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Indicated diagrams of a low temperature differential Stirling engine using flat plates as heat exchangers
Renewable Energy 85 (2016) 973e980
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Indicated diagrams of a low temperature differential Stirling engine using flat plates as heat exchangers Yoshitaka Kato* Oita University, 700 Dan-noharu, Oita-shi, Oita, 870-1192, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 March 2014 Received in revised form 11 June 2015 Accepted 20 July 2015 Available online xxx
Indicated diagrams of a low temperature differential (LTD) Stirling engine (SE) were obtained. The evaluation of LTDSE performance was carried out using the results. The heat source temperatures were 75, 80, 85, 90 and 95 Celsius. The working fluid was air with a mean pressure of atmospheric pressure. The shape of the heat exchangers was flat. The stroke volume of the power piston was 3.9 cc, and the stroke volume of the displacer was 238 cc. The LTDSE did not have any regenerators. The maximum indicated power was 3.34 mW. The polytropic exponents becomes larger than 1.4 before the displacer reached dead center, and the working fluid temperatures fluctuated. These behaviors suggest that the heat exchanger did not work effectively. The evaluation of LTDSE performance was carried out using “the maximum fluctuation of ensemble averaged working fluid temperature”. The value is the fluctuation of the internal energy per the heat capacity, and has dimensions of temperature. The obtained values were from 3.2 to 4.7 C. The comparison of these values with actual temperature differences suggests that the indicated work of conventional LTDSE was much lower than the thermodynamic upper limit. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Low temperature differential Stirling engine Indicated diagram Polytropic exponent Internal energy
1. Introduction The aim of the study presented in this paper is the development of a desktop 100 W level low temperature differential (LTD) Stirling engine (SE) with a heat source temperature below 100 C. The aim of the development is to provide distributed power generation equipment for which maintenance is possible on location. In the utilization of a heat source that is not fuel combustion, SE has advantages over various internal combustion engines. Although LTDSEs can generate brake power from a heat source for which exergy is low, the poor power output prevents the practical use of LTDSEs. The heat source temperature which is considered to be a low temperature is not defined clearly. However, present study discusses an LTDSE with a heat source temperature below 100 C since the aim of present study is to contribute to realization of a desktop 100 W level LTDSE. The preceding studies on LTDSEs are much less than studies of conventional SEs. A few reports suggested that an LTDSE could generated watt-level power with a heating of which temperature was approximately 100 C. However, it is
Abbreviations: LTD, low temperature differential; SE, Stirling engine. * Department of Mechanism and Energy System Engineering, Oita University, 700 Dannoharu, Oita-shi, Oita 870-1192, Japan. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.renene.2015.07.053 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
difficult to find out specific ways to improve an LTDSE performance. For example, the evaluation of a regenerator effect requires comparisons of indicated diagrams. Therefore, the data of an LTDSE which does not have a regenerator are required. And, the evaluation methods to compare different LTDSEs. An LTDSE is an SE that can operate under the conditions in which the temperature difference between the heat source and the heat sink is low. In terms of cold side, heat sink is usually atmospheric air or water, except for a cryogenic SE, in which the heat sink is some type of liquefied gas [1,2]. The heat source temperature which is considered to be a low temperature is not defined clearly. For example, Hirata et al. [3] did not refer to their SE as an LTDSE although the SE was operated with an exhaust gas from a Diesel engine. On the contrary, Takeuchi et al. [4] referred to their SE as an LTDSE. The SE described Takeuchi was operated with the 300 C oil. Therefore, an SE that is not heated by combustion directly can be referred to as an LTDSE. However, the review by Kongtragool and Wongwises [5] described LTDSEs from other solar powered SEs, where the heat source is also not combustion heat. Generally, 100 C is considered to be low as a temperature of a heat source. An LTDSE that can operate with a heat source temperature of below 100 C can utilize the latent heat of water. In addition, commodity plastic is available for the material of the LTDSE at this temperature. Therefore, the target temperature of a
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Nomenclature BN C Cv M N P 0 Pm Taverag U V V0 Wout
Beale number [W/(bar$cc$Hz)] constant specific heat [J/(kg$K)] mass of working fluid [kg] engine speed [Hz]/polytropic exponent pressure of working fluid [Pa] mean pressure used for the estimation by Beale number [bar] temperature averaged by the mass of working fluid in an instance [K] internal energy [J] volume of working fluid volume used for the estimation by Beale number [cc] brake power used for the estimation by Beale number [W]
heat source is below 100 C in this study, as mentioned above. The term “LTDSE” has been researched and developed is over a shorter period of time than conventional SEs operating with high temperature heat sources. The first low-temperature difference Stirling engine was presented at the International University Center in Dubrovnik as early as 1983 [6,7]. Ohyagi et al. [8] reported the experimental data for an LTDSE at utilized atmospheric air as the working fluid and was operated with a temperature difference between the heat source and the heat sink of approximately 18 C. Kongtragool and Wongwises [9e11] reported the effect of some parameters on brake power experimentally. Karabulut et al. [12] reported that the beta configuration SE could operate with the hot end temperature of 93 C. In the case of LTDSEs, model LTDSEs are more common. However, there are some reports that LTDSE generated watt-level power with a heating of which temperature was approximately 100 C. Schleder and Zoppke [13] reported a practical LTDSE called “Sunwell50”. The SE worked as a water pump, and the energy source was sunlight. Hoshino and Yoshihara [14] reported two beta-type free piston SEs with expansion space temperature of 100 C. These equipments had flexure springs. One of the engines that Hoshino and Yoshihara reported is based on the test models of a free piston SE converter which was developed for a demonstration of solar heat energy utilization for future aerospace applications. This is a rare case in which a conventional SE operating with a high temperature heat source was converted to an LTDSE. In another engine they reported, the working fluid was helium with a mean pressure of 0.5 MPa. According to their report, the piston power output, which is the difference between the indicated power and the work required to move the displacer, was 11.8 W, although the electrical power output from the mismatched linear alternator was approximately 1 or 2 W. In this condition, the frequency of the piston and the displacer may be 35 Hz with strokes of 8 mm, and the expansion space temperature was 100 C; the coolant temperature was 20 C. Those reports suggest that an LTDSE for practical use can be realized. However, the thermodynamic discussions to improve the indicated work have not been sufficient. As Kato [15] reported, the temperature difference between the hot space and cold space was approximately one tenth of the temperature difference between the heat source and heat sink. The result suggests that the indicated work of an LTDSE was approximately one tenth of upper limit of the ideal p-V diagram. In addition, the brake power of the LTDSE that
Asai and Kato [16] presented was not increased whereas the size of the LTDSE was different order of magnitude than the size of the compared LTDSE. The data was not enough to clarify the reason that the larger size did not provide the more power. As these cases, the discussion of indicated diagrams is required to improve an LTDSE performance. Although Ohyagi et al. [8] showed indicated diagrams, a thermodynamic discussion was not included. The discussion was focused on mechanical efficiency instead. Muramatsu and Tanaka [17] discussed the effect of phase angle on the indicated diagram. In those experiments, the temperature differences were relatively low. However, their equipment was an alpha configuration. An alpha configuration has different layout of heat exchangers from a gamma configuration. In addition, the temperature difference of the discussed experiments was 120 C. Therefore, the report by Muramatsu and Tanaka cannot be utilized directly for the gamma configuration LTDSE in which the heat source temperature is below 100 C. Considering above, the indicated diagrams of a gamma configuration SE must be obtained under the condition of which heat source temperature is lower than 100 C. The method of performance evaluation is also required to further improvement of LTDSE. Beale number BN [18] is used for the evaluation of SE performance, and is well known. Beale number BN is defined by Eq. (1). However, Beale number BN is not suitable for an LTDSE, since Beale number BN is positively correlated with the temperature difference between cold side and hot side. In case of an LTDSE, the dominant factor is not a heat resistance of a heat exchanger. The heat source temperature is dominant factor in an LTDSE. Therefore, the temperatures of heat source and heat sink must be considered in the evaluation of LTDSE performance. 0 Wout ¼ BN Pm Vn0
(1)
The preceding studies have not shown experimental indicated diagrams of LTDSEs. And, except for an indicated work, evaluation methods of an indicated diagram to discuss an LTDSE performance have never been proposed. This paper presents the indicated diagrams of LTDSE in which heat exchangers were flat in shape and which did not have regenerator. The heat source temperatures of all the operation were lower than 100 C. In addition, the fluctuation of internal energy is discussed based on the indicated diagrams. In the discussion, the evaluation method for LTDSE performance is proposed. 2. Choice of heat exchangers' layout LTDSEs can be categorized according the layout of heat exchangers. Fig. 1 shows an LTDSE in which the inner surfaces of the displacer chamber work as heat exchangers, and Fig. 2 shows an LTDSE that has external independent heat exchangers. This paper discusses the LTDSE shown in Fig. 1, since the previous works mentioned below suggested that the type of LTDSE shown in Fig. 1 can obtain higher engine speed than the LTDSE shown in Fig. 2. KATO and Oba [19] carried out a numerical calculation using SCM20 [20]. SCM20 is a numerical simulation program for designing Stirling cycle machines. The calculated specifications were decided by considering the 10 W class LTDSE [21,22]. The followings are assumed. The working fluid is atmospheric air. The power piston and displacer move sinusoidally. The phase angle between the power piston and displacer is 90 . The heat source temperature is 80 C. The heat sink temperature is 20 C. In the LTDSE of which inner surfaces of the displacer chamber work as heat exchangers, two models of heat transfer were adopted. One is the model provided by Haramura and Nakamura [23], and the other model assumed that all of the working fluid in the displacer
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transfer surface significantly, since the inner surface of displacer chamber is large. 3. Experimental method 3.1. Experimental apparatus
Fig. 1. Schematic view of an LTDSE in which the inner surfaces of the displacer chamber work as heat exchangers.
