Chapter 10

Question 1

Define quasi-one-dimensional flow.

Answer 1

Quasi-one-dimensional flow occurs when the properties in a flow only significantly vary in one direction. This occurs if dA/dx of a nozzle or diffuser is very small.

Ref: Pg 693

Question 2

For quasi-one-dimensional flow, what cases the flow properties to change as a function of x?

Answer 2

The area change.

Question 3

Is quasi-one-dimensional flow an exact or approximate model?

Answer 3

Approximate

Question 4

Are the equations that describe quasi-one-dimensional flow exact or approximate.

Answer 4

Exact

Question 5

What are the assumptions for quasi-one-dimensional (Q1D) flow?

Answer 5

1. Steady
2. Inviscid
3. Adiabatic

Question 6

Since Q1D considers steady, adiabatic, inviscid flow, are there any dissipative mechanisms?

Answer 6

No

Question 7

In regards to the area velocity relation, if M approaches 0, what does this tell you about the cross section and the flow type?

Answer 7

1. The flow is incompressible.

2. Au = Constant

Question 8

In regards to the area velocity relation, if the flow is subsonic (0<=M<1) what does an increase in velocity tell you about the duct area change?

Answer 8

An increase in velocity (positive du) is associated with a decrease in area (negative dA) and vv.

Question 9

In regards to the area velocity relation, if the flow is subsonic (0<=M<1) what does an decrease in velocity tell you about the duct area change?

Answer 9

An decrease in velocity (negative du) is associated with a increase in area (positive dA) and vv.

Question 10

In regards to the area velocity relation, if M>1, an increase in velocity is associated with how change in area?

Answer 10

An increase in velocity is associated with an increase in area and vv.

Question 11

In regards to the area velocity relation, if M>1, a decrease in velocity is associated with how change in area?

Answer 11

An decrease in velocity is associated with an decrease in area and vv.

Question 12

For supersonic flow (M>1) describe how velocity changes in a diverging and converging duct.

Answer 12

1. Converging duct: Velocity Decreases
2. Diverging duct: Velocity Increases

This is the opposite of subsonic flow.

Question 13

In regards to the area velocity relation, if the flow is sonic (M=1) dA/A is equal to what? What does this imply physically?

Answer 13

dA/A = 0
> Mathematically this means that there is a minimum or maximum in the area distribution of the nozzle. However, physically speaking this means that the area is at a minimum (you are at the throat of the nozzle).

Question 14

For a gas to expand isentropically from subsonic to supersonic speeds, it must flow through what type of duct?

Answer 14

A convergent-divergent duct.

Question 15

In a convergent/divergent duct, the flow at the minimum area is ____.

Answer 15

Sonic

Question 16

With regards to the area Mach number relation, what does the equation tell you as far as how the Mach number changes in a nozzle?

Answer 16

The Mach number in the nozzle is a function of the ratio of the area to the critical area (sonic throat area) only.

Question 17

True or False

A<a></a>

Answer 17

True

A > A^*

Question 18

For a convergent/divergent nozzle with M1<1, how does the Mach number change as it flows from the reservoir, through the throat, and into the bell?

Answer 18

It increases into the throat, and then continues to increase so long as the area of the bell continues to increase. At the end of the bell where the area change stops the Mach number reaches a steady value.

Question 19

For a convergent/divergent nozzle with M1 < 1, how does the static to total pressure ratio change with x?

Answer 19

The ratio starts out at a value 1 in the reservoir and then continues to decrease sharply as flow moves through the throat. Toward the base of the bell the ratio begins to reach a steady value.

Question 20

For a convergent/divergent nozzle with M1 < 1, how does the static to total temperature ratio change with x?

Answer 20

The ratio starts out at a value of 1 and then decreases smoothly through the throat and the bell.

Question 21

To accelerate a gas through a nozzle, what must be present?

Answer 21

A pressure gradient.

Question 22

For air to move through a nozzle, what is the required relationship between the exit pressure and the inlet pressure?

Answer 22

The exit pressure must be lower than the inlet pressure.

Question 23

Describe (in detail) the flow of air through a convergent/divergent nozzle where the exit pressure is just slightly below in the inlet pressure.

Answer 23

The small pressure difference will cause a slight wind to blow through the duct at low sub-sonic speeds. The Mach number will increase as air flows into the throat, reaching a maximum at the throat. The Mach number at the throat will not reach Mach 1. Downstream of the throat the subsonic flow encounters a divergent duct and slows down.

Question 24

For sub-sonic flow through a convergent/divergent nozzle, what are the controlling factors that affect flow properties and how many isentropic solutions exist.

Answer 24

1. pe/po and A/At

2. Infinite

Question 25

For sub-sonic flow through a convergent/divergent nozzle, how is mass flow rate affected by the exit pressure?

Answer 25

Mass flow through the duct increases as pe decreases.

Note: This is only true for Mach numbers less than 1.

Question 26

Describe chocked flow.

Answer 26

When the exit pressure is low enough to attain sonic conditions in the throat, the mass flow rate after the throat is constant.

Question 27

What is the pressure p_e6 refer to?

Answer 27

P_e6 represents the proper isentropic value for the design exit Mach number, which exists immediately upstream of the normal shock wave standing at the exit.

Question 28

What is the pressure p_e5 refer to?

Answer 28

The static pressure behind a normal shock at the design Mach number of the nozzle.

Question 29

What conditions must exist for a convergent/divergent duct to be considered “over-expanded?”

Answer 29

p_e6 < pb < p_e5

Question 30

What conditions must exist for a convergent/divergent duct to be considered “under-expanded?”

Answer 30

pb< p_e6

Question 31

True or False

The shape of a diffuser can vary depending on the flow regime.

Answer 31

`True

Question 32

In a semi-qualitative sense, describe the use of total pressure with respect to work.

Answer 32

The total pressure of a flowing gas is a measure of the capacity of the flow to perform useful work. Any loss of total pressure during a process is indicative of inefficiency.

Question 33

Define a diffuser with respect to useful work.

Answer 33

A diffuser is a duct designed to slow an incoming gas flow to a lower velocity at the exit of the diffuser with as small a loss in total pressure as possible.

Question 34

Why can an ideal diffuser never be achieved in practice?

Answer 34

It is extremely hard to decelerate supersonic flow without generating shockwaves in the duct. Shockwaves increase the total entropy and render the flow non-isentropic (ideal diffusers are always considered isentropic). In addition, the boundary layer on the wall of the diffuser causes an additional entropy increase.

Question 35

What are the three main problems associated with a normal shock diffuser wind tunnel configuration?

Answer 35

1. Normal shocks are the strongest possible shocks and therefore result in the largest total pressure loss.
2. It is extremely difficult to hold normal shock waves stationary at the exit.
3. The test model would create oblique shockwaves which would further complicate the downstream flow.

Question 36

What is the main source of total pressure loss in a supersonic wind tunnel?

Answer 36

The diffuser.

Question 37

Which is more efficient in terms of total pressure loss?

1. Oblique shock diffusers.
2. Normal Shock diffuser.

Answer 37

Oblique shock diffusers.

Question 38

What is an “unstarted” supersonic wind tunnel?

Answer 38

A wind tunnel in which a normal shock stands inside the CD nozzle and causes subsonic flow throughout.

Question 39

Describe the effect of shockwave interactions with the boundary layer in a diffuser.

Answer 39

The adverse pressure gradient across the shock causes the boundary layer to separate from the nozzle wall. A lambda-type shock pattern occurs at the two feet of the shock near the wall and the core of the nozzle flow, now separated from the wall, flows downstream at an almost constant area.