Modeling and Trajectory Optimization of Water Spray Cooling in a Liquid Piston Air Compressor

An efficient and sufficiently power dense air compressor/expander is the key element in a Compressed Air Energy Storage (CAES) approach. Efficiency can be increased by improving the heat transfer between air and its surrounding materials. One effective and practical method to achieve this goal is to use water droplets spray inside the chamber when air is compressing or expanding. In this paper, the air compression cycle is modeled by considering one-dimensional droplet properties in a lumped air model. While it is possible to inject water droplets into the compressing air at any time, optimal spray profile can result in maximum efficiency improvement for a given water to air mass ratio. The corresponding optimization problem is then defined based on the stored energy in the compressed air and the required input works. Finally, optimal spray profile has been determined for various water to air mass ratio using a general numerical approach to solve the optimization problem. Results show the potential improvement by acquiring the optimal spray profile instead of conventional constant spray flow rate. For the specific compression chamber geometry and desired pressure ratio and final time used in this work, the efficiency can be improved up to 4%. INTRODUCTION Gas compression and expansion has many applications in pneumatic and hydraulic systems, including in the Compressed Air Energy Storage (CAES) system for offshore wind turbine that has recently been proposed in [1, 2]. Since the air compressor/expander is responsible for the majority of the storage energy conversion, it is critical that it is efficient and sufficiently powerful. This is challenging because compressing/expanding air in high compression ratios (200-300) heats/cools the air greatly, resulting in poor efficiency, unless the process is sufficiently slow which reduces power [3]. There is therefore a trade-off between efficiency and power. Most attempts to improve the efficiency or power of the air compressor/expander aim at improving the heat transfer between the air and its environment. One approach is to use multi-stage processes with inter-cooling [4]. Efficiency increases as the number of stages increase. To improve the efficiency of the compressor/expander with few stages, it is necessary to enhance the heat transfer during the compression/expansion process. A liquid piston compression/expansion chamber with porous material inserts has been studied in [5]. The porous material greatly increases the heat transfer area and the liquid piston prevents air leakage. Numerical simulation studies of fluid flow and enhanced heat transfer in round tubes filled with rolled copper mesh are studied in [6]. Application of porous inserts for improving heat transfer during air compression has also been investigated [7]. In addition, the compression/expansion trajectory can be optimized and controlled to increase the efficiency for a given power or to increase power for a given efficiency [3, 7–9]. Another approach to increase the air compression efficiency is to employ a water spray. The large number of small size droplets with a high heat capacity can provide a high total surface area for heat transfer [10–12]. However, the presence of significant liquid volume in the piston chamber must also be accommoProceedings of the ASME 2013 Heat Transfer Summer Conference HT2013 July 14-19, 2013, Minneapolis, MN, USA