Mesh convergence error estimations for compressible inviscid fluid flow over airfoil cascades using multiblock structured mesh

Q4 Chemical Engineering
Adam Tater, J. Holman
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引用次数: 0

Abstract

This work deals with estimations of errors, which are a consequence of a finite spatial discretisation that appears while solving differential equation numerically. More precisely, it deals with the estimation of errors that occur while computing compressible inviscid fluid flow over 2D airfoil cascades. This flow is described by the 2D Euler equations that are solved by the finite volume method in their conservative form. Numerical computations are performed on structured meshes consisting of four blocks, so the number of cells in the mesh can be easily adjusted. In this work, two estimation methods are used. Firstly, the grid convergence index is used to estimate the amount of cells needed to obtain certain accuracy of the solution. Secondly, the Richardson extrapolation is used to approximate the exact solution from a series of solutions obtained with meshes of different sizes. This analysis is performed on a well-known compressor cascade, which is composed of NACA 65 series airfoils. The obtained results should lead to a reasonable choice of the number of elements in a computational mesh based on the required accuracy of the solution and therefore also to computational time reduction while performing airfoil cascade computations. The results indicate that even for very precision demanding applications, 100 000 is a sufficient number of cells in a mesh.
用多块结构网格估计翼型叶栅可压缩无粘流体流动的网格收敛误差
这项工作涉及误差的估计,这是在求解微分方程时出现的有限空间离散化的结果。更准确地说,它处理的误差估计,而发生的计算可压缩的无粘流体流动在二维翼型叶栅。这种流动用二维欧拉方程来描述,用有限体积法以其保守形式求解。在由四个块组成的结构化网格上进行数值计算,因此网格中的单元数可以很容易地调整。在这项工作中,使用了两种估计方法。首先,利用网格收敛指数估计获得一定精度解所需的单元数;其次,利用Richardson外推法从不同尺寸网格的一系列解中逼近精确解。该分析是在一个著名的压气机叶栅上进行的,该叶栅由NACA 65系列翼型组成。所获得的结果应导致一个合理的选择在一个计算网格的元素的数量基于所需的精度的解决方案,因此也计算时间减少,同时执行翼型级联计算。结果表明,即使对于精度要求很高的应用,100,000个网格中的单元数量也足够了。
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来源期刊
Applied and Computational Mechanics
Applied and Computational Mechanics Engineering-Computational Mechanics
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
14 weeks
期刊介绍: The ACM journal covers a broad spectrum of topics in all fields of applied and computational mechanics with special emphasis on mathematical modelling and numerical simulations with experimental support, if relevant. Our audience is the international scientific community, academics as well as engineers interested in such disciplines. Original research papers falling into the following areas are considered for possible publication: solid mechanics, mechanics of materials, thermodynamics, biomechanics and mechanobiology, fluid-structure interaction, dynamics of multibody systems, mechatronics, vibrations and waves, reliability and durability of structures, structural damage and fracture mechanics, heterogenous media and multiscale problems, structural mechanics, experimental methods in mechanics. This list is neither exhaustive nor fixed.
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