Analysis of High-Order Source Terms in Throughflow Solutions

Abstract

Classical throughflow methodologies, due to their oversimplified assumptions regarding dimensionality reduction, result in a significant reliance on empirical inputs. This paper introduces a rigorous dimensionality reduction approach, building upon Adamczyk’s average-passage approach, wherein four averaging operators are incorporated into the Navier–Stokes equations. This method dispels the conventional assumptions of time averaging and passage periodicity inherent in primary equations, simultaneously addressing circumferential non-uniformity in the flow field through the inclusion of high-order source terms in the equations. The study employs a time-marching numerical method to solve the averaged equations and offers a comprehensive discussion on the influence and role of high-order source terms, derived from three-dimensional unsteady Reynolds-averaged Navier–Stokes results, in throughflow solutions. The transonic fan case’s results presented in this paper underscore the critical significance of high-order source terms in throughflow calculations, particularly concerning temporal and circumferential fluctuations. At the design point, considering temporal correlations reveals the wake recovery effect, resulting in a 3% increase in flow capacity, alongside heightened pressure ratio and efficiency. Conversely, incorporating circumferential correlations, intricately associated with steady flow structure, induces a 5% reduction in flow capacity, accompanied by a decrease in pressure ratio and efficiency. This paper advocates for the accurate modeling of high-order source terms and identifying computational error sources to improve the precision of throughflow solutions, though the actual modeling of these terms is not the focus of this paper.