Derivation of the optimal internal cooling geometry of a prismatic slab: Comparison of constructal and non-constructal geometries

摘要

This paper investigates the thermal performance of a prismatic slab internally cooled by a bundle of staggered tubes. Four tube arrangements are considered, each case having three constructal levels of cooling tubes; for each case a single ratio between two consecutive tube level diameters is adopted, the constructal ratio paradigm defining one of the four geometries.rnThe mass flow rate of the cooling fluid through the tube bundle is constant, enters the slab from its root and is ejected from the tip. The remaining boundary conditions imposed on the system reproduce those of an internally cooled gas turbine blade.rnThe initial configuration for each case is the one prescribed by the constructal design paradigm, and is described in a previous paper by the same authors: this geometry resulted from a simple 2-D constructal "optimisation" in which the pressure drop along the tubes was neglected.rnA completely 3-D approach is proposed here instead: a local analysis of thermal field of both the slab and the tubes suggests that the constructal cooling strategy is not the best one for compact heat exchange purposes where it is more convenient to exploit the entry length effects to achieve the best performance.