Open Access Journal Journal of Power Technologies 98 (1) (2018) 97–105
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Comparison of the Brayton–Brayton Cycle with the Brayton–Diesel Cycle
Mateusz Mostowy∗, Łukasz Szabłowski∗ Institute of Heat Engineering, Warsaw University of Technology, 21/25 Nowowiejska Street, 00-665 Warsaw, Poland
Abstract This article is a comparative analysis of two systems: Brayton–Brayton and Brayton–Diesel. These two systems were both compared with a simple cycle of a gas turbine as a benchmark. The paper compares and contrasts the various advantages and disadvantages of the systems. The comparison with the simple cycle was made possible by having the same mass flow of air at the inlet of the gas turbine compressor for all analyzed cases (in the case of the Brayton–Brayton system—at the inlet of the compressor of the first gas turbine). Compared to the simple cycle, the Brayton–Brayton cycle has greater power and the Brayton–Diesel less. In terms of efficiency both systems outperformed the simple cycle, with the Brayton–Diesel system achieving slightly better results than the Brayton-Brayton.
Keywords: Gas turbine; Brayton-Brayton; Brayton–Diesel
1. Introduction nate when assessing a gas turbine with a regeneration sys- tem are: This text deals with issues surrounding modification of a simple cycle gas turbine, in particular harnessing waste • power output N, MW, or net shaft work N j, kJ/kg], heat energy. Available literature contains a wealth of infor- • mation about the simple cycle gas turbine combined with the thermal efficiency ηc, %. steam cycle (Combined Cycle) [1], but there is little on other However, other factors can apply depending on the circum- types of complex cycles. Sometimes it is economically un- stances, such as the power ramp up rate, MW/minute, space justifiable to build an additional steam cycle, other times it is requirement, m2, and weight of the unit, t. This paper ana- simply unfeasible for other reasons, such as space restraints lyzes the cycles from the thermodynamic point of view, ignor- on oil rigs. Then alternative solutions to the Combined Cy- ing the space requirement, m2, and weight of the unit, t. As cle—in the shape of other types of complex gas turbine cy- the analysis was static, the ramp up rate, MW/minute, was cles—should be explored. Examples of other complex cy- ignored as well. Essentially, the most important factors from cles are: Brayton-Brayton, Brayton–Diesel, Brayton with fuel the economic point of view are generated power N, MW, and cells [2–5], Brayton combined with Organic Rankine Cycle . thermal efficiency ηc, %. Hence, when comparing the Bray- The methods for modeling fuel cells are described in [6–8] ton–Brayton and Brayton–Diesel cycles, the focus shall be and some experimental studies in [9]. There is also a pos- on which has higher N, MW, (N j, kJ/kg]) and/or ηc, %. sibility to combine the Brayton cycle (microturbines) with the The literature is a rich source of information on Bray- Stirling engine. Some information on the modeling and test- ton–Brayton cycles. Theoretical bases are included for ex- ing of Stirling engines can be found in [10–15]. ample in [16]. Information about the industrial applications Central to this paper is a comparative analysis of two of the Brayton–Brayton cycle (the Air Bottoming Cycle) or methods: Brayton–Brayton cycle and the Brayton–Diesel cy- about themselves are included in [17]. Information is scarce cle. on industrial applications of Brayton–Diesel cycles, suggest- Determining which of these two cycles is better depends ing limited interest. . The literature has multiple resources on the criteria selected. The two factors that generally domi- on piston expanders in the Diesel cycle. They are used for example in gas reduction stations for energy recovery [18]. The present research looked at the thermal efficiency η , ∗Corresponding author c Email addresses: [email protected] (Mateusz Mostowy), %, and net shaft work N j, kJ/kg, of the Brayton–Brayton [email protected] (Łukasz Szabłowski) and Brayton–Diesel cycles and investigated the influence of cen84959_ch09.qxd 4/26/05 5:45 PM Page 508
508cen84959_ch09.qxd| Thermodynamics 4/26/05 5:45 PM Page 510 q Fuel in Combustion chamber
3 Heat 2 exchanger
wnet 3 Compressor Turbine 510 | Thermodynamics 2 cen84959_ch09.qxd 4/26/05 5:45 PM Page 508 wnet Compressor Turbine Fresh Exhaust 1 produce 21.6 MW (29,040 hp). The regeneration also reduces the exhaust tem- cen84959_ch09.qxd 4/26/05 5:45 PM Page 508 air gases 4 perature from 600°C (1100°F) to 350°C (650°F). Air is compressed to 3 atm FIGURE 9–29 1 4 before it enters Heatthe intercooler. Compared to steam-turbine and diesel- An open-cycle gas-turbine engine. exchanger 508 | Thermodynamics propulsion systems, the gas turbine offers greater power for a given size and q Fuel weight, high reliability,q long life, and morein convenient operation. The engine Combustion out chamber start-upFIGURE 9–30time has been reduced from 4 h required for a typical steam- propulsion3A closed-cycle system gas-turbine to engine.less than 2 min forHeat a gas turbine. Many modern marine Journal of Power Technologies 98 (1) (2018) 97–105 exchanger 508 | Thermodynamics 2 propulsion systems use gas turbines together with diesel engines because of the wnet 3 Compressor highTurbine fuel consumption of simple-cycle2 gas-turbine engines. In combined diesel qin wnet Fuel w Combustion T 3-4 Isentropic expansionand (ingas-turbine a turbine) systems, diesel is used to provide for efficientnet low-power and 3 Compressor Turbine chamber wturbine Fresh4-1 Constant-pressure Exhaustheat rejection 1 air cruisegases operation,4 and gas turbine is used when high speeds are needed. The T-s and P-v diagrams of an ideal Brayton cycle are shown in Fig. 9–31. P = const. Heat In gas-turbine power plants, the ratio of the compressor work to the tur- 3 q FIGURENotice Back9–29 workthat all four processes of the Brayton cycle are executed1 in steady- 4 in exchanger bine work, called the back work ratio,Heatis very high (Fig. 9–34). Usually 2 4 An open-cycleflow devices; gas-turbine thus, engine. they should be analyzed as steady-flow processes. When exchanger 2 the changes in kinetic andmore potential than energies one-half are neglected, of the theturbine energy workbal- output is used to drive the compres- N qout 3 ance for a steady-flow process can be expressed, on a unit–mass basis, as q Compressor sor. The situation is even worse when the isentropicout efficiencies of the com- Turbine 2 1 P = const. wcompressor qin qout win wout hexit hinlet (9–15) 1 pressor2 1 and the2 turbine areFIGURE low. 9–30 This is quite in contrast to steam power w Therefore, heat transfers plants,to and from where the working the backfluidnet are workA closed-cycle ratio is gas-turbine only a engine.few percent. This is not surpris- Figure 2: TheFIGURE fraction 9–34 of the turbines work used to drive the compressor (a) T-s diagram Compressor q Turbineh h c T T (9–16a) Fresh Exhaust (source: [19]) ing,in however,3 2 p 1 3 since2 2 a liquid is compressed in steam power plants instead of 1 air gases 4 The fraction of the turbineand work used a gas, and the steady-flow work is proportional to the specific volume of the P to drive the compressorT is called the q h h3-4 c IsentropicT T expansion (in a turbine)(9–16b) workingout3 4 1fluid.p 1 4 1 2 back work ratio. 