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SUMMARY A general model for an irreversible solar‐driven Brayton multi‐step heat engine is presented. The model incorporates an arbitrary number of turbines (Nt) and compressors (Nc) and the corresponding reheating and intercooling processes; thus, the solar‐driven Ericsson cycle is a particular case where Nt, Nc → ∞. For the solar collector, we assume linear heat losses, and for the Brayton multi‐step cycle, we consider irreversibilities arising from the non‐ideal behavior of turbines and compressors, pressure drops in the heat input and heat release, heat leakage through the plant to the surroundings, and non‐ideal couplings of the working fluid with the external heat reservoirs. We obtain the collector temperatures at which maximum overall efficiency ηmax is reached as a function of the thermal plant pressure ratio, and a detailed comparison for several plant configurations is given. This maximum efficiency is obtained in two cases: when only internal irreversibilities are considered and when both internal and external irreversibilities (which corresponds to the fully irreversible realistic situation) are simultaneously taken into account. Differences between both situations are stressed in detail. In the fully irreversible realistic case, it is possible to perform an additional optimization with respect to the pressure ratio, ηmax∗. In particular, this double optimization leads to a valuable increase in efficiency (between 34% and 65%) for a plant with two turbines and two compressors compared to the simple solar‐driven one‐turbine one‐compressor Brayton engine. Copyright © 2012 John Wiley & Sons, Ltd.

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.