A COMPLETE CROCCO-INTEGRAL FOR 2-DIMENSIONAL LAMINAR BOUNDARY-LAYER FLOW OVER AN ADIABATIC WALL FOR PRANDTL-NUMBERS NEAR UNITY

The so-called Crocco integral establishes a relation between the veloc ity and temperature distributions in steady boundary layer how. It cor responds to an exact solution of the flow equations in the case of uni ty Prandtl number and an adiabatic wall, where it reduces to the condi tion that the total enthalpy remains constant throughout the boundary layer, irrespective of pressure gradient and compressibility. The effe ct of Prandtl number is usually incorporated by assuming a constant re covery factor across the entire boundary layer, Strictly, however, thi s modification is in conflict with the conservation-of-energy principl e. In search of a more complete expression for the Crocco integral the present study applies an asymptotic solution approach to the energy e quation in constant-property flow. The analysis of self-similar bounda ry layer solutions results in a formulation of the Crocco integral whi ch correctly incorporates the effect of Prandtl number to first order, and that is complete in the sense that it satisfies the energy conser vation requirement. Furthermore, the result is found to be applicable not only to self-similar boundary layers,but also to provide a solutio n to the laminar flow equations in general as well. The effect of vary ing properties is considered with regard to the extension of the expre ssion to more general flow conditions. In addition to the asymptotic e xpression for the Crocco integral, asymptotic solutions are also obtai ned for the recovery factor for various classes of flows.