A NEW COMPACT HEAT ENGINE

Transcription

1 A NEW COMPACT HEAT ENGINE by Miodrag NOVAKOVI] Original scientific aer UDC: 536.8:621.4 BIBLID: , 6 (2002), 1, The Differential Cylinder Heat Engine (DCHE) reorted consists of two different size cylinders with istons where four assages (channels) enable fluid communications between cylinders. The istons are connected in oosition to share the wor. As the channels are oen and closed by movement of istons the woring fluid assing through the adequate channel is heated, cooled or let adiabaticaly flown from one cylinder to the other. The arrangement enables different thermodynamic cycles to be erformed. Here the Brayton cycle is chosen by adequate choice of volume ratio and by ositioning the channel aertures. During isobaric arts of the cycle the gas is adequately heated or cooled when assing through corresonding channel. During these rocess temeratures remain constant (and different) in each cylinder. The erformance of the engine is analyzed and the arameters and efficiency determined. Introduction The concet of Stirling engine and Stirling cycle aears to attract the interest of researchers and inventors although it aroaches to its bycentenary 1. The Stirling engine is still further develoed and succesfully alied 2. The concet of external combustion engine is more and more attractive for develoing countries as it allows free choice of inexoensive and not olluting fuels, including agricultural waste. The roosed concet may be characterized as further develoment of external combustion engine at mechanical simification. Basic concet of DCHE The basic DCHE engine consists of two different size cylinder where the woring fluid by movement of istons is transferred from one to the other cylinder adiabatic or with the external heat exchange during the fluid transfer. Several ossible arragments of differential cylinder are ossible. Differential Cylinder Heat Engine 45

2 THERMAL SCIENCE: Vol. 6 (2002), No. 1, (DCHE) with two coaxial cylinders is chosen for easy exlanation of erformance (Fig. 1). It can be seen that the volume of one cylinder increases while the other decreases (left large cylinder, right small cylinder). One should note that when the istons move in such a way as to increase the volume in the large cylinder (to right) the woring fluid is in exansion. The movement in oosite direction is comression. Figure 1. Variable differential cylinder arrangement The thermodynamic sys tem such as this one con sist ing of fluid (gas) in two arts of same res sure P which arts could have dif fer ent tem er a tures is a com os ite one. One should have in mind that due to the lin ear na ture of the ideal gas equa tion, all ideal gas laws are valid for this comosit sys tem. If M re re sents the to tal mass (M l + M s ), vol ume V reresents total volume (V l + V s ) and temerature T re re sents av er age tem er a ture (T l M l /M + T s M s /M)in the P, V, T, M re la tions. The four chan nels are fit ted with one-way valve, er mit ting only one way flow of gas. It should be noted that for ev ery o si tion of cou led is tons and the sense of their move ments there is al ways one chan nel oen for as sage of gas from one cyl in der to the other. When the is tons moves to ward right, the fluid flows from small cyl in der to the large one in ex an sion as more sace is ro vided in the large one in ex an sion as more sace is ro vided in the large cyl in der then lost in small cyl in der. 46

3 Novaovi}, M.: A New Comact Heat Engine De ending on the o si tion of is tons and the sense of move ments the flow is achieved through a articular channel, heated, cooled or adi a batic channel. If, during exansion it flows through non-heated chan - nel C 2 (Fig. 2) we have an adi a - batic ex an sion and the tem er - a tures in cyl in ders and the res - sure will fall. If it flows through heated chan nel C 1 then the joint res sure may dro, rise or re - main con stant de end ing on the tem er a ture in crease. The heat ing can be ad justed that the res sure does not change nor the tem er a tures in the cyl in ders. Dur ing such heat - ing ro cess tem er a tures in both cyl in ders re main con stant but the av er age tem er a ture rises as amount of hot gas in the large cyl in der is in creas ing. The res sure of both arts is rac ti cally the same, as the res sure dro due flow ing fluid may be very small. Trans ferring all the gas from small cyl in der to the large one in creases its vol ume r times (the vol ume ra tio). In creasing its tem er a ture in heated as sage at same ra tio r times the ideal gas res - sure re mains same be ing roortional to temera - ture. Sim i lar rea son ing a lies for flow in cooled channel. It should be noted that the DCHE ro - cesses of fluid ass ing the each four chan nels, cor - re sond to four ro - cesses in a Brayton cy cle energy lant comonents (Fig. 3) 3, 4. Figure 2. The heat engine with differential cylinder Figure 3. The Brayton cycle (1) Flow in heated channel C 1 (see Fig. 2) Exansion in the boiler; (2) Flow in adiabatic channel C 2 (see Fig. 2) Exansion in the turbine; (3) Flow in cooled channel C 3 (see Fig. 2) Comression in the condenser; (4) Flow in adiabatic channel C 4 (see Fig. 2) Comression in the comressor 47

4 THERMAL SCIENCE: Vol. 6 (2002), No. 1, Thermodynamic roerties of the DCHE The erformance of the DCHE is reresented on P-V diagram in Fig The hihghest temerature required for rocess T HS is the heat source (reservoir) temerature. It can be deduced from a comeat isobaric rocess P 1 = const, assuming that whole gas is heated to T HS. The T is the heat sin temerature and can be found from isobaric rocess P 3 = const, assuming that the whole gas is cooled to T. In analysis of the DCHE s erformance it is useful to use the following dimensionless arameters: T t HS PH V r T P V L H L (1) Substituting the exressions for V H (V 3 ) and V L (V 1 ) in deffinition of the dimensionless arameter r we have D d r (2) Figure 4. The DCHE on P-V diagram where D and d are the diameters of the large and the small cylinder resectively. Alying adequate equations T/V = = const, and PV = const for isobaric and adiabatic rocesses of the cycle resectively, all the P, V, T data for oints 1, 2, 3 are exressed as function P L, V L, T l and dimensionless arameters and r (see Table 1). The temerature of cold and hot source, T, T HS are also determined (oints 6 and 5 resectively in Fig. 4) T T l 1 (3) T HS T r l 1 (4) It should be noted that there is no fluid with temerature T 2 and T 4, these temeratures corresond to mixed temerature of the fluid in large and small cylinder (V l and V s ). Using the eq. (3) the temeratures of oints 1, 2, 3, 4 are also exressed by T (see Table 1). It is useful to find the relation between the arameters. Combining the eq. (1a) with the exressions for T HS and T one can get the following relation t = r (5) 48