Fig. 2. Schematic view of an LTDSE that has external independent heat exchangers.
chamber flows only in the radial direction with a uniform distribution of velocity. According to the feasibility study, the maximum engine speed of the LTDSE that has independent heat exchangers is 136 rpm since the work to move the displacer increases more than the work obtained from the power piston. In most of model Stirling engines, the heat exchanger is the inner surface of a cylinder or a displacer chamber. In particular, the model SEs made by students, which were introduced by Isshiki et al. [24], tended to depend on the inner surface of a cylinder for heat exchange. In case of a conventional SE operated with a high temperature heat source, the adoption of external independent heat exchangers expands the heat transfer surface significantly. However, in case of a gamma configuration LTDSE, the adoption of external independent heat exchangers does not increase heat
Table 1 shows the specifications of the LTDSE used in the experiments. The experimental apparatus is shown in Fig. 3. In this paper, the upper surface of the displacer chamber worked as a cooler between the heat sink and the working fluid. And, the bottom surface of the displacer chamber works as a heater between the heat source and the working fluid. The shapes of these heat exchangers were flat. The heat sink was atmospheric air or water. The temperature of the atmospheric air was controlled at 20 C. The heat source was the hot water. This hot water did not contact the bottom of the tested LTDSE directly. The bottom of the LTDSE and the hot bath composed a closed section. The hot water filled the closed section with a steam. The steam provided by the hot water heated the tested LTDSE. The hot water temperature was one of the parameters. The phase angle is the difference of the phase angle between the power piston and the displacer. The phase angle in this study is not the difference of volume variations between expansion space and compression space. The phase angle of the measured LTDSE was approximately 140e150 , and the values differed depending on whether the power piston went to the top dead center or to the bottom dead center. Off-set crank mechanism causes such difference of phase angle. Although the phase angle of an LTDSE is generally 90 , the difference between a working fluid pressure and a buffer pressure prevents a progress of a cycle during approximately half of the piston strokes. In case of the adopted phase angle, the pressure difference which prevents a progress of a cycle appears during approximately quarter of the piston stroke. The power piston of the measured LTDSE was composed of a syringe provided by Tsubasa Industry Co. LTD. The working fluid was air, and the buffer pressure was atmospheric pressure. The diameter of the displacer rod was less than 1 mm. Therefore, this paper neglects the volume change caused by the motion of the displacer. The error caused by neglecting this factor is less than 0.0064%. For the pressure measurement in the displacer chamber, the inner pressures of both the hot space and the cold side were measured. The pressure sensor heads were Keyence AP-41A, which have a rated pressure range from 101.3 to 101.3 kPa. The resolution in standard mode was 0.1 kPa, and the response was 1 ms. The amplifier for the pressure sensor head was a Keyence AP-44. A USB oscilloscope Picoscope4424 was used as an A/D converter to send the data of the pressure and crank angle to a personal computer. The resolution of the pressure measurement was 0.167 kPa because of the resolution of the A/D converter. The analog output from the
Table 1 Specifications of the engine. Total volume of displacer chamber [cm3] Volume of displacer [cm3] Stroke volume of displacer [cm3] Stroke volume of power piston [cm3] Height of displacer chamber [cm] Bore of displacer chamber [cm] Height of displacer [cm] Diameter of displacer [cm] Stroke of displacer [cm] Compression ratio Phase angle [degree]
523 95 238 3.9 4.5 12.8 1.0 12.3 2.0 1.009 140e150
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Fig. 3. Measurement system.
AP-44 was from 1 to 4 V, and the range of the analog output was correlated with the rated pressure range of AP-41A. The resolution of the 12bit oscilloscope in the range of from 5 to 5 V is approximately 0.0033 V, which becomes approximately 0.167 kPa. Although a calibration had been carried out using a mercury manometer and a water manometer, it was only used as confirmation that the pressure measurement system had sufficient accuracy for this study. The pressure data were processed by a software low-pass filter of the PicoScope when the pressure was measured. The experiments to determine the filtered frequency was conducted in advance. To obtain the data for the crank angle, a Keyence FU, which consists of a digital fiver sensor FS-N10 Series and an FS-N11N was used. The A/D converter used for the pressure measurement was also used for the crank angle. The rotary disk for the crank angle measurement had slits every 5 for crank angles of 0e350 . On the rotary disc, the area from 350 to 360 was shaded to clarify the position of the top dead center. The end of this shaded area indicated a crank angle of 0 , and the signal in this shaded area was used to trigger the measurement by the oscilloscope. In this paper, a crank angle of 0 indicates the top dead center at which the volume of working fluid is minimum, and the power piston is at the lowest position in the cylinder of the actual equipment. For the temperature measurement, a USB TC-08 thermocouple data logger, which was provided by Pico Technology, sent the data from the thermocouples to the personal computer. T type thermocouples with a diameter of 0.3 mm measured the temperatures of the working fluid in the displacer chamber. K type thermocouples with a diameter of 0.3 mm measured the outer surface temperatures of the heat exchangers, the atmospheric temperature, and the temperature of the steam that worked as the heat source. The temperature data were recorded every 0.1 s by the USB TC-08 thermocouple data logger and the software, and 6 points that contained the temperature measured by the thermistor in the TC08 thermocouple data logger were recorded in the experiments. Therefore, the temperature data were recorded every 0.6 s. The error of the thermocouple was less than 0.6 C when all of the thermocouples and the thermistor were compared. The brake power was not measured due to its low value. Although the measurement of the brake power is interesting, the brake power measurement reduces the experimental conditions in which the LTDSE can operate because of the load caused by the measurement equipment. An investigation of the method to measure the weak brake power does not improve the LTDSE directly. 3.2. Experimental procedures As mentioned above, the atmospheric temperature was controlled to be 20 C. The room temperature was measured near
the equipment during the experiments. The bottom of the SE was heated by steam. The steam was generated by a thermostated bath. To avoid leakage of the steam, the gap between the thermostated bath and the SE was sealed. In the experiments in which the temperature of the cold side heat exchanger was controlled, water cooled system kept the surface temperature of the cold side heat exchanger. The measurement of indicated diagram was started after the measurement temperatures of the operating LTDSE were stable. The parameters were the hot water temperature and the treatment of the cold side heat exchanger temperature. The hot water temperatures were 75, 80, 85, 90 and 95 C. The temperature was measured by the thermometer of a thermostated bath. A hot water temperature of 75 C was the lower limit at which the LTDSE could operate. In terms of the treatment the cold side heat exchanger temperature, both the water-cooled conditions and the air-cooled conditions were performed. 4. Experimental results and discussion 4.1. Temperature distributions and indicated diagrams Tables 2, 3 and Fig. 4 show the experimental data. This paper presents each experiment according to the hot water temperature and the heat sink. In the test name, the number indicates the hot water temperature. For the character following the number, “C” means the experiment in which the temperature of the cold side heat exchanger was 25 C, and “N” means the experiment in which the cold side heat exchanger was cooled by natural convection of surrounding air. Fig. 4 shows the data obtained every 5 of the crank angle from 0 to 350. The pressure data this paper presents are the pressure of the working fluid on the cold side because the measurement system described above did not show a significant pressure difference in the working fluid between the hot side and cold side. In present experiments, the maximum indicated power was 3.34 mW, and the maximum indicated power per unit of the displacer stroke volume was 28 mW/L. The pressure difference between maximum and minimum in each of Fig. 4 is less than the half of that reported by Ohyagi et al. [8]. However, when the values of Beale number divided by Carnot efficiency are compared, the values of present study is a few times of the value of the experimental result reported by Ohyagi et al. The value of the experimental result reported Ohyagi et al. was yielded by the brake power 0.96 mW; the mechanical efficiency 0.915; the buffer pressure 101.3 kPa; the stroke volume of the displacer 1152 cm3; the engine speed 12 rpm; the hot side temperature 22 C; and the cold side temperature 4 C. When Beale number was obtained, a volume was defined by a stroke volume of each displacer, and a brake power was exchanged
