Improved, robust, axial line singularity method for bodies of revolution

Hemsch, Michael J.

doi:10.2514/3.25318

Journal of Aircraft

1990

DOI: 10.2514/3.25318

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Improved, robust, axial line singularity method for bodies of revolution

Michael J. Hemsch

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1992

1994

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Cited by 3 publications

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Solution of the axisymmetric inverse problem by higher‐order line doublets

Zedan¹

1994

Numerical Methods in Fluids

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SUMMARYThe axial singularity inverse method for designing bodies of revolution has been improved by using higher-order doublet elements. The performance of the method for various element orders and other solution parameters is presented in detail. The results indicate that the method is generally more robust, less sensitive to insets and has a better-conditioned coefficient matrix compared with the source method of the same order. The condition number of the matrix is shown to increase with the thickness of the body, the order of the method, the number of elements and the degree of stretching of the node distribution. In general, good performance is attained for most bodies even with f, as low as 2 by using 10-12 second-order doublet elements with insets greater than 0-02L from rounded ends. Increasing the insets to 0.06L appears to improve the accuracy of the method for most bodies but slows its convergence.

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Solution of the axisymmetric inverse problem by higher‐order line doublets

Zedan¹

1994

Numerical Methods in Fluids

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Tuning the axial singularity method for accurate calculation of potential flow around axisymmetric bodies

Zedan

1994

Aeronaut. j.

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The performance of axial line singularity methods has been investigated systematically for various solution parameters using carefully chosen test cases. The results indicate that increasing the number of elements and using stretched node distribution improves the solution accuracy until the matrix becomes near-singular. The matrix condition number increases with these parameters as well as with the order of intensity variation and profile thickness. For moderate fineness ratios, the linear methods outperform zero-order methods. The linear doublet method performs best with control points at the x-locations of nodes while the source methods perform best with control points mid-way between nodes. The doublet method has a condition number an order of magnitude lower than the source method and generally provides more accurate results and handles a wider range of bodies. With appropriate solution parameters, the method provides excellent accuracy for bodies without slope discontinuity. The smoothing technique proposed recently by Hemsch has been shown to reduce the condition number of the matrix; however it should be used with caution. It is recommended to use it only when the solution is highly oscillatory with a near-singular matrix. A criterion for the optimum value of the smoothing parameter is proposed.

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Prediction of vortex shedding from forebodies with chines

Mendenhall

Lesieutre

1992

Journal of Aircraft

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Improved, robust, axial line singularity method for bodies of revolution

Cited by 3 publications

References 20 publications

Solution of the axisymmetric inverse problem by higher‐order line doublets

Solution of the axisymmetric inverse problem by higher‐order line doublets

Tuning the axial singularity method for accurate calculation of potential flow around axisymmetric bodies

Prediction of vortex shedding from forebodies with chines

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