The front of the two-dimensional rectangular grid is formed by the x - z plane. In this model, the surface tension is modelled as a body force F sf, which is non-zero only at the bubble interface and is given by the gradient of the colour function, F sf = σκ( x) ∇ c ( x, t), where σ is the surface tension and κ( x) is the local mean curvature of the bubble interface κ( x, t) = − ∇( n/| n|), where n is the vector normal to the bubble interface.Īll our simulations were carried out in a rectangular column using a uniform two-dimensional cartesian-coordinate grid. The continuum surface force model 3 is used to model the force arising from surface tension acting on the gas-liquid interface. The mass and momentum conservation equations are considered to be homogeneous. The liquid and gas velocities are assumed to equilibrate over a very small distance, and essentially u k = u at the bubble interface, where the subscript k corresponds to either liquid or gas. The colour function indicates the fraction of the computational cell that is filled with liquid, and varies between 0, if the cell is completely occupied by gas, and 1, if it consists only of liquid.The location of the bubble interface is tracked in time by solving a balance equation for this function, (∂ c ( x, t)/∂ t)+ ∇˙( u c ( x, t) = 0, where u is the velocity vector. The VOF method defines a fractional volume or ‘colour’ function c ( x, t), which is a function of position vector xand time, t. The finite-difference VOF model uses a donor-acceptor algorithm 2 to obtain and maintain an accurate and sharp representation of the gas-liquid interface. The round-trip efficiency is about 15%.The VOF model resolves the transient motion of the gas and liquid phases using the Navier-Stokes equations, and accounts for the topology changes of the gas-liquid interface induced by the relative motion between the dispersed gas bubble and the surrounding liquid. About 15 MWh of energy is stored over a 10 hour period. This system consumes about 10 MW of power during charging and produces about 1.8 MW of power during discharging. Both are used to help refrigerate high-pressure air in the chiller to reduce liquefaction power consumption. The high-grade cold store captures waste cold of liquid air from the evaporation process and the low-grade cold store captures waste cold from the turbine exhaust. The low-grade hot store captures waste heat from the compression process and uses it to boost the temperature of air going entering the turbines, increasing power production. To improve round-trip efficiency of the charge and discharge cycles, three thermal stores were added. The high-pressure air is expanded through a 3-stage turbine with reheating to produce power. This causes the liquid air to vaporize and build up 6.5 MPa of pressure. In the power generation system, liquid air is pumped from the storage tank to the evaporator where it is heated from about 80 K to ambient temperature. The cold low-pressure air that did not liquefy passes through the opposite side of the chiller to refrigerate the high-pressure air before returning to the compressor to complete the cycle. The remaining portion of high-pressure air is sent through an expander to cool the air while recovering some power. This causes a some of the air to liquefy due to the Joule-Thomson effect. A portion of the high-pressure air is cooled by the chiller and then expanded via the throttle valve. In the liquefaction system, a 4-stage intercooled compressor pressurizes air to 10 MPa. When there is high power demand, the system expands the stored liquid air to produce power based on the Rankine cycle. The cold liquid air is stored in a low-pressure insulated tank until needed. When there is excess power, the system liquefies ambient air based on a variation of the Claude cycle. This example models a grid-scale energy storage system based on cryogenic liquid air. Simulation Results from Simscape Logging.
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