Revista Mexicana de Física ISSN: 0035-001X [email protected] Sociedad Mexicana de Física A.C. México Aragón-González, G.; Cano-Blanco, M.; Canales-Palma, A.; León-Galicia, A. Developing and testing low cost LTD Stirling engines Revista Mexicana de Física, vol. 59, núm. 1, febrero-, 2013, pp. 199-203 Sociedad Mexicana de Física A.C. Distrito Federal, México Available in: http://www.redalyc.org/articulo.oa?id=57030970033 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative THERMODYNAMICS Revista Mexicana de F´ısica S 59 (1) 199–203 FEBRUARY 2013 Developing and testing low cost LTD Stirling engines G. Aragon-Gonz´ alez´ ¤, M. Cano-Blanco, A. Canales-Palma, and A. Leon-Galicia´ PDPA, Universidad Autonoma´ Metropolitana-Azcapotzalco, Av. San Pablo # 180. Col. Reynosa. Azcapotzalco, 02200, D.F. Telefono´ y FAX: (55) 5318-9057. ¤e-mail: [email protected] Received 30 de junio de 2011; accepted 25 de agosto de 2011 The construction of miniature LTD Stirling engine prototypes, developed with low-cost materials and simple technologies is described. The protypes follow the Ringbom motor array, without mechanical linkages to actuate the displacer piston. Different designs, sizes, materials and mechanisms components have been tested. The power piston has been replaced with a flexible diaphragm and the mechanisms linkages were constructed with piano steel wire. Power output and efficiency experimental measurements are presented for two miniature LTD Stirling engines, the MM7 model from American Stirling Company and our simplest low cost model. A reasonable design to build low cost engines, rendering brake power and thermal efficiencies about 40 % those obtained with similar commercial engines, but only 5 % the cost has been obtained. Keywords: Stirling cycle; LTD machines; Ringbom motors; power and thermal efficiency measurement. Se describe la construccion´ de prototipos de maquinas´ Stirling LTD miniatura, desarrollados con materiales de bajo costo y tecnolog´ıas sencillas. Se apegan al modelo de motor Ringbom, sin eslabones mecanicos´ para actuar el piston´ de desplazamiento. Se han sometido a prueba diferentes disenos,˜ tamanos,˜ materiales y componentes para los mecanismos. El piston´ de potencia se remplazo´ con un diafragma flexible y los eslabones de los mecanismos se construyeron con alambre cuerda de piano. Se presentan mediciones experimentales de la potencia y la eficiencia para dos maquinas´ Stirling LTD miniatura, el modelo MM7 de American Stirling Company y del mas´ sencillo de nuestros modelos de bajo costo. Se obtuvo un buen diseno˜ para construir maquinas´ de bajo costo, que entrega 40 % de potencia y eficiencia termica´ desarrollada por modelos comerciales semejantes, pero con solo´ 5% del costo. Descriptores: Ciclo Stirling; maquinas´ LTD; motores Ringbom; medicion´ de potencia y eficiencia termica.´ PACS: 01.50.Kw; 01.50.Pa; 07.10.Pz; 07.20.Pe 1. Introduction For example the waste heat rejected to the environment from several industrial or manufacturing processes. The operation of several thermal machines, devices designed to convert internal energy in mechanical work, is well de- scribed using the thermodynamic power cycle concept. One of these engines is the Stirling motor, a device that follows a four times closed regenerative cycle operating with an ideal gas as the working substance The main subject of Robert Stirling’s original design was a heat exchanger, called originally “economiser” for its en- hancement of fuel economy to run the engine. The heat ex- changer takes up a part of the energy of hot gas leaving the expansion chamber to deliver it when the cold gas goes back to the chamber. Now it is generally known as ’regenerator’. The ideal gas undergoes successive expansions and com- pressions, due to the heat exchanging from hot and cold tem- perature sources. The ideal Stirling cycle consists of four thermodynamic processes (Fig. 1 below): 3-4, the gas is ex- ternally heated and undergoes an isothermal expansion; 4-1, the gas transfers heat to the regenerator and follows an iso- choric cooling process; 1-2, the gas undergoes an isothermal compression, transferring with the cool temperature source; 2-3, the compressed gas receives heat from the regenerator and follows an isochoric process [1]. A Stirling engine is not an internal combustion engine; it receives the heat from any external high temperature source. FIGURE 1. Ideal regenerative Stirling cycle. 200 G. ARAGON-GONZ´ ALEZ,´ M. CANO-BLANCO, A. CANALES-PALMA, AND A. LEON-GALICIA´ where pm is the medium cycle pressure (bar), Vp the power piston stroke (m3), f the cycle frecuency (Hz). This dimen- sionless parameter Bn is called Beale number [7]. Typical values for the Beale number are 0.11 to 0.15 when consider- ing high temperature differential engines [8]. 