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# Computational Fluid Dynamics – Turbulence Modelling – Shear Stress Transport Model

1 - Question

The Shear Stress Transport model is a hybrid of _________

a) the standard k-ε model and the k-ω model

b) the standard k-ε model and the RNG k-ε model

c) the realizable k-ε model and the RNG k-ε model

d) the realizable k-ε model and the k-ω model

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Answer: aExplanation: For boundary layers with adverse pressure gradients, the standard k-ε model does not perform well. To overcome this problem, the other models were devised. But, those are sensitive to the arbitrary constants used. So, the Shear Stress Transport model combines the standard k-ε model and the k-ω model to get the advantages of both.

2 - Question

Which of these is unmodified for the Shear Stress Transport model and the k-ω model?

a) Reynolds stress calculation and the k-equation

b) Reynolds stress calculation and the ε-equation

c) The k-equation and the ε-equation

d) Reynolds stress calculation, the k-equation and the ε-equation

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Answer: aExplanation: For a Shear Stress Transport model, the k-equation and the calculation of the Reynolds stresses are the same as used in the standard k-ω model. The equation for the transport of ε is transformed into the ω-equation by using the relationship ε=kω.

3 - Question

Which of these statements holds true regarding the Shear Stress Transport model?

a) In the near-wall region, the k-ε model is transformed into k-ω model

b) In the near-wall region, the standard k-ε model is used

c) In regions far from the wall, the k-ε model is transformed into k-ω model

d) In regions far from the wall, the k-ω model is used

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Answer: aExplanation: The Shear Stress Transport model uses a transformation of the k-ε model into a k-ω model in the near-wall region. In the region far from the wall, it uses the standard k-ε model as it gives satisfactory results there.

4 - Question

When compared to the standard ε-equation, the transformed ω-equation has _________

a) the same number of terms

b) an extra dissipation term

c) two extra source terms

d) an extra source term

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Answer: dExplanation: While transforming the ε-equation into the ω-equation, an extra source term arises. It is called the cross-diffusion term. This cross diffusion term is modified using external blending functions.

5 - Question

The σk value used in the Shear Stress Transport model is ________

a) -1

b) 1

c) 2

d) -2

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Answer: bExplanation: The constants used in the Shear Stress Transport model are revised to optimize the performance. The σk value used for the k-equation is 1. The σω1 value used for the ω-equation of the near-wall region is 2. The σω2 value used for the ω-equation of the far region is 1.17.

6 - Question

Which of these problems may occur because of the hybrid nature of the Shear Stress Transport model?

a) Non-linearity

b) Inconsistency

c) Numerical instability

d) Inaccuracy

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Answer: cExplanation: As the modelling equations vary from the converted k-ω model in the near-wall region to the standard k-ω model in the far away region, numerical instabilities may arise in the computed eddy viscosities.

7 - Question

The blending function used in the Shear Stress Transport model is a function of _____________

a) Turbulent kinematic viscosity, the ratio of turbulence and distance from the wall

b) Turbulence Reynolds number, turbulent kinematic viscosity and distance from the wall

c) Turbulence Reynolds number, the ratio of turbulence and turbulent kinematic viscosity

d) Turbulence Reynolds number, the ratio of turbulence and distance from the wall

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Answer: dExplanation: The blending function is a function of lt/y and Rey. Where, lt→ Ratio of turbulence. y→ Distance from the wall. Rey→ Reynolds number based on the y-distance.

8 - Question

The blending function is __________ at the wall and __________ in the far field.

a) 0,→1

b) 0,→∞

c) 1,0

d) 1,∞

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Answer: aExplanation: The blending function is chosen in a way that it becomes zero at the wall and tends to unity in the far-field region. Also, it should produce a smooth transition around a distance halfway between the boundary layer’s edge and the wall.

9 - Question

A limiter is imposed on _________ to improve the performance in adverse pressure gradients and wake regions.

a) the Reynolds number

b) the eddy viscosity

c) the k-value

d) the ε-value

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Answer: bExplanation: There are two limiters used in the Shear Stress Transport model. One of these is on the eddy viscosity. This is done to improve the performance of the model when there are adverse pressure gradients or with wakes. These are the places where the k-ε model fails.

10 - Question

The turbulent kinetic energy production is limited to prevent the build-up of turbulence in __________ regions.

a) far-field

b) near-wall

c) stagnation

d) trailing

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Answer: cExplanation: In the stagnation region, the velocities will be zero. So, there is no possibility of turbulence there. The model should be limited to prevent unrealistic turbulence in the stagnation region.