Thermodynamic Analysis of Vuilleumier Heat Pumps

Abstract

It has been 101 years since a Swiss-American engineer called Rudolph Vuilleumier conceived an idea on how to generate a heat pump device that would operate using heat at high temperature as energy input. The device that he invented, the Vuilleumier machine, utilized working gas expansion and compression at three variable volume spaces in order to pump heat from a low to a moderate temperature level. The interesting characteristic of the Vuilleumier machine is that the induced volume variations are realized without the use of work, but thermally. This is the reason why it has a potential to operate at modern applications where the pollution of the environment is not a choice. It is a perfect candidate for such applications, as it consists only of metallic parts and inert gas. Using these units for heating and cooling buildings, large energy savings can be accomplished as they can be operated at small scale in common buildings or at large scale providing heat power to entire building blocks without using fossil fuels. The use of Vuilleumier machines for industrial applications or inside vehicles is also a feasible option. Another field where these machines have already been involved is the cryogenics, as they are also able to provide refrigeration at very low temperatures like the very similar and well-known Stirling refrigerators. The possible uses of Vuilleumier machines can only be confined be the limits of imagination of the people being involved with them. The development of the Vuilleumier machines has been an ongoing process since the first patent of Rudolph Vuilleumier in 1918, aiming at the design of efficiently operating heat pumps and cryogenic refrigerators. However, the research on this type of regenerative machines is not yet very extensive and analytical. The present dissertation, aims at the knowledge advancement on Vuilleumier machines, providing an additional effort to broaden the research on this field. In the past, several industries and universities have been engaged with the development of these machines. At first, the research was performed in USA for the production of cryogenic refrigerators for space use. The US Army, the US Air Force and NASA collaborated with companies such as R.C.A., Philips, AiResearch, Hughes Aircraft and Kinergetics and managed to realize space missions with Vuilleumier cryogenic refrigerators. Later cryogenic refrigerator research initiated in Japan and Korea also, where heat pumps for heating buildings were also developed for companies such as Mitsubishi, Daikin, Sanyo and Kawasaki. In Europe, mainly in Germany and Denmark, two decades after the cryogenic refrigerators development in USA, universities and companies focused their research on Vuilleumier heat pumps and many experimental units were built and tested. The Technical University of Munich, the Technical University of Denmark, Dortmund University and the collaboration BVE-Thermolift are among them. Nowadays, the research is still active in USA and Europe for heat pumps and in Japan and China for cryogenic refrigerators mostly. Although many prototypes have been produced during all these years, Vuilleumier machines still exhibit low performance and efficiency due to inherent thermodynamic and aerodynamic losses. An accurate description and understanding of these complicated phenomena is required in order build competitive machines for modern applications. Considering the heat pumps, the volume specific heat power has to be increased compared to other heat pump devices. Vuilleumier machines are bulky because of the low pressure ratio accomplished. In addition, the efficiency has a potential of further improvement with the design of more effective heat exchangers and regenerators and the reduction of flow losses. For the cryogenic refrigerators, the efficiency is insignificant, but the cooling capacity and the refrigeration temperature are of great importance and there are still a lot of improvements that can be done, such as applying new materials or reducing the thermal losses. In the present dissertation in Chapter 1 the fundamental parts of regenerative machines, the thermal and mechanical compressor are presented, which coupled form a Stirling heat pump. Then, the operation of the same Stirling machine as a prime mover, as a heat pump or as a refrigerator is explained and it follows a presentation of the connection between two Stirling machines to form a heat actuated heat pump like a Vuilleumier machine. Several configurations and types of the Vuilleumier machines are presented together with their operation and their benefits and disadvantages. An extensive presentation of the evolution of Vuilleumier machines from their first patent until now is conducted in Chapter 2. All available studies, patents, books and reports are cited for both heat pumps and cryogenic refrigerators and the work of each researcher is briefly discussed. The theoretical or experimental performance of various Vuilleumier cryogenic refrigerators and heat pumps is summarized in corresponding tables and also all the Vuilleumier related US patents. In Chapter 3 the types of existing models that are used for the prediction of the performance of Stirling engines are presented together with one-dimensional thermodynamic models generated, in the context of this dissertation, especially for Vuilleumier machines. At first, the construction of the ideal isothermal model is presented. It follows the ideal adiabatic model and the thermodynamic segmentation of the machine into work-heat converting control volumes. Then the application of this model on real machines is discussed and the results of a comparison between the two ideal models are also presented. Chapter 3 includes in addition the description of several losses inherent in a Vuilleumier machine and the physics behind the derivation of equations that calculate their values. Finally, a validation of the developed computer codes according to the thermodynamic models is conducted by comparison with experimental data. In Chapter 4 there is a comprehensive three-dimensional Computational Fluid Dynamics (CFD) simulation of a Vuilleumier machine that was designed for this purpose at three different operating speeds. At first, existing CFD studies on Stirling engines are presented and then there is an analytical description of the designed machine, the boundary conditions applied, the computational grid used and all the equations that were utilized for the generation of this numerical model. For the simulation, a commercial CFD software was used. The results from the simulation are presented next, providing details about the thermodynamic and fluid mechanics quantities distribution in every space of the machine and the interaction between them. Useful 3D illustrations of the temperature, the pressure and the velocity are given too. Moreover, calculation of heat and work transfer between the machine and the surrounding is performed for all three speeds. Then, heat transfer coefficients are derived in relationship with the Reynolds number of the flow. Finally, the efficiency of the designed Vuilleumier machine is calculated and it is compared against experimental data.