3. Low temperature difference Stirling en- gines In 1982 Kolin developed a Stirling engine to produce me- chanical work from a temperature source lower than the boil- ing water [9]. In 1992 James R. Senft received a request from the National Aeronautics and Space Administration (NASA) FIGURE 2. Gamma engine with separate cylinders. to build a Stirling engine operating with a very low tem- perature difference (LTD motors). Senft built the N-92 en- The net work output W (J) for the ideal cycle is, [2]: gine [10]; this Stirling engine runs with ¢T as low as 6±C and even with the heat produced with a warm hand on a cold V1 W = mR ln (TH ¡ TC ) (1) day V2 Several researchers are developing new LTD Stirling en- where m (kg) is the mass of the gas enclosed by the engine, R gines [11-13], to fit them to some low temperature difference (J/kgK) is the specific gas constant, V (m3) is the enclosed 1 or use several sources of waste heat. The Mexico City sub- gas volume with the power piston at highest position in its way company has recently expressed his interest to build and cylinder, V (m3) is the gas volume with the power piston at 2 use 1 (kW) Stirling engines. The purpose is to make use of lowest point, T (K) is the temperature of the engine hot-side H the heat generated in the electric train systems or obtained and T (K) is the temperature of the engine cold-side. C from solar collectors, to provide electric power for the light- ing system in the train stations. Even though the initial fi- 2. Power production on a Stirling engine nancing may be expensive, this request may be satisfied with LTD Stirling The thermal efficiency of any Stirling engine is defined as the ratio of the power output to the heat transferred from the high temperature source. Schmidt developed a model to predict the power output of a Stirling machine, [3-5]; the working substance is treated as an ideal gas and the compression and expansion as isothermal processes. The gas changes of volume in any Stirling engine are synchronized with the cyclic piston stroke, from the upper to the lower dead point; they can be expressed with a sinu- soidal function. The theoretical predictions from the Schmidt model approach to the behaviour observed in real engines, for any of the mechanical Stirling engines configurations. These mechanical configurations are generally divided into three groups known as ®, ¯ and γ arrangements. Alpha engines have two pistons in separate cylinders which are connected in series by a heater, regenerator and cooler. Both Beta and Gamma engines use displacer-piston arrangements, the Beta engine having both the displacer and the piston in an in-line cylinder system, whilst the Gamma engine uses separate cylinders (Fig. 2) From the initial Schmidt analysis several other authors have proposed mathematical models for Stirling engine ther- modynamic analysis. Chen and Giffin [6] identified 25 dif- ferent models. Beale proposed an empirical equation to cal- culate the power output of the Stirling engine, by: w_ Bn = (2) pmVpf FIGURE 3. Ringbom miniature engine (Carl Aero Co.). Rev. Mex. Fis. S 59 (1) (2013) 199–203 DEVELOPING AND TESTING LOW COST LTD STIRLING ENGINES 201 Miniature LTD Ringbom γ engines develop power in the order of 1 to 10 (mW), shaft torques below 3£10¡4 (Nm), angular speeds under 500 (rpm) with thermal efficiencies be- low 0.1% (Fig. 3). They are built sometimes as scientific toys, but can be employed with didactic purposes and to ex- plore the limits of useful low temperature difference. It is also possible to measure its power output and thermal efficiency, using simple methods and common instruments available in almost any engineering school [15]. Equation (2) cannot be used to calculate the power output of LTD Ringbom Stirling engines. Walker [16] proposed an empirical equation for these engines, with BN in function of the cold to hot engine temperatures ratio, ¿ = TC /TH : BN = 0:034 ¡ 0:052¿ (3) Kongtragool [17] proposed the modified Beale number: · ¸ w_ (1 + ¿) MBn = (4) pm Vp f (1 ¡ ¿) Typical MBN values for LTD engines are 0.25 to 0.35. 4. Testing LTD Ringbom engines There are not any other means to know the thermal efficiency and real power output from any thermal engine, but perform- ing measurements from primary variables. A testing facility was built to measure LTD Ringbom miniature engine perfor- mance [15]. The very low power figures (no more than 10 mW), made compulsory to adapt typical testing designs to measure brake power and heat transferred from the high temperature source, without using expensive laboratory instruments (Fig. 4). The testing procedure consists of supplying the heat QH (W) by electric means, measuring voltage and electric cur- rent (QH = ¢V i).