This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Turbulence Modelling – RNG K Epsilon”.

1. The RNG k-ε model comes under which of these types of the turbulence models?

a) Two-equation model

b) One-equation model

c) Algebraic model

d) Second-order closure models

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Explanation: The RNG k-ε model is a variation of the k-ε model. So, the RNG k-ε model also has two extra transport equations like the k-ε model. It comes under the two-equation turbulence models.

2. What does the abbreviation RNG in the RNG k-ε model stand for?

a) Random number generator

b) Renormalization group

c) Renormalization generator

d) Random number group

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Explanation: The RNG in the RNG k-ε model means renormalization group. This method was invented by Yakhot and Orszag of Princeton University. This is invented to overcome the disadvantages of the k-ε model.

3. The RNG k-ε model makes assumptions for ___________

a) dynamic eddy viscosity

b) kinematic eddy viscosity

c) small-scale turbulence

d) large-scale turbulence

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Explanation: The statistical mechanics approach has led to new mathematical formalizations. A limited number of assumptions regarding the statistics of small scale turbulence is made in this RNG k-ε model.

4. The effects of the small-scale turbulence are ____________

a) normalized

b) assumed

c) neglected

d) represented by random forcing functions

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Explanation: In the Navier-Stokes equations, the effects of small-scale turbulence are replaced by random forcing functions in the RNG k-ε model. In the Large Eddy Simulation method, these are neglected.

5. The effective dynamic eddy viscosity is ___________

a) the addition of molecular dynamic viscosity and dynamic eddy viscosity

b) the ratio of molecular dynamic viscosity and dynamic eddy viscosity

c) the product of molecular dynamic viscosity and dynamic eddy viscosity

d) molecular dynamic viscosity to the power of dynamic eddy viscosity

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Explanation: The small scales of motion in the governing equations are replaced by the larger scale motions and modified viscosity. This modified effective viscosity is the addition of molecular dynamic viscosity and dynamic eddy viscosity.

6. The dynamic eddy viscosity used in the RNG k-ε model is ____________

a) half of the that of the k-ε model

b) the same as that of the k-ε model

c) twice that of the k-ε model

d) thrice that of the k-ε model

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Explanation: The dynamic eddy viscosity used in the RNG k-ε model is the same as that of the k-ε model. The equation used is

μ

_{t}=ρC

_{μ}\(\frac{k^2}{\varepsilon}\).

7. What is the value of C_{μ} in the RNG k-ε model?

a) 0.0545

b) 0.0645

c) 0.0845

d) 0.0745

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Explanation: The value of C

_{μ}is 0.0845. This is useful in finding the turbulent dynamic viscosity and hence the effective dynamic viscosity of the RNG k-ε model. This value is obtained by comparing to the existing turbulence model data.

8. div[α_{k}μ_{eff}grad k] is the diffusion term in the transport equation of the turbulent kinetic energy. α_{k} represents ____________

a) effects of internal thermal energy

b) effects of turbulent kinetic energy

c) effects of large-scale turbulence

d) effects of small-scale turbulence

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Explanation: The effect of small-scale turbulence is used while representing the diffusion of turbulent kinetic energy in its transport equation as α

_{k}. In a similar way, the transport equation for the rate of dissipation of the turbulent kinetic energy contains α

_{ε}.

9. The Reynolds stress term used in the RNG k-ε model is given by 2μ_{t} S_{ij}-2⁄3 ρkδ_{ij}. What does the term δ_{ij} represent?

a) Kronecker delta

b) Euler delta

c) Hermann delta

d) Cartesian delta

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Explanation: The rate of dissipation of the turbulent kinetic energy in different directions are given by the equation ε

_{ij}=

^{2}⁄

_{3}ρδ

_{ij}. Here, the term δ

_{ij}is the Kronecker delta. This value becomes zero if i≠j. If i=j, it becomes 1.

10. The term representing the effect of small-scale eddies in diffusion terms of the k transport equation and ε transport equations take the values ___________ and ____________

a) 1.49, 1.49

b) 1.39, 1.39

c) 1.39, 1.49

d) 1.49, 1.39

View Answer

Explanation: The terms mentioned in the question are α

_{k}and α

_{ε}. These terms take the same value for the RNG k-ε model. The values are 1.39 both. These are obtained from the experimental data.

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