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# Computational Fluid Dynamics – Turbulent Schmidt Number

1 - Question

Turbulent Schmidt number is the ratio of ____________

a) turbulent viscosity to turbulent diffusivity

b) turbulent diffusivity to turbulent viscosity

c) turbulent rate to turbulent diffusivity

d) turbulent diffusivity to turbulent rate

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Answer: aExplanation: Turbulent Schmidt number gives the ratio of turbulent transfer of momentum to the turbulent transfer of mass. It is given by

Turbulent Schmidt number=TurbulentviscosityTurbulentdiffusivity.

2 - Question

Turbulent Prandtl number is the ratio of ____________

a) turbulent transport of heat to turbulent transport of momentum

b) turbulent transport of momentum to turbulent transport of heat

c) turbulent viscosity to turbulent transport of heat

d) turbulent transport of heat to turbulent viscosity

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Answer: b

Explanation: Prandtl number is the ratio of transport of momentum to transport of heat. Turbulent Prandtl number is

Turbulent Prandtl number=TurbulentviscosityTurbulentdiffusivity.

3 - Question

What is the unit of turbulent Schmidt/Prandtl number?

a) m2/s

b) It is dimensionless

c) m2/s2

d) m/s2

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Answer: bExplanation: Both viscosity and diffusivity are in the same units. As the turbulent Schmidt or Prandtl number is the ratio of viscosity to conductivity, the number becomes dimensionless. So, it does not have units.

4 - Question

According to Reynolds analogy, what is the value of turbulent Schmidt number?

a) -1

b) 0

c) 1

d) ∞

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Answer: cExplanation: Reynolds analogy states that “because of eddy mixing, the values of turbulent viscosity and turbulent diffusivity will be fairly close to each other”. So, dividing both we will get unity. Therefore, turbulent Schmidt or Prandtl number becomes unity.

5 - Question

Which of these is correct when the turbulent Prandtl number is unity?

a) Turbulent diffusivity is zero

b) Turbulent viscosity is zero

c) The flow becomes laminar

d) The velocity and temperature profiles are identical

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Answer: dExplanation: When the turbulent Prandtl number is one, both turbulent viscosity and turbulent diffusivity are the same. So, the velocity and temperature profiles near the solid boundary or wall become identical.

6 - Question

Turbulent Prandtl number is used in CFD to ____________

a) change viscosity profiles

b) change temperature profiles

c) modulate heat transfer results

d) modulate velocity profiles

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Answer: cExplanation: Prandtl number relates momentum transfer and heat transfer in a turbulent flow. So, it is used in turbulent flows with heat transfer. In general CFD problems, it is used to tune the heat transfer results.

7 - Question

Turbulent Prandtl number is useful in __________

a) SST

b) DNS

c) LES

d) RANS

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Answer: dExplanation: RANS is Reynolds-Averaged Navier-Stokes equations. RANS is a method used to solve the turbulent flows with modified Navier-Stokes equations. The turbulent Prandtl number is used here to solve the problem.

8 - Question

Turbulent Schmidt number is used to solve ____________

a) mass transfer in a turbulent boundary layer

b) compressible flows

c) boundary layer flows

d) heat transfer in a turbulent boundary layer

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Answer: aExplanation: As the turbulent Schmidt number relates momentum and mass transports, it is used to solve mass transfer in turbulent boundary layers. In general, it is used along with the Reynolds analogy.

9 - Question

The range of turbulent Schmidt number is ___________

a) 0.2 to 3.5

b) 0.2 to 1.5

c) 1 to 3.5

d) 0 to 0.2

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Answer: aExplanation: According to the experiments, the turbulent Schmidt number ranges from 0.2 to 3.5. Only when using the Reynolds analogy, the approximation becomes a value near unity. Otherwise, this value varies.

10 - Question

The range of turbulent Prandtl number is ___________

a) 0.5 to 0.7

b) 0.7 to 0.9

c) 0.9 to 1.5

d) 1.5 to 1.7

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Answer: bExplanation: The average value of the turbulent Prandtl number is 0.85. The experimental turbulent Prandtl number value varies from 0.7 to 0.9. It stays below unity.