ME4438 Computational Fluid Dynamics End of Semester Exam Paper 2019-20 QUESTION 4. (30 marks total) 4(a),...

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ME4438 Computational Fluid Dynamics End of Semester Exam Paper 2019-20 QUESTION 4. (30 marks total) 4(a), (8 marks) Briefly explain, within the context of a turbulent flow, what is meant by; A turbulent eddy; A length scale; A frequency: The energy cascade. 4(b). (6 marks) The transient 3D, laminar flow Navier-Stokes equation in the x-direction is given by 8( 2 + (puv) = - +V (\u) at ax Page 5 of 5 Describe how the technique known as direct numerical simulation goes about solving this equation for a turbulent flow. 4(c). (12 marks) The x-momentum equation for ID (in the x-direction), transient, incompressible flow is given by (pu) (puu) dp a'u dx ax di dx Use the technique known as Reynolds decomposition and time averaging to formulate a version of the above equation which is applicable to a turbulent flow. Clearly indicate which terms in the time averaged version are called the Reynolds stresses. 4(d), (4 marks) The eddy viscosity can be written in the following form; , =cpV, where c, is a constant, V, is the velocity associated with the eddy movement around the flow field, and I, is the distance travelled by an eddy before it dissipates its energy in another part of the flow field. Starting from the equation given for ,, and using an order of magnitude analysis, show that the eddy viscosity can be expressed in terms of the eddy kinetic energyk, and the viscous dissipation rate &. ME4438 Computational Fluid Dynamics End of Semester Exam Paper 2019-20 QUESTION 4. (30 marks total) 4(a), (8 marks) Briefly explain, within the context of a turbulent flow, what is meant by; A turbulent eddy; A length scale; A frequency: The energy cascade. 4(b). (6 marks) The transient 3D, laminar flow Navier-Stokes equation in the x-direction is given by 8( 2 + (puv) = - +V (\u) at ax Page 5 of 5 Describe how the technique known as direct numerical simulation goes about solving this equation for a turbulent flow. 4(c). (12 marks) The x-momentum equation for ID (in the x-direction), transient, incompressible flow is given by (pu) (puu) dp a'u dx ax di dx Use the technique known as Reynolds decomposition and time averaging to formulate a version of the above equation which is applicable to a turbulent flow. Clearly indicate which terms in the time averaged version are called the Reynolds stresses. 4(d), (4 marks) The eddy viscosity can be written in the following form; , =cpV, where c, is a constant, V, is the velocity associated with the eddy movement around the flow field, and I, is the distance travelled by an eddy before it dissipates its energy in another part of the flow field. Starting from the equation given for ,, and using an order of magnitude analysis, show that the eddy viscosity can be expressed in terms of the eddy kinetic energyk, and the viscous dissipation rate &.