This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Turbulent Viscosity”.

1. The value of turbulent viscosity is fairly close to that of __________

a) Turbulent diffusivity

b) Newton’s viscosity

c) Kinematic viscosity

d) Dynamic viscosity

View Answer

Explanation: Transport of momentum is due to viscosity and transport of heat or mass is due to diffusivity. In turbulent flows, both of these are due to the same mechanism which is eddy mixing. So, the value of turbulent viscosity is considered to be close to that of turbulent diffusivity.

2. Which of these scientists introduced turbulent viscosity?

a) Kolmogorov

b) Smagorinsky

c) Prandtl

d) Boussinesq

View Answer

Explanation: Boussinesq introduced the concept of eddy viscosity or turbulent viscosity in turbulent flows. Boussinesq equated the turbulent stresses to the mean flow. Here, the new constant of proportionality called the turbulent viscosity was introduced.

3. The kinematic turbulent viscosity is __________

a) equal to the product of turbulent length and time scales

b) equal to the product of turbulent length and velocity scales

c) proportional to the product of turbulent length and velocity scales

d) proportional to the product of turbulent length and time scales

View Answer

Explanation: By using dimensional analysis, the relationship between kinematic turbulent viscosity, turbulent length and time scales can be established using the dimensional analysis. It can be expressed as

ν

_{t}∝vl

Where,

ν

_{t}→ Kinematic turbulent viscosity.

v → Turbulent velocity scale.

l → Turbulent length scale.

4. The dynamic turbulent viscosity is ___________

a) equal to the product of turbulent length and time scales

b) proportional to the product of turbulent length and time scales

c) proportional to the product of kinematic turbulent viscosity and density of the fluid

d) equal to the product of kinematic turbulent viscosity and density of the fluid

View Answer

Explanation: Dynamic viscosity is the product of kinematic viscosity and density in general. This applies to the turbulent viscosities also.

μ

_{t}=ρν

_{t}

Where,

ν

_{t}→ Kinematic turbulent viscosity.

μ

_{t}→ Dynamic turbulent viscosity.

ρ → Density.

5. __________ relates turbulent viscosity and diffusivity.

a) Reynolds number

b) Reynolds analogy

c) Reynolds-Averaged Navier-Stokes equations

d) Favre-Averaged Navier-Stokes equations

View Answer

Explanation: Reynolds analogy relates the turbulent momentum and heat transfer. It states that “both of these (turbulent momentum and heat transfer) are due to the same mechanism called turbulent eddies and hence the values of turbulent viscosity and diffusivity will be close to each other”.

6. Which of these models solves a system for the turbulent kinematic viscosity?

a) DNS

b) LES

c) Spalart-Allmaras

d) RANS

View Answer

Explanation: Spalart- Allmaras is a model for solving turbulent flow especially invented for aerospace problems. It gives good results for turbulent boundary layer models. It solves the transport equation for turbulent kinematic viscosity.

7. The units of kinematic and dynamic turbulent viscosities are ___________ respectively.

a) m/s^{2} and kg m/s

b) m^{2}/s^{2} and kg/m s

c) m^{3}/s and kg m/s

d) m^{2}/s and kg/m s

View Answer

Explanation: The units of turbulent viscosities are the same as the viscosities given by Newton’s law. The unit of kinematic turbulent viscosity is m

^{2}/s. The unit of dynamic viscosity is kg/m s.

8. Which of these is not a turbulent viscosity model?

a) k-ω

b) k-ε

c) DNS

d) SST

View Answer

Explanation: The models k-ε, k-ω and SST are all models which include turbulent viscosity. DNS stands for Direct Numerical Simulation which is the basic model to solve turbulent flows. It does not involve turbulent viscosities.

9. In the k-ε model, the turbulent viscosity is given as ___________

a) μ_{t}∝k/ε

b) μ_{t}∝k^{2}/ε

c) μ_{t}=k/ε

d) μ_{t}=k^{2}/ε

View Answer

Explanation: In the k-ε model, the turbulent dynamic viscosity is given in terms of k and ε. The relation is given as

μ

_{t}∝k

^{2}/ε.

10. Which of these models is made different from its parent model by turbulent viscosity?

a) Realizable k-ε model

b) k-ε model

c) Spalart-Allmaras model

d) SST model

View Answer

Explanation: The realizable k-ε model is a variant of the k-ε model. The realizable k-ε model is different from its parent that a new turbulent viscosity is formulated. Another variation is that a new transport equation for the dissipation rate is formed.

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