4-1 Constant-pressure heat rejection q 1 Then the thermal efficiency of the ideal Brayton4 cycle under the cold-air- FIGURE 9–29 in Heat A power plant with a high back work ratio requires a larger turbine to Figure 1: An open–cycle gas turbine engine (source: [19]) standard assumptions becomes The T-s and P-v diagrams of an ideal Brayton cycle are shown in Fig. 9–31. 2 3 exchangerP = const. provide the additional power requirements of the compressor. Therefore, the An open-cycle gas-turbine engine. q Notice that all four processes of the Brayton cycle are executed in steady- s = const. s = const. in wnet qout cp T4 T1 T1 T4 T1 1 h 4 1 2 1 > 2 th,Brayton q 1turbinesq flow1 used devices; in thus,gas-turbine they1 should powerbe analyzed plants as steady-flow are larger processes. than When those used in steam the parameters on the results in both cycles. Nowadays in- in in cp T3 T2 T2 T3 T2 1 2 the changes1 in kinetic2 and 1 potential> 2energies are neglected, the energy bal- q power plants of the same net power output. out ance for a steady-flow process can be expressed, on a unit–mass basis, as vestors very rarely decide to build a simple cycle gas tur- Processes 1-2 andqout 3-4 are isentropic, and P2 P3 and P4 P1. Thus, 4 bine out of concerns over efficiency and the environment. 1 1 P = const. T P k 1 k P k 1 k qT q w w h h (9–15) 2 2 1 2> 3 1 2> 1 in3 out 2 1 in out 2 exit inlet qout As fuel prices are a major issue, there is a drive to utilize to FIGURE 9–30 T1 Developmenta P1 b Therefore,a P4 heatb transfers ofT4 Gasto and fromTurbines the working fluid are the greatest extent the energy available, including by adding v Substituting these equationss into the thermal efficiency relation and simpli- A closed-cycle gas-turbine engine.The gas turbine has experiencedqin h3 h2 phenomenalcp T3 T2 progress (9–16anda ) growth since its heat recovery features to existing systems. fying give 1 2 FIGUREFigure 9–31 3: p-v and T-s diagrams for the Brayton cycle (source: [19])first successfuland development in the 1930s. The early gas turbines built in the The comparative analysis determined which of the two cy- P 1 T-s and P-v diagrams for the ideal h 1 q h h (9–17)c T T (9–16b) 1940sth,Brayton and evenk 1 k 1950s outhad 4 simple-cycle1 p 1 4 1 2 efficiencies of about 17 percent cles of interest is better and show advantages and disadvan- Brayton cycle. r p1 2> q Then the thermal efficiency of the ideal Brayton cycle under the cold-air- tages of the Brayton–Diesel cycle. The comparative analysis in because of the low compressor and turbine efficiencies and low turbine inlet • 2 → 3 Constant-pressure heat addition; standard assumptions becomes was facilitated by the fact that the cycles were a modification 2 3 temperatures due to metallurgical limitations of those times. Therefore, gas T 3-4 Isentropic expansion (in a turbine) s = const. s = const. w q c T T T T T 1 3 • → Isentropic expansion (in the turbine); net out p 1 4 1 2 1 4 1 of the same simple cycle gas turbine. 3 4 turbines foundhth,Brayton only limited1 use1 despite their1 versatility1 > 2 and their ability to qin qin c T T T T T 1 4-1 Constant-pressure heat rejection burn a variety of fuels. The effortsp 1 to3 improve2 2 2 1the3> 2 cycle2 efficiency concen- • 4 → 1 Constant-pressure heat rejection. Processes 1-2 and 3-4 are isentropic, and P P and P P . Thus, trated in three areas: 2 3 4 1 2. Materials and Methods The T-s and P-v diagrams of an ideal Brayton1 cycle are shown4 in Fig. 9–31.T P k 1 k P k 1 k T P = const. Processes occurring in the gas turbine, plotted on the p-v 2 2 1 2> 3 1 2> 3 qout q Notice that all four processes of the Brayton cycle are executed in steady-T1 a P1 b a P4 b T4 In order to comparein the Brayton–Brayton and the Bray- and T-s diagrams, were shown in the Fig. 3. 1. Increasing the turbine inlet (or firing) temperatures This has 4 v ton–Diesel cycle, both need to be modifications offlow the same devices; thus, they should be analyzed as(b) P -steady-flowv diagram been processes. theSubstituting primary Whenthese approach equations into taken the thermal to improve efficiency gas-turbinerelation and simpli- efficiency. The tur- fying give simple cycle gas turbine. Modeling cycles withthe different changes 2.1.2.in kinetic Calculation and potential model FIGUREenergies 9–31 are neglected,bine theinlet energy temperatures bal- have increased steadily from about 540°C (1000°F) in 2 1 q T-s and P-v diagrams for the ideal h (9–17) boundary conditions would hamper anyout determination as The entire system was modeled in the program HYSYS.the 1940s to 1425°C (2600°F)th,Brayton and1 evenk 1 k higher today. These increases were ance for a steady-flow process can be expressed, on a unit–mass basis, as r 1 2> to which cycle delivers a greater increase in efficiency and The most commonly used fuelBrayton in the cycle. gas turbine enginesmade is possible by the development ofp new materials and the innovative cool- 1 q q w w h h (9–15) power. P = const. natural gas.1 in Its compositionout 2 1 in is shownout 2 in Tableexit 1. inleting techniques for the critical components such as coating the turbine blades Methane is the predominant constituent part of naturalwith ceramic layers and cooling the blades with the discharge air from the 2.1. Simple cycle (benchmark) Therefore, heatgas. transfers To facilitate to calculations,and from the the working fuel (p. 4 influid Fig. are 4) was s compressor. Maintaining high turbine inlet temperatures with an air-cooling 2.1.1. Thermodynamic(a) T-s diagram