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# Computational Fluid Dynamics – Mixing Length Turbulence Model

The mixing length model defines the turbulence dynamic viscosity as a function of ____________

a) position

b) mean flow properties

c) fluctuating components

d) velocities

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Answer: aExplanation: The mixing length model is a variation of the RANS model. It does not need any additional transport equations. It describes the stresses in terms of a simple algebraic formula for the turbulent dynamic viscosity as a function of position.

The mixing length model links _____________ with _____________

a) length scale with mean flow properties

b) velocity scale with mean flow properties

c) length scale with position coordinates

d) velocity scale with position coordinates

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Answer: bExplanation: The large eddies directly interact with the mean flow properties and extract energy from them. So, there is a strong connection between the mean flow properties and the behaviour of the large eddies. So, the velocity scale is linked with the mean flow properties.

If ν_{t} is the turbulent kinematic viscosity, l_{m} is the mixing length and U is the mean flow velocity in the x-direction, which of these gives the Prandtl mixing length model equation?

a) νt=l2m∣∣∂U∂x∣∣

b) νt=l2m∣∣∂U∂y∣∣

c) νt=lm∣∣∂U∂y∣∣

d) νt=l2m∣∣∂U∂x∣∣

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Answer: b

Explanation: Prandtl mixing length model is an attempt to give the transport of momentum in terms of Reynolds stresses. νt=l2m∣∣∂U∂y∣∣ gives the Prandtl mixing length model.

The value of mixing length depends on ____________

a) small eddies

b) large eddies

c) turbulence

d) time scales

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Answer: cExplanation: The mixing length model defines the Reynolds stresses in terms of velocity gradients, mixing length and density of the fluid. Turbulence is a function of the flow. So, if the turbulence changes, the Reynolds stresses should change. This change is accounted by changing the mixing length.

For a 2-D flow, what is the mixing length of the mixing layer turbulence model?

a) 0.1 of layer width

b) 0.09 of layer width

c) 0.08 of layer width

d) 0.07 of layer width

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Answer: dExplanation: Mixing length varies for different turbulent flows. For free turbulent flow of the mixing layer type, the mixing length is 0.07 times of the layer width. Mixing layer turbulent flow occurs due to the interaction of two flows with various velocities.

What is the mixing length for the outer layer of a 2-D turbulent boundary layer?

a) 0.09 times the boundary layer thickness

b) 0.08 times the boundary layer thickness

c) 0.07 times the boundary layer thickness

d) 0.06 times the boundary layer thickness

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Answer: aExplanation: For a turbulent boundary layer problem, the mixing length varies for different layers of the flow. For the 2-D case, the mixing length of the outer boundary layer is 0.09 times the boundary layer thickness.

The mixing length model can be used to get the turbulent scalar fluxes also using _____________

a) turbulent Prandtl/Reynolds number

b) turbulent Reynolds/ Schmidt number

c) turbulent Prandtl/Schmidt number

d) turbulent Reynolds/Nusselt number

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Answer: cExplanation: Mixing length model uses the turbulent viscosity coefficients. If a relationship can be established between the turbulent viscosity and turbulent diffusivity, the model can be used for turbulent scalar fluxes. This relationship is established by the Turbulent Prandtl/Schmidt number.

Mixing length model cannot be used for _____________

a) turbulent jets

b) turbulent mixing layers

c) turbulent wakes

d) turbulent flows with separation

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Answer: dExplanation: Mixing length model is ideal for predictions of thin turbulent shear flows such as turbulent jets, wakes, boundary layers and mixing lengths. But, they will not be able to predict flows with separation or even recirculation.

Consider a turbulent flow of viscosity μ_{t}, diffusivity Γ_{t} and Prandtl/Schmidt number σ_{t}. Let Φ be a flow property which can be decomposed into Φ=Φ+Φ’. What is the turbulent scalar flux given by?

a) –ρu’Φ’=Γ_{t}∂Φ∂x

b) –ρu’Φ’=Γ_{t}∂Φ∂x

c) –ρu’Φ’=μ_{t}∂Φ∂x

d) –ρu’Φ’=μ_{t}∂Φ∂x

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Answer: a

Explanation: By using the mixing length model, the scalar flux can be given by the mean flow property Φ. Since the equation is in general for a flow property, the general term diffusivity only can be given and not the viscosity. So, the relationship is given by –ρu’Φ’=Γ_{t}∂Φ∂x.

The mixing length for a 2-D turbulent boundary layer depends on ____________

a) the distance from the wall and the boundary layer thickness

b) the distance from the wall and von Karman’s constant and dimensionless distance

c) von Karman’s constant

d) the boundary layer thickness

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Answer: bExplanation: The mixing length for a 2-D turbulent boundary layer is given by κy[1-exp(y+/26)]. Where, κ is the von Karman’s constant which is equal to 0.41. y is the distance from the wall. y+ is the dimensionless distance.