The present study presents a one-dimensional liquid-piston compressor model with an embedded two-dimensional submodel. The submodel is for calculating heat conduction across a representative internal plate of a porous heat exchanger matrix within the compression space. The liquid-piston compressor is used for Compressed Air Energy Storage (CAES). Porous-media-type heat exchangers are inserted in the compressor to absorb heat from air as it is compressed. Compression without heat transfer typically results in a temperature rise of a gas and a drop in efficiency, for the elevated temperature leads to wasted thermal energy, due to cooling during subsequent cooling back to ambient temperature. The use of heat exchangers can reduce the air temperature rise during the compression period.

A typical numerical model of a heat exchanger is a one-dimensional simplification of the two-energy-equation porous media model. The present authors proposed a one-dimensional model that incorporates the Volume of Fluid (VOF) method for application to the two-phase flow, liquid piston compressor with exchanger inserts. Important to calculating temperature distributions in both the solid and fluid components of the mixture is heat transfer between the two, which depends on the local temperature values, geometry, and the velocity of fluid through the matrix. In the one-dimensional model, although the axial temperatures vary, the solid is treated as having a uniform temperature distribution across the plate at any axial location. This may be in line with the physics of flow in most heat exchangers, especially when the exchangers are made of metal with high thermal conductivity. However, it must be noted that for application to CAES, the gas temperature in the compression chamber rises rapidly during compression and the core of the solid wall may heat up to a different temperature than that of the surface, depending on the geometry, solid material of the exchanger and fluid flow situation. Therefore, a new, one-dimensional model with embedded two-dimensional submodel is developed to consider two-dimensional heat conduction in a representative solid plate. The VOF concept is used in the model to handle the moving liquid-gas interface (liquid piston).

The model gives accurate solutions of temperature distributions in the liquid piston compression chamber. Six different heat exchangers with different length scales and different materials are simulated and compared.

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