A working fluid with a flow rate of $1~kg/s$ enters a heater at a pressure of $1~MPa$ and temperature $150~^\circ C$, which raises its temperatures to $300~^\circ C$. It then enters a turbine, does work, loses pressure and temperature, and exits at $0.5~MPa$ and $200~^\circ C$ at the same flow rate. The bypass valve's purpose is to control the work output of the turbine by bypassing some of the working fluid from the inlet stream directly to the outlet stream. Suppose that we're free to make all the "simplifying assumptions" for this problem. Suppose also that initially the opening fraction of the bypass valve is $0\%$ i.e., the valve is fully closed. My questions are:
- How would the pressure and flow rate change as the bypass valve opening fraction is varied ($0\%$ means fully closed, $100\%$ means fully opened)? In particular, I'm interested to know them at points A, B, X, Y and E.
- Would a high pressure stream at Y intercepting the low pressure stream at E raise the pressure and flow rate of the latter? How could that be quantified?
- Could the valve's opening fraction be linearly related to flow rate and pressure? Meaning, could it assumed that flow rate and pressure at point B would be halved if the valve was half-open ($50\%$ opening fraction)?
- What would be the simplest way to model this valve?
Some questions might seem redundant, but I listed them to get a thorough response, for clarity and understanding. Also, all the numbers are arbitrary and any unreported quantities could be assumed. Thank you.