Table 2 Data from the experiments in which the cold side heat exchanger temperature was controlled. Test name
75C
80C
85C
90C
95C
Heat source temperature [ C] Heat sink
75 Water
80 Water
85 Water
90 Water
95 Water
Room temperature [ C] Heat exchanger (cold side) [ C] Working fluid (cold side) [ C] Working fluid (hot side) [ C] Heat exchanger (hot side) [ C]
20 25 25 44 67
20 25 26 49 73
20 25 26 51 78
20 25 28 55 83
20 25 28 56 87
Cycle [sec] Indicated work [mJ] Indicated power [mW]
1.79 3.84 2.15
1.57 3.61 2.30
1.60 3.82 2.39
1.58 4.64 2.94
1.30 4.34 3.34
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Table 3 Data from the experiments in which the cold side heat exchanger temperature was not controlled. Test name
75N
80N
85N
90N
95N
Hot water [ C] Heat sink
75 Air
80 Air
85 Air
90 Air
95 Air
Room temperature [ C] Heat exchanger (cold side) [ C] Working fluid (cold side) [ C] Working fluid (hot side) [ C] Heat exchanger (hot side) [ C]
20 27 28 47 68
20 29 29 48 73
20 30 31 52 78
20 32 33 56 84
20 33 35 60 88
Cycle [sec] Indicated work [mJ] Indicated power [mW]
1.75 3.4 1.94
1.81 3.74 2.07
1.69 3.91 2.31
1.78 4.80 2.70
1.60 4.40 2.75
for an indicated power. And, working fluid temperatures were used to calculate Carnot efficiencies. Fig. 5 shows the correlation between the temperature difference of the two heat exchangers and the indicated power. The indicated work of the SE is affected by the load. In the case of the LTDSE, the indicated work is not sufficiently higher than the friction horsepower. Therefore, a small difference in the friction affects the indicated work as a load and obscures the correlation between the temperature difference of the two heat exchangers and the indicated work. As shown in both Tables 2 and 3, the indicated works were not directly proportional to the temperature difference of the two heat exchangers. In test “95N” and test “95C”, the time taken for the cycles were shorter than the values estimated from others, and the indicated works were smaller than the values estimated from others. The behavior of both the test “95N” and the test “95C” suggests that a high engine speed causes a reduction of a time taken for heat transfer. A reduction of a time taken for heat transfer causes a thin indicated diagram. In Tables 2 and 3, the indicated work was not directly proportional to the temperature difference in the working fluid. In case of Schmidt cycle, an indicated work is directly proportional to a temperature difference in a working fluid. However, the temperature distributions of both hot side and cold side are assumed to be uniform in such ideal cycle. In case of actual LTDSE, a temperature of each side is not uniform as Kato [25] presented a CFD results. Therefore, the temperatures measured by one thermocouple were not representative of the space in present study. The temperature differences between the heat source and the surface of the heat exchanger were approximately 7 C. Although the temperature difference of 7 C affected the LTDSE performance, the temperature difference had better not to be discussed based on the present data. In Tables 2 and 3, the indicated power often increased when the heat source temperature increased by 5 C. Therefore, these temperature differences may not be negligible. If the capacity of the thermostated bath was poor, LTDSE operation may lower the temperature. However, the indicated power in each experiment was enough lower than the capacity of the thermostated bath providing steam. Therefore, The temperature difference between the heat source and the heat exchanger is caused by heat losses, and is specific to the present experiments. Each experiment obtained each mean pressure of the working fluid as shown in Fig. 4. A mean pressure of a working fluid is affected by the total mass and temperature distribution of working fluid. A difference between a mean pressure and buffer pressure affects whether or not an LTDSE can operate, since the difference between working fluid pressure and buffer pressure give a force of a piston. In case of present experiments, the buffer pressure was atmospheric pressure. Therefore, the mean pressure does not depend on the experimental condition.
Fig. 4. Indicated diagrams of the experiments shown in Tables 2 and 3.
4.2. Incomplete heat exchange The behavior of the polytropic exponent suggests that the heat exchangers on the walls of displacer chamber did not work effectively. Fig. 6 shows the polytropic exponents calculated from all the indicated diagrams in Fig. 4. A polytropic exponent is defined by Eq. (2), and the polytropic exponents on Fiture 6 were obtained by Eq (3). In the region in which the polytropic exponent is negative, the gradient of the indicated diagram is positive. This process shows either that the working fluid obtains internal energy during the
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And, in the range of crank angle 300 e360 , the total volume of the working fluid becomes greater, and the cold side of the displacer chamber becomes greater. However, the polytropic exponents became larger than 1.4 before the displacer reached dead center in Fig. 6. As mentioned above, during such ranges, the change of internal energy inhibits the progress of the process. As shown in Tables 2 and 3, the temperatures of two heat exchangers were different from the working fluid. Therefore, the heat exchangers worked at any moment in the displacer chamber of both the expanding side and the contracting side. When the displacer was going to the dead center at the neighborhood of the dead center, another side heat exchanger worked less than the heat exchanger the displacer was approaching. 4.3. Temperature fluctuation of working fluid Fig. 5. Correlation between the temperature difference of the two heat exchangers and the indicated power.
Fig. 6. The polytropic exponents were greater than 1.4 before the displacer reached the dead centers.
expansion process or that the working fluid loses internal energy during the compression process. During the process, the change of the internal energy promotes the progress of the process. When the polytropic exponent is greater than the adiabatic exponent, the change of internal energy inhibits the progress of the process. During such processes the work from outside promotes the processes. In ideal gas, the adiabatic exponent is same as the ratio of specific heat. Therefore, the adiabatic exponent can be assumed as 1.4.
pV n ¼ C n¼
ln
Fig. 8 shows that the working fluid temperatures fluctuated. The working fluid temperatures in Tables 2 and 3 are time averages. The width of the fluctuation was less than 1 C. Although Fig. 8 shows the temperature fluctuation of only one experimental condition, such temperature variations of the working fluid occurred in all other experiments. This temperature fluctuation shown in Fig. 8 does not contradict the discussion caused by Fig. 6. If the following two assumptions are reasonable, it is reasonable that the temperatures of the hot side and cold side fluctuate concurrently as shown in Fig. 8. One of the assumptions is that the working fluid flowing into the expanding side dilutes the temperature of an expanding side of a displacer chamber. This assumption is reasonable in present LTDSE which did not have any regenerator. Another assumption is that the working fluid temperature approaches the temperature of the heat exchanger in the contracting side of a displacer chamber. It has not been confirmed experimentally yet. The range of the temperature fluctuation in Fig. 8 is on same order as the temperature change caused by an adiabatic process. However, the width would be affected by a location of the temperature measuring point. The width of temperature fluctuation in each space cannot be evaluated quantitatively. In addition, Fig. 6 suggests that the process in the LTDSE was not an adiabatic process. Therefore, the present data cannot clarify whether or not the compression and expansion by the power piston affected the temperature fluctuations in the displacer chamber. It is confirmed that the working fluid temperature fluctuated. 4.4. Internal energy fluctuation The maximum fluctuation of ensemble averaged working fluid temperature is defined by Eq. (4), under the assumption that the
(2) p2 p1
V 1 ln 1 V2
(3)
In a kinematic SE, after a displacer reaches a dead center, a polytropic exponent is absolutely greater than 1.4 until a power piston reaches a dead center. It is easily clarified without any experiments. The displacer motion of the present experiments is shown in Fig. 7. In Fig. 7, the crank angle 0 is the bottom dead center of the power piston, and the crank angle 180 is the top dead center of the power piston. As Fig. 7 shows, in the range of crank angle 140 e180 , the total volume of the working fluid becomes smaller, and the hot side of the displacer chamber becomes greater.
