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# Computational Fluid Dynamics – Turbulence Modelling – RNG K Epsilon

1 - Question

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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Answer: aExplanation: 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 - Question

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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Answer: bExplanation: 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 - Question

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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Answer: cExplanation: 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 - Question

The effects of the small-scale turbulence are ____________

a) normalized

b) assumed

c) neglected

d) represented by random forcing functions

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Answer: dExplanation: 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 - Question

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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Answer: aExplanation: 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 - Question

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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Answer: bExplanation: 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 μt=ρCμk2ε.

7 - Question

What is the value of Cμ in the RNG k-ε model?

a) 0.0545

b) 0.0645

c) 0.0845

d) 0.0745

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Answer: cExplanation: The value of Cμ 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 - Question

div[αk μeff grad k] is the diffusion term in the transport equation of the turbulent kinetic energy. αk 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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Answer: dExplanation: The effect of small-scale turbulence is used while representing the diffusion of turbulent kinetic energy in its transport equation as αk. In a similar way, the transport equation for the rate of dissipation of the turbulent kinetic energy contains αε.

9 - Question

The Reynolds stress term used in the RNG k-ε model is given by 2μt Sij-2⁄3 ρkδij. What does the term δij represent?

a) Kronecker delta

b) Euler delta

c) Hermann delta

d) Cartesian delta

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Answer: aExplanation: The rate of dissipation of the turbulent kinetic energy in different directions are given by the equation εij = 2⁄3 ρδij. Here, the term δij is the Kronecker delta. This value becomes zero if i≠j. If i=j, it becomes 1.

10 - Question

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

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Answer: bExplanation: The terms mentioned in the question are αk and αε. 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.