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# Computational Fluid Dynamics – Turbulence Modelling – Averaging Methods

The methods of averaging are collectively called as ______________

a) Reynolds averaging

b) Boussinesq averaging

c) Kolmogorov averaging

d) Schmidt averaging

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Answer: aExplanation: The averaging techniques include time averaging, Spatial averaging and ensemble averaging. These are collectively called the methods of averaging. They are used to simplify the algebra without actually disturbing the accuracy much.

What are the methods of averaging used to?

a) To decompose the flow variable

b) To get the mean component of the flow variable

c) To get the remove the fluctuating component

d) To solve the flow variables

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Answer: bExplanation: By Reynolds decomposition, the flow variables are decomposed into mean and fluctuating components. These methods of averaging are used to get the mean component during this decomposition.

Which of these averaging methods is useful for any kind of turbulent flows?

a) Ensemble averaging

b) Time averaging

c) Volume averaging

d) Spatial averaging

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Answer: aExplanation: Ensemble averaging is a method used in statistical mechanics. Here, it is used as one of the methods of averaging. This is suitable for any type of turbulent flows including unsteady turbulent flows.

Which of these represent time averaging?

a) 1V∫VϕdV

b) limV→∞1V∫VϕdV

c) 1T∫t+Ttϕdt

d) limT→∞1T∫t+Ttϕdt

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Answer: d

Explanation: Time averaging represents the average of the flow variable based on a time interval ‘T’. It uses integration to sum up the flow variables at different times and then divides by the time interval limT→∞1T∫t+Ttϕdt.

The governing equations which are averaged using these methods of averaging are used in _____________

a) DNS model

b) SST model

c) RANS model

d) k-ε model

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Answer: cExplanation: The governing Navier-Stokes equation is averaged using the Reynolds averaging techniques and these averaged equations are used in the RANS method. This is the reason why the technique is named the Reynolds-Averaged Navier-Stokes equations method.

Time averaging method is useful for ____________

a) unsteady turbulent flows

b) steady turbulent flows

c) turbulent boundary layer flows

d) mixing flows

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Answer: bExplanation: Time averaging method is useful when we have to decompose the turbulent flow variables into mean and fluctuating components based on time. They are particularly applicable for steady turbulent flows.

Which of these represent spatial averaging?

a) 1V∑ϕ

b) limV→∞1V∫VϕdV

c) 1T∫TϕdT

d) 1N∫NϕdN

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Answer: b

Explanation: Spatial averaging represents the mean based on a particular space interval or volume. So, equation limV→∞1V∫VϕdV represents spatial averaging.

Ensemble averaging represents the average of ____________

a) unsteady quantities

b) steady quantities

c) identical quantities

d) mean quantities

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Answer: cExplanation: This is useful for identical quantities. Identical in the sense, that they have similar properties in some concern. A number of quantities which have the simultaneous variations can be averaged using this method.

Which of these represent ensemble averaging if ‘N’ represents the number of identical quantities?

a) 1N∫NϕdN

b) limN→∞1N∫NϕdN

c) 1N∑Ni=1ϕi

d) limN→∞1N∑Ni=1ϕi

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Answer: d

Explanation: Ensemble averaging is based on identical flow variables. It sums up the identical variables and then takes the average. The equation is limN→∞1N∑Ni=1ϕi.

Spatial averaging is suitable for ____________

a) homogeneous turbulent flows

b) unsteady turbulent flows

c) turbulent boundary layer flows

d) mixing flows

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Answer: aExplanation: Spatial averaging finds the average of a quantity based on a spatial interval or volume. It is suitable for homogeneous turbulent flows. In homogeneous flows, the properties are invariant under the arbitrary translation of the coordinate axes.