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V. Minea / Applied Thermal Engineering 69 (2014) 143e154 147 1200 120 1000 100 800 80 600 60 400 40 200 20 00 80 85 90 95 100 105 110 115 120 Waste heat inlet temperature, °C (a) 80 85 90 95 100 105 110 115 120 Waste heat inlet temperature, °C (b) Variable feed pump speed: 0-60 Hz Cooling fluid inlet temperature = const = 20°C ORC-50 Variable feed pump speed: 0-60 Hz Cooling fluid inlet temperature = const = 20°C ORC-50 Fig. 3. Expander inlet pressure (a) and temperature (b) as functions of waste heat inlet temperatures at feed pump variable speed (0e60 Hz) and constant cooling fluid inlet temperature (20 C); r: relative (gauge) pressure. wet or saturated vapour at the expander inlet port), the machine would be able to operate correctly and provide maximum power output corresponding to the actual operating conditions [13]. Fig. 5a shows the thermodynamic cycle of a representative run (AD-14) with waste heat and cooling fluids entering the evaporator and condenser at constant temperatures of 105 C and 20 C, respectively. This test was achieved with an evaporator pinch point of about 3.5 C and reasonable condenser sub-cooling (7.7 C). It can be seen that, with an average mass flow rate of 1.93 kg/s, the temperature of the organic fluid at the evaporator exit did not exceed the critical temperature, and that the evaporator super- heating was as low as 4 C. Also, the actual temperature of the vapour leaving the expander (state 6a) was lower than the normal value (state 6) because of the colder liquid injected on both sides of the expander. Under these operating conditions, the net power output or the screw expander was 37.5 kW, i.e. about 75% of the maximum design power output of the ORC-50 prototype machine. The measured energetic balance of test AD-14 (Fig. 5b) was ach- ieved with a net heat-to-electricity conversion energetic efficiency of 7.57% (see Section 3.1.3.1). 3.1.2. Net power output The net power output of the ORC-50 machine was affected, among other parameters, by the waste heat and cooling fluid inlet temperatures, in other words, by the cycle temperature lift. Table 2 shows the extent to which the net power output depends on the expander inlet pressures and temperatures, expansion ratios, and cycle temperature lift at variable feed pump speeds (0e60 Hz) and a constant cooling fluid inlet temperature (20 C). Table 2 (and Fig. 6a) shows that the net power output increased linearly with waste heat inlet temperature, which varied from 85 C to 115 C, associated temperature lift (see Fig. 2), and organic fluid flow rates (see Fig. 4a) at all cooling fluid inlet temperatures (15, 20, 25, 25 and 30 C). For example, with the cooling fluid entering the ORC-50 machine at 20 C, the net power output increased from 19.2 kW to 43 kW (i.e. by 55.3%) when the waste heat inlet Table 2 Net power outputs as functions of waste heat inlet temperatures and pressures increase. temperature increased from 85 C to 115 C. Also, with waste heat entering the ORC-50 machine at 100 C, the net power output dropped from 35.9 kW to 29.8 kW, i.e. by about 17%, when the cooling fluid temperature increased from 15 C (winter conditions) to 30 C (summer conditions). In other words, by using waste heat at the highest available temperatures and higher temperature lifts, the ORC net power output could be proportionally improved. Conversely, for example, at the same waste heat source inlet tem- perature (90 C), the expander electrical power output increased by about 28.3% (i.e., from 20.2 kW to 28.23 kW) when the cooling fluid inlet temperature dropped from 30 C to 15 C. This means that when the cooling water inlet temperature dropped by 1 C, the power output increased by 4.7%. Fig. 6b shows differently the impact of the cooling fluid inlet temperature on the net power output when the waste heat inlet temperature increased from 85 C to 105 C. It can be seen that, with a constant waste heat inlet temperature of 85 C, the ORC-50 machine’s net power output decreased by 19.4% when the cooling fluid inlet temperature increased from 15 C to 30 C. On the other hand, with the waste heat inlet temperature remaining constant at 105 C, the net power output dropped by 12.3% when the cooling fluid inlet temperature increased from 15 C to 30 C. 3.1.3. Heat-to-electricity conversion efficiency The vast majority of industrial applications of ORC machines involve irreversible processes in each component of the cycle that generate internal and external entropy. Among other effects, the process irreversibility makes it impossible to convert all of the available thermal energy into useful work and lowers the cycle overall efficiency [2]. Internal entropy generation is caused by friction (such as a pressure drop in the pipes) and unrestrained expansion (mainly in the expander), while external irreversibility is caused by heat transfers over finite temperature differences from hot to cold fluids (mainly in the pre-heater, evaporator and condenser), or by mechanical work transfers during the expander’s expansion process. The maximum reversible work that a given power cycle would be able to generate during a completely reversible process until it reaches a state in equilibrium with the surroundings (i.e. at same pressure and temperature with the environment), is known as exergy (or availability). A net entropy increase rate is related to the exergy destruction rate [2]. The degree of irreversibility (i.e. the decrease in exergy of the control mass plus the decrease in exergy of the heat transfer processes at the heat source’s temperature minus the increase in exergy of the environment that receive the actual work) can thus be expressed in terms of the exergy destruction rate, which differs for each component of the ORC cycle. For example, the evaporator and condenser, where the heat transfer processes aren’t isobaric, make the largest contribution to the ORC cycle’s overall exergy destruction rate, being the key Waste heat inlet temperature, TIN (C) waste 85 90 95 100 105 Temperature increase, Expander inlet pressure and temperature (see Fig. 5) Expansion ratio, P5/P6a 7.71 8.0 8.2 8.3 8.4 Net power output, W_ net (kW) 22.3 26.4 31 35 39.9 TIN waste ( C) 65 70 75 80 85 TIN cool p5 (kPa, r) 581 656 745 830 911 T5 (C) 79 83 86.4 91 94 Expander inlet pressure, kPa,r Expander inlet temperature, °CPDF Image | Power generation with ORC machines low-grade waste heat
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