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The verification of mathematical models for multistage reciprocating compressors is crucial for ensuring their accuracy and reliability. In this study, we used different machine learning (ML) models to verify the results of MATLAB-based models of single-stage reciprocating compressors, multistage reciprocating compressors without intercoolers, and multistage reciprocating compressors with intercoolers to simulate the real-world operating conditions of a reciprocating compressor. The verification focuses on key performance indicators, such as the pressure–volume (PV) graph, outlet temperature graph, volumetric efficiency, and pressure ratio graph. The MATLAB model computes thermodynamic parameters, such as the power required, outlet pressure, and outlet temperature for various operating conditions. The MATLAB model produced the following results for single-stage compressor: the outlet pressure increased by 1.6 times the inlet pressure of the compressor, the volume reduced by 20% of the volume at the inlet of the single-stage compressor, and the outlet temperature increased by 30% of the inlet temperature. In the case of a multistage compressor without an intercooler, the outlet pressure increased by about 3.3–3.6 times the inlet pressure of the compressor; the volume reduced by 60% of the volume at the inlet, and the outlet temperature increased by 35% in comparison to the inlet temperature of the multistage compressor without an intercooler. Subsequently, in the case of a multistage compressor with an intercooler at the first stage of compression, the pressure increased by three times the inlet pressure; at the second stage of compression, the pressure increased by six times the inlet pressure of the compressor, the volume was reduced by approximately 80%, and the intercooler maintained the increase in outlet temperature by 30%, limiting it and preventing excessive expansion of air in the compressor and increasing the efficiency of the compressor by 12% in comparison to the multistage compressor without an intercooler. In addition, the results generated by all the machine learning models used in the study were in correlation with the results generated by the MATLAB model for all three compressors, with an accuracy of approximately 90% or more for almost all the models implemented for prediction. By comparing the predicted outputs from the ML model with the MATLAB-generated results, the accuracy and consistency of the simulation were assessed. This study aims to bridge the gap between traditional mathematical modeling and modern data-driven validation techniques to ensure robustness in compressor performance predictions.

The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations.

The capacity control system of reciprocating compressor has great significance for the contribution of energy conservation and emission reduction. The parameters of the actuator and hydraulic system within a reciprocating compressor stepless capacity control system play a decisive role in its control accuracy, mechanical reliability, and mechanical security. The actuators and hydraulic system parameters of the same stage are in conflict with each other. Therefore, the actuator and the multistage reciprocating compressor are studied here, specifically through multiobjective optimization using the Nondominated Sorting Genetic Algorithm (NSGA)-II. The multiobjective optimization design was performed on a two-dimensional (2D) reciprocating compressor test bench. When the spring stiffness of the first stage spring was 27358 N m−1, the spring stiffness of the second stage spring was 23315 N m−1, the inlet oil pressure was 296.62 N, the impact velocity of ejection was 0.4215 m s−1, and the total indicated power deviation was 12.05 kW; the objective functions were optimized. Compared with traditional parameters, the inlet oil pressure, spring stiffness, and impact velocity were all reduced. This parameter optimization design lays the foundations for global optimization designs for stepless capacity control systems.