See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/334657385 Thermodynamic analysis, performance numerical simulation and losses analysis of a low cost Stirling engine V-Type, and its impact on social development in remote areas Conference Paper · June 2011 CITATIONS READS 0 2,936 4 authors: Walter Arias Daniel Flórez-Orrego University of Maryland, College Park École Polytechnique Fédérale de Lausanne 14 PUBLICATIONS 56 CITATIONS 110 PUBLICATIONS 485 CITATIONS SEE PROFILE SEE PROFILE Hector I. Velasquez Silvio De Oliveira Junior National University of Colombia University of São Paulo 38 PUBLICATIONS 438 CITATIONS 220 PUBLICATIONS 2,142 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Worldwide Exergy Community: aeronautics View project Integration and Optimization in the Chemical Process Industry View project All content following this page was uploaded by Daniel Flórez-Orrego on 24 July 2019. The user has requested enhancement of the downloaded file. SEE PROFILE Proceedings of ECOS 2011 Novi Sad, Serbia July 4–7, 2011 Thermodynamic analysis, performance numerical simulation and losses analysis of a low cost Stirling engine V-Type, and its impact on social development in remote areas W. Ariasa, H.I. Velásqueza, D. Floreza and Oliveira Junior S b a b Universidad acional de Colombia, Sede Medellín, Colombia, wariasr@unal.edu.co, CA Mechanical Engineering Department, Polytechnic School, University of São Paulo, Brazil Abstract: This study is aimed to develop an analysis and numerical simulation on the performance of a low cost Stirling Engine V-type, built with locally available technology, with the goal of being an alternative energy technology for its implementation in non-interconnected rural areas, based on renewable sources. The detailed method includes an energy and exergy analysis for each process of the cycle and numerical simulation in MATLAB®. The selected model was the adiabatic model, due to better approximation to real engine performance compared to the isothermal model. To increase the accuracy, the internal irreversibilities caused by pressure drops, incomplete (non-ideal) regeneration, heating, and cooling processes were included. The actual efficiency result was 34%, being the effectiveness of the regeneration process the one that most impact generated on it (approximately 80% of total losses). In addition, based on the measuring of energy sources (radiation and biomass), technical feasibility was predicted. Finally, to simulate the evolution in the social development of the area since the incorporation of energy technologies, a system dynamics model was used with a holistic approach. The result was the necessity of including other parameters in addition to technical and economic feasibility, such as monitoring and accompaniment in the early stages and subsequent assimilation of their management and operation to the entire community, allowing them to present a sustainable development based on the use and value generation. Keywords: Numerical Simulation, Stirling Engine, Exergy Analysis. 1. Introduction Due to the growth in energy demand, environmental issues and high dependence on fossil fuels, the need to find sustainable alternative sources of energy conversion emerges. Stirling engine performance meets these demands, which has one theoretical efficiency equivalent to that of Carnot, it also uses any heat sources (biomass, solar energy, combustion gases) and the pollution generated is smaller than the conventional engines [1-4]. The simple construction, and its manufacture being the same as the reciprocating internal combustion engine, and when produce in a large number of units per year, the Stirling engine would obtain the economy of scale and could be built as a cheap power source for developing countries. For solar electric generation in the range of 1–100 kWe, the Stirling engine was considered to be the cheapest, Although the Stirling engine efficiency may be low, reliability is high and costs are low [5]. Moreover, the International Energy Agency estimates that in 2008, 1.5 billion people, or 22% of the world’s population, had no access to electricity, of whom 85% live in rural areas [20]. In Colombia, there are geographically isolated regions, not connected to the National Transmission System, these areas represent 66% of the territory, and about 15% (3'000 .000 people) of the total population [6,7]. In 2008, service coverage in non-interconnected areas was 76% [7]. State policy has focused on promoting fossil fuel-based projects reaching more than 96% of total generation in diesel plants [6.8]. Two studies [9.10] carried out on the potential availability of agricultural and agro-industrial residues, found that in Colombia the Stirling micro-generators implement 3767 alternative is