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Let's say I have a simple condenser inside of a HVAC system with 1 point of entry(Super-heated Vapour) and 1 point of exit(Saturated Liquid) for my refrigerant r134a.

  • A pipe passes through it with water for heat transfer reasons. I know at all times the $\dot{m}_W$ (mass flow rate) of that water and the EWT (Entry Water Temperature) and LWT (Leaving Water Temperature) via sensors.
  • The condenser is an isobaric process, so pressure at entry $P_1$ = pressure at exit $P_2$. Pressure is known at all times via sensors.
  • I also know the entry temperature $T_1$ via sensors. Its enthalpy $H_1$ and entropy $S_1$ at entry are known via tables.
  • Because I know the pressure at exit $P_2$ and its a saturated liquid, I know other thermodynamic data: $T_2$, $H_2$, and $S_2$.
  • Lastly, I know control measurement like compressor speed and guide vane opening, so I assume, I can estimate the mass flow rate entering my condenser (not sure how?). I also have access to geometric data of condenser.

To my understanding, inside the condenser, that gas becomes a liquid via heat transfer, and the condenser container is at all times, partly filled with R134a liquid and gas.

Given the above info, how would I use energy/mass conservation, fluid equation/ Bernouilli equation to calculate the depth of water inside my condenser tank?

I want to make a least-square/Gauss estimator of my liquid level given known measurements, and that predictive equation to compare with an actual sensor we already have. It's to get liquid level feedback signals for my control system when its value is outside of my liquid level sensor measuring range.

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