Compressible Flow: Flow in nozzles

[aznkid310]

Homework Statement

I am currently studying for finals, and I am really confused about compressible flow in nozzles. Some questions I have:

1) What is exactly is the condition for choked flow for converging, diverging, and converging-diverging nozzles?
2) When can we assume that the back pressure pb = pe (exit pressure)?
3) What is the condition for shock waves to form? How do we know when to check for them? How do we know where they are (ie in the throat, just upstream/downstream...)
4) What is the design pressure and design conditions? What do we use these for?

Homework Equations

Not choked: p0 > pb > p* where p0 = stagnation pressure (no velocity)
pb = back prz
p* = critical prz
Choked: pb < p*

Shock wave if: p*>pb>pe (where?)

The Attempt at a Solution

 

[Valkarie]

1) For a converging nozzle, the condition for choked flow is when the back pressure (pb) is less than the critical pressure (p*). For a diverging nozzle, the condition for choked flow is when the back pressure is greater than the critical pressure. For a converging-diverging nozzle, the condition for choked flow is when the back pressure is equal to the critical pressure. 2) We can assume that the back pressure pb = pe (exit pressure) when the flow is choked. This is because when the flow is choked, there is a maximum mass flow rate and the pressure at the exit must be equal to the back pressure in order to maintain this mass flow rate. 3) Shock waves form when the critical pressure (p*) is greater than the back pressure (pb) but less than the exit pressure (pe). The shock wave can form anywhere in the nozzle, depending on the flow conditions. To check for shock waves, we can calculate the Mach number at various points in the nozzle and compare it with the critical Mach number. If the Mach number is greater than the critical Mach number, then a shock wave will form. 4) The design pressure and design conditions are used to determine the operating parameters of the nozzle. The design pressure is the pressure at which the nozzle is designed to operate, and the design conditions are the flow conditions such as Mach number and temperature at which the nozzle is designed to operate.

 

[Mene]

I can provide some general information and guidelines for understanding compressible flow in nozzles. However, without specific context or equations, it may be difficult to give a complete response.

1) The condition for choked flow in a nozzle is when the back pressure (pb) is equal to or less than the critical pressure (p*). For a converging nozzle, choked flow occurs at the throat where the cross-sectional area is the smallest. For a diverging nozzle, choked flow occurs at the exit where the cross-sectional area is the largest. For a converging-diverging nozzle, choked flow can occur at either the throat or the exit, depending on the design and operating conditions.

2) The assumption that the back pressure is equal to the exit pressure (pb = pe) can be made when the flow is fully expanded at the exit. This typically occurs when the back pressure is equal to or less than the critical pressure.

3) Shock waves form when the back pressure is greater than the critical pressure, but less than the exit pressure (p*>pb>pe). The exact location of the shock wave in the nozzle will depend on the design and operating conditions. To check for shock waves, you can use the equations provided in your course material to calculate the back pressure and compare it to the critical and exit pressures.

4) Design pressure and design conditions refer to the specific operating conditions and pressures that a nozzle is designed for. These are important for ensuring that the nozzle can handle the expected flow and prevent any damage or failure. These values are typically determined through calculations and simulations, taking into account the specific application and requirements.

In summary, understanding compressible flow in nozzles requires knowledge of the flow conditions, pressure ratios, and design considerations. It is important to carefully analyze and calculate these parameters in order to properly design and operate a nozzle.