Fig. 7. The position of the displacer and the crank angle which is 180 at the top dead center of the power piston.
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hot side and the cold side were approximately from 20 to 30 C. The differences in the working fluid temperature between the hot side and the cold side were much higher than the maximum fluctuations of ensemble averaged working fluid temperature. These comparisons suggest that the indicated work of present LTDSE was much lower than the thermodynamic upper limit in each experimental condition. 5. Conclusions Indicated diagrams and temperatures of working fluid were obtained by operating the LTDSE. The heat source temperatures were 75, 80, 85, 90 and 95 C. The maximum indicated power was 3.34 mW, and the maximum indicated power per unit of the displacer stroke volume was 28 mW/L. In obtained indicated diagrams, the polytropic exponents becomes larger than 1.4 before the displacer reached dead center. The behavior of the polytropic exponents suggests that the heat exchanger did not work effectively when the displacer was far. The working fluid temperatures fluctuated. The temperature fluctuations do not contradict the discussion caused by politropic exponent. In addition, “the maximum fluctuations of ensemble averaged working fluid temperature” were calculated for the evaluation. The value is the fluctuation of the internal energy per the heat capacity, and has dimensions of temperature. The obtained values were much lower than the actual temperature differences in present experiments. The comparison suggests that the indicated work of conventional LTDSE was much lower than the thermodynamic upper limit.
Fig. 8. Temperature fluctuations of the working fluid in Test 80C.
working fluid is an ideal gas. It is available to evaluate the thermodynamic performance of the LTDSE. The value is the fluctuation of the internal energy per the heat capacity as Eq. (5) shows and is not affected by the size of the LTDSE. The temperature distribution in the SE is not uniform; therefore, the averaged temperature is not the actual value. This maximum fluctuation of ensemble averaged working fluid temperature is less than the temperature difference between the heat source and the heat sink. Therefore, the comparison of “maximum fluctuation of ensemble averaged working fluid temperature” with the temperature difference between the heat source and the heat sink helps to evaluate thermodynamic performance.
DTaverage ¼
DðpVÞ mR
(4)
DTaverage ¼
DU mCv
(5)
Eqs. (4) and (5) requires the mass of working fluid. The mean volume and the mean working fluid temperature cause estimated mass of working fluid. Although the estimated mass of working fluid causes errors, the error is negligible in the discussion below. Since maximum fluctuation of ensemble averaged working fluid temperature was much lower than the temperature difference between heat source and heat sink in each test condition. If the mass of working fluid was calculated using the heat source temperature or the heat sink temperature, the obtained value causes same discussion. The value DpV is the difference between the maximum pV and the minimum pV in each test condition. The maximum fluctuations of ensemble averaged temperature were from 3.2 to 4.7 C in present experiments. The values were lower than the difference in the working fluid temperature between the hot side and the cold side. In addition, as Tables 2 and 3 show, the differences in the working fluid temperature between the
Acknowledgments The study was supported by ESPEC Foundation for Global Environment Research and Technology (Charitable Trust). References [1] T. Ishikawa, T. Otaka, M. Ito, Operating characteristics of a small size Stirling machine as a cryogenic heat engine (in Japanese), in: Koichi Hirata, Hiroshi Sekiya, Makoto Nohtomi, Masatoshi Shinoki, Yuki Ueda, Toshio Otaka, Yoshitaka Kato, Noboru Kagawa, Shinji Suzuki, Makoto Takeuchi, Makoto Tanaka, Fujio Toda, Kazuhiro Hamaguchi, Yoshihiko Haramura, Yoshikatsu Hiratsuka, Tetsushi Biwa, Takeshi Hoshino (Eds.), Symposium on Stirling Cycle: Proceedings of the 13th Symposium on Stirling Cycle; 2010 Dec 7e8; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2010, pp. 93e94. [2] K. Hirata, Y. Niki, Y. Ichikawa, K. Miki, Performance of cold energy used Stirling engine with New-type heat exchanger (in Japanese), in: Koichi Hirata, Hiroshi Sekiya, Makoto Nohtomi, Masatoshi Shinoki, Yuki Ueda, Toshio Otaka, Yoshitaka Kato, Noboru Kagawa, Shinji Suzuki, Makoto Takeuchi, Makoto Tanaka, Fujio Toda, Kazuhiro Hamaguchi, Yoshihiko Haramura, Yoshikatsu Hiratsuka, Tetsushi Biwa, Takeshi Hoshino (Eds.), Symposium on Stirling Cycle: Proceedings of the 13th Symposium on Stirling Cycle; 2010 Dec 7e8; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2010, pp. 95e96. [3] K. Hirata, E. Ishimura, M. Kawada, T. Akazawa, M. Iida, Development of a marine heat recovery system with Stirling engine generators, in: The Japan Society of Mechanical Engineer (Ed.), The 13th International Stirling Engine Conference: Proceedings of the 13th International Stirling Engine Conference; 2007 Sep 23e26; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2007, pp. 331e336. [4] M. Takeuchi, Y. Abe, S. Suzuki, Z. Nakaya, A. Kitahara, Development of 10 kW class low temperature difference indirect heating Stirling engine using aþ -type mechanism, in: The Japan Society of Mechanical Engineer (Ed.), The 13th International Stirling Engine Conference: Proceedings of the 13th International Stirling Engine Conference; 2007 Sep 23-26; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2007, pp. 42e45. [5] B. Kongtragool, S. Wongwises, A review of solar-powered Stirling engines and low temperature differential Stirling engines, Renew. Sustain. Energy Rev. 7 (2003) 131e154. [6] I. Kolin, S.K. Kolin, M. Golub, Geothermal Electricity Production by Means of the Low Temperature Difference Stirling Engine [homepage on the Internet], The International Geothermal Association, Bochum, Germany, 2000 [updated 2010 Sep 15; cited 2012 Feb 9]. Available from: http://www.geothermalenergy.org/pdf/IGAstandard/WGC/2000/R0856.PDF.
