Fluid Dynamics: Expansion Fan and Fanno Line

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the effect of a lower gamma value on the expansion angle in an expansion fan?

A lower gamma value results in a smaller expansion angle due to higher compressibility.

Describe the condition under which the mass flow becomes choked in a supersonic flow.

Mass flow becomes choked when the upstream flow loses information due to critical length constraints.

What happens to the Mach number when the length of a Fanno flow duct exceeds its critical length?

The inlet Mach number decreases as the flow is retarded by the sound wave.

Explain the transition behavior of flow downstream of a normal shock in supersonic conditions.

Downstream of a normal shock, the flow transitions to a subsonic solution and accelerates toward sonic conditions. Signup and view all the answers

What is the effect of increasing length beyond critical in supersonic flow in terms of shock wave behavior?

Increasing length beyond critical strengthens the shock wave, which can sit exactly at the inlet, resulting in subsonic flow. Signup and view all the answers

How does temperature change in Rayleigh flow as the velocity approaches sonic speeds?

As the velocity approaches sonic speeds in Rayleigh flow, temperature decreases due to compressibility effects. Signup and view all the answers

What causes shock formation in supersonic flow sections, and what are the potential outcomes?

Shock forms due to increased back pressure at the exit, leading to either mid-shock halting or subsonic curve following. Signup and view all the answers

What role does thermal choking play in the context of variable area ducts?

Thermal choking can occur from mass or pressure addition, leading to potential burning, thus requiring variable area ducts. Signup and view all the answers

What occurs at the inlet of a scram jet when it is initially unstarted?

Subsonic combustion occurs. Signup and view all the answers

Describe the state of flow when a rocket's nozzle is over-expanded.

The exhaust gas pressure is higher than the supersonic isentropic exit pressure but lower than ambient pressure. Signup and view all the answers

What happens to the gas flow after it passes through the oblique shock wave at the nozzle exit?

The flow is turned towards the centerline and undergoes compression. Signup and view all the answers

How does the oblique shock wave behave at the center plane of the nozzle?

It reflects outward from the center plane as it cannot penetrate it. Signup and view all the answers

What is the role of the contact discontinuity in the interactions of the exhaust gases?

It serves as a boundary where pressure remains constant as flow meets free-stream air. Signup and view all the answers

What type of waves are set up at the intersection of the reflected shock wave and the contact discontinuity?

Expansion waves of the Prandtl-Meyer type are established. Signup and view all the answers

How does the gas flow change as it passes through the Prandtl-Meyer compression waves?

The flow is turned back towards the centerline and undergoes an increase in pressure. Signup and view all the answers

What is the significance of the repeated interactions of expansion and compression waves?

They lead to the continuous adjustment of pressure until it equals ambient pressure. Signup and view all the answers

Why is the pattern formed by the expansion and compression waves often described as diamond-shaped?

The interactions of these waves create unique flow patterns resembling diamonds. Signup and view all the answers

What is the outcome of the flow stabilization within the scram jet nozzle as the cycle repeats?

The flow stabilizes with pressure matching ambient pressure while remaining parallel to the centerline. Signup and view all the answers

Study Notes

Expansion Fan

Expansion fan occurs when the last layer near the wedge turns faster than the top layer.
Lower gamma values (higher compressibility) lead to less expansion angle.
"Dnyu" represents the change in expansion angle, unlike "theta" for compression.
Mass choking prevents upstream information from reaching the downstream.

Fanno Line

In supersonic flow, significant Mach number changes occur with small length variations, as seen in graphs.
In a constant-area duct Fanno flow, increasing duct length beyond a critical length (L*) causes incoming flow retardation and reduces the inlet Mach number.
Increased length leads to a reduced flow at the inlet, causing higher inlet temperature due to friction.
L* is larger at lower Mach numbers.
Increasing length beyond the critical point in supersonic flow creates a normal shock.
The shock position depends on velocity; it stays at the inlet.
Downstream flow becomes subsonic and accelerates towards sonic.
Inlet Mach number remains unchanged in subsonic flows.
Critical length matches subsonic solution for achieving supersonic conditions.
Further increasing length creates a stronger compression/shock wave at the inlet (spillage).
This creates a subsonic flow choosing a higher curve to accelerate to sonic speeds.

Rayleigh Flow

In Rayleigh flow, velocity approaches sonic up to a point determined by 1/sqrt(gamma).
Temperature decreases; the compressibility effect is more significant with decreasing density.
Supersonic flow doesn't hold as much heat as subsonic flow, as seen in diagrams.
Shock formation in supersonic flows forces a selection of subsonic curves towards sonic velocity.
Shock formation is due to increased back pressure at the exit.
Shocks can either halt in the middle or follow a path, choosing a subsonic solution to match exit pressure.
Shock movement is possible (shifts).

Choking

Mass addition or increased pressure (e.g., fuel injection against flow) can cause choking.
Thermal choking can lead to burning.
Variable-area ducts are used to manage these issues.
In an unstarted scramjet, an inlet shock creates subsonic combustion.

Over-Expanded Nozzle

Rocket nozzles are designed for higher altitudes.
At engine start, flow is over-expanded (exhaust gas pressure, pe, higher than supersonic isentropic exit pressure but lower than ambient pressure, pa).
This creates an oblique shock at the nozzle exit plane.
Gases undergo compression after passing through the oblique shock, eventually reaching ambient pressure.
The oblique shock reflects off the centerline to create expansion and compression waves that increase pressure to ambient pressure.
Iterative expansion-compression leads to the diamond patterns observed in such flows.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the concepts of expansion fans and Fanno lines in fluid dynamics. Understand how changes in geometry affect flow characteristics in supersonic conditions. This quiz covers the underlying principles and implications of shock positions and flow behavior.