Optimization of a More Realistic System The Otto Cycle

The desired objective corresponds to the absolute maximum (or minimum) of H over the range of the set of the control variables u. 

If one maximizes the mean power produced, the energy per cycle, one obtains an explicit pathway for the cycle, the volume (or piston displacement) and temperature as functions of time. Such an optimal pathway is sketched schematically but in fact from real calculations of the optimal Carnot-like cycle with heat leak and friction, in Fig. 14.2. 

The Otto cycle is essentially the cycle describing the internal-combustion automobile engine. This is a four-stroke cycle, in contrast to the simpler two-stroke Carnot cycle and the various others, such as the Stirling and Brayton cycles, that operate on a single oscillation of the piston. The Otto cycle consists of an intake expansion, a compression, an expansion resulting from ignition 

The most striking characteristic of the optimized time path is the marked deviation from sinusoidal motion in the power stroke, the first stroke shown at the beginning of the cycle. The piston accelerates very rapidly as the fuel-air mixture ignites and then, most important, the piston moves out at essentially its maximum rate. This is precisely what enables this optimized cycle to transform as much of the heat energy as possible into work before it can leak out of the cylinder into the surroundings. 

What can such optimization achieve One criterion is the effectiveness, sometimes called the second-law efEciency, which is the ratio of the work done by the process to that it would do reversibly. The conventional Otto cycle used for this analysis would have an effectiveness of 0.633 the most effective of the optimized engines modeled in the analysis but with a maximum piston velocity of 22.4m/s would be 0.698 with no velocity constraint, that would go only to 0.705. The model used in the analysis dissipates about 3/5 of its total losses as friction and 2/5 as heat loss. If the engine chosen as the conventional basis for comparison were to lose only about 30% of its total through friction and 70% through heat leak, the effectiveness of the optimized engine would be as much as 17% greater than the conventional engine. 

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Optimization of a More Realistic System The Otto Cycle 139... 

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