description modeled as 100%q methane. h h c T T (9–16a) in 3 2 p 1 3 2 2 technique requires the combustion temperature to be higher to compensate for The principle of the operation of a simple cycle gas turbine The fresh air (p. 1 in Fig. 4) used in all the processes in the and cycle1 was modeled in accordance with ISO conditionsthe [21]. cooling effect of the cooling air. However, higher combustion tempera- is based on the differences between the work used to com- tures increase the amount of nitrogen oxides (NO ), which are responsible for pressP fresh air in the compressor and the work obtained by Fresh air relative humidity was obtained through appropri- x qout h4 h1 cp T4 T1 (9–16b) the expansion of the exhaust gases in the turbine (Fig. 1). ate molar proportion of individual factors1 at the2 inletthe of the formation of ozone at ground level and smog. Using steam as the coolant Fresh air at ambient parameters is compressed inThen the com- the thermalcompressor efficiency (p. 1 in Fig.of 4).the ideal Brayton cycle allowedunder thean increasecold-air- in the turbine inlet temperatures by 200°F without an qin pressor, where its temperature and pressure rise. The air increase in the combustion temperature. Steam is also a much more effective 2 3 standard assumptions becomes at high pressure then flows into the combustion chamber 1Should be noted that at the moment of “adding” fuel, the workingheat transfer medium than air. where combustions = const. starts unders = const. constant pressure. Then hot mediumw is no longer theq same air but is ac mixtureT ofT air and fuel T T T 1 net out p 1 4 1 2 1 4 1 exhaust gases expand in the turbine to ambient pressure.hth,Brayton 1 1 1 1 > 2 qin qin c T T T T T 1 Power is generated on the shaft. p 1 3 2 2 2 1 3> 2 2 To generate power (net work Wnet) on the shaft the work Table 1: Composition of natural gas as a percentage of volume (source: [20]) Processes 1-2 and 3-4 are isentropic, and P2 P3 and P4 P1. Thus, obtained in the turbine Wturbine must be higher than the work gas % of volume 1 4 k 1 k k 1 k used in the compressor Wcompressor. This is shown in Fig. 2. T2 P2 1 2> P3 1 2> T3 CH4 98.39 The thermodynamic cycleq whichout describes the gas turbine C2H6 0.44 T1 a P1 Cb H a0.16P4 b T4 engine is called the Brayton cycle after its inventor [19]. The 3 8 v C4H10 0.07 cycle comprises( fourb) P internally-v diagram reversible processes:Substituting these equations intoC5H 12the thermal0.03 efficiency relation and simpli- N2 0.84 fying give CO2 0.07 FIGURE• 1 → 29–31Isentropic compression (in the compressor); 1 T-s and P-v diagrams for the ideal h 1 (9–17) — 98 — th,Brayton k 1 k Brayton cycle. r p1 2> Journal of Power Technologies 98 (1) (2018) 97–105
Fuel Table 2: ISO conditions for fresh air (source: [21]) Combustion chamber ambient pressure 1.013 bar ambient temperature 15◦C GT1 fresh air relative humidity 60% N1 (gas turbine) Compressor 1 Turbine 1
Fresh Table 3: Molar proportion at the inlet of the compressor (p. 1 in Fig. 4) Exhaust gases air (source: own work) Heat exchanger components molar proportions, % mass proportions, %
water H2O 1.01 0.6331 nitrogen N2 78.20 76.2194 oxygen O2 20.79 23.1475
N GT2 2 Compressor 2 Turbine 2 The Peng-Robinson equation was used as the equation of (air turbine) state of the gas. Fresh The parameters of individual system components are air Exhaust gases summarized in Table 4. In order to obtain the characteristics of thermal efficiency Figure 5: Scheme of the Brayton–Brayton cycle (source: based on the [19]) ηc as a function of the pressure ratio Π pressure in point 2 (in Fig. 4) was changed in the next calculations. The range a) Simple cycle gas b) Brayton-Brayton cycle c) Combined cycle T turbine of changed values was: from 1.013 bar to 50 bar with step 3 3 3 0.1 bar. The characteristics of net shaft work N j were ob- tained in a similar manner. 4 4 7 4 7 The simple cycle gas turbine model created in HYSYS was 2 2 8 2 9 shown in Fig. 4. 6 6 8 1 1 5 1 5 2.2. Brayton–Brayton cycle 2.2.1. Thermodynamic description s
The principle of operation of the Brayton–Brayton cycle Figure 6: T-s diagrams for: a) Brayton cycle, b) Brayton–Brayton cycle, c) is based on the use of exhaust heat from the simple cy- combined cycle (source: own work) cle gas turbine. When the hot gases leave the gas turbine they are not released to the atmosphere but go instead to the heat exchanger. The heat exchanger works exactly like • 6 → 7 Constant-pressure heat addition; a combustion chamber for another gas (air) turbine. This • 7 → 8 Isentropic expansion (in the turbine); way, more power is generated (but on two shafts) after burn- ing the same amount of the fuel. The scheme of the Bray- • 8 → 5 Constant-pressure heat rejection. ton–Brayton cycle is shown in Fig. 5. The thermodynamic cycle which describes the Bray- Processes occurring in the Brayton–Brayton cycle plotted ton–Brayton cycle consists of two Brayton cycles. The on the T-s diagram, were shown in Fig. 6 b). first—GT1—cycle was described in section 2.1.1 on page 98. The second—GT2—cycle comprises four internally 2.2.2. Calculation model reversible processes (as in GT1): The entire system was modeled in HYSYS software. The parameters of the fuel, fresh air and gas equation of state • → 5 6 Isentropic compression (in the compressor); were as described in section 2.1.2 on page 98. Pressure, temperature, relative humidity, components of the fresh air in the bottom part of the Brayton–Brayton cycle were modeled A Thermal efficiency 31,08 % 15,00 C 1499 C Net shaft work 463,8 kJ/kg 50,00 bar 12,00 bar ADJ-1 in accordance with the ISO conditions [21] (like in the simple sprawnosc Power 268,3 MW 17,25 kg/s jed_moc_wew 595,7 kg/s cycle). 4 1,0000 1499 C 5a This scheme consists of two Brayton cycles coupled to- 12,00 bar combustion chamber 595,7 kg/s gether with the heat exchanger. The air part of the cycle 2 G 401,4 C 5 861,6 C 15,00 C (GT2 in Fig. 5) takes ambient air which is then heated in 12,00 bar mix 1,000 bar 1,013 bar 595,7 kg/s 578,5 kg/s 5b the heat exchanger (exhaust gases-fresh air). The heat ex- 1499 C 1 504,2 MW 6 235,9 MW 12,00 bar changer was modeled so that it cools exhaust gases from 0,00 kg/s 3 7 Compressor Turbine the gas turbine (GT1 in Fig. 5) with a fixed temperature dif- ference value equal to 100◦C (difference between p. 4 and 7 Figure 4: Simple cycle gas turbine modeled in HYSYS (source: own work) in Fig. 5). Then the heated air expands in turbine 2.
