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  • 1
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    Computation of a Single Airfoil Gust Response and Gust-Cascade Interaction Using the CE/SE Method (2004)
    In:  CASI
    Details
    Publication Date: 2019-07-10
    Description: The problems 1 and 2 in Category 3 are solved using the space-time conservation element and solution element (CE/SE) method. Problem 1 concerns the acoustic field generated by the interaction of a harmonic vertical gust with a single isolated airfoil. Problem 2 models rotor-stator interaction in a 2D cascade. Both problems involve complex geometries and flow physics including vortex shielding and acoustic radiation. An unstructured triangular mesh is used to solve both problems. For problem 2, the Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Numerical solution of both near and far fields of problem 1 are presented and compared with a frequency-domain solver GUST3D and a time-domain high-order Discontinuous Spectra Element Method (DSEM) solutions. For problem 2, numerical solutions on the blade surface, inlet and outlet planes are presented.
    Keywords: Acoustics
    Type: Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems; 115-126; NASA/CP-2004-212954
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  • 2
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    Applications of the Space-Time Conservation Element and Solution Element (CE/SE) Method to Computational Aeroacoustic Benchmark Problems (2000)
    In:  CASI
    Details
    Publication Date: 2019-07-10
    Description: The Internal Propagation problems, Fan Noise problem, and Turbomachinery Noise problems are solved using the space-time conservation element and solution element (CE/SE) method. The problems in internal propagation problems address the propagation of sound waves through a nozzle. Both the nonlinear and linear quasi 1D Euler equations are solved. Numerical solutions are presented and compared with the analytical solution. The fan noise problem concerns the effect of the sweep angle on the acoustic field generated by the interaction of a convected gust with a cascade of 3D flat plates. A parallel version of the 3D CE/SE Euler solver is developed and employed to obtain numerical solutions for a family of swept flat plates. Numerical solutions for sweep angles of 0, 5, 10, and 15 deg are presented. The turbomachinery problems describe the interaction of a 2D vortical gust with a cascade of flat-plate airfoils with/without a downstream moving grid. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. All the comparisons demonstrate that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple and efficient manner. Furthermore, the simple non-reflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well in 1D, 2D and 3D problems.
    Keywords: Acoustics
    Type: Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems; 133-159; NASA/CP-2000-209790
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  • 3
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    Prediction of Sound Waves Propagating Through a Nozzle Without/With a Shock Wave Using the Space-Time CE/SE Method (2000)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The benchmark problems in Category 1 (Internal Propagation) of the third Computational Aeroacoustics (CAA) Work-shop sponsored by NASA Glenn Research Center are solved using the space-time conservation element and solution element (CE/SE) method. The first problem addresses the propagation of sound waves through a nearly choked transonic nozzle. The second one concerns shock-sound interaction in a supersonic nozzle. A quasi one-dimension CE/SE Euler solver for a nonuniform mesh is developed and employed to solve both problems. Numerical solutions are compared with the analytical solution for both problems. It is demonstrated that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple way. Furthermore, the simple nonreflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well.
    Keywords: Acoustics
    Type: NASA/TM-2000-209937 , E-12283 , NAS 1.15:209937 , Aerospace Sciences; Jan 10, 2000 - Jan 13, 2000; Reno, NV; United States
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  • 4
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    Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves (1999)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.
    Keywords: Acoustics
    Type: NASA/TM-1999-209659 , NAS 1.15:209659 , E-12030 , AIAA Paper 2000-0474 , 38th Aerospace Sciences; Jan 10, 2000 - Jan 13, 2000; Reno, NV; United States
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  • 5
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    A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method (2015)
    In:  CASI
    Details
    Publication Date: 2019-07-12
    Description: The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.
    Keywords: Numerical Analysis; Astronautics (General)
    Type: NASA/TM-2015-218743 , E-19071 , GRC-E-DAA-TN21438
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