Computational Fluid Dynamics Multiple Choice Questions on “Turbulence Modelling – Turbulent Scale”.
1. Small eddy scales are called as ___________
a) Batchelor scales
b) Taylor micro-scales
c) Kolmogorov micro-scales
d) Integral length scales
Answer: c
Clarification: The smallest eddies with dominating viscosity are called Kolmogorov micro-scales. It is named after the Russian scientist Andrey Kolmogorov who carried out works on the structure of turbulence in the 1940s.
2. What do the length, velocity and time-scale ratios mean?
a) The ratio of large-scale and characteristic properties
b) The ratio of small-scale and characteristic properties
c) The ratio of small and large scale eddies
d) The ratio of actual and characteristic properties
Answer: c
Clarification: The time-scale ratio is the ratio between small-scale time (of small-scale eddies) and large-scale time (of small-scale eddies). Similarly, the length and velocity-scale ratios are also the ratios between small and large-scale lengths and velocities.
3. What is the relationship between Length-scale ratio and Reynolds number (Re)?
a) Re3/4
b) Re-3/4
c) Re1/2
d) Re-1/2
Answer: b
Clarification: Length scale ratio is obtained by estimation of the dissipation rate in the large scale flow features.
Length-scale ratio= Re-3/4.
4. Small-scale eddy motions have ___________
a) does not vary from the energy losses of the large-scale eddy motions
b) the same order of energy losses as the large-scale eddy motions
c) decreased energy losses
d) increased energy losses
Answer: d
Clarification: Small-scale eddy motions are dissipative. The energy associated with these motions is converted into thermal internal energy. This leads to increased energy losses associated with the turbulent flows.
5. The Reynolds number associated with the smallest scale of motion in the turbulent flow is ____________
a) 0.1
b) 1
c) 10
d) 100
Answer: a
Clarification: The smallest scales of motion in the turbulent flows are dominated by viscous flows. They are associated with a Reynolds number 1. The smallest scales are those for which inertia and viscous flows are the same.
6. Express the time-scale ratio in terms of Reynolds number (Re).
a) Re-1/4
b) Re3/4
c) Re-1/2
d) Re1/2
Answer: c
Clarification: The ratio of time-scales is obtained using the length scale ratios. It is given by
Time-scale ratio= Re-1/2.
7. To establish the relationship between turbulent scales and the Reynolds number, which of these methods is used?
a) Statistical averaging
b) Dimensional analysis
c) Weighted averaging
d) Geometric algebra
Answer: b
Clarification: The ratio of large and small scales of turbulent flows can be given in terms of the Reynolds number. These relations are established using dimensional analysis. Dimensional analysis is a method which compares the dimensions in both the sides of the equations to set the relationship.
8. The behaviour of large eddies depend on __________
a) Viscosity and time scales
b) Velocity and time scales
c) Time and length scales
d) Velocity and length scales
Answer: d
Clarification: Velocity and length of the large eddies will be large. The variation of flow with time is not much. Thus, they are not dependent much on the time scales. Instead, they are dependent on the velocity and length scales.
9. When the Reynolds number increases, the difference between the large and small scales ____________
a) increases
b) decreases
c) remains constant
d) cannot be defined
Answer: a
Clarification: As the Reynolds number increases, the flow becomes more turbulent. This increases the difference between the large and small eddies (the difference between the large and small scales). It is called scale separation.
10. Which of these is equal to the velocity-scale ratio?
a) Re-3/4
b) Re-1/3
c) Re-1/4
d) Re-2/4
Answer: b
Clarification: Once the length and time-scale ratios are known, we can get the velocities scale ratios using these two. It is given by
Velocity-scale ratio = Re-1/4.