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# Computational Fluid Dynamics – Turbulence Modelling – Boundary Conditions

If n is the spatial coordinate, in the outlet or symmetry boundaries, which of these following is correct for a k-ε model?

a) \frac{\partial k}{\partial n}=0; \frac{\partial\varepsilon}{\partial n}=0

b) \frac{\partial^2 k}{\partial n^2}=0; \frac{\partial\varepsilon}{\partial n}=0

c) \frac{\partial k}{\partial n}=0; \frac{\partial^2 \varepsilon}{\partial n^2}=0

d) \frac{\partial ^2 k}{\partial n^2}=0; \frac{\partial^2 \varepsilon}{\partial n^2}=0

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Answer: a

Explanation: In general, for any flow property, the gradients will be zero for the outlet or symmetry boundaries. In the same way, for a k-ε model, the gradients of the variables k and ε are zero. This is given by the equations \frac{\partial k}{\partial n}=0; \frac{\partial\varepsilon}{\partial n}=0.

Boundary conditions near the solid-walls for a k-ε model depends on ___________

a) Eddy viscosity

b) Reynolds number

c) ε-value

d) k-value

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Answer: bExplanation: The behaviour of the boundary conditions depends on the Reynolds number. Near the wall, the k-ε model does not perform well. So, wall functions are used. This again depends on the Reynolds number of the flow only.

Which of these values vanish near the wall boundary?

a) Velocity and turbulent viscosity

b) Velocity and Reynolds number

c) Velocity and k-value

d) k-value and Reynolds number

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Answer: cExplanation: Near the wall boundary, the velocity of the flow is reduced by the friction of the wall. So, velocity vanishes. The variable k stands for turbulent kinetic energy. As the kinetic energy depends on the velocity, when velocity vanishes, k also will vanish.

In the low Reynolds number turbulence models, the first internal grid point is placed in the ___________

a) log-law layer

b) buffer layer

c) inertial sub-layer

d) viscous sub-layer

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Answer: dExplanation: It is difficult to model the flow in the buffer layer. So, the low Reynolds number models place the first internal grid point in the viscous sub-layer and the high Reynolds number models place it in the inertial sub-layer skipping the buffer layer.

When k and ε values are not available, for inlet boundary conditions, they are ____________

a) obtained from turbulence intensity

b) assumed to be zero

c) assumed to be unity

d) obtained from Reynolds number

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Answer: aExplanation: At the inlet boundary conditions, the k and ε values must be specified for the k-ε model. In most of the industrial CFD applications, these values will not be known. So, they are obtained from the turbulence intensity and the characteristic length of the model.

Which of these is correct about the first internal node of a k-ε model?

a) k-equation is not solved

b) ε-equation is not solved

c) Both k and ε-equations are not solved

d) Both k and ε-equations are solved simultaneously

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Answer: bExplanation: In the k-ε model, the ε-equation is not solved at the first interior point near the wall. Instead, this value is obtained by the condition that the turbulent kinetic dissipation rate will be equal to its production rate.

Which of these equations give the turbulence intensity?

a) V⃗ ‘.V⃗ ‘¯¯¯¯¯¯¯¯¯¯¯¯¯√V⃗ .V⃗ √

b) V⃗ .V⃗ √V⃗ ‘.V⃗ ‘¯¯¯¯¯¯¯¯¯¯¯¯¯√

c) V⃗ ‘¯¯¯¯¯¯√V⃗ √

d) V⃗ √V⃗ ‘¯¯¯¯¯¯√

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Answer: a

Explanation: The turbulence intensity which is used to get the k and ε-values for the inlet boundary conditions is

Ti=V⃗ ‘.V⃗ ‘¯¯¯¯¯¯¯¯¯¯¯¯¯√V⃗ .V⃗ √ Where,

V⃗ → Velocity vector.

The relationship between the turbulence intensity Ti and the turbulence kinetic energy k is given by ___________

a) k=12Ti(v⃗ .v⃗ )

b) k=12T2i(v⃗ .v⃗ )

c) k=12T2i(v⃗ .v⃗ )

d) k=12Ti(v⃗ .v⃗ )

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Answer: b

Explanation: To find the turbulent kinetic energy k using the turbulence intensity value, the following formula is used.

k=12T2i(v⃗ .v⃗ )

Where,

v⃗ → Velocity vector.

The range of values of the turbulent kinetic energy is ___________

a) 50 to 75%

b) 11 to 20%

c) 1 to 10%

d) 0 to 1%

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Answer: cExplanation: The value of turbulence intensity lies between 1% and 10%. The values below 1% are considered to be very less and the values above 10% are considered to be a high one.

The formula to find ω from the k-value obtained using the turbulence intensity is ____________

a) ω=k3/2l2

b) ω=k3/2l

c) ω=k1/2l2

d) ω=k1/2l

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Answer: d

Explanation: The ε and the ω-values should be obtained from k-value in the k-ε and k-ω models. The formulae used to get these values are

ε=Cμk32l

ω=k12l

Where,

l → Turbulent length scale.

C_{μ} → A dimensionless constant.