economically viable, especially in non-interconnected and/or rural areas, there is a similarly strong solar energy potential, reaching averages of radiation throughout their territory, with a daily multi-year average close to 4.5 kWh/m2, suitable for proper utilization [11]. This paper presents a Stirling engine as a technical alternative, economically and socially viable in the search for energy solutions in such areas, using its natural resources. Because of this, the thermodynamic analysis and numerical simulation of a low-cost Stirling engine prototype is done. And finally we will analyze the incorporation of this new technology in social development in the area. 2. Thermodynamics of Stirling cycle engine The Stirling engine uses a compressible fluid as the working fluid (Hydrogen, Helium or Air) in a closed system, Fig. 1a and Fig. 1b show the classic diagram of the Stirling cycle PressureVolume and Temperature –Entropy, which consists of four processes: an isothermal expansion (heat addition from the external source), isothermal compression (heat rejection to the external sink), a rejection (internal heat transfer from the working fluid to the regenerator) and heat addition (internal heat transfer from the regenerator back to the working fluid at constant volume). Aside from having an equal theoretical efficiency to Carnot efficiency, the Stirling engine has the advantage to work with two constant volume processes, instead of two isentropic processes; increasing the p-v diagram area and therefore the work done (Fig. 1a), also it has the maximum mechanical performance compared with another reciprocating thermal engines at the same working conditions[5,15]. The analysis using the first and second laws of thermodynamics to the four ideal Stirling cycle processes is taken into account to establish the ideal adiabatic model used to simulate the performance of the prototype in the four processes mentioned before, in which, additionally, a decoupled analysis of the irreversibilities due to pumping losses and imperfect heat exchanger was performed (regenerator, heater and cooler) [13, 14] Fig.1. Thermodynamic Stirling cycle: a) P-V diagram, b) T-S diagram. [12] 3. Mathematical model of the Stirling engine There are three widely detailed mathematical and documented analysis, discriminated according to the methodology proposed by Martini, Dyson and Chen [14,17,18], a first analysis or the Zero Order was proposed by W. Beale, he noted that the output of many Stirling engines with similar specifications is given by (1) [17], although this method cannot analyze the power loss and heat, is used as a first design approach [3,18]. Pot= b P*f*Vswe (1) An analysis of first order was made by G. Schmidt called isothermal analysis, which is the most complicated it can be solved analytically due to its closed-form solution is to approximate the sinusoidal volumetric variations, see Fig. 2 [14,17,18]. Fig. 2. Sinusoidal volume variation [19] However, the given results by this analysis are incongruous, indicating that the heater and cooler are redundant, because all the heat is transferred through the working spaces. This paradox is due to the compression and expansion spaces are kept at the respective cooler and heater temperature, prompting the 3768 calculated efficiency equals the Carnot efficiency, which is usually 2 or 3 times the actual efficiency of Stirling engines [1,13,14,19]. A second order analysis was developed by Finkelstein. He modified the Schmidt analysis, changing the isothermal to adiabatic conditions, allowing the heat transfer to occur only through the heater and cooler. Furthermore, this analysis has the feature to be decoupled, i.e. the irreversibilities are treated separately from the ideal model; e.g. the losses due to pressure drops and heat losses, are calculated and subtracted from the adiabatic ideal work, increasing the accuracy of work done and efficiency calculated, compared to the actual engine, and allows to detail and quantify the power losses [13,14]. 3.1. Adiabatic Analysis To carry out the prototype numerical simulation, the adiabatic analysis model was selected, due to the above mentioned advantajes, also it was taking into account the aproximations and assumptions indicated by Finkeltein [14] and later by Urieli [19] and Herzog [20]: • Leakage of gas to the outside of the engine, including crank case, is assumed to be zero. • Any pressure drops due to flow resistances and pressure differentials needed to accelerate the working gas are neglected. Hence, the pressure has at a given instant the same value everywhere inside the engine and varies only with time. • Equal to the schmidt model, to simulate the prototype by the adiabatic model, it is necesary to approach the expansion and compresion