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Table 4: Parameters of individual system components in Fig. 4 (source: own work) no. on Fig. 4 pressure p, bar temperature T, ◦C mass flow m˙ , kg/s efficiency, % compressor—in 1 1.013 15 578.5 80 compressor—out 2 changed – – fuel 4 50 15 changed - turbine—in 5 – changed – 80 turbine—out 6 1.013 – – efficiency was modeled as isentropic efficiency compressor out pressure was changed after every calculation to get definite pressure ratio turbine in temperature value was changed at 900◦C, 1200◦C, 1500◦C fuel mass flow was changed in such a way as to receive a certain temperature after the combustion chamber
A Table 5: Reference parameters of the gas part in the Brayton–Brayton cycle Thermal efficiency 25,57 % 15,00 C 899,2 C Net shaft work 149,2 kJ/kg 50,00 bar 9,935 bar fuel_amout_regulation (source: own work) sprawnosc jed_moc_wew Power 97,26 MW 7,601 kg/s 586,1 kg/s ◦ 1,0000 temperature T3, C optimal pressure ratio Π,- 2c 899,2 C 472,4 C 2a sigma 9,935 bar 1,013 bar 900 9.8 combustion_chamber B1: sigma 0,7385 586,1 kg/s 586,1 kg/s 1200sigma 19.3 2 G 1500 35.8 360,7 C 3 4 15,00 C 9,935 bar mix1 1,013 bar 2b 578,5 kg/s 899,2 C 1 9,935 bar 296,4 MW 210,2 MW 0,00 kg/s 3a In order to examine the possibility of applying the Bray- 1a Turbine_1 Compressor_1 ton–Brayton cycle to increase the thermal efficiency of the 90,04 C 372,4 C Optimizer - simple cycle gas turbine, it was necessary to demonstrateSpreadsheet 15,00 C 1,95 bar 1,95 bar 1,013 bar 6 7 288,1 C the impact of various system variables. These variables100,0 C 752,0 kg/s heat_exchanger 1,013 bar 34,42 C 5 8 57,63 MW 68,60 MW were: delta_T_wymiennik67,21 C 124,5 C 5a 7a Compressor_2 1,013 bar Turbine_2 • pressure ratio of the compressor in the bottom part (air 586,1 kg/s 4a part) ΠGT2; WYMIENNIK_SPRAWDZENIE
• mass flow of the compressor in the bottom part (air part) Figure 7: Brayton–Brayton cycle modeled in HYSYS (source: own work) m˙ GT2. • Brayton cycle (as in gas turbines); The characteristics of the efficiency of the whole system as a function of the pressure ratio ΠGT2 and the mass flow m˙ GT2 • Diesel cycle (as in cars). of the air part ηc = f (ΠGT2, m˙ GT2) were designated for spe- cific parameters of the gas part of the system (GT1 in Fig. 5). When the hot gases leave the gas turbine they are not re- These parameters were: leased to the atmosphere, but go to the heat exchanger. The heat exchanger warms part of the air from the compressor. • pressure ratio of the compressor in the gas part Π; After that the warmed air goes to the piston expander. In the piston expander power on the shaft is generated. After ex- • temperature after the combustion chamber (n. 3 in T3 pansion, the air is not released directly to the atmosphere, Fig. 5). but goes first to the turbine from the gas turbine cycle. Af- As reference parameters in the gas part, the optimal pres- ter expanding in the turbine, the air is released to the atmo- sure ratios for 3 temperatures were chosen: sphere (once again through the heat exchanger). Notewor- Parameters of individual system components are summa- thy is that the Brayton–Diesel cycle is a combination of the rized in Table 6. turbo-machine and the piston-machine. A chart of the Bray- The Brayton–Brayton cycle model created in HYSYS was ton–Diesel cycle is shown in Fig. 8. shown in Fig. 7. The thermodynamic cycle which describes the Bray- ton–Diesel cycle consists of two Brayton cycles. The gas turbine cycle was described in section 2.1.1. The Diesel cy- 2.3. Brayton–Diesel cycle cle comprises four internally reversible processes: 2.3.1. Thermodynamic description The principle of operation of the Brayton–Diesel cycle is • 1D → 2D Isentropic compression (in a compressor); based partially on the use of the exhaust heat from the sim- • 2D → 3D Constant-pressure heat addition; ple cycle gas turbine (as in the Brayton–Brayton cycle). This cycle consists of two different cycles: • 3D → 4D Isentropic expansion (in a turbine);
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Spark Fuel ■ Spark plug injector 9–6 DIESEL CYCLE: THE IDEAL CYCLE FOR COMPRESSION-IGNITION ENGINES AIR Journal of Power Technologies 98 (1) (2018) 97–105 Air–fuel The Diesel cycle is the ideal cycle for CI reciprocating engines. The CI mixture Fuel spray engine, first proposed by Rudolph Diesel in the 1890s, is very similar to the SI engine discussed in the last section, differing mainly in the method of Table 6: Parameters of individual system components in Fig. 7 (source: own work) initiating combustion. In spark-ignition engines (also known as gasoline no. on the Fig. 7 pressure p, bar temperature T, ◦C mass flow m˙ , kg/s efficiency, % engines), the air–fuel mixture is compressed to a temperature that is below cen84959_ch09.qxd 4/26/05 5:44 PM Page 500 compressor 1—in 1 1.013 15 578.5 80 the autoignition temperature of the fuel, and the combustion process is initi- compressor 1—out 2 changed – – ated by firing a spark plug. In CI engines (also known as diesel engines), fuel 2c 50.000 15 changedGasoline engine – Diesel engine the air is compressed to a temperature that is above the autoignition temper- turbine 1—in 3 – changed – 80 ature of the fuel, and combustion starts on contact as the fuel is injected into FIGURE 9–20 turbine 1—out 4 1.013 – – this hot air. Therefore, the spark plug and carburetor are replaced by a fuel heat exchanger constant value 4T = 100◦C (difference between T and T ) In diesel engines, the spark plug is injector in diesel engines (Fig. 9–20). 500 | Thermodynamics4 7 replaced by a fuel injector, and only compressor 2—in 5 1.013 15 changed 80 In gasoline engines, a mixture of air and fuel is compressed during the Spark Fuel air is compressed■ during the compressor 2—out 6 changed Spark 9–6 DIESEL CYCLE: THEcompression IDEAL CYCLEstroke, and the compression ratios are limited by the onset of plug ◦ injectorcompression process. turbine 2—in 7 – T4 − 100 C – 80 FOR COMPRESSION-IGNITIONautoignition or engineENGINES knock. In diesel engines, only air is compressed dur- turbine 2—out 8 1.013 –AIR – ing the compression stroke, eliminating the possibility of autoignition. P Air–fuel The Diesel cycle is the ideal cycle Therefore,for CI reciprocating diesel engines engines. can Thebe designed CI to operate at much higher com- engine, first proposed by Rudolph Diesel in the 1890s, is very similar to the efficiency was modeled as isentropic efficiency mixture Fuel spray qin pression ratios, typically between 12 and 24. Not having to deal with the SI engine discussed in the last section, differing mainly in the method of 2 3 problem of autoignition has another benefit: many of the stringent require- compressor 1 out pressure was changed