An Iterative Inverse Design Method Based on Aerodynamic Streamline Equations

Yu, Jianzhong; Paraschivoiu, Ion; Saeed, Farooq

doi:10.2514/6.2003-214

Cited by 1 publication

(2 citation statements)

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“…This might be caused by taking the same constant D in Eqs. (17) and (26) for the entire airfoil. The problem can be solved by treating the constant D as a function of curvature lengths, but it is more convenient to use nonuniform relaxation.…”

Section: Nonuniform Relaxationmentioning

confidence: 99%

“…Therefore in this research, different relaxation factors are employed and varied between 0.3 and 5 in Eqs. (17) and (26), and are adjusted automatically according to the amplitudes of geometric perturbations and the pressure differences. Relaxation factors should be selected in such a way that the convergence speed to the target values should be more uniform at every point of the airfoil.…”

Section: Nonuniform Relaxationmentioning

confidence: 99%

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Iterative Inverse Design Method Based on Streamline Equations

Paraschivoiu

Saeed

2004

Journal of Aircraft

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Aerodynamic characteristics are very sensitive to airfoil leading-edge geometry, and its accurate treatment is a limitation of many existing design methods. The objective of the present research is to develop an interactive inverse design method that is not only efficient but can also treat the leading-edge region accurately. In the formulation of the method, a small-perturbation geometric equation is deduced from the streamline momentum equations, the continuity equation, and the isentropic relations with the geometry similarity assumption of near streamlines to the airfoil surface. Moreover, the transonic correction is considered in the aforementioned equation with the assumption for the effects of waves reflected from the free surface (sonic line) because the method based on the surface flow values cannot take into account the transonic characteristics such as wave interference. The geometric perturbation normal to the airfoil surface is then calculated by solving this second-order initial value ordinary differential equation iteratively to obtain an airfoil design. Techniques such as airfoil smoothing, nonuniform relaxation, and the strained coordinate transfer are employed to accelerate convergence. The airfoil design cases demonstrate the remarkable efficiency and accuracy of the method not only for compressible flows but also for low-speed flows. Moreover, the method allows the leading-edge shape to be determined accurately and, thus, to overcome the deficiency of many of the related methods.

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Section: Nonuniform Relaxationmentioning

confidence: 99%

Section: Nonuniform Relaxationmentioning

confidence: 99%