volume variation to sinusoidal form (Fig. 3), since the drive mechanism is a crankshaft (Eq. 2,3) 1 [13,14,19,20]. Ve = Vcle + 1/ 2 Vswe ( 1+ cos (θ + α + π) ) (2) dVe = - 1/2 Vswe sin(θ + α + π ) dθ (3) • The engine turns at constant speed. Therefore, time and crank angle are proportional to each other. • Both, the compression and expansion space, volumes, are adiabatic. The temperature in these spaces is uniform but varies during a cycle due to changes in pressure, volume and gas coming from/leaving to the adjacent cooler and heater space, respectively • The heat transfer conditions for the cooler space are sufficiently good to keep the gas inside the cooler space, volume Vk, at constant uniform temperature Tc at all times. The same holds true for the heater space, volume Vh and uniform temperature Th. • The heat transfer conditions are sufficient to keep the temperature distribution inside the regenerator, volume Vr , linear, varying from Tc where the regenerator is connected to the cooler to Th at the heater side. • An ideal gas is used as working fluid and the ideal gas law : PV = mRT (4) Cp − Cv = R (5) K = Cp Cv du = Cv (T ) dT dh = Cp (T ) dT (6) (7) (8) This model split the engine into five parts: heater, regenerator, cooler and expansion and compression spaces as is showd in Fig 3 furthermore the gas temperature in each of the control volumes is shown, the graphic also shows the control limits through which the enthalpy passes given the mass flow. 3.1.1. Mass and energy conservation laws Additionally to the restrictions or aproximations given in numeral 3.1, the mass and energy conservation laws were used to formulate the governing diferential Relevant equations to each part of the Fig. 3 initially, thermodynamics basic equations are applied to a volume control for a piston/cylinder device and a heat exchanger with one inlet and one outlet mass flux, como se muestra en Fig. 4. 1 The equations shown are for the expansion space, these are similar to the compression space 3769 dV dm e = dθ p= p V e + e dp dθ γ dθ RT he (11) MR Vc Vk Vh Ve Vr ln ( Tr Tc + + + + Tr − Tc Tc Tk Th Te 1 dVc 1 dVe − γp + + T dθ T dθ he ck dp = Vc V V V V + γ k + r + h + e Tk Tr Th The Tck Fig. 3. Ideal Adiabatic Model [1] Fig. 4. Generic volume control [13] To deduce the governing equations is convenient derivate in function of the crankshaft angle (dθ) instead of the time. To find the pressure equation (13) in function to the angle, as well as its differential (14), natural logarithm is applied to the ideal gas equation (4) and afterwards it is derived in function of the crankshaft angle to obtain (9). this equation is applied to the three heat exchangers, where the volume and the temperature are constant, obtaining the mass differential in these spaces (10). Similarly to find the mass differential on expansion and compression spaces(11, 12), the energy conservation equation is applied in conjunction with the ideal gas relations (5-8). Finally these five equations are replaced into the mass conservation equation, obtaining (12) and (13). 1 dp 1 dV 1 dm 1 dT + = + p dθ V dθ m dθ T dθ dmhx dp = mhx p (9) ) (12) (13) The mass flows equations in a control volume are found through the mass conservation principle, applying this equation to each one of the volumes described by the Fig 4, (14-17) are obtained. dm mck = − c (14) dθ dmc mkr = mck − (15) dθ dm mhe = mrh − h (16) dθ dmh mrh = mhe + (17) dθ The equations for temperature (18) into the compression and expansion spaces were found by deriving in function of the crankshaft angle the ideal gas equation (4). dTe 1 dp 1 dVe 1 dme = Te( + − ) dθ p dθ Ve dθ me dθ (18) To determinate the heat transference in the heater, cooler and regenerator, the energy equation is applied to each of the spaces along with the ideal gas equation (4) and the relation of the calorific capacities equations (5-8): dQ r Vr C v dp (19) = − C p (Tkr m kr − Trh m rh ) dθ R dθ dQ h V h C v dp = − C p (Trh m rh − The m he ) dθ R dθ (10) (20) The equations that describe the work differential for the compression and expansion spaces and the total are: 3770 dWe dV =p e dθ dθ (21) dW dWe dWc = + dθ dθ dθ (22) of the Reynolds number and the fanning friction factor). St * Awgr TU = (23) 2 Ar Due to the non-linearity of the temperature differential equations (18), it is necessary to apply numeric methods to solve them as well as the whole equations system here detailed. 