# Computational Fluid Dynamics Questions and Answers – Free and Wall Turbulence

This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Free and Wall Turbulence”.

1. The process which is responsible for spreading of turbulent flows in the flow direction is __________
a) Pluming
b) Entrainment
c) Turbulent mixing
d) Turbulent generation

Explanation: While turbulent flows burst out of its region, fluid from the surrounding is drawn into the turbulent region. This is the process of entrainment. This is the cause of spreading of turbulent flows in the flow direction.

2. Which of these terms represent the burst of turbulent activity to the outer region?
a) Crisis
b) Intermittency
c) Turbulent burst
d) Turbulent jumps

Explanation: Intermittency is the irregular alteration of phases. In turbulent flows, it is seen in the irregular alteration between the turbulent and non-turbulent region of jet flow. Intermittency represents the burst of turbulent activity to the surrounding region.

3. A turbulent jet is formed because ___________
a) A region of high-speed flow is surrounded by a stationary fluid
b) An object disturbs the flow
c) Interaction between an object and a fast moving fluid
d) Interaction of fast and slow moving fluids

Explanation: In mixing layers, the interaction of fast and slow moving fluids create turbulence. A turbulent wake is created by an object which disturbs the flow. When a high-speed flow is surrounded by a stationary fluid, the turbulent jet is formed.

4. The velocity of a free turbulent flow at any particular distance in the cross-stream direction is a function of ___________
a) The ratio of the distance in the cross-stream direction from the centreline and half-width at that cross section
b) The source velocity
c) The cross-stream velocity of the source
d) The velocity in the flow direction of the source

Explanation: The velocity at any point in the cross-stream direction at a particular cross section depends on the ratio of the distance from the centreline and the half width of the cross-stream.

5. Turbulent entrainment leads to ___________
a) Increase in the magnitude of the velocity gradients in the flow direction
b) Increase in the magnitude of the velocity gradients in the cross-stream direction
c) Decrease in the magnitude of the velocity gradients in the flow direction
d) Decrease in the magnitude of the velocity gradients in the cross-stream direction

Explanation: Because of the entrainment of the surrounding fluid, the velocity gradients decrease in magnitude in the flow direction. This also decreases the difference between the speed of the wake fluid and its surroundings.

6. Which of these is correct for mixing layer turbulent flows?
Note:
Umax → Maximum velocity at a particular cross-section
Umin → Minimum velocity at a particular cross-section
y → Distance in the cross-stream direction from the centre line at the cross section
b → Cross-stream half width
U → Velocity at the distance ‘y’.
a) $$\frac{U}{U_{max}-U_{min}}=a(\frac{y}{b})$$
b) $$\frac{U_{max}-U}{U_{max}-U_{min}}=b(\frac{y}{b})$$
c) $$\frac{U}{U_{max}}=c(\frac{y}{b})$$
d) $$\frac{U-U_{min}}{U_{max}-U_{min}}=d(\frac{y}{b})$$

Explanation: For mixed flows, the velocity is dependent on minimum velocity. This corresponds to the velocity of the slow-moving fluid. Maximum velocity corresponds to the fast-moving fluid. The function is given by
$$\frac{U-U_{min}}{U_{max}-U_{min}}=d(\frac{y}{b})$$.

7. If y is the distance in the cross-stream direction from the centre line at a particular cross-section b → Cross-stream half width. The mean velocity gradients and all the velocity fluctuations become zero when the value $$\frac{y}{b}$$ ___________
a) goes above unity
b) goes below unity
c) goes above zero
d) goes below zero

Explanation: The value $$\frac{y}{b}$$ going above 1 means that y crosses b and goes out of the turbulent region. So, the velocity gradients and its fluctuations also will become zero when the value $$\frac{y}{b}$$ goes above 1.

8. Which of these is correct for turbulent jets?
Note:
Umax → Maximum velocity at a particular cross-section
Umin → Minimum velocity at a particular cross-section
y → Distance in the cross-stream direction from the centre line at the cross section
b → Cross-stream half width
U → Velocity at the distance ‘y’.
a) $$\frac{U}{U_{max}-U_{min}}=a(\frac{y}{b})$$
b) $$\frac{U_{max}-U}{U_{max}-U_{min}}=b(\frac{y}{b})$$
c) $$\frac{U-U_{min}}{U_{max}-U_{min}}=c(\frac{y}{b})$$
d) $$\frac{U}{U_{max}}=d(\frac{y}{b})$$

Explanation: For a turbulent jet, the minimum velocity is zero corresponding to the stationary surrounding fluid. So, the equation becomes
$$\frac{U}{U_{max}}=d(\frac{y}{b})$$.

9. The mean velocity gradient is zero at the centreline for ___________
a) jets
b) mixing flows
c) mixing flows and wakes
d) jets and wakes

Explanation: For turbulent flows at jets and wakes, the sign must change at the symmetry line. The symmetry line is the centreline here. For the sign change to be possible, the velocity gradients should reach zero at this line.

10. The velocity at cross-stream of a turbulent wake is calculated using the formula
$$\frac{U_{max}-U}{U_{max}-U_{min}}=b(\frac{y}{b})$$
Note:
Umax→ Maximum velocity at a particular cross-section
Umin→ Minimum velocity at a particular cross-section
y → Distance in the cross-stream direction from the centre line at the cross section
b → Cross-stream half width
U → Velocity at the distance ‘y’
The minimum velocity here corresponds to _____________
a) Velocities at the edges
b) Velocities just downstream of the object
c) Velocities of the surrounding free stream
d) Velocities at the centreline

Explanation: $$\frac{U_{max}-U}{U_{max}-U_{min}}=b(\frac{y}{b})$$ is the formula used to calculate the velocity at a distance from the centre-line in the cross-stream direction. The minimum velocities here corresponds to the starting of the wake, which is just downstream of the object.

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