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# Computational Fluid Dynamics – Turbulent Boundary Layer

For flows over a flat plate, at length scales near to the length of the flat plate, which of these is correct?

a) Inertial force is zero

b) Inertial force is large

c) Inertial force is equal to viscous force

d) Viscous force is large

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Answer: bExplanation: Reynolds number depends on the length scale taken for the calculation. At the length scales near to that of the length of the flat plate, the Reynolds number will be high. Therefore, the inertial forces will be large.

The mixing length model links _____________ with _____________

a) length scale with mean flow properties

b) velocity scale with mean flow properties

c) length scale with position coordinates

d) velocity scale with position coordinates

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Answer: bExplanation: The large eddies directly interact with the mean flow properties and extract energy from them. So, there is a strong connection between the mean flow properties and the behaviour of the large eddies. So, the velocity scale is linked with the mean flow properties.

If ν_{t} is the turbulent kinematic viscosity, l_{m} is the mixing length and U is the mean flow velocity in the x-direction, which of these gives the Prandtl mixing length model equation?

a) νt=l2m∣∣∂U∂x∣∣

b) νt=l2m∣∣∂U∂y∣∣

c) νt=lm∣∣∂U∂y∣∣

d) νt=l2m∣∣∂U∂x∣∣

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Answer: b

Explanation: Prandtl mixing length model is an attempt to give the transport of momentum in terms of Reynolds stresses. νt=l2m∣∣∂U∂y∣∣ gives the Prandtl mixing length model.

The value of mixing length depends on ____________

a) small eddies

b) large eddies

c) turbulence

d) time scales

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Answer: cExplanation: The mixing length model defines the Reynolds stresses in terms of velocity gradients, mixing length and density of the fluid. Turbulence is a function of the flow. So, if the turbulence changes, the Reynolds stresses should change. This change is accounted by changing the mixing length.

For a 2-D flow, what is the mixing length of the mixing layer turbulence model?

a) 0.1 of layer width

b) 0.09 of layer width

c) 0.08 of layer width

d) 0.07 of layer width

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Answer: d

Explanation: Mixing length varies for different turbulent flows. For free turbulent flow of the mixing layer type, the mixing length is 0.07 times of the layer width. Mixing layer turbulent flow occurs due to the interaction of two flows with various velocities.

The fluid layer which is in contact with a smooth wall is called ____________

a) Inviscid layer

b) Linear sub-layer

c) Log-law layer

d) Wake-law layer

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Answer: bExplanation: In the fluid layer which is in contact with a smooth wall, the value of dimensionless velocity and dimensionless cross-stream distance tend to be the same. Because of this linear relationship, the layer is named linear sub-layer.

What is the range of y+ in the viscous sub-layer?

a) 0<y+<20

b) 0<y+<5

c) 0<y+<10

d) 0<y+<15

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Answer: bExplanation: This is the layer which is in immediate contact with the smooth wall. It obeys Newton’s law of viscosity. The shear stress in this layer is constant and approximately equal to that of the wall. It extends from the wall till y+ reaches 5.

The layer with viscous and turbulent stresses in equal magnitude is called _____________

a) Viscous sub-layer

b) Log-law layer

c) Buffer layer

d) Velocity-defect layer

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Answer: cExplanation: The layer above the linear sub-layer has equally important turbulent and viscous stresses. Neither of these is dominating nor inconsiderable. A layer in this area where both the viscous and turbulent stresses are of equal magnitude is called the buffer layer.

What is the other name of the velocity-defect law?

a) Linear law

b) Log law

c) Law of the wall

d) Law of the wake

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Answer: dExplanation: Velocity defect law is applicable to the layer far away from the wall. This layer has less viscous effects and inertia forces are dominating here. The velocity-defect law is otherwise called the law of the wake.

What is the range of y+ in the log-law layer?

a) 30<y+<500

b) 20<y+<500

c) 30<y+<400

d) 20<y+<400

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Answer: aExplanation: The log-law layer extends outside the viscous or linear sub-layer. Here, both viscous and turbulent effects are important. It ranges between 30<y+<500. It is called log-law layer because of the logarithmic relationship between u+ and y+.