in accordance with Table 5 initiating combustion. In spark-ignitionments engines placed (also on the known gasoline as gasoline can now be removed, and fuels that are less engines), the air–fuelIsentropic mixture is compressed to a temperature that is below ◦ ◦ ◦ refined (thus less expensive) can be used in diesel engines. turbine 1 in temperature value was changed at 900 C, 1200 C, 1500 C the autoignition temperature of the fuel, and the combustion process is initi- v The fuel injection process in diesel engines starts when the piston ated by firing a spark plug. In CI engines (also known as diesel engines), fuel mass flow was changed in such a way to receive a certain temperature after the combustion chamber Isentropic approaches TDC and continues during the first part of the power stroke. Gasoline engine Diesel engine the air is compressed to a temperature4 that is above the autoignition temper- Therefore, the combustion process in these engines takes place over a ature of the fuel, and combustionq starts on contact as the fuel is injected into compressor 2 in mass flow was changed as 50%, 60%, 70%, 80%, 90%, 100%, 110%, 120%,FIGURE 130% 9–20 of the mass flow in compressor 1 out longer interval. Because of this longer duration, the combustion process in this hot air. Therefore, the1 spark plug and carburetor are replaced by a fuel In diesel engines, the spark plug is the ideal Diesel cycle is approximated as a constant-pressure heat-addition compressor 2 out pressure value was changed in such a way to receive a pressure ratio of the air part ΠGT2 from 2 to 10 with step 0.1 injector in diesel engines (Fig.v 9–20). replaced by a fuel injector, and only In gasoline(a) P- v diagramengines, a mixture of process.air and fuelIn fact,is compressed this is the during only theprocess where the Otto and the Diesel air is compressed during the compression stroke, and the compressioncycles ratios differ. are The limited remaining by the onsetthree ofprocesses are the same for both ideal compression process. autoignition or engine knock. In dieselcycles. engines, That only is, air process is compressed 1-2 is isentropicdur- compression, 3-4 is isentropic T ing the compression stroke, eliminatingexpansion, the possibility and 4-1 ofis autoignition.constant-volume heat rejection. The similarity P P 3 Therefore, diesel engines can be designedbetween to theoperate two atcycles much is higher also apparentcom- from the P-v and T-s diagrams of Fuel qin 2 qin pression ratios, typically between 12the and Diesel 24. Notcycle, having shown to indeal Fig. with 9–21. the Combustion chamber 3 3D 2D D problem of autoignition has another benefit:Noting many that ofthe the Diesel stringent cycle require- is executed in a piston–cylinder device, ments placedP = constant on the gasoline can now be removed, and fuels that are less Isentropic 4D which forms a closed system, the amount of heat transferred to the working Compressor Turbine G refined2D (thus less expensive) can be usedfluid inat diesel constant engines. pressure and rejected from it at constant volume can be v q Generator The fuel injection processout in dieselexpressed engines as starts when the piston 6 Isentropic 4 approaches TDC and continues during the first part of the power stroke. 1 Heat 4 D v = constant q w u u S q P v v u u Therefore, the combustion process in these enginesin takesb,out place3 over2 ain 2 1 3 2 2 1 3 2 2 exchanger q 1D exhaust 5 out longer interval. Because of this longer duration, the combustion process in h h c T T (9–10a) 1 3 2 p 3 2 Fresh gases D the ideal Diesel cycle is approximated as a constant-pressure heat-addition 1 2 air v s and 7 Piston expander process. In fact, this is the only process where the Otto and the Diesel cycles differ. The remaining three processes are the sameq foru bothu Sidealq u u c T T (9–10b) out 1 4 out 4 1 v 1 4 1 2 8 Figure 9: p-v and T-s diagrams forFIGURE thecycles. Diesel9–21 That cycle is, (source: process[19]) 1-2 is isentropic compression, 3-4 is isentropic Then the thermal efficiency of the ideal Diesel cycle under the cold-air- G T-s andexpansion, P-v diagrams and for4-1 the is ideal constant-volume heat rejection. The similarity T standard assumptions becomes Generator Dieselbetween cycle. the two cycles is also apparent from the P-v and T-s diagrams of qin the Diesel cycle, shown in Fig. 9–21. wnet qout T T T1 T4 T1 1 3 h 1 1 4 1 1 1 > 2 T7 − TNoting6 that the Diesel cycle is executedth,Diesel in a piston–cylinderq q device, k T T kT T T 1 P = constant σ = (1) in in 1 3 2 2 2 1 3> 2 2 4 T −whichT forms a closed system, the amount of heat transferred to the working 2 4 fluid6 at constant pressure and rejected from it at constant volume can be Figure 8: Scheme of the Brayton–Brayton cycle (source: own work) qout where: T7—temperature of theexpressed heated as air after the heat S exchanger, T6v—temperature = constant of the heatedq airin afterwb,out theu3 com-u2 qin P2 v3 v2 u3 u2 1 1 2 1 2 pressor, T4—temperature of the exhaust gases after the tur- h h c T T (9–10a) 3 2 p 1 3 2 2 • 4D → 1D Constant-volume heat rejection. bine. s and (b) T-s diagram Then the heated air expands in the piston expander. S qout u1 u4 qout u4 u1 cv T4 T1 (9–10b) The processes occurring in the Diesel cycle, plotted on the FIGUREIn order 9–21 to examine the possibility of applying the Bray- 1 2 Then the thermal efficiency of the ideal Diesel cycle under the cold-air- p-v and T-s diagrams, were shown in Fig. 9. ton–DieselT-s and P-v diagrams cycle tofor increasethe ideal the thermal efficiency of the Diesel cycle. standard assumptions becomes simple cycle gas turbine, it was necessary to demonstrate w q T T T1 T4 T1 1 h net 1 out 1 4 1 1 1 > 2 the impact of various system variables.th,Diesel Theseq variablesq k T T kT T T 1 2.3.2. Calculation model in in 1 3 2 2 2 1 3> 2 2 were: The entire system was modeled in the program HYSYS. The parameters of fuel, fresh air and the gas equation of • mass flow in the Diesel cycle m˙ 2_D; state were described in subsection 2.1.2. This scheme con- • pressure ratio in the Diesel cycle Π (compression ratio sists of the Brayton cycle and the Diesel cycle coupled to- D r). gether with the heat exchanger. The Diesel part of the cycle (the piston expander in Fig. 8) takes compressed air which As the reference parameters in the Diesel part, optimal pres- is then heated in the heat exchanger (exhaust gases-fresh sure ratio for 1 temperature was chosen: air). The heat exchanger was modeled so as to cool exhaust The parameters of individual system components are gases from the gas turbine (Fig. 8) with a fixed recovery ratio summarized in Table 8. of 0.85. Brayton–Diesel cycle model created in HYSYS was shown Recovery ratio: on Fig. 10.
