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# Computational Fluid Dynamics – Turbulence Modelling – Concept of Y +

The value y+ is important only when we deal with ___________

a) turbulent boundary layers

b) turbulent jets

c) free turbulent mixing layers

d) turbulent wakes

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Answer: aExplanation: The value of y+ depends on the distance from the wall. So, the concept of y+ is also valid only when we solve turbulent boundary layer problems. The turbulent boundary layer has different sub-layers based on this y+ value.

The value of y+ is used while finding ___________

a) eddy kinematic viscosity for the turbulent boundary layers

b) mixing length for the turbulent boundary layers

c) eddy dynamic viscosity for the turbulent boundary layers

d) kinetic energy for the turbulent boundary layers

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Answer: b

Explanation: The formula for finding the mixing length for turbulent boundary layers is

l_{m} = κy[1−exp(−y+26)]

While the other parameters like eddy kinematic viscosity, eddy dynamic viscosity and the kinetic energy do not depend on the y^{+} value.

The concept of y+ is not used in which of these laws?

a) Law of the wall

b) Law of the wake

c) Log law

d) Linear law

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Answer: bExplanation: All these laws are used in modelling turbulent boundary layers. The law of the wake depends on the function of the distance from the wall and the boundary layer thickness. It does not depend on the y+ value.

Let y be the distance from the wall, u_{t} be the shear velocity and ν be the kinematic viscosity. Which of these equations define y^{+}?

a) y^{+}=y/u_{t}ν

b) y^{+}=u_{t}ν/y

c) y^{+}=(y u_{t})/ν

d) y^{+}=u_{t}/yν

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Answer: c

Explanation: y^{+} is the ratio of the product of the distance from the wall boundary and the shear velocity to the kinematic viscosity. This is given by the equation y^{+}=y u_{t}/ν. This is why the value of y^{+} increases with the distance from the wall.

What is shear velocity?

a) Square of the ratio of density to wall shear stress

b) Square root of the ratio of density to wall shear stress

c) Square of the ratio of wall shear stress to density

d) Square root of the ratio of wall shear stress to density

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Answer: dExplanation: Shear velocity is used while defining the y+. It otherwise called the friction velocity. It is the square root of the ratio of wall shear stress to density. It has the same unit as that of normal velocity.

What is the unit of y^{+}?

a) y^{+} is dimensionless

b) m

c) m^{2}

d) 1⁄m

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Answer: a

Explanation: y^{+} is dimensionless length. It does not have any dimensions. This can be again proved from the equation

y^{+} (unitless and dimensionless)= y(m)ut(ms)/ν(m2s).

Wall function cannot be used when ___________

a) y^{+}<30

b) y^{+}>30

c) y^{+}<20

d) y^{+}>20

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Answer: a

Explanation: For low Reynolds number turbulent models, wall function can be used to integrate the function. This wall function cannot be used if the value of y^{+} is not more than 30. If the value of y^{+} is less than 30, the wall function is invalid.

What is the range of y^{+} in the buffer layer?

a) 0 < y^{+} < 5

b) 5 < y^{+} < 30

c) 30 < y^{+} < 500

d) 10 < y^{+} < 20

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Answer: b

Explanation: Buffer layer has the turbulent forces and the viscous forces in equal magnitude. In this layer, the range of y^{+} is 5 < y^{+}<30. 0 < y^{+} < 5 is for the linear or viscous sub-layer. The buffer layer lies just above the viscous sub-layer.

The value of y

^{+}is 50. Which layer does it belong to?

a) Inertia dominated layer

b) Velocity defect layer

c) Log-law layer

d) Law of the wake layer

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Answer: cExplanation: 30 < y+ < 500 is the range of y+ where the value of u+ varies logarithmically with the y+ value. It is called the log-law layer. As the value 50 falls in this range, it belongs to the log-law layer.

The value of y+ at the intersection between the linear profile and log-law is ___________

a) 20

b) 5

c) 30

d) 11.63

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Answer: dExplanation: Though the layer varies from viscous sub-layer to buffer layer when y+ crosses the value 5, the variation is still linear. This linear variation becomes logarithmic variation when y+ crosses 11.63 to be exact.