Calculation of steam regenerators
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The regenerator uses high-temperature steam to heat the water inside it in order to store heat, which is then supplied as steam to the external system. The known values are: the pressure inside the regenerator is P1, the pressure in the external system is P2, the volume of the regenerator is V. For the saturated water and saturated steam inside the regenerator, their masses are M_water and M_vapor respectively; their internal energies are U_water and U_vapor; and their enthalpies are H_water and H_vapor. And under pressures P1 and P2, what are the formulas for the densities of water ρ_water1, ρ_vapor1, ρ_water2, ρ_vapor2? How can we determine how many tons of steam are stored in the heat accumulator at the pressures applied to the external network?
For such problems, we need to use the heat balance equation for the regenerator. Ideally, the heat storage capacity of a thermal accumulator should equal the difference between the heat input and the heat output. In this case, the energy of the heated water and steam inside the heat store can be expressed as: U_in = M_water * U_water + M_vapor * U_vapor (input energy). Then, we calculate the energy supplied by the heat store to the external system. According to the law of mass continuity, during the process of heat storage and release by the regenerator, the total mass M of the substances contained within it remains constant; that is, M_water + M_vapor = M (the total mass of substances in the regenerator). Therefore, we can infer that the amount of steam supplied to the external network is M, and the enthalpy of this steam at pressure P2 is H_Steam 2. Therefore, the energy supplied to the external network is: U_out = M * H_steam2 (output energy). By comparing the two formulas above, we can obtain: M_water * U_water + M_steam * U_steam = M * H_steam2. Solving this equation yields the value of M, which represents the required amount of steam. However, this is an ideal situation; in practice, factors such as the heat loss and efficiency of the heat storage device also need to be taken into account. .