1 Pk − c2 ); 2 νt = cµ k . • TASK 3 [5 points]: Discretize the equations using central difference and a non-equidistant mesh. Note that you need to keep k and  positive to avoid divergence of the solution. To achieve that, put all negative source terms in SP where S = SP ΦP + SU . For example, the dissipation term in the k equations should be in the SP and look similar to: SP = − k ∆y or SP = − k ∆V (depending on how you integrate the equations). • TASK 4 [3 points]: Write down the steps of the algorithm for solving this problem in Matlab. ∂ = 0. For the boundary conditions use U = k = ∂y 3 Use channel height of 2 m, ρ = 1 kg/m , uτ = 1 m/s and use − ∂P ∂x = τw . Use a Gauss-Seidel solver. • TASK 5 [8 points] Simulate this flow using Matlab. Plot the velocity profile. Please submit the following on Canvas under FINAL exam submission: – A pdf file containing the work for TASK 1, 2, 3, and 4; The plot from TASK 5, and a printout of the code from TASK 5. The work from TASKS 1 – 4 can be scanned papers, an exported one-note document or have any other form, as long as everything is legible and the submission is a single pdf file. – A zipped folder with all your work on the assignment, including the final .m file. 1 ...
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