Theoretical limits on the heat regeneration degree. (November 2020) - Kronberg, Alexander; Glushenkov, Maxim; Knoke, Torben; Kenig, Eugeny Y.
Highlights: It is easy to overlook a violation of the 2nd law in analysis of heat exchangers. Maximum permissible degree of heat exchange between two fluids is derived. Fluid temperatures at the pinch point can easily be obtained. Realistic heat regeneration efficiencies can be evaluated. Heat exchange efficiency is determined by technical and thermodynamic limitations. Abstract: Heat regeneration is important in numerous heat engines and energy-intensive processes. The theoretical analysis of this non-steady-state process becomes highly complicated when working fluid properties change significantly, as in processes with the phase change of a working fluid or near its critical point. Usually, simplifying assumptions are made; for instance, in the preliminary design of regenerative type heat engines, perfect regeneration or a certain regeneration efficiency is commonly assumed. However, this can result in violation of the second law of thermodynamics and lead to erroneous conclusions with respect to the engine performance. In this paper, the maximum thermodynamically permissible degree of heat exchange between two fluids with specified amounts, initial temperatures and pressures is derived. The analysis is performed for a general-type heat exchanger, with arbitrary flow arrangements and conditions. A simple determination method for the fluid temperature at the pinch point is proposed. When the pinch point is achieved away from the ends of a heat exchanger, the fluid temperatures at these ends are determined, too. The results of the derivation are illustrated graphically to clarify their physical significance and examples of the calculation of the regeneration efficiency are provided. The derived simple equation for the maximum heat exchange enables to avoid violations of the second law in heat exchange studies and permits the maximum possible efficiency of a heat exchanger to be estimated. The equation can also be used as a preliminary criterion for selection and/or design of working fluids optimal for particular power or refrigeration (heat pump) cycles. The maximum degree of energy exchange between two fluids is shown to be determined by the maximum enthalpy difference at the same temperature; this temperature can generally deviate from the inlet temperatures, as in case of fluids with complex temperature and pressure dependant heat capacities.