Numerical evaluation of finite length tubes effects in Stirling engines heaters

¹ CNR Istituto di Scienze e Tecnologie per l’Energia e la Mobilità Sostenibili, Napoli 80124, Italy
² ENEA Italian National Agency for New Technologies, Energy and Sustainable Economic Development Energy Technologies and Renewable Sources Department (TERIN), ICT Division, Portici Research Center, Portici, 80055, Italy

^* Corresponding author: francescosaverio.marra@stems.cnr.it

Abstract

The performance of Stirling engines is directly related to the amount of energy that, in the form of heat, participates in the thermodynamic cycle. A peculiar characteristic of this type of engine is the closed circuit of the working fluid, implying a periodic admission and extraction, ideally involving the whole working fluid, of the heat exchanged during the cycle without any exchange of material with the external environment. Several correlations have been proposed in the literature to predict the heat exchange in the hot side heat exchangers, but most of them are based on nondimensional numbers, usually expressed in terms of an oscillatory Reynolds number and a non-dimensional length, that even if they take into account the amplitude and frequency of the oscillating flow inside the tube with respect to its diameter, do not include any dependency upon the length of the tube. Nevertheless, the length of the tube can have a great impact on the performance of a Stirling engine. The heater forms a significant part of the dead volume of the engine, making the optimization of the volume to surface ratio necessary. The friction losses increase by increasing the length of the tubes, determining a negative impact while the exchange surface increases. Even the Nusselt number in the inner side of the tubes changes along the length, achieving the largest values alternatively in the first portions of the tube lengths because of entrance effects (Graetz problem). The picture is made even more complex because of the special velocity profiles that develop in oscillating flows in tubes. One of the effects less investigated in previous studies, which we could call a “breathing effect”, regards the amount of working fluid that, in a real engine, can effectively travel from the hot side to the cold side, thus reaching the conditions of nominal heat exchange with the thermal source and sink of the cycle. An idealized configuration has been devised to investigate, using CFD simulations, these effects. Results reporting how the friction coefficient and the Nusselt number depend on the finite length of the tube will be illustrated.