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# MCQs on Turbulence Modelling

How does the turbulent boundary layer vary with respect to the Reynolds number?

a) Rex–15

b) Rex–14

c) Rex–12

d) Rex-2

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a

Explanation: The turbulent boundary layer thickness in an incompressible flow is given by:

δ = 0.37xRe−1/5x

Thus the turbulent boundary layer thickness varies as Rex-1/5 whereas in case of laminar flow, it varies as Rex-1/4.

What is the skin friction drag for an incompressible turbulent flow with Reynolds number = 1.5 × 107 over a flat plate?

a) 2.72 × 10-3

b) 5.41 × 10-3

c) 3.82 × 10-3

d) 2.91 × 10-3

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a

Explanation: Given, Rec = 1.5 × 107

The skin friction drag over a flat plate for an incompressible turbulent flow is given by:

Cf = 0.074Re1/5c

Substituting the values,

Cf = 0.0741.5×1071/5=0.07427.24 = 2.72 × 10-3

Turbulent boundary layer is considered to be a combination of inner and outer layer.

a) True

b) False

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a

Explanation: Turbulent boundary layer consists of inner and outer layers. There is a viscous – dependent part of the profile very close to the surface and different length scaling parameters are needed for the remaining Reynolds – stress – dependent part of the profile.

Why are turbulence models used?

a) Define reynolds stress for closure problems

b) Model hypersonic flows

c) Lack of system to accurately find turbulent flow characteristic

d) Closure of continuity equation

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a

Explanation: While solving Navier’s Stokes equation for turbulent flow which governs the velocity, pressure of the fluid, the quantity is decomposed into mean and fluctuating components. While solving these using RANS equation, we get a reynolds stress term that needs to be closed in order to solve it. Hence we make use of turbulence modeling which defines these reynolds stresses in terms of the known averaged quantities.

What are the shortcomings of DNS?

a) Possible for low Reynolds number

b) Low scale resolution

c) Time consuming

d) Possible for high Reynolds number

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a

Explanation: The DNS solves the time – dependent Navier’s Stokes equation by resolving eddies of all scales for a sufficient time before reaching statistical equilibrium. The only shortcoming is that DNS is only applicable for low Reynolds number flow which has simple geometry.

Which of these models compute large vortexes directly while neglecting small scale eddies?

a) DNS

b) LES

c) RANS

d) FANS

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b

Explanation: In Large Eddy simulation, large eddies are computed by resolving large time and length scales. In LES, the smaller length scales are ignored making it an economical and less time consuming than DNS.

One equation turbulence model account for the history effects such as turbulent energy, diffusion and convection.

a) True

b) False

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b

Explanation: One equation turbulence model only solves one turbulent transport equation mostly the kinetic energy. It is the two equation turbulent model that accounts for the history effects such as turbulent energy, diffusion and convection.

Which of these is a two – equation model?

a) Baldwin – Lomax model

b) Prandtl’s equation model

c) Spalart – Allmaras model

d) K – Epsilon model

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d

Explanation: K – epsilon model is a two – equation model which includes two transport equations representing the turbulent flow properties. The first transport equation is solved is the turbulent kinetic energy, and the second one is the turbulent dissipation rate.

Which of these models solves turbulent kinetic energy and specific dissipation?

a) K – omega model

b) K – epsilon model

c) RANS model

d) RNG – LES model

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a

Explanation: K – omega is one of the popular turbulence model. It is a two-equation model which solves two transport equations – turbulent kinetic energy and specific dissipation. Turbulent kinetic energy determines the energy whereas the specific dissipation determines the turbulence scale.

Which of these models is a hybrid of LES and RANS?

a) DNS model

b) DES model

c) WALE model

d) RNG – LES model

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b

Explanation: DES model is a hybrid of LES and RANS model and makes use of advantages of both. For treating near – wall regions, DES works like the RANS model and for rest of the region, it works as the LES model.