Vuilleumier machine speed-effect investigation with CFD and analytical model George Dogkas ⇑ , Panagiotis Bitsikas, Dimitrios Tertipis, Emmanouil Rogdakis National Technical University of Athens, 9 Heroon Polytechniou St., 15780 Zografou, Athens, Greece article info Article history: Received 13 May 2019 Received in revised form 28 July 2019 Accepted 31 July 2019 Keywords: Vuilleumier Speed Heat pump 3D CFD 1D model abstract A one-dimensional analytical model and a three-dimensional CFD numerical model were used for the investigation of the effect that the rotational speed has on several thermodynamic quantities and the per- formance of a Vuilleumier machine. The machine, was designed as a combination of two opposing Stirling engines. The one-dimensional program was based on the energy balance at each control volume in order to calculate the energy flow inside the machine and then losses were added. On the other hand, the CFD model utilized fundamental conservation equations at each of the numerous computational cells which resulted to accurate calculations at every dimension. It was able to provide the heat transfer coefficients inside the heat exchangers that were in turn utilized by the analytical model. The pressure drop was computed directly at each space by the numerical model and with equations for flow losses from the bibliography by the analytical model. Pressure drop increased significantly with the speed. The effectiveness of the regenerators was evaluated by an existing analytical model and resulted to reduce drastically with the drop of speed. The effectiveness plays very important role on the efficiency of the machine. Furthermore, there appears to be a discrepancy between the heat flow in the heat exchang- ers and the wall-gas temperature difference at high speeds which has to be examined according to the oscillatory nature of the gas flow. Heat transfer coefficients were generated in relationship with the Reynolds number for each speed investigated, yielding less thermal resistance when the speed is high. Finally, the change of heat amounts through the four heat exchangers and change of the efficiency of the Vuilleumier machine with the speed, resulted to be similar with experimental data. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Heat pumps, refrigerators and work-producing engines that are capable of absorbing energy from an external heat source are an interesting machine type, due to the large variety of available heat sources. Combustion of fossil fuels is a potential heat source, but heat can be absorbed from renewable sources such as biomass or concentrated solar radiation. Moreover, radioisotopes and waste energy of large scale plants are two additional viable options. Vuilleumier machines are one type of these heat pumps. They can be used either for heating and cooling spaces such as buildings, or as refrigerators at very low temperatures (cryocoolers). Rudolph Vuilleumier first presented a theoretical such machine in 1918 [1]. Vuilleumier machines normally operate at a wide range of temper- atures and employ inert working gas (Helium). Due to the fact that Vuilleumier heat pumps absorb heat from an external source, they are electrically independent. The ability of these machines to utilize renewable sources makes them environmentally friendly. Other advantages offered by Vuilleumier machines is the produc- tion of low levels of noise and vibrations and their long lifetime. Vuilleumier machines are associated with Stirling Engines and refrigerators. A Stirling Engine absorbs heat from an external hot source and rejects heat to a sink that is usually under the temper- ature of the surroundings. As the heat source is hotter than the heat sink, a Stirling Engine has a positive work output. On the con- trary, a practical Stirling refrigerator absorbs heat at temperature lower to 0 °C and rejects heat to the ambience. As a result, a Stirling refrigerator requires work input. Similar is the operation of a Stir- ling heat pump for producing heat. The operation of a Vuilleumier heat pump can be viewed as the combination of two Stirling machines. The first machine is an engine operating between a high and a moderate temperature that produces work, while the other is heat pump operating between a low and a moderate temperature that requires work input. Two design objectives for Vuilleumier machines are to keep mechanical losses low and to achieve good heat transfer from and to the working fluid. These objectives conflict because HEs https://doi.org/10.1016/j.ijheatmasstransfer.2019.118513 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: geodogas@mail.ntua.gr (G. Dogkas). International Journal of Heat and Mass Transfer 143 (2019) 118513 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt