Engineering Questions with Answers - Multiple Choice Questions

Computational Fluid Dynamics – Turbulence Modelling – Boundary Conditions

1 - Question

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

View Answer

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.

2 - Question

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
View Answer Answer: b
Explanation: 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.

3 - Question

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
View Answer Answer: c
Explanation: 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.

4 - Question

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
View Answer Answer: d
Explanation: 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.

5 - Question

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
View Answer Answer: a
Explanation: 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.

6 - Question

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
View Answer Answer: b
Explanation: 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.

7 - Question

 Which of these equations give the turbulence intensity?
a) V⃗ .V⃗ ¯¯¯¯¯¯¯¯¯¯¯¯¯V⃗ .V⃗ 
b) V⃗ .V⃗ V⃗ .V⃗ ¯¯¯¯¯¯¯¯¯¯¯¯¯
c) V⃗ ¯¯¯¯¯¯V⃗ 
d) V⃗ V⃗ ¯¯¯¯¯¯

View Answer

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.

8 - Question

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 )

View Answer

Answer: b
Explanation: To find the turbulent kinetic energy k using the turbulence intensity value, the following formula is used.
k=12T2i(v⃗ .v⃗ )
v⃗ → Velocity vector.

9 - Question

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%
View Answer Answer: c
Explanation: 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.

10 - Question

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

View Answer

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
l → Turbulent length scale.
Cμ → A dimensionless constant.

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