This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Turbulence Modelling – Kolmogorov Energy Spectrum”.

1. Kolmogorov micro-scales can be expressed in terms of ___________

a) Rate of dissipation of turbulent energy and fluid viscosity

b) Turbulent energy and fluid velocity

c) Fluid velocity and viscosity

d) Turbulent energy and fluid viscosity

View Answer

Explanation: Kolmogorov micro-scales can be expressed in terms of the rate of energy dissipation of the turbulent flow and the fluid viscosity. It uses the statement that the rate of production of turbulent energy and the rate of dissipation should be balanced.

2. Kolmogorov spectral energy is a function of ____________

a) Velocity

b) Wavenumber

c) Kinematic viscosity

d) Dynamic viscosity

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Explanation: Kolmogorov spectral energy is, in general, a function of the wavenumber. The wavenumber is, in turn, a function of wavelength (λ) given by

κ=\(\frac{2\pi}{\lambda}\).

3. Spectral energy is equal to ___________

a) Kinetic energy per unit mass per unit wavenumber

b) Rate of dissipation of turbulent energy per unit mass per unit wavenumber

c) Rate of dissipation of turbulent energy per unit wavenumber

d) Kinetic energy per unit wavenumber

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Explanation: All the fluctuating properties of a turbulent flow contain some energy. The spectral energy can be given as the kinetic energy per unit mass per unit wavenumber of fluctuations around the wavenumber.

4. What is the unit of spectral energy?

a) \(\frac{m}{s^2}\)

b) \(\frac{m^3}{s^2}\)

c) \(\frac{m^2}{s^3}\)

d) \(\frac{m^2}{s^2}\)

View Answer

Explanation: Spectral energy is the kinetic energy per unit mass per unit wavenumber. So, the unit of spectral energy is given by

\(\frac{kg m^2}{s^2}×\frac{1}{kg}×m=\frac{m^3}{s^2}\).

5. What is the range of length and frequency of the Kolmogorov micro-scale eddies respectively?

a) 0.1 to 1 mm, around 1 kHz

b) 1-10 mm, around 10 kHz

c) 0.01 to 0.1 mm, around 10 kHz

d) around 10 mm, 0.1 to 0.01 kHz

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Explanation: The smallest scales of motion in a turbulent flow is called the Kolmogorov micro-scale. They have a wavelength of around 0.01 to 0.1 mm and frequencies around 10 kiloHertz. They have Reynolds number very near to one.

6. If ν is the kinematic viscosity and ε is the rate of dissipation of turbulent energy, to which of these terms is the spectral energy of Kolmogorov micro-scale eddies proportional to?

a) ν^{5/3} ε^{1/3}

b) ν^{3/2} ε^{1/2}

c) ν^{1/2} ε^{3/2}

d) ν^{5/4} ε^{1/4}

View Answer

Explanation: Kolmogorov argued that the behaviour of the smallest turbulent eddies depends on the rate of dissipation of turbulent energy. But, later studies revealed that only the spectral energy of the smallest turbulent eddies depends on the rate of dissipation of turbulent energy and the relationship is given by spectral energy∝ν

^{5/4}ε

^{1/4}.

7. The size of the eddies and the wavenumber are __________

a) inversely proportional

b) directly proportional

c) not related to each other

d) related but it varies according to the energy

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Explanation: Wavenumber is the frequency of eddies and the size will be related to the wavelength. So, the size and wavenumber are inversely proportional. The large eddies have low wavenumber and the small eddies have high wavenumbers.

8. ____________ is associated with high wavenumbers.

a) Conduction

b) Dissipation

c) Kinetic energy

d) Potential energy

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Explanation: High wavenumbers represent small eddies. Dissipation is associated with small eddies and kinetic energy is associated with large eddies. This is given by the relation between energy and wavenumber.

9. _____________ are called the inertial sub-range of turbulence.

a) Kolmogorov micro-scale

b) Small scale eddies

c) Intermediate scale eddies

d) Large scale eddies

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Explanation: Transfer of energy from large eddies to small eddies is called the energy cascade. The transfer brings turbulent kinetic energy from large scales to small scales. The intermediate range in this transfer is called the inertial sub-range.

10. If κ is the wavenumber and ε is the rate of dissipation of turbulent energy, which of these is proportional to the spectral energy of the inertial sub-range of turbulence?

a) κ^{-5/3}ε^{-2/3}

b) κ^{5/3}ε^{-2/3}

c) κ^{5/3}ε^{2/3}

d) κ^{-5/3}ε^{2/3}

View Answer

Explanation: The spectral energy in terms of the wavenumber and the rate of dissipation of turbulent energy is given by E(κ)∝κ

^{-5/3}ε

^{2/3}. Where the proportionality constant is 1.5 (obtained experimentally)

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