Numerical error evaluation for tip clearance flow calculations in a centrifugal compressor
Résumé
Since globally mesh independent solution are still beyond available computer resources for industrial cases, a method to quantify locally the numerical error is proposed. The design of experiments method helps selecting mesh parameters that influence the tip clearance solution, so that additional meshes are computed to evaluate the numerical error on the shroud friction coefficient.
In the field of CFD applied to turbomachinery, this study results from a partnership between ENSICA, Liebherr-Aerospace Toulouse and Numeca International. This paper focuses on numerical error evaluation for RANS simulations, applied to centrifugal compressor flow field calculations. CFD is now commonly used for centrifugal compressor design optimization, but, as Hutton and Casey develop in [1], there is an urging demand for improved quality and trust in industrial CFD. Indeed, this stresses the need for comprehensive and thorough numerical error evaluation, namely the process of verification, as defined for example by Oberkampf and Trucano in [2]. Unfortunately, 3D turbulent calculations for turbomachinery components are still very demanding in computational resources and, to the knowledge of the author, there is no published result concerning comprehensive verification of the entire flow field in centrifugal compressors. As a first step on the way to achieve that, this paper presents a method aiming at the obtention of a numerical solution that can be regarded as locally mesh-independent. In other words, the objective is to compute the flow field on a grid such that the solution obtained has a specific region where the numerical error is negligible. It has long been recognized that the tip clearance of a centrifugal compressor is of paramount importance for aerodynamic performances, which means that accurately predicting the flow field in this region is crucial for accurate prediction of performances by means of CFD codes. Numerous studies have been published that compare numerical and experimental results in the tip region. However, in these studies, numerical error still remains an issue; for instance Basson and Lakshminarayana [3] show excellent comparisons with experiments, but they attribute the remaining discrepancies to insufficient grid resolution. Indeed, accurate predictions of global effects, such as efficiency, require a fine description of flow details. Therefore, friction at the shroud endwall is the concern of the study, since it is a very sensitive indicator of the quality of the velocity profile’s prediction at the wall.
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