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Chapter 4: Modeling Two-phase pressure drops strongly depend on the vapor quality. They are generally expressed by: (33) where the Fanning friction factor ftp depends on the vapor quality and v̄=x⋅vg+(1−x)⋅vl . The total pressure drop is thus obtained by integrating numerically over the exchanger length and by assuming that the vapor quality evolves linearly in the heat exchanger with axial coordinate: 1 2⋅ftpv̄⋅G2 Δptp=∫ D dx⋅L (34) 0h where x is the vapor quality. The condensation heat transfer coefficient is estimated with an expression derived from the Kuo correlation (Kuo et al., 2005), established in the case of a vertical plate heat exchanger fed with R410A: h =C⋅(0.25⋅Co−0.45⋅FR0.25+75⋅Bo0.75) (35) tp l Where Frl is the Froude Number in saturated liquid state, Bo the boiling number and Co the convection number. The heat transfer coefficient correlation is quality-dependent. However, in this model, an average heat transfer coefficient is considered. For this reason, the two-phase heat transfer correlations are integrated by assuming that vapor quality variation is linear with length, the average heat transfer coefficient: Model validation Δ p t p 2 ⋅ f t p v̄ ⋅ G 2 dL= D h 1 h̄=∫h dx (36) tp tp 0 To calibrate the model described above, the experimental data of the first ORC test bench is used. The proposed model is slightly simplified: ➢ The ambient heat losses are neglected since the heat exchangers are well insulated. It was shown in Figure 12 that these losses are very low, the energy unbalance between both sides of the heat exchangers being almost negligible. ➢ The pressure drops are neglected because no accurate pressure drop measurement was installed on the test rig. Experimental results however showed that these pressure drops were very limited in the evaporator. 15PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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