So I'm imagining that the heated refrigerant and water at controlled boiling point being in a type of heat exchanger where two copper pipes are twisted to gether and covered in insulation, the hot refrigerant liquid water side has pipes narrow in diameter to contain the pressure in the refrigerant and efficiently heat the liquid water. The boiling water passes through the enclosed turbine and into wider pipes of the same setup that allow for the expanded water vapor to cool next to the expanded refrigerant. can you give me an estimate on the difference in diameter of the pipes, as well as an efficiency estimate?

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Poe
To estimate the pipe diameters and efficiency of your proposed heat exchanger system, we need to consider several factors, including fluid dynamics, heat transfer principles, and the specific conditions of your system. Here’s a breakdown of how to approach this:
1. Pipe Diameter Estimation
A. Hot Refrigerant Side
- Objective: The diameter of the pipes carrying the hot refrigerant should be narrow enough to maintain pressure but also allow for efficient heat transfer.
- Typical Values: For refrigerant lines, common diameters range from 0.5 inches (about 12.7 mm) to 2 inches (about 50.8 mm), depending on the flow rate and pressure.
Assumption: Let’s assume you choose a diameter of 0.75 inches (19 mm) for the refrigerant side.
B. Boiling Water Side
- Objective: The diameter of the pipes carrying the boiling water should be wider to allow vapor expansion and minimize pressure drop while ensuring sufficient flow.
- Typical Values: For water flow in heat exchangers, a diameter of 1.5 inches (38 mm) to 3 inches (76 mm) is common.
Assumption: Let’s choose a diameter of 1.5 inches (38 mm) for the boiling water side.
2. Diameter Ratio
- Diameter of Refrigerant Pipe: 0.75 inches (19 mm)
- Diameter of Water Pipe: 1.5 inches (38 mm)
Ratio:
Diameter Ratio=Diameter of Water PipeDiameter of Refrigerant Pipe=1.50.75=2\text{Diameter Ratio} = \frac{\text{Diameter of Water Pipe}}{\text{Diameter of Refrigerant Pipe}} = \frac{1.5}{0.75} = 2Diameter Ratio=Diameter of Refrigerant PipeDiameter of Water Pipe=0.751.5=2
3. Efficiency Estimate
A. Heat Transfer Efficiency
- Heat Exchanger Efficiency: The efficiency of heat exchangers can vary widely (typically between 70% and 95%) depending on design and operational conditions. For a well-designed system using copper pipes and proper insulation, an efficiency of around 85% can be a reasonable estimate.
B. Overall System Efficiency
- Turbine Efficiency:
- The efficiency of the turbine in converting thermal energy to mechanical energy is typically between 70% and 90%. Assuming 80% efficiency for the turbine.
- Overall Efficiency Calculation:
- The overall efficiency (ηoverall\eta_{overall}ηoverall) can be estimated as:
ηoverall=ηheat exchanger×ηturbine\eta_{overall} = \eta_{heat\ exchanger} \times \eta_{turbine}ηoverall=ηheat exchanger×ηturbine
\eta_{overall} = 0.85 \times 0.80 = 0.68 \text{ (or 68%)}
Summary
- Estimated Pipe Diameters:
- Hot Refrigerant Pipe: 0.75 inches (19 mm)
- Boiling Water Pipe: 1.5 inches (38 mm)
- Diameter Ratio: 2:1
- Estimated Overall Efficiency: Approximately 68%
Conclusion
This setup, using a narrower pipe for the hot refrigerant and a wider one for the boiling water, allows for efficient heat transfer while accommodating the pressure dynamics of the system. The estimated overall efficiency of around 68% reflects a practical balance between heat exchange and energy conversion processes.
If you have specific conditions or parameters you'd like to adjust or further explore, please let me know!