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[7] J.R. Senft, An Introduction to Low Temperature Differential Stirling Engines, first ed., Moriya Press, River Falls WI, 1996. [8] Y. Ohyagi, F. Toda, K. Nakajima, K. Kikuchi, Performance analysis of low temperature difference Stirling engine: behavior of mechanism efficiency (in Japanese) [homepage on the Internet], in: Tokyo, Japan: 7th Symposium on Stirling Cycle, 2003 [cited 2014 Mar 27]. Available from: http://ci.nii.ac.jp/ naid/110002490316. [9] B. Kongtragool, S. Wongwises, A four power-piston low-temperature differential Stirling engine using simulated solar energy as a heat source, Sol. Energy 82 (6) (2008) 493e500. [10] B. Kongtragool, S. Wongwises, Performance of a twin power piston low temperature differential Stirling engine powered by a solar simulator, Sol. Energy 81 (7) (2007) 884e894. [11] B. Kongtragool, S. Wongwises, Performance of low-temperature differential Stirling engines, Renew. Energy 32 (4) (2007) 547e566. [12] H. Karabulut, H.S. Yücesu, C. Çınar, F. Aksoy, An experimental study on the development of a b-type Stirling engine for low and moderate temperature heat sources, Appl. Energy 86 (1) (2009) 68e73. €glichkeiten und grenzen der leistungssteigerung [13] F. Schleder, H. Zoppke, Mo von Niedertemperatur-Stirlingmotoren (in German) [homepage on the Internet], Fachhochschule Trier, Trier, German, 2005 [updated 2005 Nov 18; cited 2014 Mar 27]. Available form, http://www.wald-rlp.de/fileadmin/ website/fawfseiten/fawf/downloads/Projekte/Seeg/NTStirling.pdf. [14] T. Hoshino, S. Yoshihara, Initial performance tests of free piston Stirling engines for low temperature applications (in Japanese), in: Toshio Otaka, Shinji Suzuki, Makoto Takeuchi, Masatoshi Shinoki, Yuki Ueda, Yoshitaka Kato, Noboru Kagawa, Hiroshi Sekiya, Makoto Tanaka, Fujio Toda, Makoto Nohtomi, Kazuhiro Hamaguchi, Yoshihiko Haramura, Koichi Hirata, Yoshikatsu Hiratsuka, Tetsushi Biwa, Takeshi Hoshino (Eds.), Symposium on Stirling Cycle: Proceedings of the 14th Symposium on Stirling Cycle; 2011 Dec 7e8; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2011, pp. 19e22. [15] Y. Kato, Experimental method of thermodynamic optimization for regenerator volume of model Stirling engine as engineering education in provinces, in: The Japan Society of Mechanical Engineer (Ed.), The 13th International Stirling Engine Conference: Proceedings of the 13th International Stirling Engine Conference; 2007 Sep 23e26; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2007, pp. 347e352. [16] Y. Asai, Y. Kato, Low temperature difference model Stirling engine with the displacer swept volume of over 1 litter (in Japanese) [homepage on the Internet], in: Tokyo, Japan: 13th Symposium on Stirling Cycle, 2010 [cited 2014 Mar 27]. Available from: http://ci.nii.ac.jp/naid/110008742258. [17] A. Muramatsu, M. Tanaka, A study on small temperature difference alpha-type
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Stirling engine (in Japanese) [homepage on the Internet], in: Yokohama, Japan: 10th symposium on Stirling Cycle, 2006 [cited 2014 Mar 27]. Available from: http://ci.nii.ac.jp/naid/110006637247. B. Kongtragool, S. Wongwises, Investigation on power output of the gammaconfiguration low temperature differential Stirling engines, Renew. Energy 30 (2005) 465e476. Y. Kato, T. Oba, Evaluation by Numerical Simulation about Simplification of Heat Exchangers in Low Temperature Difference Stirling Engine (in Japanese) [homepage on the Internet], in: National Symposium on Power and Energy Systems 2010, 2010 [cited 2014 Mar 31]. Available from: http://ci.nii.ac.jp/ naid/110008740051. I. Yamashita, K. Hamaguchi, N. Kagawa, K. Hirata, Y. Momose, Design of Stirling Engine (in Japanese), first ed., Power-sha, Tokyo, 2009. S. Iwamoto, F. Toda, K. Hirata, Performance analysis for low temperature difference Stirling engine (behavior of mechanism efficiency) (in Japanese), in: the Japan society of mechanical engineers (Ed.), 74th JSME Fall Annual Meeting, Proc. of 74th JSME Fall Annual Meeting vol.III; 1996 Sep 21e23; Kyoto Japan, The Japan Society of Mechanical Engineers, Tokyo, 1996, pp. 487e488. K. Hirata, 10 W Class Low Temperature Difference Stirling Engine [homepage on the internet]. Tokyo, Japan: Hirata K, 2002 [cited 2014 Mar 27]. Available from: http://www.nmri.go.jp/eng/khirata/stirling/kiriki/10wse/index.html. Y. Haramura, K. Nakamura, Heat transfer due to annular jet induced by displacer motion (in case that whole surface is heated) (in Japanese) [homepage on the Internet], in: Tokyo, Japan: 12th Symposium on Stirling Cycle, 2009 [cited 2014 Mar 27]. Available from: http://ci.nii.ac.jp/naid/110008009306. N. Isshiki, M. Matsuo, I. Fujii, Report on the 9th and 10th Stirling techno rally, in: The Japan Society of Mechanical Engineer (Ed.), The 13th International Stirling Engine Conference: Proceedings of the 13th International Stirling Engine Conference; 2007 Sep 23e26; Tokyo Japan, The Japan Society of Mechanical Engineers, Tokyo, 2007, pp. 370e375. Y. Kato, Numerical analysis of flows around channel shape heat exchanger in low temperature differential Stirling engine (in Japanese), in: the Japan society of mechanical engineers (Ed.), Mechanical Engineering Congress, 2012 Japan, Proc. of Mechanical Engineering Congress, 2012 Japan; 2012 Sep 9e12; Kanazawa Japan, The Japan Society of Mechanical Engineers, Tokyo, 2012, p. S202033.
Yoshitaka Kato B. Sc; 1998 (Tokyo Metropolitan University, Japan), M. Sc. 2000 (Tokyo Institute of Technology, Japan), Ph.D. 2003 (Tokyo Institute of Technology, Japan), Research Associate 2003e2015 (Oita University, Japan).
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Indicated diagrams of a low temperature differential Stirling engine using flat plates as heat exchangers Yoshitaka Kato* Oita University, 700 Dan-noharu, Oita-shi, Oita, 870-1192, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 March 2014 Received in revised form 11 June 2015 Accepted 20 July 2015 Available online xxx
Indicated diagrams of a low temperature differential (LTD) Stirling engine (SE) were obtained. The evaluation of LTDSE performance was carried out using the results. The heat source temperatures were 75, 80, 85, 90 and 95 Celsius. The working fluid was air with a mean pressure of atmospheric pressure. The shape of the heat exchangers was flat. The stroke volume of the power piston was 3.9 cc, and the stroke volume of the displacer was 238 cc. The LTDSE did not have any regenerators. The maximum indicated power was 3.34 mW. The polytropic exponents becomes larger than 1.4 before the displacer reached dead center, and the working fluid temperatures fluctuated. These behaviors suggest that the heat exchanger did not work effectively. The evaluation of LTDSE performance was carried out using “the maximum fluctuation of ensemble averaged working fluid temperature”. The value is the fluctuation of the internal energy per the heat capacity, and has dimensions of temperature. The obtained values were from 3.2 to 4.7 C. The comparison of these values with actual temperature differences suggests that the indicated work of conventional LTDSE was much lower than the thermodynamic upper limit. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Low temperature differential Stirling engine Indicated diagram Polytropic exponent Internal energy
1. Introduction The aim of the study presented in this paper is the development of a desktop 100 W level low temperature differential (LTD) Stirling engine (SE) with a heat source temperature below 100 C. The aim of the development is to provide distributed power generation equipment for which maintenance is possible on location. In the utilization of a heat source that is not fuel combustion, SE has advantages over various internal combustion engines. Although LTDSEs can generate brake power from a heat source for which exergy is low, the poor power output prevents the practical use of LTDSEs. The heat source temperature which is considered to be a low temperature is not defined clearly. However, present study discusses an LTDSE with a heat source temperature below 100 C since the aim of present study is to contribute to realization of a desktop 100 W level LTDSE. The preceding studies on LTDSEs are much less than studies of conventional SEs. A few reports suggested that an LTDSE could generated watt-level power with a heating of which temperature was approximately 100 C. However, it is
Abbreviations: LTD, low temperature differential; SE, Stirling engine. * Department of Mechanism and Energy System Engineering, Oita University, 700 Dannoharu, Oita-shi, Oita 870-1192, Japan. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.renene.2015.07.053 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
difficult to find out specific ways to improve an LTDSE performance. For example, the evaluation of a regenerator effect requires comparisons of indicated diagrams. Therefore, the data of an LTDSE which does not have a regenerator are required. And, the evaluation methods to compare different LTDSEs. An LTDSE is an SE that can operate under the conditions in which the temperature difference between the heat source and the heat sink is low. In terms of cold side, heat sink is usually atmospheric air or water, except for a cryogenic SE, in which the heat sink is some type of liquefied gas [1,2]. The heat source temperature which is considered to be a low temperature is not defined clearly. For example, Hirata et al. [3] did not refer to their SE as an LTDSE although the SE was operated with an exhaust gas from a Diesel engine. On the contrary, Takeuchi et al. [4] referred to their SE as an LTDSE. The SE described Takeuchi was operated with the 300 C oil. Therefore, an SE that is not heated by combustion directly can be referred to as an LTDSE. However, the review by Kongtragool and Wongwises [5] described LTDSEs from other solar powered SEs, where the heat source is also not combustion heat. Generally, 100 C is considered to be low as a temperature of a heat source. An LTDSE that can operate with a heat source temperature of below 100 C can utilize the latent heat of water. In addition, commodity plastic is available for the material of the LTDSE at this temperature. Therefore, the target temperature of a
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Nomenclature BN C Cv M N P 0 Pm Taverag U V V0 Wout
Beale number [W/(bar$cc$Hz)] constant specific heat [J/(kg$K)] mass of working fluid [kg] engine speed [Hz]/polytropic exponent pressure of working fluid [Pa] mean pressure used for the estimation by Beale number [bar] temperature averaged by the mass of working fluid in an instance [K] internal energy [J] volume of working fluid volume used for the estimation by Beale number [cc] brake power used for the estimation by Beale number [W]