4. Losses Analysis The power loss analysis assesses the heat transference effectiveness as well as the pressure drop in the three heat exchangers. The advantage of this decoupled method is that a detailed accounting of the losses is produced which is useful in design modifications, sin embargo however, it has a disadvantage in front of the coupled method, since the relationships between the various subsystems are neglected, even though the coupled analysis is generally more complex, makes also significant assumptions and some decoupling occurs by the use of this method [13,17]. West claims that the simpler decoupled analysis is not established to be inferior to the more complex "third order" or coupled analysis [13]. Creswick, Qvale, Rios, Walker, Senft, and Smith were some pioneers using this approach [1,5,13]. In general, both, the coupled and decoupled approaches are valid; the decoupled method was selected given that it fits to the requirements of this project because it has been supported and validated with empirical data [3,13,16,21], and verges the calculated results to the ones given by a real engine, letting parametrize the power losses . In this analysis, the process is approximated to a Quasi-steady flow (since the real nature of the flow in a Stirling Engine is oscillatory), in which it is assumed that on each stage of the cycle, the flow behaves as a stable fluid. The effect of the non-ideal regenerator is modeled by the Number of transfer Units (NTU), which it is in function of the Stanton number (23). In order to calculate the Stanton number, the modified analogy of Reynolds had to be considered, which can be used even in presence of pressure gradients (24) [22,23] where fr is the Reynolds friction factor (equals to the product St = fr 2 Re Pr 0 .67 (24) The Reynolds friction factor (fr) depends on the regimen of the flow which is given by the Reynolds number, for laminar Flow (Re<2000), it is calculated using the annular flow laminar equation; for turbulent flow (it is assumed from Re>2000), it is calculated using the Blasius equation [22]. So the effectiveness of the regenerator can be calculated by (25) and the heat lost by (26). TU ε= (25) 1 + TU Qrloss = ( 1 − ε)(Qr max − Qr min ) (26) The heater and the cooler effectiveness is related with the temperature reached by the fluid when passing through it, which for the real case ( < 1), is lower than the temperature of the walls of the exchangers, decreasing the performance of the engine, when operating between temperature limits lower than the heater and cooler walls temperatures (Fig. 5). This analysis determinates the difference between temperatures using heat transference equations by convection (27), taking into account the heat lost due to the imperfect regenerator and the heat transference coefficient for each of the spaces (28). Th = Twh − h= (Qh − Qrloss ) * freq hh Awgh fr µCp 2d h Pr 2 (27) (28) 3 The fluid friction associated with the flow through the heat exchangers will in fact result in a pressure drop across all the heat exchangers which has the effect of reducing the power output of the engine [21]. The actual work is found subtracting the lost work to the ideal adiabatic work (29-31) [19, 21, 22]: 3771 parameters such as the expansion phase advance angle advance equal 90°, for the regenerator was inserted a stainless steel foil (it was took thermal conductivity as 25 W ), for detail m*K specifications of the Stirling engine prototype see Table 1. Fig. 5. Actual performance of Stirling Engine [22] W = ∫ p ( dVe + dV c ) − ∫ ∑ ∆pdV e (29) 2π dV 3 ∆W = ∫ ∑i =1 ∆pi e dθ dθ 0 ∆p = − 2 frµuV 2 d hid A (30) (31) Where u is the speed fluid, V is the void volume, A is the internal free flow area, µ is the gas dynamic viscosity, calculated through the Sutherland equation[21,22] 5. Prototype The objective of this study is to design a Stirling engine as micro-generation alternative (power about 0,5kW – 1kW). Because of that, the construction of the Stirling engine has to be attached to the local restrictions. The V-type Stirling engine is easier to build than other types of configuration, given that its construction can be commenced from a commercial V-type compressor. Equation (1) was used, with the goal to dimension the compressor [3], the compressor operating frequency was selected as the engine operating frequency factor in (1) and the reference pressure factor in (1) was the 80% of the maximun operating pressure. Power output was 605W for a 1,5KW compressor and its price is the half price of another compressor (2.2- 3.8 KW), besides the increase in power is not equivalent to the price increase, because of that, 1.5KW compressor was selected. Figure 6 shows the prototype, in the heater and cooler were attached seven internal fin (due to space restriction), to increase the wetted area of each one. also the expansion piston and the regenerator were insulated to decreased the heat losses. The compressor has established 6. Energy Potential in Remote Areas Two studies [9,10] concerning the availability potential of agricultural and agro-industrial waste, concluded that the implementation of