A three-energy equation model and estimation of effective thermal properties for transient analysis of bi-disperse packed bed thermocline storage system

For the first time, a complete set of the volume averaged governing equations based on a three-energy equation model has been proposed to attack the transient thermal response of a bi-disperse packed bed thermocline storage system, in which its void is filled by smaller particles (i.e. solid filler). Effective permeability, stagnant thermal conductivity and effective thermal conductivities for three individual phases, namely, the fluid phase, large particle phase and small particle phase of the bi-disperse packed bed storage system, have been evaluated taking full account of tortuosity and appealing to a volume averaging theory. Subsequently, the three individual energy equations in the three-energy model were coupled and analytically solved to reveal a transient behavior of the temperature fields of the individual phases. The effective discharging efficiency of the bi-disperse packing is found to decrease substantially as compared with that of the mono-disperse packing under equal pumping power. Though one can save a substantial initial cost by filling the void by solid fillers, one must pay a penalty of a higher cost in running the bi-disperse packed bed thermocline storage system. The analysis presented in this study serves to estimate both initial and running costs of a bi-disperse packed bed thermocline storage system.