heat source is below 100 C in this study, as mentioned above. The term “LTDSE” has been researched and developed is over a shorter period of time than conventional SEs operating with high temperature heat sources. The first low-temperature difference Stirling engine was presented at the International University Center in Dubrovnik as early as 1983 [6,7]. Ohyagi et al. [8] reported the experimental data for an LTDSE at utilized atmospheric air as the working fluid and was operated with a temperature difference between the heat source and the heat sink of approximately 18 C. Kongtragool and Wongwises [9e11] reported the effect of some parameters on brake power experimentally. Karabulut et al. [12] reported that the beta configuration SE could operate with the hot end temperature of 93 C. In the case of LTDSEs, model LTDSEs are more common. However, there are some reports that LTDSE generated watt-level power with a heating of which temperature was approximately 100 C. Schleder and Zoppke [13] reported a practical LTDSE called “Sunwell50”. The SE worked as a water pump, and the energy source was sunlight. Hoshino and Yoshihara [14] reported two beta-type free piston SEs with expansion space temperature of 100 C. These equipments had flexure springs. One of the engines that Hoshino and Yoshihara reported is based on the test models of a free piston SE converter which was developed for a demonstration of solar heat energy utilization for future aerospace applications. This is a rare case in which a conventional SE operating with a high temperature heat source was converted to an LTDSE. In another engine they reported, the working fluid was helium with a mean pressure of 0.5 MPa. According to their report, the piston power output, which is the difference between the indicated power and the work required to move the displacer, was 11.8 W, although the electrical power output from the mismatched linear alternator was approximately 1 or 2 W. In this condition, the frequency of the piston and the displacer may be 35 Hz with strokes of 8 mm, and the expansion space temperature was 100 C; the coolant temperature was 20 C. Those reports suggest that an LTDSE for practical use can be realized. However, the thermodynamic discussions to improve the indicated work have not been sufficient. As Kato [15] reported, the temperature difference between the hot space and cold space was approximately one tenth of the temperature difference between the heat source and heat sink. The result suggests that the indicated work of an LTDSE was approximately one tenth of upper limit of the ideal p-V diagram. In addition, the brake power of the LTDSE that
Asai and Kato [16] presented was not increased whereas the size of the LTDSE was different order of magnitude than the size of the compared LTDSE. The data was not enough to clarify the reason that the larger size did not provide the more power. As these cases, the discussion of indicated diagrams is required to improve an LTDSE performance. Although Ohyagi et al. [8] showed indicated diagrams, a thermodynamic discussion was not included. The discussion was focused on mechanical efficiency instead. Muramatsu and Tanaka [17] discussed the effect of phase angle on the indicated diagram. In those experiments, the temperature differences were relatively low. However, their equipment was an alpha configuration. An alpha configuration has different layout of heat exchangers from a gamma configuration. In addition, the temperature difference of the discussed experiments was 120 C. Therefore, the report by Muramatsu and Tanaka cannot be utilized directly for the gamma configuration LTDSE in which the heat source temperature is below 100 C. Considering above, the indicated diagrams of a gamma configuration SE must be obtained under the condition of which heat source temperature is lower than 100 C. The method of performance evaluation is also required to further improvement of LTDSE. Beale number BN [18] is used for the evaluation of SE performance, and is well known. Beale number BN is defined by Eq. (1). However, Beale number BN is not suitable for an LTDSE, since Beale number BN is positively correlated with the temperature difference between cold side and hot side. In case of an LTDSE, the dominant factor is not a heat resistance of a heat exchanger. The heat source temperature is dominant factor in an LTDSE. Therefore, the temperatures of heat source and heat sink must be considered in the evaluation of LTDSE performance. 0 Wout ¼ BN Pm Vn0
(1)
The preceding studies have not shown experimental indicated diagrams of LTDSEs. And, except for an indicated work, evaluation methods of an indicated diagram to discuss an LTDSE performance have never been proposed. This paper presents the indicated diagrams of LTDSE in which heat exchangers were flat in shape and which did not have regenerator. The heat source temperatures of all the operation were lower than 100 C. In addition, the fluctuation of internal energy is discussed based on the indicated diagrams. In the discussion, the evaluation method for LTDSE performance is proposed. 2. Choice of heat exchangers' layout LTDSEs can be categorized according the layout of heat exchangers. Fig. 1 shows an LTDSE in which the inner surfaces of the displacer chamber work as heat exchangers, and Fig. 2 shows an LTDSE that has external independent heat exchangers. This paper discusses the LTDSE shown in Fig. 1, since the previous works mentioned below suggested that the type of LTDSE shown in Fig. 1 can obtain higher engine speed than the LTDSE shown in Fig. 2. KATO and Oba [19] carried out a numerical calculation using SCM20 [20]. SCM20 is a numerical simulation program for designing Stirling cycle machines. The calculated specifications were decided by considering the 10 W class LTDSE [21,22]. The followings are assumed. The working fluid is atmospheric air. The power piston and displacer move sinusoidally. The phase angle between the power piston and displacer is 90 . The heat source temperature is 80 C. The heat sink temperature is 20 C. In the LTDSE of which inner surfaces of the displacer chamber work as heat exchangers, two models of heat transfer were adopted. One is the model provided by Haramura and Nakamura [23], and the other model assumed that all of the working fluid in the displacer
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transfer surface significantly, since the inner surface of displacer chamber is large. 3. Experimental method 3.1. Experimental apparatus
Fig. 1. Schematic view of an LTDSE in which the inner surfaces of the displacer chamber work as heat exchangers.
Fig. 2. Schematic view of an LTDSE that has external independent heat exchangers.
chamber flows only in the radial direction with a uniform distribution of velocity. According to the feasibility study, the maximum engine speed of the LTDSE that has independent heat exchangers is 136 rpm since the work to move the displacer increases more than the work obtained from the power piston. In most of model Stirling engines, the heat exchanger is the inner surface of a cylinder or a displacer chamber. In particular, the model SEs made by students, which were introduced by Isshiki et al. [24], tended to depend on the inner surface of a cylinder for heat exchange. In case of a conventional SE operated with a high temperature heat source, the adoption of external independent heat exchangers expands the heat transfer surface significantly. However, in case of a gamma configuration LTDSE, the adoption of external independent heat exchangers does not increase heat
Table 1 shows the specifications of the LTDSE used in the experiments. The experimental apparatus is shown in Fig. 3. In this paper, the upper surface of the displacer chamber worked as a cooler between the heat sink and the working fluid. And, the bottom surface of the displacer chamber works as a heater between the heat source and the working fluid. The shapes of these heat exchangers were flat. The heat sink was atmospheric air or water. The temperature of the atmospheric air was controlled at 20 C. The heat source was the hot water. This hot water did not contact the bottom of the tested LTDSE directly. The bottom of the LTDSE and the hot bath composed a closed section. The hot water filled the closed section with a steam. The steam provided by the hot water heated the tested LTDSE. The hot water temperature was one of the parameters. The phase angle is the difference of the phase angle between the power piston and the displacer. The phase angle in this study is not the difference of volume variations between expansion space and compression space. The phase angle of the measured LTDSE was approximately 140e150 , and the values differed depending on whether the power piston went to the top dead center or to the bottom dead center. Off-set crank mechanism causes such difference of phase angle. Although the phase angle of an LTDSE is generally 90 , the difference between a working fluid pressure and a buffer pressure prevents a progress of a cycle during approximately half of the piston strokes. In case of the adopted phase angle, the pressure difference which prevents a progress of a cycle appears during approximately quarter of the piston stroke. The power piston of the measured LTDSE was composed of a syringe provided by Tsubasa Industry Co. LTD. The working fluid was air, and the buffer pressure was atmospheric pressure. The diameter of the displacer rod was less than 1 mm. Therefore, this paper neglects the volume change caused by the motion of the displacer. The error caused by neglecting this factor is less than 0.0064%. For the pressure measurement in the displacer chamber, the inner pressures of both the hot space and the cold side were measured. The pressure sensor heads were Keyence AP-41A, which have a rated pressure range from 101.3 to 101.3 kPa. The resolution in standard mode was 0.1 kPa, and the response was 1 ms. The amplifier for the pressure sensor head was a Keyence AP-44. A USB oscilloscope Picoscope4424 was used as an A/D converter to send the data of the pressure and crank angle to a personal computer. The resolution of the pressure measurement was 0.167 kPa because of the resolution of the A/D converter. The analog output from the
Table 1 Specifications of the engine. Total volume of displacer chamber [cm3] Volume of displacer [cm3] Stroke volume of displacer [cm3] Stroke volume of power piston [cm3] Height of displacer chamber [cm] Bore of displacer chamber [cm] Height of displacer [cm] Diameter of displacer [cm] Stroke of displacer [cm] Compression ratio Phase angle [degree]
523 95 238 3.9 4.5 12.8 1.0 12.3 2.0 1.009 140e150
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Fig. 3. Measurement system.
