A new equation representing the performance of kinematic Stirling engines

Abstract

Previous work carried out for the last eight years resulted in the proposal of a complete system of dimensionless groups in order to represent the performance of dierent kinematic Stirling engine con®gurations. When looking for experimental support for the proposed model, some differences between the performances of several prototypes were observed. In this paper an equation is introduced to be applied to all known kinematic engines and to their whole range of performance. The coecients appearing in this equation can be computed from temperature and geometrical dimensionless ratios and from experimental measurements at the maximum indicated power operating point. The meaning of those coecients is interpreted and their usefulness to provide an engine performance overview is shown. The quasi-static simulation and the characteristic Mach number at the maximum indicated power operating point appear to be interesting criteria in order to evaluate the performance of prototypes. NOTATION a, b dimensionless coecients of the friction factor A xx cross-sectional area (m 2 ) C f friction factor L length (m) n s engine speed (r/s) N B Beale number N MA characteristic Mach number n s V 1a3 E a RT C p N p characteristic pressure number p m V 1a3 E a " RT C p N SG N MA N re local instantaneous Reynolds number N RE characteristic Reynolds number p m V 2a3 E n s a "RT C N SG N 2 MA N SG characteristic Stirling number p m a"n s N TCR characteristic regenerator thermal capacity number & r c r T C ap m N W West number N characteristic regenerator thermal diusivity number r aV 1a3 E RT C p p m mean pressure (Pa) P B brake power (W) P ind indicated power (W) r crank radius (m) r hx hydraulic radius (m) R speci®c gas constant (J/kg K) T temperature (K) u local instantaneous¯uid velocity (m/s) V swept volume (m 3 ) V dx dead volume (m 3 ), Y 1 dimensionless coecients of the mechanical losses of the indicated power r regenerator material thermal diusivity (m 2 /s) xx dimensionless cross-sectional area parameter A xx raV E adiabatic coecient 1 , F F F , n angles and other dimensionless parameters of the drive mechanism, normalized by the crank radius dimensionless indicated power P ind ap m V E n s B dimensionless brake power P B ap m V E n s mec dimensionless mechanical losses of the indicated power À B ÁP ind ap m V E n s mec mechanical eciency B a swept volume ratio V C aV E ! dimensionless parameter as de®ned in text ! hx dimensionless hydraulic radius parameter r hx ar heThe MS was

Using GMDH Neural Networks to Model the Power and Torque of a Stirling Engine

“…Also, statistical properties of data set are shown in Table 1. [35,36] Based on the approach described in the preceding section, the polynomial generated for the Stirling engine for torque is formulated as follows: …”

“…In the present work, a model is developed incorporating GMDH and Stirling engine experimental [35,36] outcomes for the first time. The results are verified against experimental values.…”

“…The results are verified against experimental values. In the study, 112 configuration numbers, obtained from prior experimental works [35,36], are utilized for both training the polynomial NN and estimation. Inputs for the NN model are temperature of the hot working fluid, pressure and fuel, while the outputs are torque and power.…”

Connectionist intelligent model estimates output power and torque of stirling engine

“…[50][51][52][53][54][55][56][57][58]. Rotation speeds, temperature of heat source, stirling engine type are considered as input of the LSSVM and PSO-ANN models.…”

“…A point to consider is that the improved SVM procedure, [46] profits from the pros of the earlier version of the approach as well. The regression deviation of the LSSVM [46] model is identified as the difference between the estimated characteristic and measured values, [50][51][52][53][54][55][56][57][58] that is noticed as an extension to the limitation of the optimization quandary. In conventional SVM model, the regression errors are commonly optimized in the calculations; however, in the LSSVM, [46] the deviation is mathematically determined [40,[46][47][48][49][74][75][76][77][78].…”