Two distinct steady state models have been programmed to calculate heat transfer and pressure loss from a saturated CO2 vapor in a vertical U-tube to the surrounding grout and earth. The work began with calculations of the individual heat transfer coefficients from vapor, from the condensing vapor, and from the liquid to the tube, and then from the U-tube to the surrounding grout and earth. According to computations for the tube to the earth reviewed in the ASHARE Handbook and relevant literature on the coefficients inside the tube, all reviewed in the paper, the internal heat transfer coefficient area products, hA, for CO2 condensing in a 3/4 inch tube diameter are much higher than the ground heat transfer coefficient; the ground heat transfer coefficient limits the heat transfer in the U-tube. A homogeneous model assumed that the vapor-liquid mixture in the tube is represented by a fluid whose properties and heat transfer coefficients are a weighted average between those of the vapor and the liquid present at the point. The homogeneous model has been developed by the mass balance, momentum balance, energy balance, enthalpy property, equation of state, and phase equilibrium of liquid and vapor CO2. The equations of the model have been numerically calculated in Matlab by solver ODE4 (Runge-Kutta). Measured values of heat transfer were closed to values calculated by the model. Measurements of the pressure loss over the U-tube were significantly higher than those predicted by the model. Based on the assumption that the pressure differences in the U-tube between the inlet and outlet are mainly due to the presence of liquid CO2 in the up and down legs, a new simplified model has been created and the simulation results have been compared with the experimental results. Greater agreement between measured and predicted pressure losses was achieved. This study is useful in understanding heat transfer and pressure loss of CO2 condensing in a vertical U-tube transferring heat to the earth.
Steady State Heat Transfer Models of CO2 Condensing in a Vertical U-Tube
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Hu, Y, & Archer, DH. "Steady State Heat Transfer Models of CO2 Condensing in a Vertical U-Tube." Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition. Volume 7: Fluid Flow, Heat Transfer and Thermal Systems, Parts A and B. Vancouver, British Columbia, Canada. November 12–18, 2010. pp. 1693-1700. ASME. https://doi.org/10.1115/IMECE2010-39112
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