ME7724 - Computational Fluid Dynamics - Engineering Assignment Help

Assignment Task

Learning Outcomes
The following module learning outcomes and professional body learning outcomes are tested in this assessment:
(LO1) Define and analyse engineering fluid flow problems using the Navier Stokes equations. Simplify flow problems and solve them exactly. (SM1m, SM2m, G1)
(LO2) Construct appropriate solid models for CFD analysis, setup the solution domain and generate suitable surface and volume grids via meshing tool. (SM3m, SM5m)
(LO3) Understand both flow physics and mathematical properties of governing Navier- Stokes equations and define appropriate boundary conditions. (EA3m)

The aims of this individual assignment are two fold:
(1) to investigate the analytical solution derived from Navier-Stokes (NS) equations through simplification process
(2) to construct mesh over typical curved geometry models, reflecting known physical flow features of near wall viscous layer and run simple CFD simulations

Question 1

(1.a) The analytical solutions of laminar flow through a circular pipe (Figure Q1.a) can be derived by solving the simplified 3-D Navier-Stokes governing equations in cylindrical form (available from lecture notes or general literature. All references you use in your work should be provided in your submission in the Reference section to avoid plagiarism). In this task, you are required:
(1.a.i). To simplify the 3-D unsteady compressible Navier-Stokes equations to axisymmetric 2-D steady incompressible laminar flow equations. Ignore the effects of gravity. You should include all the key steps and provide reasons for the simplifications.

(1.a.ii.) From the simplified equations in Question1.a.i., derive the analytical solution of streamwise velocity profile u(r) using the appropriate boundary conditions. Derive also the equation for the volumetric flow rate Q and calculate it at given conditions (R=1m, µ=0.25 Pa.s, dp/dx= -1 Pa/m). Create the velocity plots in Excel and discuss and analyse the results in detail.

(1.b) Turbulence modelling remains one of the main challenges in CFD modelling and simulations. Questions in this section of the assignment are related to turbulence modelling. In your answers you could use the lecture notes and also literature materials. All references used in your work should be provided in your submission in the Reference section to avoid plagiarism.
(1.b.i). Discuss the main differences between the Reynolds Averaged Navier Stokes (RANS) turbulence approach and the Large Eddy Simulation (LES) turbulence approach. Provide some examples where RANS and LES would be suitable to use in the simulations.

(1.b.ii). Near wall treatment is important in CFD modelling because the flow features in near wall region are different from the freestream region far from the wall. Dimensionless velocity analysis from a wide variety of turbulent duct and boundary layer flows conclude the ‘Law of the wall’.

Question 2 

Use the available meshing tools in ANSYS to generate mesh and perform CFD calculations using ANSYS-CFX for the three-dimensional air flow over I.S.A.960 aerofoil (points coordinates file is provided on CANVAS) at the following given conditions:
Angle of attack: 0 degrees
Free stream flow velocity: chose any value between 20 m/s – 40 m/s
Free stream flow temperature: 20 °C
Chord length: 1 m
The generated unstructured mesh should reflect the key physical flow features, e.g. viscous boundary layer, rapid changes in flow field, etc. Also discuss and comment on mesh quality. To create the 3D slice of the aerofoil, extrude the 2D profile with 0.1 m depth. For this question you need to undertake the followings:
(a) Calculate the air flow Reynolds number (based on chord length), and Mach number and determine the flow status (laminar or turbulent, compressible or incompressible), select and justify the appropriate turbulence model (if required);
(b) Choose the right boundary layer thickness calculation formula; and estimate its value to be used in meshing procedure and demonstrate that inflation layers properly reflect the physical viscous layer

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