Fluid Dynamics: Expansion Fan and Fanno Line
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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.

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

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

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

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

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

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

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

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

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

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

<p>Subsonic combustion occurs.</p> Signup and view all the answers

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

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

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

<p>The flow is turned towards the centerline and undergoes compression.</p> Signup and view all the answers

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

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

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

<p>It serves as a boundary where pressure remains constant as flow meets free-stream air.</p> 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?

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

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

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

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

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

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

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

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

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

Flashcards

Over-Expanded Nozzle

When a rocket's nozzle is designed for higher altitudes, but starts at sea level, the exhaust gas pressure is higher than the ambient pressure, leading to an oblique shock wave forming at the nozzle exit.

Oblique Shock Wave Formation

The flow of gases gets compressed as they move away from the nozzle exit, passing through the oblique shock wave.

Reflected Shock Wave

The oblique shock wave reflects outward from the center plane of the nozzle, causing further compression of the gases.

Contact Discontinuity

The contact discontinuity is a boundary where the outer edge of the gas flow meets the free stream air. Pressure and flow direction are the same on both sides.

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Prandtl-Meyer Expansion Waves

Prandtl-Meyer expansion waves are generated at the intersection of the reflected shock wave and the contact discontinuity. These waves expand the gas flow to reduce pressure to ambient pressure.

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Reflected Prandtl-Meyer Waves

The Prandtl-Meyer expansion waves reflect from the center plane, turning the flow back parallel to the centerline but causing further pressure reduction.

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Prandtl-Meyer Compression Waves

Reflected Prandtl-Meyer waves meet the contact discontinuity and reflect as compression waves, increasing the pressure to ambient and turning the flow back towards the centerline.

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Reflected Compression Waves

The compression waves further reflect from the center plane, increasing pressure above ambient and turning the flow parallel to the nozzle centerline.

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Diamond Patterns

The process of expansion and compression waves interacting leads to the diamond patterns observed in the rocket's exhaust plume.

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Equilibrium Flow

The flow continues to cycle through expansion and compression waves until the gas pressure reaches ambient pressure and the flow is parallel to the nozzle centerline.

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What is an expansion fan?

An expansion fan is created when the flow expands around a wedge. The fluid near the wedge turns more quickly than the upper layers, causing a fan-like expansion of the flow.

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What is the difference between the expansion angle (Dnyu) and the compression angle (theta)?

The expansion angle (Dnyu) is the change in direction of the flow during an expansion fan. Unlike the compression angle (theta), Dnyu decreases as the Mach number increases, meaning the expansion becomes less pronounced.

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What occurs when a flow becomes choked?

Choking occurs when the flow reaches the maximum mass flow rate possible through the given duct. Once choked, the upstream flow cannot influence the downstream flow.

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What is Fanno flow?

A Fanno flow is a flow in a constant area duct where friction causes the flow to decelerate, increasing temperature and entropy.

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What is the critical length (L*) in Fanno flow?

The critical length (L*) is the maximum length a duct can have before a normal shock forms. Beyond this point, the flow becomes subsonic.

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What is Rayleigh flow?

Rayleigh flow is an adiabatic, frictionless flow in a variable area duct. It's characterized by the conservation of stagnation enthalpy. In Rayleigh flow, velocity increases or decreases towards sonic velocity depending on the heat addition/removal.

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What happens when a shock wave forms in supersonic Rayleigh flow?

In Rayleigh flow, for supersonic flow, when a shock wave forms at supersonic section, the flow chooses subsonic curve and later attains sonic velocity. This happens due to increased back pressure at the exit of the duct, causing the flow to slow down.

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What is thermal choking?

Thermal choking occurs when the flow reaches a maximum heat addition/removal rate, leading to burning or pressure waves. To handle this, variable area ducts are used to control the flow.

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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.

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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.

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