June 2019 501H3 - Question Paper PDF

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Candidate Number501HTHE UNIVERSITY OF SUSSEXMSc and MEng ( year 4 ) EXAMINATION 2019 May/June 2019 (A2)COMPUTATIONAL FLUID DYNAMICSAssessment Period: May/June 2019 (A2)DO NOT TURN OVER UNTILINSTRUCTED TO BY THE LEADINVIGILATORCandidates must attempt THREE out of FOUR questionsDuration: 2 hoursIf all...

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Candidate Number

501H3

THE UNIVERSITY OF SUSSEX MSc and MEng (year 4) EXAMINATION 2019 May/June 2019 (A2)

COMPUTATIONAL FLUID DYNAMICS Assessment Period:

May/June 2019 (A2)

DO NOT TURN OVER UNTIL INSTRUCTED TO BY THE LEAD INVIGILATOR Candidates must attempt THREE out of FOUR questions Duration: 2 hours If all four questions are attempted, all will be marked, but the lowest mark will not be counted in the total for the paper. At the end of the examination the question paper and any answer books/answer sheets, used or unused, will be collected from you before you leave the examination room. Examination handout: None

501H3

1.

COMPUTATIONAL FLUID DYNAMICS

Below a 2-dimensional finite volume mesh is shown. The mesh is structured and equidistant. The flow variables (𝜌, 𝑢, 𝑣, 𝑝) are stored at the mid points of cells (𝑃, 𝑊, 𝐸, 𝑁, 𝑆). Derive the following terms for the cell with the midpoint P, using the flow variables at the at the mid points of cells

a. the total mass flux into the cell [5 marks] b. the total x-momentum flux due to convective transport (i.e. due to the bulk flow) into the cell [5 marks] c. total pressure force acting on the cell in x-direction [5 marks] d. accumulation of x-momentum in the cell [5 marks]

2. a. What difficulties would arise if a density-based CFD code is used to simulate a low Mach number flow field? [4 marks] b. Explain the differences between Reynolds Averaged Navier Stokes (RANS) simulations, Large Eddy simulations (LES) and Direct Numerical simulations (DNS). [6 marks] c. Derive the Poisson equation for pressure from the incompressible flow equations given below. 𝜕𝑢𝑗 =0 𝜕𝑥𝑗 𝜕𝜌𝑢𝑖 𝑢𝑗 𝜕𝜏𝑖𝑗 𝜕𝑝 𝜕𝑢𝑗 =− + − 𝜕𝑡 𝜕𝑥𝑖 𝜕𝑥𝑖 𝜕𝑥𝑗 [10 marks]

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501H3 3.

COMPUTATIONAL FLUID DYNAMICS The steady-state convection-diffusion equation for a 1-dimensional system is given as: 𝜕(𝜌𝑢𝜙) 𝜕𝜙 𝜕 = (𝜇 𝜕𝑥 ) 𝜕𝑥 𝜕𝑥 Answer the following questions to solve this equation numerically using the equi-distant mesh shown below:

a. Determine the discretised form of the convective term using 1st order Forward Differencing Scheme [5 marks] b. Discretize the diffusive term with 2nd order Central Differencing Scheme [5 marks] c. Show how to implement the Dirichlet boundary conditions: 𝜙 = 0 𝑎𝑡 𝑥 = 0 and 𝜙 = 1 𝑎𝑡 𝑥 = 1 [5 marks] d. Explain briefly how you can solve the obtained algebraic equation set. [5 marks]

4. a. Explain the “law of the wall” with the help of a figure. [7 marks] b. Explain how the law of the wall can be used to formulate “wall functions”. [5 marks] c. What are the advantages and disadvantages of wall functions? [8 marks]

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