Constructal vapor compression refrigeration (VCR) systems design

•We introduce a mathematical model for constructal VCR systems design.•The heat exchangers refrigerant phase and temperature distributions are depicted.•Optimal system pressure ratio, area allocation and compressor size are found.•Three refrigerants are tested with the model, i.e., R1234yf, R22, and R410A.•The maxima are sharp, showing a second law efficiency ∼400% variation. This paper introduces a mathematical model and a structured procedure to optimize the internal structure (heat exchanger areas) and pressure ratio of a vapor compression refrigeration system so that the refrigeration rate, the coefficient of performance (COP), and second law efficiency are maximized. The heat exchanger (condenser and evaporator) model equations are written based on the effectiveness-NTU method with the aim of achieving fast and accurate results for possible application in systems engineering design. The optimization is subjected to fixed system total heat transfer surface, A (or number of transfer units, N), and desired compressor power input, W̃cp. Two levels of optimization are investigated: (i) the compressor pressure ratio, pr=pc/pe, and (ii) the internal structure, which basically accounts for the relative sizes of evaporator and condenser heat transfer surfaces. The pressure ratio and the available heat exchanger area allocation are selected optimally so that system performance is maximized. In such condition, the refrigerant fluid morphs optimally in two and three sections, respectively, in the evaporator (superheating and two-phase), and condenser (superheating, two-phase, and subcooling), which are determined by the model. Three different refrigerants are tested with the model, i.e., R1234yf, R22, and R410A. Numerical results show that the optimized internal structure and pressure ratio are “robust” with respect to changes in refrigerant and system total number of transfer units. The optimized internal structure and pressure ratio are a result of an optimal balance among the several system irreversibilities (e.g., thermal contact between streams). The maxima found are sharp, showing a second law efficiency ∼400% variation within the tested range of the optimized parameters, highlighting the importance of exploring the system tradeoffs.