5 Novaovi}, M.: A New Comact Heat Engine Ther mal ef fi ciency of the Brayton cy cle is 6, 7 h 1 1 (6) from eq. (6) it is clear that the 3 P L V L r T l r 1/ T r thermal efficiency of the Brayton 4 P L V L 1/ T l T 1/ cycle increases with the cycle s 5 P L V L r T l 1/ T ressure ratio. The DCHE has 6 P limitation that deends on the L V L T l r ( 1)/ T temerature ratio T HS /T. T HS is the temerature of the heat reservoir and deends on the used fuel. T is the lowest available temerature, i. e. The temerature of the surrounding. So, for the given temerature ration t the DCHE has a maximum heat efficiency when the ressure ratio has a maximum value. It is obvious that the lowest ossible volume ratio r min will be when V 2 V 1 and V 3 V 4, whence V r P min V 1 1 P 3 4 combining with eq. (5) one can get Table 1. The DCHE s state roerties max P V T T 1 P L V L T l ( 1)/ T 2 P L V L r 1/ T l r ( 2)/ T r ( 1)/ 1 1 t (7) The DCHE s maximum useful wor of a cycle er unit mass The useful wor er unit mass in a cycle is W = q ex q comr having in mind q ex = C (T 2 T 3 ) and q comr = C (T 1 T 4 ) substituting for T 1, T 2, T 3 and T 4 from Table 1 (last column): W * m W ( r r ) C T 1 1 (8) whence, with eq. (5) and 1 = 1/, we have 49

6 THERMAL SCIENCE: Vol. 6 (2002), No. 1, W * W m r t r t r r t (9) C T Where W m * is a the dimensionless useful wor er unit mass. The maximum value of W m * at given the occures when the first derivative with resect to r is zero: * ( Wm ) tconst 1 r t 1 r t 1 r t 0 (10) r The nonlinear eq. (10) is solved by Newton-Rhason iteration technique. Results and discussion Figure 5 shows a lot of thermal efficiency of the DCHE vs. temerature ratio t. The curve ETHAMAX reresent the case of the theoretical maximum ossible h for the given t. The other curve (WMMAX) reresents the values of h for the given t when the maximum useful wor is achieved er unit mass. The following Fig. 6 gives us the value of D/d vs. t. Finally in Fig. 7 the values of dimensionless useful wor er unit mass (eq. 9) vs. t is given, with arameters of WMMAX (eq. 10) and with T = 300 K. Figure 5. Thermal efficiency of the DCHE vs.t Figure 6. The DCHE s cylinders ratio vs. t Figure 7. Dimensionless wor of the DCHE vs. t 50

7 Novaovi}, M.: A New Comact Heat Engine Nomenclature C J/gK secific heat caacity at constant nnressure C v [J/gK] secific heat caacity of constant nnvolume D m diameter of the large cylinder d m diameter of the small cylinder secific heat ratio = C /C V M [g] total mass of woring fluid M l [g] mass of woring fluid in large cylinder M s [g] mass of woring fluid in small nncylinder P Pa ressure P H [Pa] high ressure P L [Pa] low ressure Q H J total heat given to the cycle nnat high temerature Q C J total heat extracted from the nncycle in condenser Gree symbols q J/g heat exchanged er 1 g of iworing fluid r volume ratio r min theoretical minimal volume ratio of DCHE s J/g Enthroy T K absolute temerature T K temerature of cold source sin T HS K temerature of hot source Te [K] temerature of woring fluid in large cylinder V L [m 3 ] volume of woring fluid after comresion V H [m 3 ] volume of woring fluid after exansion V l m 3 volume of large cylinder V s volume of small cylinder W J/g useful wor dimensionless useful wor W m * t h Pressure ratio Temerature ratio Thermal efficiency References 1 Organ, A. J., Analysis of the Gas Turbine Rotary Regenerator, Proc. Instn. Mech. Engs., Vol. 211 (1977), Part D, SIGMA Eletrotenis A.S. N-1550 Helen, Norway 3 Chicurel, R., A Modified Otto Engine for Fuel Economy, Alied Energy, 38 (1988), Aly, S. E., Diesel Engine Waste Heat Power Cycle, Alied Energy, 29 (1988), Šarenac, R. Z., MSc thesis, Deartment of Mechanical Engineering, University of Novi Sad, Novi Sad, Yugoslavia (1980) 6 Van Wylen, G. J., Thermodynamics, John Wiley and Sons, New Yor, Novaovi}, M., Djuri}, M., Technical Thermodynamics, Faculty of Technology, University of Novi Sad, Novi Sad, Yugoslavia, 1998 Author s address: M. Novaovi} Faculty of Technology, University of Novi Sad Bul. Cara Lazara 1, Novi Sad, Yugoslavia Paer submited: May 15, 2002 Pare revised: July 1, 2002 Paer acceted: Setember 1,