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Table 7: Reference parameters of the Diesel part in the Brayton–Diesel cycle (source: own work) ◦ temperature T3, C optimal pressure ratio Π,– 1200 19.3
Parameters of the entire Brayton-Diesel system A fuel_amount_regulation sprawnosc Thermal efficiency 37,14 % jed_moc_wew Net shaft work 214,8 kJ/kg 15,00 C 1200 C Sprawnosc cieplna ukladu
419,7 C 382,4 C A A 3,00 bar 2,308 bar 1d reg_sigma same_density Figure 11: Brayton–Diesel cycle modeled in the program HYSYS (source: 200,0 kg/s 1,216 kg/m3 15,00 C 6,014 kJ/kg-C 6,029 kJ/kg-C own1,013 work)bar 41,68 2_D 3_D 4_D 200,0 kg/s 1 149,1 C heat_exchanger 8,186 MW 216,3 C 1,216 kg/m3 3,000 bar 3,000 bar R_moc piston_expaner(adiabatic_expansion) 5,406 kJ/kg-C 200,0 kg/s 380,4 C 200,0 kg/s 94,46 m3/s 1,013 bar 5,484 kJ/kg-C GT1: Compression ratio 2,170 C1 585,2 kg/s E-1 Efficiency of the piston expander 80,00 % 4a Diesel part of the whole mass flow rate 34,57 % T3 = 900 ◦C, Π=9,8 Uklad Diesla 28 Power from piston expander (point in Diesel diagram 3->4->1) 29,48 MW 174,7 C Power of the Diesel system (takes into account the compressive power) 1,922 MW Heat exchanger: 1,576 bar 200,0 kg/s 25 ∆T = 100 ◦C 3ddd 10,78 MW Figure 10: Brayton–Diesel cycle modeled in the program HYSYS (source: 28 energiaD 22
419,7 C 299,7 C own work) kopiowanie_expander 3,000 bar 1,694 bar 24 200,0 kg/s [%] 19 c
3dddd 4dddd η -26,10 MW 20 energiaDD 16 As it was not possible to model the pistonsprezarka_tlokowa expander in 16 HYSYS, a spreadsheet package was used. Thermodynamic 12 13 8 2 relationships which make possible to calculate the power and 3 10 4 efficiency of the Diesel part were included in the spread- 4 5
thermal efficiency 6 7 25
10 7 , 95
sheet. It then became possible to make the calculations. , 80
, 8 65 , 50
, 9 4
35 [–] 289 , 20 347 , 10
The thermodynamic relationships included in the spread- 05 404 , 462 , ABC mass flow of the GT2 ˙ 520
578 Π 636
sheet are as follows: 694 pressure ratio of the GT2 m 752 ABC [kg/s] • Power of the Diesel part:
Rys. 1. Sprawność cieplna ηc w układzie N = N + N − N (2) Figure 12: The thermal efficiency ηc of the Brayton–Brayton cycle for the D 3D→4D 4D→1D 1D→2D Brayton–Brayton.◦ Temperatura T = 900 C temp. T3 = 900 C (source: own3 work)◦ where: N3D→4D—power obtained by the expansion of the (źródło: opracowanie własne) piston expander, N4D→1D—power obtained by the constant- volume heat dissipation, N1D→2D—power consumed for the 3. Results and discussion compression of the fresh air in the gas turbine compressor. 3.1. Brayton–Brayton cycle • Power obtained by the expansion of the piston expander The thermal efficiency ηc of the Brayton–Brayton cycle N : 3D→4D as a function of the mass flow rate m˙ GT2 and pressure ra- tio ΠGT2 of the bottom part ηc = f (ΠGT2, m˙ GT2) are pre- read from the program HYSYS (modeled as the expanding sented in Figures 12–14. The plot for the temperature turbine) ◦ T3 = 900 C—Fig. 12. ◦ • Power obtained by the constant-volume heat dissipation Plot for the temperature T3 = 1200 C—Fig. 13. ◦ N4D→1D: Plot for the temperature T3 = 1500 C—Fig. 14. As can be seen from Figures 12–14, determining the ef- N m · ρ−1 · p − p (3) 4D→1D = ˙ 2_D ( 4_D 1) ficiency of the Brayton–Brayton invoves a very complex re- where: m˙ 2_D—the mass flow of the air to the Diesel part, lationship, combining many parameters of the two gas tur- ρ—density of the fresh air, pi—the pressure in the point i. bines. • Power consumed for the compression of the fresh air in These parameters are: temperature after the combustion chamber of GT1, pressure ratio in GT1, parameters of heat the gas turbine compressor N1→2: exchanger, pressure ratio in GT2, mass flow of air in GT2 (in ˙ L1D→2D = m˙ 2_D · (h2_D − h1) (4) relation to the mass flow in the GT1). where: hi—the enthalpy at point i. Thermal efficiency depends more strongly on the pressure The screenshot of the spreadsheet included in the Diesel ratio ΠGT2 than on the mass flow m˙ GT2. Power output in the part was shown in Fig. 11: Brayton–Brayton cycle is the sum of the power generated in It must be noted that in all calculations only results that the GT1 and GT2 part. The division of the power generated match the physical limitations were taken into account. as a function of ΠGT2 was shown in Fig. 15.
