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Energies 2020, 13, 370 16 of 31 Table 2. Performance metrics and cycle parameters at the optimum and four sub-optimum points for the single flow split with a dual expansion cycle. All temperatures are in ◦C. TIT x ηTOT ηth φ T2 T4 T5 T6 T7 T8 T9 T10 Tout 550 1 0.35 1 500 0.30 500 0.50 400 0.40 400 0.60 22.30 26.62 83.77 64.1 14.18 16.93 83.77 64.1 18.76 22.39 83.77 64.1 16.33 19.50 83.77 64.1 15.76 18.82 83.77 64.1 441.4 236.2 225.4 324.9 232.7 233.9 73.8 395.3 80.7 64.1 131.9 55.3 62.1 62.1 395.3 274.5 268.2 379.2 283.3 278.9 124.6 302.6 106.2 95.9 178.3 95.5 99.7 65.9 302.6 244.1 221.4 298.6 208.0 229.7 128.0 114.1 114.1 114.1 114.1 114.1 1 Optimum values of the decision variables. If the mass flow fraction, x, is decreased from the optimum (x = 0.30), the CO2 temperature at the outlet of HTR and entering the LTT is markedly reduced. This results in a temperature at the outlet of LTT lower than the compressor outlet temperature (T8 < T2) and the consequent exclusion of LTR. Conversely, if x is increased (x = 0.50), the temperature at the inlet of LTT increases and approaches the temperature at the outlet of HTT (T7 → T4). On the other hand, the heat at the exhaust from both HTT and LTT is only partially recovered, as demonstrated by the high temperature at the inlet of the cooler (T10 > 120 ◦C). The penalty in ηth and ηTOT deriving from the low x is much higher than that attheEnherigiehs2x0.20I,n13d,exed,theslopeoftheresponsesurfaceismuchsteeperfordecrementsof1x6offro31mthe optimum rather than for increments, as clearly shown by the distance between the contour lines at the high x. Indeed, the slope of the response surface is much steeper for decrements of x from the constant ηTOT in Figure 7. optimum rather than for increments, as clearly shown by the distance between the contour lines at The decrease of TIT (TIT = 400 ◦C in Table 2) implies a contextual decrease of the maximum cycle constant ηTOT in Figure 7. temperature and inlet temperature to LTT, without involving any gain in heat extraction from the heat The decrease of TIT (TIT = 400 °C in Table 2) implies a contextual decrease of the maximum cycle source. Thus, the overall effect is the decrease of ηth and ηTOT. temperature and inlet temperature to LTT, without involving any gain in heat extraction from the Figure 8 shows the T–s diagram of the single flow split with a dual expansion cycle at the optimum heat source. Thus, the overall effect is the decrease of ηth and ηTOT. point. The power cycle is actually composed of two partially superimposed Brayton cycles: The first Figure 8 shows the T–s diagram of the single flow split with a dual expansion cycle at the elementary cycle (in blue) operates between the minimum and maximum temperatures and receives optimum point. The power cycle is actually composed of two partially superimposed Brayton cycles: heat Tfrhoemfirtshteelheemaetnstoauryrcey;ctlehe(insebcloune)doeplermatesnbtaertyweceyncltehe(imn ipninmku)mreacnodvemrsaxhimeautmfrotempthereaetuxrheasuasntdof the first cryeceleivaensdhetahterfreofomrethreahcehaetssaoulorcwe;erthmeasxecimonudmeltemepnetarraytucryec.leA(cicnoprdinink)glrye,ctohvertshehremataflroeffimctiheency of exhaust of the first cycle and therefore reaches a lower maximum temperature. Accordingly, the elementary topping cycle 1 is the ratio between the net power produced by the mass flow rate, m, and thermal efficiency of elementary topping cycle 1 is the ratio between the net power produced by the the heat input from the external heat source (as per Equation (5)). Instead, the thermal efficiency of the mass flow rate, m, and the heat input from the external heat source (as per Equation (5)). Instead, the elementary bottoming cycle 2 is the ratio between the net power produced by m2 and the heat input thermal efficiency of the elementary bottoming cycle 2 is the ratio between the net power produced from the exhaust of topping cycle 1 (as per Equation (6)). by m2 and the heat input from the exhaust of topping cycle 1 (as per Equation (6)). FigurFeig8u.rSei8n.gSliengflloewfloswplsiptlwitiwthithdudaulaleexxppaansiion layoutt::TT––ssddiaigargarmamofothfethoeptoimptuimuthmermthoedrmynoadmyicnamic cycle maximizing η . The cooling profile of the heat source is superimposed. cycle maximizing η T.OThe cooling profile of the heat source is superimposed. TOT Table 3 shows that despite the lower TIT, the thermal efficiency of elementary cycle 2 is almost 10% higher than that of elementary cycle 1 due to the recuperative layout. While the topping elementary cycle enables an effective heat extraction from the external heat source (φ = 83.77%), the bottoming cycle enables an effective heat recovery from the exhaust of the high temperature CO2 turbine.PDF Image | Novel Supercritical CO2 Power Cycles for Waste Heat Recovery
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