AP-44 was from 1 to 4 V, and the range of the analog output was correlated with the rated pressure range of AP-41A. The resolution of the 12bit oscilloscope in the range of from 5 to 5 V is approximately 0.0033 V, which becomes approximately 0.167 kPa. Although a calibration had been carried out using a mercury manometer and a water manometer, it was only used as confirmation that the pressure measurement system had sufficient accuracy for this study. The pressure data were processed by a software low-pass filter of the PicoScope when the pressure was measured. The experiments to determine the filtered frequency was conducted in advance. To obtain the data for the crank angle, a Keyence FU, which consists of a digital fiver sensor FS-N10 Series and an FS-N11N was used. The A/D converter used for the pressure measurement was also used for the crank angle. The rotary disk for the crank angle measurement had slits every 5 for crank angles of 0e350 . On the rotary disc, the area from 350 to 360 was shaded to clarify the position of the top dead center. The end of this shaded area indicated a crank angle of 0 , and the signal in this shaded area was used to trigger the measurement by the oscilloscope. In this paper, a crank angle of 0 indicates the top dead center at which the volume of working fluid is minimum, and the power piston is at the lowest position in the cylinder of the actual equipment. For the temperature measurement, a USB TC-08 thermocouple data logger, which was provided by Pico Technology, sent the data from the thermocouples to the personal computer. T type thermocouples with a diameter of 0.3 mm measured the temperatures of the working fluid in the displacer chamber. K type thermocouples with a diameter of 0.3 mm measured the outer surface temperatures of the heat exchangers, the atmospheric temperature, and the temperature of the steam that worked as the heat source. The temperature data were recorded every 0.1 s by the USB TC-08 thermocouple data logger and the software, and 6 points that contained the temperature measured by the thermistor in the TC08 thermocouple data logger were recorded in the experiments. Therefore, the temperature data were recorded every 0.6 s. The error of the thermocouple was less than 0.6 C when all of the thermocouples and the thermistor were compared. The brake power was not measured due to its low value. Although the measurement of the brake power is interesting, the brake power measurement reduces the experimental conditions in which the LTDSE can operate because of the load caused by the measurement equipment. An investigation of the method to measure the weak brake power does not improve the LTDSE directly. 3.2. Experimental procedures As mentioned above, the atmospheric temperature was controlled to be 20 C. The room temperature was measured near
the equipment during the experiments. The bottom of the SE was heated by steam. The steam was generated by a thermostated bath. To avoid leakage of the steam, the gap between the thermostated bath and the SE was sealed. In the experiments in which the temperature of the cold side heat exchanger was controlled, water cooled system kept the surface temperature of the cold side heat exchanger. The measurement of indicated diagram was started after the measurement temperatures of the operating LTDSE were stable. The parameters were the hot water temperature and the treatment of the cold side heat exchanger temperature. The hot water temperatures were 75, 80, 85, 90 and 95 C. The temperature was measured by the thermometer of a thermostated bath. A hot water temperature of 75 C was the lower limit at which the LTDSE could operate. In terms of the treatment the cold side heat exchanger temperature, both the water-cooled conditions and the air-cooled conditions were performed. 4. Experimental results and discussion 4.1. Temperature distributions and indicated diagrams Tables 2, 3 and Fig. 4 show the experimental data. This paper presents each experiment according to the hot water temperature and the heat sink. In the test name, the number indicates the hot water temperature. For the character following the number, “C” means the experiment in which the temperature of the cold side heat exchanger was 25 C, and “N” means the experiment in which the cold side heat exchanger was cooled by natural convection of surrounding air. Fig. 4 shows the data obtained every 5 of the crank angle from 0 to 350. The pressure data this paper presents are the pressure of the working fluid on the cold side because the measurement system described above did not show a significant pressure difference in the working fluid between the hot side and cold side. In present experiments, the maximum indicated power was 3.34 mW, and the maximum indicated power per unit of the displacer stroke volume was 28 mW/L. The pressure difference between maximum and minimum in each of Fig. 4 is less than the half of that reported by Ohyagi et al. [8]. However, when the values of Beale number divided by Carnot efficiency are compared, the values of present study is a few times of the value of the experimental result reported by Ohyagi et al. The value of the experimental result reported Ohyagi et al. was yielded by the brake power 0.96 mW; the mechanical efficiency 0.915; the buffer pressure 101.3 kPa; the stroke volume of the displacer 1152 cm3; the engine speed 12 rpm; the hot side temperature 22 C; and the cold side temperature 4 C. When Beale number was obtained, a volume was defined by a stroke volume of each displacer, and a brake power was exchanged
Table 2 Data from the experiments in which the cold side heat exchanger temperature was controlled. Test name
75C
80C
85C
90C
95C
Heat source temperature [ C] Heat sink
75 Water
80 Water
85 Water
90 Water
95 Water
Room temperature [ C] Heat exchanger (cold side) [ C] Working fluid (cold side) [ C] Working fluid (hot side) [ C] Heat exchanger (hot side) [ C]
20 25 25 44 67
20 25 26 49 73
20 25 26 51 78
20 25 28 55 83
20 25 28 56 87
Cycle [sec] Indicated work [mJ] Indicated power [mW]
1.79 3.84 2.15
1.57 3.61 2.30
1.60 3.82 2.39
1.58 4.64 2.94
1.30 4.34 3.34
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Table 3 Data from the experiments in which the cold side heat exchanger temperature was not controlled. Test name
75N
80N
85N
90N
95N
Hot water [ C] Heat sink
75 Air
80 Air
85 Air
90 Air
95 Air
Room temperature [ C] Heat exchanger (cold side) [ C] Working fluid (cold side) [ C] Working fluid (hot side) [ C] Heat exchanger (hot side) [ C]
20 27 28 47 68
20 29 29 48 73
20 30 31 52 78
20 32 33 56 84
20 33 35 60 88
Cycle [sec] Indicated work [mJ] Indicated power [mW]
1.75 3.4 1.94
1.81 3.74 2.07
1.69 3.91 2.31
1.78 4.80 2.70
1.60 4.40 2.75
for an indicated power. And, working fluid temperatures were used to calculate Carnot efficiencies. Fig. 5 shows the correlation between the temperature difference of the two heat exchangers and the indicated power. The indicated work of the SE is affected by the load. In the case of the LTDSE, the indicated work is not sufficiently higher than the friction horsepower. Therefore, a small difference in the friction affects the indicated work as a load and obscures the correlation between the temperature difference of the two heat exchangers and the indicated work. As shown in both Tables 2 and 3, the indicated works were not directly proportional to the temperature difference of the two heat exchangers. In test “95N” and test “95C”, the time taken for the cycles were shorter than the values estimated from others, and the indicated works were smaller than the values estimated from others. The behavior of both the test “95N” and the test “95C” suggests that a high engine speed causes a reduction of a time taken for heat transfer. A reduction of a time taken for heat transfer causes a thin indicated diagram. In Tables 2 and 3, the indicated work was not directly proportional to the temperature difference in the working fluid. In case of Schmidt cycle, an indicated work is directly proportional to a temperature difference in a working fluid. However, the temperature distributions of both hot side and cold side are assumed to be uniform in such ideal cycle. In case of actual LTDSE, a temperature of each side is not uniform as Kato [25] presented a CFD results. Therefore, the temperatures measured by one thermocouple were not representative of the space in present study. The temperature differences between the heat source and the surface of the heat exchanger were approximately 7 C. Although the temperature difference of 7 C affected the LTDSE performance, the temperature difference had better not to be discussed based on the present data. In Tables 2 and 3, the indicated power often increased when the heat source temperature increased by 5 C. Therefore, these temperature differences may not be negligible. If the capacity of the thermostated bath was poor, LTDSE operation may lower the temperature. However, the indicated power in each experiment was enough lower than the capacity of the thermostated bath providing steam. Therefore, The temperature difference between the heat source and the heat exchanger is caused by heat losses, and is specific to the present experiments. Each experiment obtained each mean pressure of the working fluid as shown in Fig. 4. A mean pressure of a working fluid is affected by the total mass and temperature distribution of working fluid. A difference between a mean pressure and buffer pressure affects whether or not an LTDSE can operate, since the difference between working fluid pressure and buffer pressure give a force of a piston. In case of present experiments, the buffer pressure was atmospheric pressure. Therefore, the mean pressure does not depend on the experimental condition.
