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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

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By means of spatially 1 discriminate dimensional analysisf \ a complete system of dimensionless groups is proposed to describe the thermodynamic performhnce of thdfinematic Stirling en@.) From experimental results, homogeneous dimensionless indicated power equations are deduced, as well as equations corresponding to the maximum indicated power operating point. Spatial discrimination evidences conceptual diflerences between quantities, reduces the number of dimensionless parameters and improves the design method based on dynamic similarity. NOTATION

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This paper presents a preliminary design method based on dynamic similarity and quasistatic simulation. The proposal improves methods based on Beale and West correlations and provides the engine speeds corresponding to the maximum indicated powers and the achievement of indicated power maps. The dimensionless factor of indicated power losses provides a new viewpoint for engine analysis and design. In support of the method, experimental GPU-3 test results have been reanalysed, proving the accuracy of maximum indicated power predictions and providing values of the dimensionless factor of indicated power losses. Scaling factors corresponding to strict dynamic similarity are supplied for several typical cases. Similarity relaxation criteria are also recommended to be used when strict dynamic similarity leads to inadequate specifications for the derivative. Some numerical examples illustrate the method.

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