Steam flow rate in 2-chamber steam engine system

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Discussion Overview

The discussion revolves around the flow rate of steam in a two-chamber steam engine system, specifically focusing on the phases of operation and the conditions affecting steam flow between the chambers. The inquiry is conceptual, aiming to understand the dynamics of steam flow during different phases of the engine's operation.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes a system with a duct (P1) and a piston chamber (P2), detailing the isobaric heating process and the expansion of air in P2 that lifts the piston.
  • The participant notes that the volumetric flow rate between P1 and P2 is not conserved due to the piston lifting mechanism.
  • The participant seeks to understand how to find the flow rate of steam entering P2 during phase 2 and after the piston is locked in phase 3.
  • Another participant questions the terminology used, asking for clarification on whether "air" was meant to refer to "steam."
  • The original poster confirms that they are indeed referring to steam, specifying that it is not boiling steam.
  • A participant raises a question regarding the boundary conditions at the end of P1, inquiring whether it is dead-ended or at constant pressure.
  • The original poster responds that P1 is at constant pressure and is twice as long as P2, expressing interest in whether the expansion of heated moist air can lift the piston in P2.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specifics of the boundary conditions or the implications of the steam flow on the piston movement. Multiple viewpoints and questions remain unresolved.

Contextual Notes

The discussion includes assumptions about the system's configuration and the nature of the steam, which may influence the analysis of flow rates. The specifics of the boundary conditions and their impact on the system's behavior are not fully defined.

Denniskwantas
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Our system of interest has a duct on the left and a piston chamber on the right that make the shape of the letter T rotated 90º clockwise. The smaller tube on the left is abbreviated as P1 has an unspecified length while the piston chamber is P2. The air in P2 heats up and expands while the pressure remains constant (isobaric process). That said, heat energy (q) is supplied to the piston chamber to heat up the air and lift the piston up simultaneously.

In phase 2, the heated air escapes to P1 via the opening and heat energy is still supplied to the chamber to continue lifting the piston up. Caveat: The volumetric flow rate between P1 and P2 is not conserved because part of it goes to lifting the piston.

In phase 3, the heat supply is cut off and the position of the piston is locked in by some mechanism. The heat and vapor accrued in the isobaric expansion process in P1 will flow to P2.
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2.jpg
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The question is conceptual rather than finding the exact number. How can I find the flow rate of the steam as it enters P2 in phase 2 and when the piston's position is locked in phase 3 ?

Here are all the relevant equations, rewritten in LaTex.

Screen Shot 2021-10-23 at 9.40.19 AM.png


This is the general equation for mass flow rate which equals to the product of steam density, steam velocity and the area of the opening between P1 and P2 .

Recently I've found another equation for steam flow rate in a pipe.
https://www.physicsforums.com/attachments/291039

d : Pipe Inner Diameter (m)
v : Steam Velocity (m/s)
V : Specific volume (m³/kg)
m_s : Steam Flow Rate (kg/h)

Source: TLV
 
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You refer to air. Did you mean steam?
 
Yep. Steam it is. But it's not boiling steam though.
 
And what is the boundary condition at the far end of P1? Is it dead ended, or is it at constant pressure? Or something else?
 
As for the boundary conditions though, the P1 tube would be twice as long as P2 and yes, the P1 is at constant pressure with P2 as well.

I'm really interested in knowing whether the expansion of the heated moist air could lift the piston in P2 in any capacity.
 

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