Stirling micro-generator in Colombia is economically feasible. Specially in noninterconected and/or rural areas, since the agricultural waste of harvest (rice husk, sugar cane harvest waste, pulp of coffee and cocoa, among others), besides the planted and natural forests waste is 12.968 MWh/year. However this is not entirely usable, there are limitations on use, such as competition, i.e. the energy product (waste) has a specific destination, the knowledge involved to the transformation in energy, and the availability, indicating the amount, timing of cultivation and processing technology in energy. This limitations define the actual, useful and available energy (Fig. 7). To determinate the gained temperature from the agricultural and forest waste combustion was necessary to resort to previous studies, for the case of the direct combustion of cane bagasse was obtained a stack gas temperature of 517°C and a furnace temperature of 841°C (16% bagasse cane moisture) [24]. For rice husk was obtained a bed temperature of 600°C – 800°C [25], for wood and bark (sawdust of pine and spruce), temperature of 680°C was achieved (measured at a distance of 70 mm from the burner). Similarly Colombia count with a high solar energy potential, reaching a multiannual diary average close to 4,5kW/ m2 (highlighting the peninsula of La Guajira with a daily average of 6.0 kWh/ m2 and the Orinoco, with a value slightly lower), suitable for proper exploitation [11]. It was selected a specific area (Latitude 12.5 and Longitude -71.5), to analyze the solar radiation potential. 3772 with a projected area of 2 m2 and built with commercial aluminum rings, and similar climatic conditions, the focus achieved a temperature of 450 ±20°C. Other studies show focus temperature between 675°C and 800°C [28]. 12000 Gross energy potential 10000 MWh/Year 8000 Available energy potential 6000 4000 Useful or additional energy (effic 55%) 2000 0 Fig. 6. Low cost Stirling Engine V-type Fuel oil production Figure 8 show the results, with a minimum and maximum radiation of 0.24KW/m2 and 0.90KW/m2, respectively and a diary average of 0.66KW/m2 [26]. Based on an experimental study [27] about a parabolic solar concentrator Waste Forest waste Fig. 7 agricultural waste useful energy [10] Insolation KW/m2 Table 1.Technical feature and operating conditions of the Stirling engine prototype. Parameter Value/Type Engine type Alpha Drive type Sinusoidal Working fluid Air/Hydrogen Compression / Expansion space 0.0 clearance volume (m3) Compression/Expansion space 7.10 × 10-5 swept volume (m3) expansion phase angle advance 90 (degrees) Cooler /Heater type Slots Width of slot (m) 2.45 × 103 Height of slot (m) 3.40 × 102 Heat exchanger length (m) 6.77 × 102 Number of slots 7 Regenerator configuration Tubular Housing external diameter(m) 4.4 ×102 Housing internal diameter (m) 3.8 ×102 Regenerator length (m) 0.177 Operating frequency (Hz) 90 Regenerator material Stainless steel wrapped foil Matrix type matrix Unrolled length of foil (m) 2.025 Foil thickness (m) 2×10-4 Mean pressure (Pa) 8.6 × 105 Charging pressure(Pa) 6.2 × 105 Cold sink temperature (K) 320.15 Hot source temperature (K) 773.15 Alcohol production 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Experimental Data y = -0,0292x 2 + 0,6878x - 3,1472 R² = 0,9998 0 2 4 6 8 10 12 14 16 18 Hour GMT -5:00 Fig. 8 Insolation Incident on a horizontal surface (KW/m2)[26] 6. Numerical Simulation and Results The prototype was analysed by using MATLAB®, through the Isothermal, adiabatic and Simple routines presented by Urieli and Berchowitz [19,21]. To determinate the heater temperature, the energy potential in rural and non-interconnected areas was taking into account, listed in Table 1. It also was used the four order Runge Kutta (RK4) method to solve the differential equations. This numerical simulation method was validated with the D90 (90cc) Andy Ross Stirling engine [21], similarly this method was used by Scollo [3]. Prior to perform the numeric integration, the method stabilizes the gas temperature calculating them by RK4 and comparing them before and after a complete cycle, achieving the steady state when their difference is lower than 1°C. Then it calculates the volumes and their derivates for each crankshaft angle by means of (2) and (3) for the compression and expansion, 3773 Table 2 shows that the real power using air and hydrogen as working gas is respectively 24% and 71% of the ideal power, noticing the inefficiency of the air, due to the greater amount of heat lost through the regenerator, plus the least amount of heat transferred to the cooler and the heater and therefore a lower rate of temperature compared to hydrogen. The pressure limits were increased in the nonideal model, due to the temperature ratio (Th/Tc) decreased, from 2.23 to 1.39, being the pressure function of this ratio (Eq. 12). This is observed in Fig. 10. 