Constructal Theory: Tree-Shaped Flows and Energy Systems for Aircraft

Attention is drawn to constructal theory and design, which relies on global maximization of performance in the pursuit of flow system architecture. Exergy analysis establishes the theoretical performance limit. Thermodynamic optimization (or entropy generation minimization) brings the design as closely as permissible to the theoretical limit. The design is destined to remain imperfect because of constraints (finite sizes, times, and costs). Improvements are registered by spreading the imperfection, for example, flow resistances, through the system. Resistances compete against each other and must be optimized together. Optimal spreading means geometric form. System architecture is generated by the constructal principle: constrained global optimization and constraints in a morphing flow medium. In flows that connect a volume (or area) with one point, the resulting structure is a tree of low-resistance links, and high-resistance interstices. These structures are robust, diverse, and everywhere. A key example is the extraction of maximum exergy from a hot-gas stream that is cooled and discharged into the ambient. The optimal configuration consists of a heat transfer surface with a temperature that decays exponentially in the flow direction. Additional examples show that the complete structure of a heat exchanger for an environmental control system can be derived based on this method.