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Stirling engine based units are considered among the most effective alternatives for future solar applications at low power range. In order to analyze and to improve the performance of the three main subsystems of those units, namely, the solar receiver, the thermodynamic gas circuit, and the drive mechanism, simulations codes are under development worldwide. Therefore, the authors must be congratulated not only on the quality of their paper, but also on its current interest.

The authors claim that there is a good agreement between the calculated performance and the experimental results. Unfortunately, however, there is hardly any reference to the influence of velocity on either indicated power or mechanical losses. Yet, I have verified that widely accepted simulation codes can present very different degrees of accuracy depending on the operating point considered.

Organ 1 has introduced similarity criteria that evidence interrelations between the engine speed and other indicated performance parameters. Independently, Prieto and co-workers have derived the complete set of dimensionless parameters influencing the indicated performance and have proposed a method to apply similarity to analysis and design. A wide variety of prototypes has been analyzed, and a general model of performance has recently been proposed to cover wide temperature, pressure, size, and power ranges (see, for example, 2).

The influence of the Mach number, $NMA=nVe1/3/RTc,$ a kind of dimensionless engine speed, on the dimensionless indicated power, $ζ=Ni/PV¯en,$ can be expressed by means of:
$ζ=ζ0−ΦNMA−ΨNMA2$
(1)
where Φ and Ψ are dimensionless factors of the indicated power losses, and the coefficient $ζ0,$ known as quasi-static simulation, represents the theoretical thermodynamic prediction assuming an ideal cycle without any thermal or mechanical irreversibilities. Approximately, $ζ0$ can be computed by the well-known Schmidt’s model.
The values $ζmax$ and $NMA,max$ at the maximum indicated power point fulfill the following equations:
$12ζ0⩽ζmax⩽23ζ0$
(2)

$NMA,max=Φ2+3ζ0Ψ−Φ3Ψ$
(3)

$NMA,max$ can be considered as an index of engine development level, i.e., it is not an independent design parameter but a function which depends on the same parameters influencing the indicated power.

If the authors could obtain experimental measurements of $ζmax$ and $NMA,max,$ coefficients Φ and Ψ could be derived from the following equations:
$Φ=2ζ0−3ζmaxNMA,max$
(4)

$Ψ=2ζmax−ζ0NMA,max2$
(5)

On the other hand, I have recently verified that the dimensionless power of the mechanical losses, $ζmech=Nmech/PV¯en,$ is correlated to a series of dimensionless variables among which the Stirling number, $NSG=P¯/μn,$ where μ is the working fluid viscosity, stands out. $NSG$ evidences the influence of forces, viscosity, and velocity on mechanical power losses and it could be considered as a variation of a classical parameter in Tribology, usually known as the Sommerfeld number (see, for example, 3).

$ζmech$ and $NSG$ could be correlated by combining experimental brake power measurements and indicated power maps based on Eq. (1), which could confirm the accuracy of both the assumptions $n=1200 min−1$ and $μg=μs=μsh=0.4$ for helium at the operating point specified.

1.
Organ
,
A. J.
,
1991
, “
Intimate Thermodynamic Design of the Stirling Engine Gas Circuit Without the Computer
,”
Proc. ImechE (Part C): J. Mech. Engng. Sci.
,
205
, pp.
421
430
.
2.
Prieto
,
J. I.
,
Gonzalez
,
M. A.
,
Gonzalez
,
C.
, and
Fano
,
J.
,
2000
, “
A New Equation Representing the Performance of Kinematic Stirling Engines
,”
Proc. ImechE (Part C): J. Mech. Engng. Sci.
,
214
, pp.
449
464
.
3.
Orlov, P., 1975, Ingenieria de Disen˜o (Spanish edition), Mir. Moscow.