Numerical Simulation of Aeroacoustic Field in a 2D Cascade Involving a Downstream Moving Grid Using the Space-Time CE/SE
The space-time conservation element and solution element (CE/SE) method is used to solve an aeroacoustic benchmark problem regarding turbomachinery noise. It concerns the aeroacoustic field generated by the interaction of a convected gust with a 2D cascad
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s.c. Chang2 , and P. Jorgenson3
ITaitech Inc., NASA Glenn Research Center, Cleveland, Ohio 2,3NASA Glenn Research Center, Cleveland, Ohio 1 email: [email protected] 2 email: [email protected] 3 email: [email protected]
Abstract. The space-time conservation element and solution element (CE/SE) method is used to solve an aeroacoustic benchmark problem regarding turbomachinery noise. It concerns the aeroacoustic field generated by the interaction of a convected gust with a 2D cascade of flat-plate airloils with a downstream moving grid. This tests the accuracy of a numerical method and the ability to model the acoustic wave and the gust across a sliding interlace typical of those used in rotor stator interaction problems. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. The comparison shows that the CE/SE method is capable of producing accurate solutions in a simple manner.
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Introduction
The method of space-time conservation element and solution element (abbreviated as the CE/SE method) is an innovative numerical method for solving conservation laws. It is designed to be a numerical method in the field of computational fluid dynamics (CFD). Computational aeroacoustics (CAA) is one of its applications. This method is distinguished from other methods by its very conceptual basis - flux conservation in space and time. Simplicity, generality and accuracy are weighted in the development of this method. Its salient properties are summarized briefly as follows. First, both local and global flux conservations are enforced in space and time instead of in space only. Second, all the dependent variables and their spatial derivatives are considered as individual unknowns to be solved for simultaneously at each grid point. Third, every CE/SE scheme starts from a non-dissipative scheme and numerical dissipation is fully controllable, which result in very low numerical dissipation. Fourth, the flux-based specification of the CE/SE schemes give rise in a natural fashion to an extremely simple yet highly effective non-reflecting boundary condition which is an important issue in CAA. This can be contrasted to the complexity of nonreflecting boundary conditions necessary for traditional numerical methods. A detailed description of this method and the accompanied analysis can be found in [1-4]. N. Satofuka (ed.), Computational Fluid Dynamics 2000 © Springer-Verlag Berlin Heidelberg 2001
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X-Y Wang, S-C Chang, P Jorgenson
A variety of numerical tests have been performed previously to illustrate the accuracy of this method. Applications of this method to CAA problems reveal that the results are comparable to that of a 4th-order compact difference scheme even though the current solver is only 2nd-order accurate. Results show that the present solver can handle both continuous and discontinuous flows very well [5]. In this paper, the 2-D CE/SE Euler solver is applied to study turbomachinery noise. An aer
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