Fig. 4. Indicated diagrams of the experiments shown in Tables 2 and 3.
4.2. Incomplete heat exchange The behavior of the polytropic exponent suggests that the heat exchangers on the walls of displacer chamber did not work effectively. Fig. 6 shows the polytropic exponents calculated from all the indicated diagrams in Fig. 4. A polytropic exponent is defined by Eq. (2), and the polytropic exponents on Fiture 6 were obtained by Eq (3). In the region in which the polytropic exponent is negative, the gradient of the indicated diagram is positive. This process shows either that the working fluid obtains internal energy during the
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And, in the range of crank angle 300 e360 , the total volume of the working fluid becomes greater, and the cold side of the displacer chamber becomes greater. However, the polytropic exponents became larger than 1.4 before the displacer reached dead center in Fig. 6. As mentioned above, during such ranges, the change of internal energy inhibits the progress of the process. As shown in Tables 2 and 3, the temperatures of two heat exchangers were different from the working fluid. Therefore, the heat exchangers worked at any moment in the displacer chamber of both the expanding side and the contracting side. When the displacer was going to the dead center at the neighborhood of the dead center, another side heat exchanger worked less than the heat exchanger the displacer was approaching. 4.3. Temperature fluctuation of working fluid Fig. 5. Correlation between the temperature difference of the two heat exchangers and the indicated power.
Fig. 6. The polytropic exponents were greater than 1.4 before the displacer reached the dead centers.
expansion process or that the working fluid loses internal energy during the compression process. During the process, the change of the internal energy promotes the progress of the process. When the polytropic exponent is greater than the adiabatic exponent, the change of internal energy inhibits the progress of the process. During such processes the work from outside promotes the processes. In ideal gas, the adiabatic exponent is same as the ratio of specific heat. Therefore, the adiabatic exponent can be assumed as 1.4.
pV n ¼ C n¼
ln
Fig. 8 shows that the working fluid temperatures fluctuated. The working fluid temperatures in Tables 2 and 3 are time averages. The width of the fluctuation was less than 1 C. Although Fig. 8 shows the temperature fluctuation of only one experimental condition, such temperature variations of the working fluid occurred in all other experiments. This temperature fluctuation shown in Fig. 8 does not contradict the discussion caused by Fig. 6. If the following two assumptions are reasonable, it is reasonable that the temperatures of the hot side and cold side fluctuate concurrently as shown in Fig. 8. One of the assumptions is that the working fluid flowing into the expanding side dilutes the temperature of an expanding side of a displacer chamber. This assumption is reasonable in present LTDSE which did not have any regenerator. Another assumption is that the working fluid temperature approaches the temperature of the heat exchanger in the contracting side of a displacer chamber. It has not been confirmed experimentally yet. The range of the temperature fluctuation in Fig. 8 is on same order as the temperature change caused by an adiabatic process. However, the width would be affected by a location of the temperature measuring point. The width of temperature fluctuation in each space cannot be evaluated quantitatively. In addition, Fig. 6 suggests that the process in the LTDSE was not an adiabatic process. Therefore, the present data cannot clarify whether or not the compression and expansion by the power piston affected the temperature fluctuations in the displacer chamber. It is confirmed that the working fluid temperature fluctuated. 4.4. Internal energy fluctuation The maximum fluctuation of ensemble averaged working fluid temperature is defined by Eq. (4), under the assumption that the
(2) p2 p1
V 1 ln 1 V2
(3)
In a kinematic SE, after a displacer reaches a dead center, a polytropic exponent is absolutely greater than 1.4 until a power piston reaches a dead center. It is easily clarified without any experiments. The displacer motion of the present experiments is shown in Fig. 7. In Fig. 7, the crank angle 0 is the bottom dead center of the power piston, and the crank angle 180 is the top dead center of the power piston. As Fig. 7 shows, in the range of crank angle 140 e180 , the total volume of the working fluid becomes smaller, and the hot side of the displacer chamber becomes greater.
Fig. 7. The position of the displacer and the crank angle which is 180 at the top dead center of the power piston.
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hot side and the cold side were approximately from 20 to 30 C. The differences in the working fluid temperature between the hot side and the cold side were much higher than the maximum fluctuations of ensemble averaged working fluid temperature. These comparisons suggest that the indicated work of present LTDSE was much lower than the thermodynamic upper limit in each experimental condition. 5. Conclusions Indicated diagrams and temperatures of working fluid were obtained by operating the LTDSE. The heat source temperatures were 75, 80, 85, 90 and 95 C. The maximum indicated power was 3.34 mW, and the maximum indicated power per unit of the displacer stroke volume was 28 mW/L. In obtained indicated diagrams, the polytropic exponents becomes larger than 1.4 before the displacer reached dead center. The behavior of the polytropic exponents suggests that the heat exchanger did not work effectively when the displacer was far. The working fluid temperatures fluctuated. The temperature fluctuations do not contradict the discussion caused by politropic exponent. In addition, “the maximum fluctuations of ensemble averaged working fluid temperature” were calculated for the evaluation. The value is the fluctuation of the internal energy per the heat capacity, and has dimensions of temperature. The obtained values were much lower than the actual temperature differences in present experiments. The comparison suggests that the indicated work of conventional LTDSE was much lower than the thermodynamic upper limit.
Fig. 8. Temperature fluctuations of the working fluid in Test 80C.
working fluid is an ideal gas. It is available to evaluate the thermodynamic performance of the LTDSE. The value is the fluctuation of the internal energy per the heat capacity as Eq. (5) shows and is not affected by the size of the LTDSE. The temperature distribution in the SE is not uniform; therefore, the averaged temperature is not the actual value. This maximum fluctuation of ensemble averaged working fluid temperature is less than the temperature difference between the heat source and the heat sink. Therefore, the comparison of “maximum fluctuation of ensemble averaged working fluid temperature” with the temperature difference between the heat source and the heat sink helps to evaluate thermodynamic performance.
DTaverage ¼
DðpVÞ mR
(4)
DTaverage ¼
DU mCv
(5)
Eqs. (4) and (5) requires the mass of working fluid. The mean volume and the mean working fluid temperature cause estimated mass of working fluid. Although the estimated mass of working fluid causes errors, the error is negligible in the discussion below. Since maximum fluctuation of ensemble averaged working fluid temperature was much lower than the temperature difference between heat source and heat sink in each test condition. If the mass of working fluid was calculated using the heat source temperature or the heat sink temperature, the obtained value causes same discussion. The value DpV is the difference between the maximum pV and the minimum pV in each test condition. The maximum fluctuations of ensemble averaged temperature were from 3.2 to 4.7 C in present experiments. The values were lower than the difference in the working fluid temperature between the hot side and the cold side. In addition, as Tables 2 and 3 show, the differences in the working fluid temperature between the
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Yoshitaka Kato B. Sc; 1998 (Tokyo Metropolitan University, Japan), M. Sc. 2000 (Tokyo Institute of Technology, Japan), Ph.D. 2003 (Tokyo Institute of Technology, Japan), Research Associate 2003e2015 (Oita University, Japan).