Question

2. a) List the characteristics of turbulent flows and state why they are challenging to compute. [12 Marks b) The Navier-Stokes equations in two-dimensions for an incompressible fluid are given in part b) of Q1 above. When studying turbulent flows it is usual to time average these equations. Explain the process of time averaging and show which additional terms result from the time averaging process in two-dimensions for an incompressible fluid. 12 Marks c) When modelling turbulent flows the Navier-Stokes equations and the k-epsilon equations are connected via the turbulent viscosity. It is given that the turbulent viscosity and epsilon equations are: k 2 where C, 0.09 and p 1.226 kg/m. For a case where the value of the turbulent viscosity is 0.01m2 /s, the turbulent length scale is 4 cm and the free stream velocity is 10m/s calculate the turbulence intensity assuming the turbulence is isotropic. (12 Marks d) Sketch the log-law velocity profile of a turbulent boundary layer using appropriate scales in non-dimensional form and label the regions. (7 Marks] e) Give the range in terms of y+ values that it is suitable for the law-of-the-wall and state why it is useful for aerodynamic simulations. 7 Marks]

Answer 1

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