11.5 11 Pressure (bar [1bar = 100kPa]) then together with the total mass value and the temperatura in each part of the engine, pressure in calculated (12) for each crankshaft angle. With these values, it calculated the mass changes in each space and thus the mass flow rat through (14-17), with the pressure, volume and mass flow rate values for a given crankshaft angle, it used the RK4 method to calculate the variation of temperatures in the compression and expansion spaces (18), heat flux in each heat exchanger (19-20), and finally the expansion and compression spaces (21, 22) Table 2 show the adiabatic and non-ideal model results. Non-ideal regenerator, heater and cooler as well as pumping losses caused by fluid friction are considered. Air and Hydrogen were considered as working gas. The P-V diagram shown in Fig. 9, compare the engine performance with and without losses. This figure shows that the temperature difference was reduced, therefore the enclosed area of the cycle. 10.5 Non-ideal Analysis (Working gas: Air) Adiabatic Analysis 10 9.5 9 8.5 8 7.5 7 pressu re (ba r) 6.5 Table 2. 8umerical results comparison. 220 240 260 280 300 320 340 Volume (cc) Parameter Adiab Nonideal Nonideal Fig. 9 P-V diagram comparison atic (Air) (Hydrogen) Total power 943.9 231.4 675.6 The heat transfer coefficient calculated trough output (W) (Eq. 27) in the cooler, using air and hydrogen Heat transferred 1736 2683.5 1946.8 are respectively 567.45 y 965.50 (W/m2K). to the heater(W) Although the Reynolds number calculated for -906.4 Heat transferred -796.4 -1140.7 hydrogen was lower than the calculated for air, to the cooler(W) 4573.1 and 24436.5 respectively, the hydrogen Gas temperature 772.5 618.8 697.8 has larger calorific capacity than the air (ratio in heater 14-1). Gas temperature 345.3 444.1 358.1 in cooler 11.5 Non-ideal Analysis Regenerator net 0 1205.7 316.7 11 heat loss(W) 10.5 Regenerator 1 0.797 0.964 10 P-mean Non-ideal analysis effectiveness 9.5 Regenerator wall 0 24.7 24.7 P-mean Adiabatic 9 analysis heat leakage(W) 8.5 Pressure drop 0 85.5 27.9 8 Adiabatic Analysis available work 7.5 loss(KPa) 7 Thermal ideal 54.4 21.8 43.8 6.5 efficiency (%)* 0 50 100 150 200 250 300 350 400 crank angle (deg) 8.6 34.7 Actual efficiency Fig. 10. Pressure – Crank angle (%)** * Power losses are not taken into account, only considers the temperature ratio. ** This value does not take into account the power loss in shaft bearings. Figure 11 describe the temperatures in expansion and compression spaces, checking 3774 the above. It is observed the imperfect heat transfer in the cooler and heater, obtaining temperatures of 100°C below the wall temperature in the worst case. Equal to cooler, the heat transfer coefficient in heater and regenerator are larger for hydrogen than air. The opposite occurs with the Reynolds friction factor, since it decreased when using hydrogen as working gas instead of air (ratio 14). 800 750 Mean heater gas temperature X: Hydrogen O: Air Heater wall temperature=773 K this due to their wetted area is 23 times higher compared to the heater and cooler. Figure 14 show the involved energy in function of crank angle, in each heat exchanger, as well as the net work, in Fig.14 is noticeable the difference between the energy involved for regenerator and heater or cooler, being the first two or three time larger than the last two. This result is in accordance to Thombare [1]. Also is remarkable that the net energy involved in the regenerator is zero for a complete cycle (Ideal case). 700 4 1.5 Expansion space temperature 600 550 H eat exchang er pressure drop [P a] T e m p e ra tu re (K ) 650 Regenerator space temperature 500 450 400 Compression space temperature Mean cooler gas temperature 350 Cooler wall temperature =320 K 300 0 50 100 150 200 Crank angle (degrees) 250 300 350 Fig.11. Expansion, Regenerator and Compression temperature – Crank angle. x 10 1 0.5 0 -0.5 -1 -1.5 0 50 100 150 200 250 Crank angle (degrees) 300 350 Fig. 13 Heat exchanger pressure drop –Crank angle (Air) 80 Work W 60 Energy [Joules] Figure 12 show the power losses caused by imperfect functioning regenerator and pressure drops in the engine. This figure show that there are less heat losses for hydrogen than air, due to = 26,5 larger heat transfer coefficient ( to hydrogen, and 3,9 to air). The fewer amounts of losses for hydrogen is due to the mass flux are lower than calculated for air (ratio 14 – 1). Cooler Heater Regenerator 40 Heater heat Qh 20 0 Cooler heat Qk -20 Regenerator heat Qr 600 -40 0 400 Power (W) 200 50 100 150 200 250 Crank angle (degrees) 300 350 400 Fig. 14. Energy – Crank angle (Air) 0 -200 -400 -600 -800 0 7. Impact