Optimized Laminar Axisymmetrical Nozzle Design Using a Numerically Validated Thwaites Method

Abstract

This paper presents the Thwaites method as an accurate and efficient design tool for laminar, axisymmetrical nozzles. Based on historical developments, it is improved to describe internal flows with highly favorable pressure gradients in cylindrical coordinates. The calculation of the core flow velocity distribution based on the continuity equation is proposed as a replacement to other sophisticated numerical methods. A remarkably good agreement is obtained when comparing the results of the current Thwaites method against those of computational fluid dynamics (CFD) simulations, for which the integral boundary layer thicknesses are calculated with equations developed from first principles in the course of the work. This consistency among the results and the low time and resource costs of the Thwaites method confirm its applicability and usefulness as an engineering design and optimization tool.