Two-Phase Flow Heat Exchanger Analysis
Theory: an isothermal side with changing properties
Overview
I'm designing a refrigeration condenser. Since the refrigerant condenses, can I treat it as constant temperature?
During condensation it's nearly constant, and treating that side as infinite capacity rate makes the effectiveness relation very simple. But real refrigerant enters from the compressor as superheated vapour and leaves as slightly subcooled liquid. Those inlet and outlet zones have much lower heat transfer coefficients than condensation, so lumping everything as condensation misjudges the required area. The basic approach for two-phase exchangers is to split them into zones by phase state.
Effectiveness with phase change
With the phase-change side isothermal, the capacity ratio is zero and effectiveness takes this form regardless of flow arrangement (counterflow, parallel or crossflow).
Zoned area
For each zone — superheated vapour, condensation (evaporation), subcooled liquid (or superheat) — find heat $Q_k$, overall coefficient $U_k$ and log-mean temperature difference, then sum the areas.
The condenser that doubled steam-engine efficiency
The history of two-phase heat exchangers goes back to the separate condenser James Watt conceived around 1765. Newcomen's engines condensed steam by spraying water into the cylinder, cooling the whole cylinder every stroke and wasting great amounts of fuel. Watt condensed the steam in a separate vessel, keeping the cylinder hot and cutting fuel consumption sharply. Heat exchangers that condense and evaporate efficiently still decide the performance of heat engines, from power plants to refrigerators and air conditioners.
Worked examples
Example 1: heating water with steam
Steam condensing at 100 °C heats 2 kg/s of water from 20 °C (water capacity rate 8,360 W/K):
| UA | NTU | Effectiveness | Heat | Water outlet |
|---|---|---|---|---|
| 5,000 W/K | 0.60 | 0.450 | 301 kW | 56.0 °C |
| 10,000 W/K | 1.20 | 0.698 | 467 kW | 75.8 °C |
| 20,000 W/K | 2.39 | 0.909 | 608 kW | 92.7 °C |
| 40,000 W/K | 4.78 | 0.992 | 663 kW | 99.3 °C |
Each doubling of UA yields a smaller gain; beyond NTU 3 the outlet nearly reaches steam temperature, and more area buys little.
Example 2: zoning a refrigerant condenser
R134a at 0.1 kg/s enters as 70 °C superheated vapour, condenses at 40 °C and is subcooled to 35 °C. Cooling water at 1.0 kg/s enters at 30 °C in counterflow. Overall coefficients: 300 superheat, 1,500 condensing, 500 W/m²K subcool (approximate properties):
| Zone | Heat | Share of heat | Area | Share of area |
|---|---|---|---|---|
| Superheated vapour | 3.3 kW | 16% | 0.671 m² | 29% |
| Condensing | 16.3 kW | 80% | 1.410 m² | 62% |
| Subcooled liquid | 0.75 kW | 3.7% | 0.210 m² | 9% |
| Total | 20.4 kW | 100% | 2.291 m² | 100% |
The superheat zone is only 16% of the heat but needs 29% of the area.
Because gas-side heat transfer is poor. Lumping everything as condensation at 40 °C with U = 1,500 gives 1.859 m² — only 81% of the zoned total, so the exchanger would be built nearly 20% too small. In service, condensing pressure would rise to compensate, increasing compressor power. For two-phase exchangers, locate where the phase changes, split into zones, and use appropriate heat transfer correlations for each.
Example 3: pressure drop and saturation temperature
R134a saturation pressure is 293 kPa at 0 °C and 350 kPa at 5 °C, about 11.4 kPa per kelvin here. A 30 kPa pressure drop in an evaporator means saturation temperatures at inlet and outlet differ by 2.6 K — 13% of the 20 K difference between 25 °C air and 5 °C evaporation, not negligible.
Analysis workflow
- Define inlet and outlet states (superheat, quality, subcooling).
- Split into zones where phase changes and compute heat per zone.
- Select heat transfer (condensation, boiling, single phase) and pressure-drop correlations per zone.
- Include saturation shift from pressure drop and march through fine segments.
- Check correlations against test data (outlet temperatures, pressure drop).
“Air conditioning fails in midsummer”
An air conditioner's outdoor unit that should have met its rating fell short in midsummer heat. The condenser had been designed with one lumped coefficient, leaving too little area for the superheat zone; condensation slipped toward the outlet and there was almost no subcooling. High ambient raised condensing temperature further and reduced refrigerant flow — a vicious circle. Revisiting the superheat-zone area with zoned analysis gave a design with margin in the same envelope.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Lumping all as phase change | Area underestimated | Split into zones |
| Ignoring pressure drop | Wrong saturation temperature | Update pressure per segment |
| Single-phase correlations for two-phase | Coefficients far off | Flow-regime-appropriate correlations |
| Averaging high-quality regions | Dryout missed | Evaluate local quality |
| Ignoring oil in refrigerant | Lower heat transfer | Correct for oil |
I'd like to learn related topics.
Check boiling and properties with the boiling curve simulator and steam tables. Related analyses include boiling heat transfer, condensation, pool boiling CFD and thermosiphons.
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