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Table 8: Parameters of individual system components in Fig. 10 (source: own work) no. on Fig. 10 pressure p, bar temperature T, ◦C mass flow m˙ , kg/s efficiency, % compressor 1—in 1 1.013 15 578.5 80 compressor 1—out 1a changed – – compressor 2—in 2p – – m˙ 1 − m˙ 2_D 80 compressor 2—out 2 19.550 – – fuel 2c 50 15 changed – turbine 1—in 3 – 1200 – 80 turbine 1—out 3a p4_D –– turbine 2—in 3b – – – 80 turbine 2—out 4 1.013 – –
T −T recovery ratio σ = 3_D 2_D ≈ 0, 85 T4−T2_D h. e.—in 2_D changed – changed – h. e.—out 3_D – changed – – piston—BDC 4_D changed – – – Efficiency was modeled as isentropic efficiency, compressor 1 out pressure was changed after every calculation to obtain the specified pressure ratio, fuel mass flow was changed so as to receive a certain temperature after the combustion chamber, heat exchanger in the classic Diesel engine that will be the state before the fuel burns in the combustion chamber. In the analyzed model it is the inlet to the heat exchanger, heat exchanger in pressure value was changed to obtain the specified compression ratio of the Diesel part. The vales of the pressure: from 2.026 bar to 9.177 bar with step 0.1013 bar, heat exchanger in the mass flow the value of the mass flow in the Diesel part ranges from 10 kg/s to 350 kg/s, step 1 kg/s, heat exchanger out in the classic Diesel engine that will be the state after the combustion reaction in the combustion chamber ends. In the analyzed model that is inlet to the heat exchanger,Rozdział 2 Rozdział 3 heat exchanger out temperature the value was changed in such a way as to obtain the recovery ratio σ = 0.85 after every iteration, piston Bottom Dead Center piston/pistons in the piston expander are in Bottom Dead Center (after adiabatic expansion and before constant volume heat dissipation), piston1200 Bottom Dead Center pressure was changed in such a way to get same specific volume1500 at points 1 and 4_D
GT1: GT1:
T3 = 1200 ◦C, Π=19,3 36 T3 = 1500 ◦C, Π=35,8 42 Heat exchanger: Heat exchanger: 34 ∆T = 100 ◦C ∆T = 100 ◦C 40 36 32 42 34 40 38 [%] 30 [%]
c 32 c η 30 η 38 28 36 28 36 26 26 34 24 34 2 24 32 2 22 3 3 4 4 20 5 30 5 32 thermal efficiency thermal efficiency 6 22 6 25 25 10 10 7 7 , , 95 95 , , 80 80 , , 8 8 65 65 , , 50 50 , , 9 20 9 30 35 35 [–] [–] 289 289 , , 20 20 347 347 , , 10 10 05 05 404 404 , , 462 462 , , ABC ABC 520 mass flow of the GT2 ˙ 520 mass flow of the GT2 ˙ 578 578 Π Π 636 636 694 694 pressure ratio of the GT2 pressure ratio of the GT2 752 m 752 m ABC [kg/s] ABC [kg/s]
Rys. 2.1. Sprawność cieplna ηc w układzie Rys. 3.1. Sprawność cieplna ηc w układzie Figure 13: The thermal efficiency ηc of the Brayton–Brayton cycle for the Figure 14: The thermal efficiency ηc of the Brayton–Brayton cycle for the Brayton–Brayton.◦ Temperatura Brayton–Brayton.◦ Temperatura temp. T3 = 1200 C (source: own work) temp. T3 = 1500 C (source: own work) T3 = 1200 ◦C(źródło: opracowanie własne) T3 = 1500 ◦C(źródło: opracowanie własne)
◦ 3.2. Brayton–Diesel cycle • temperature T3 = 1200 C.
Power (and efficiency ηc) of the Brayton–Diesel cycle de- The most efficient combinations of the variables were com- pends strongly on the mass flow rate m˙ 2_D in the diesel part pared (Brayton-Brayton: m˙ GT2, ΠGT2; Brayton–Diesel: m˙ 2_D, (Fig. 16) and on the pressure ratio ΠD in the diesel part (com- ΠD). pression ratio r)—Fig. 17. The thermal efficiency of the analyzed cycles is shown in It is worth noting that both the mass flow rate m˙ 2_D and Fig. 18 and their power output in Fig. 19. the pressure ratio ΠD have a strong influence on the value of power generated in the Diesel cycle. 4. Conclusions
3.3. Summary It is difficult to determine in absolute terms which of the To make a meaningful assessment, the same conditions systems presented in this paper is better. Much depends were adopted as with the base gas turbine system. These on the designated purpose for the system. Both the Bray- conditions were: ton–Brayton cycle and Brayton–Diesel occupy a larger area than a conventional gas turbine system. This is due to the • mass flow rate m˙ 1 = 578.5 kg/s; presence of a large heat exchanger, in which gases are the
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237 30 3,0 236 25 2,5 GT1: 235 20 GT2 T3 = 1200 ◦C, Π=19,3 2,0 200 kg/s 234 15 150 kg/s Heat exchanger: , 233 GT1 1 5 100 kg/s 10 σ = 0, 85 232 1,0 5 50 kg/s 231 GT1: 0,5 25 kg/s 0 230 T3 = 1500 ◦C, Π=35,8 0,0 5 229 − Heat exchanger: GT2: 0,5 − 228 10 m˙ = 578,5 kg/s − ∆T = 100 ◦C ABC 1,0 power generated in the GT1 [MW] power generated in the GT2 [MW] − 1 2 3 4 5 6 7 8 9 227 15 power generated in the Diesel cycle [MW] − 2 3 4 5 6 7 8 9 10 pressure ratio ΠDiesla [–] pressure ratio Π [–] Rozdział 5 Rozdział 5 1,00 1,64 2,19 2,69 3,16 3,60 4,01 4,42 4,80 Rys. 4.1. Moc generowana w układzie compression ratio r [–] Figure 15: Power generated in the GT1 and GT2 as a function of ΠGT2 powietrznym oraz gazowym w funkcji sprężu (source:diesel1 own work) Rys. 6.1. Moc generowana w układzie części powietrznej (źródło: opracowanie FigureDiesla w17:diesel1 funkcji Power stopnia generated sprężania/sprężu in the Diesel part as a function of the pressure własne) ratio Π(Dźródło(compression: opracowanie własne) ratio r) (source: own work) 5 r = 2, 19 (ΠDiesla = 3) 0 45 5 − 10 − 3, 59 (6) 15 GT1: [%] 40 − 4, 80 (9) c T3 = 1200 ◦C, Π=19,3 20 η − Heat exchanger: 25 − σ = 0, 85 Brayton–Diesel 30 35 Brayton–Brayton − 0 50 100 150 200 250 300 350 power genereted in the Diesel cycle [MW]
mass flow in the Diesel cyclem ˙ 2 D [kg/s]