on social development in remote areas Loss heat by Non-ideal Regenerator (working gas= air) Power loss by pressure drop (working gas=air) Loss heat by Non-idea Regenerator (Working gas=Hydrogen) Power loss by pressure drop (Working gas=Hydrogen) 50 100 150 200 250 Crank angle (degrees) 300 350 Fig. 12 Power loss –Crank angle diagram Figure 13shows in detail the pressure drop for each of the heat exchangers for air (hydrogen has similar behaviour). It is noticeable that in the regenerator has the highest amount of losses, This analysis is based on a work done to simulate the behaviour of remote areas of Colombia after the incorporation of energy technologies through a holistic simulation, validated with real data [29]. The general problem is that only the initial training does not hold an energy technology 3775 implemented (renewable or not) for a long time, this is called disabilities appropriation The results (Fig. 15) shows the real power available, i.e. the use of installed capacity; in baseline scenario (without any kind of training or guided learning), the misuse of the infrastructure and the inability to efficiently exploit energy availability, implies that this becomes obsolete. due to the community lacks adequate learning processes regarding the operation and maintenance, however picks up when these impossibilities are overcome. In the technological learning scenario there is a clear trend, based on the effectiveness of investment in education and social investment. This allows an aggregate value of it and makes efficient operation. Fig. 15 real power available [29] When the technology operators through learning processes, overcome the difficulty of operating the technology and means productions, the scenario is operational learning. Taking into account that there is an barrier in learning, i.e. operating appropriation, which is overcome after years of operation. The available power decreased due to the misuse at the first years. The technological learning scenario consists of a knowledge and innovation of technology, beyond its operation and maintenance, this type of knowledge can increase the operational capacities of energy production of Goods and Services; it is satisfactory the performance in this scenario, due to different processes of exploitation of energy and innovation in the means of production, demonstrating a community development. The behaviour of human and social capital (Fig. 16), on baseline scenario tend to decrease, based on the ineffectiveness of social and educational investment, since the community lacks the means to make the investment necessary to allow sustained growth of capital. On operational learning scenario shows a clear trend toward lowering them in the early years, Fig. 16 Human and Social Capital.[29] 7. Conclusions The objective of this analysis was to simulate the performance of a low cost Stirling engine, obtaining the power output and real efficiency, also know under which scenario is feasible its implementation in a non-interconnected area of the country. The results show that the actual power was 675.6 W in the best of cases, achieving an actual efficiency of 34.6%, equivalent to 60%of the theoretical efficiency. Similarly this technology is susceptible to be implemented due to the 30% of the installed capacity in the areas is within the range of 020KW [8]. The numerical simulation allows on a first approach to analyze the temperatures and power losses behaviour in the three heat exchangers. It 3776 was found that the regenerator losses are 80% of the total losses, also due to imperfect heat transfer in the three heat exchangers and pressure drops was necessary to increase the heat furnished by 54% using air and 12% using hydrogen, being capable of optimization, similarly this simulation allows perform a sensitivity analysis in order to increase power and efficiency. The efficiency achieved with air as working gas was four times lower than that achieved with hydrogen, however the last one is more expensive and difficult to pressurize. The rural and non-interconnected areas have a large energy potential even without using, and together with a learning process which allows accumulate operational and technological capabilities, would make them self-sustainable in the long term. 8. Future perspective The next target is to realize the laboratory tests to validate the simulation and then test it in a remote area, to meet in the medium-term the social and human impact generated. Nomenclature A: C: D: F: Fr: M: N: P: Pot: Pr: Q: R: Re: S: St: T: V: W: Area Heat capacity (kJ/kg-K) Diameter (m) Frecuency (Hz) Reynolds friction factor Mass (kg) Referred to particular number Pressure (Pa) Power (W) Prandtl number Heat (W) Ideal gas constant (kJ/kmol-K) Reynolds number Specific entropy (kJ/kg-K) Stanton Number Temperature (K) Volume (m3) Work (J) Greek letter µ: Dynamic viscosity (kg/m-s) α: Expansion phase angle advance (°) γ: Heat capacity relation ε: Effectiveness θ: Crank angle (°) ϕ: Specific exergy (kJ/kg) Subscripts and Superscripts b: c: ck: cle: e: h: he: hid: hx: k: kr: p: r: rh: swe: v: wg: Beale Number Compression Compression-cooler Clearance Expansion Heater Heater-expansion Hydraulic Heat exchanger Cooler Cooler-Regenerator Constant pressure Regeneration Regenerator-Heater Swept Constant volume Wetted area Reference [1] Thombare D, Verma S.Technological development in the Stirling cycle engines. Renew Sust Energ Rev 2006; 12 : 1–38. [2] Timoumi Y, Tlili I, Nasrallah S. Performance optimization of Stirling engines,RenewEnerg2008;33:2134–2144. [3] Scollo L, Valdez P, Baron J. Design and construction of a Stirling engine prototype. Int J Hydrogen Energ 2008; 33(13) : 3506-3510. [4] Berchowitz D. Stirling Engines in Developing Countries. Conference on Small Engine and Their Fuels in Developing Countries1984Sept;Ohio, USA [5] Kongtragool B, Wongwises S. A review of solar-powered Stirling engine and low 3777 temperature difference Stirling engines. Renew Sust Energ Rev 2003;7:131-154. [6] DNP Departamento Nacional de Planeación. Programa de energización para zonas no interconectadas. Documento del Consejo Nacional de Política Económica y Social. Bogotá, Colombia: 2001 Apr. Tech. Report 3108. [7] Alliance of Rural Electrification [Internet]. Belgium – Available at: Brussels, <http://www.ruralelec.org/9.0.html> [accesed: 12.12.2010] [8] CREG Comisión de Regulación de Energía y Gas. Bases conceptuales para la regulación de la prestación del servicio de electricidad en las zonas no interconectadas. Bogotá, Colombia: 2003, Sept. Tec.Report CREG073. [9] Naso, Vincenzo. Microgeneradores “Stirling” alimentados con biomasa, Revista Palmas 1997; 18 (1): 68-73. [10] UPME Unidad de Planeación Minero Energética. Potencialidades de los cultivos energéticos y residuos agrícolas en Colombia. Bogotá, Colombia: 2003, Jul. Technical Report ANC-631 – 03 [11] IDEAM Instituto de Hidrología, Meteorología y Estudio Ambientales. Atlas de radiación solar de Colombia. Bogota, Colombia: 2005. [12] Cengel Y, Boles M. Thermodynamics an engineering approach. Reno USA. McGrawHill; 2003. [13] Malroy E. Solution of the ideal adiabatic Stirling model with coupled first order differential equations by the pasic method. [MS dissertation]. Ohio, USA: Ohio University; 1998 [14] Martini W. Nasa Stirling Engine Design, CR-168088, NASA 1983 [15] Senft J. Mechanical efficiency of heat engines. Cambridge, UK: Cambridge University Press; 2007. [16] Snyman H, Harms T, Strauss J. Design analysis method for Stirling engines. J Energy in Southern Africa 2008; 19 (3): 1-19 [17] Dyson RW, Wilson SD, Tew RC. Review of computational Stirling analysis methods. Second International Energy Conversion Engineering Conference; 2004 Aug 16-19.NASA; Cleveland, Ohio, USA. [18] Chen N, Griffin F. A review of Stirling engine mathematical models. Oak Ridge, Tennessee : Oak Ridge National Laboratory; 1983 Aug.Technical Report:ORNL/CON 135. [19] Urieli I, Berchowitz D. Stirling cycle engine analysis. Bristol, UK: Adam Hilger: 1984. [20] Herzog Siegfried, Mathematical simulation of Stirling engines. Available at:<http://mac6.ma.psu.edu/stirling/simulations/ IdealAdiabatic/index.html>[accessed 09.11.2010]. [21] Urieli Israel, Stirling Cycle Machine Analysis. Available at: <http://www.ohio.edu/people/urieli/stirling/me4 22.html> [accesed 01.03.2010] [22] Urieli Israel, A computer simulation of Stirling cycle machine. [PhD Dissertation]. Johannesburg, South Africa: University of Witwatersrand; 1977. [23] Cengel Y. Heat and mass transfer: a practical approach. Reno USA. McGraw-Hill; 2003. [24] Cundy V, Maples D, Tauzin C. Combustion of bagasse, use of an agricultural – derived waste. Fuel 1983; 62: 775-780. [25] Kuprianov V, Janvijitsakul K, Permchart W. Co-firing of sugar cane bagasse with rice husk in a conical fluidized-bed combustor. Fuel 2006; 85: 434-442. [26] Atmospheric science data center, Surface meteorology and Solar Energy. Available at:<http://eosweb.larcnasa .gov/sse/ > [accesed 01.04.2010] [27] Franco J, Cadena C, Saravia L. Multiple use comunal cookers. Sol Energy 2004; 77: 217-223. [28] Stine W, Diver R. A compendium of solar/dish Stirling technology. Pomona, California: California State Polytechnic University, Sandia National Laboratories. Technical Report: SAND93-7026UC-236. [29] Ceballos F. El proceso de incorporación de tecnologías energéticas en comunidades rurales aisladas bajo un enfoque de dinámica de sistemas [MS dissertation], Medellín, Colombia: Universidad Nacional de Colombia Sede Medellín: 2006 3778 View publication stats