Rys. 5.1. Moc generowana w układzie Figure 16: Power generated in the Diesel part as a function of the mass flow simple cycle Diesla w funkcji jej wydatku masowego 30 rate m˙ 2(_źródłoD (source:: opracowanie own własne) work) thermal efficiency working fluid on both sides (which necessitates the consid- erable size). The Brayton–Brayton cycle has greater power 25 than the simple cycle, and the Brayton–Diesel has less. Rys. 5.1. Sprawność cieplna poszczególnych Both systems outperformed the simple cycle in terms of ef- Figure 18: Thermal efficiency of the analyzed cycles (source: own work) układów z turbiną gazową dla T = 1200 C ficiency, with the Brayton–Diesel system achieving slightly 3 ◦ better results than the Brayton-Brayton. An interesting solu- (źródło: opracowanie własne) [8] J. Milewski, K. Futyma, A. Szczesniak, Molten carbonate fuel cell op- tion to increase the efficiency of the gas turbine is described eration under high concentrations of SO2 on the cathode side, IN- in [22, 23]. TERNATIONAL JOURNAL OF HYDROGEN ENERGY 41 (41) (2016) 18769–18777, 3rd International Workshop on Molten Carbonates and Related Topics (IWMC), NE Univ, Shenyang, PEOPLES R CHINA, References JUN 11-13, 2015. doi:10.1016/j.ijhydene.2016.03.121. [9] G. Cinti, U. Desideri, D. Penchini, G. Discepoli, Experimental analy- [1] K. Badyda, Perspektywy rozwoju technologii turbin gazowych oraz sis of sofc fuelled by ammonia, FUEL CELLS 14 (2) (2014) 221–230. bloków gazowo-parowych, Rynek Energii 4 (113) (2014) 74–82. doi:10.1002/fuce.201300276. [2] J. Milewski, A. Miller, Off-design analysis of MCFC hybrid system, [10] D. Thombare, S. Verma, Technological development in the stirling Rynek Energii 1. cycle engines, Renewable and Sustainable Energy Reviews 12 (1) [3] J. Milewski, A. Miller, J. Sałacinski,´ Off-design analysis of sofc hybrid (2008) 1–38. system, International Journal of Hydrogen Energy 32 (6) (2007) 687– [11] A. Chmielewski, R. Guminski,´ S. Radkowski, Chosen properties of a 698. dynamic model of crankshaft assembly with three degrees of freedom, [4] J. Milewski, T. Swiercz,´ K. Badyda, A. Miller, A. Dmowski, P. Biczel, in: Methods and Models in Automation and Robotics (MMAR), 2015 The control strategy for a molten carbonate fuel cell hybrid system, 20th International Conference on, IEEE, 2015, pp. 1038–1043. international journal of hydrogen energy 35 (7) (2010) 2997–3000. [12] A. Chmielewski, R. Guminski,´ J. M ˛aczak,S. Radkowski, P. Szulim, [5] J. Milewski, M. Wołowicz, R. Bernat, L. Szablowski, J. Lewandowski, Aspects of balanced development of res and distributed micro- Variant analysis of the structure and parameters of sofc hybrid sys- cogeneration use in poland: Case study of a µchp with stirling engine, tems, in: Applied Mechanics and Materials, Vol. 437, Trans Tech Publ, Renewable and Sustainable Energy Reviews 60 (2016) 930–952. 2013, pp. 306–312. [13] A. Chmielewski, S. Gontarz, R. Guminski,´ J. M ˛aczak,P. Szulim, Re- [6] J. Kupecki, J. Milewski, A. Szczesniak, R. Bernat, K. Motylinski, Dy- search study of the micro cogeneration system with automatic loading namic numerical analysis of cross-, co-, and counter-current flow con- unit, in: Challenges in Automation, Robotics and Measurement Tech- figuration of a 1 kw-class solid oxide fuel cell stack, International Jour- niques, Springer, 2016, pp. 375–386. nal of Hydrogen Energy 40 (45) (2015) 15834–15844. [14] K. Wang, S. R. Sanders, S. Dubey, F. H. Choo, F. Duan, Stirling cycle [7] J. Milewski, M. Wołowicz, A. Miller, R. Bernat, A reduced order model engines for recovering low and moderate temperature heat: A review, of molten carbonate fuel cell: A proposal, International Journal of Hy- Renewable and Sustainable Energy Reviews 62 (2016) 89–108. drogen Energy 38 (26) (2013) 11565–11575. [15] A. Chmielewski, S. Gontarz, R. Guminski,´ J. M ˛aczak, P. Szulim,
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200
190
180 Brayton–Brayton
[MW] 170 N 160 simple cycle
150
power output 140
130 Brayton–Diesel
120
FigureRys. 19: 5.1. PowerSprawność output of the cieplna analyzed poszczególnych cycles (source: own work) układów z turbiną gazową dla T3 = 1200 ◦C (źródło: opracowanie własne) Research on a micro cogeneration system with an automatic load- applying entity, in: Challenges in Automation, Robotics and Measure- ment Techniques, Springer, 2016, pp. 387–395. [16] K. Badyda, A. Miller, Energetyczne turbiny gazowe oraz układy z ich wykorzystaniem, Wydawnictwo Kaprint, 2014. [17] M. Korobitsyn, Industrial applications of the air bottoming cycle, Energy Conversion and Management 43 (9) (2002) 1311–1322. doi:10.1016/S0196-8904(02)00017-1. [18] Spilling Energie Systeme, Gas expansion. URL http://www.enesko.pl/images/ Spilling-expander_prospekt.pdf [19] Y. Cengel, M. Boles, Thermodynamics: An Engineering Approach with Student Resources DVD, McGraw-Hill Education, 2010. [20] R. Kiš, M. Malcho, M. Janovcová, A CFD Analysis of Flow through a High-Pressure Natural Gas Pipeline with an Undeformed and De- formed Orifice Plate, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering (2014) 606– 609. [21] F. Brooks, GE Gas Turbine Performance Characteristics. URL http://www.up.farsscript.ir/uploads/13316846411.pdf [22] R. Szewalski, Sposób podwy˙zszania sprawnosci´ obiegu energety- cznego turbiny gazowej [a method of increasing the efficiency of the gas turbine’s energy cycle] (1973). [23] P. Ziółkowski, M. Lemanski,´ J. Badur, W. Zakrzewski, Wzrost sprawnosci´ turbiny gazowej przez zastosowanie idei szewalskiego, Rynek Energii (3) (2012) 63–70.
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