Computational Fluid Dynamics of Airfoils and Wings

Garabedian, P. R.; McFadden, Geoffrey B.

doi:10.1016/b978-0-12-493280-7.50006-1

Cited by 9 publications

(3 citation statements)

References 8 publications

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“…In his pioneering contribution Lighthill (1945) solved the problem for incompressible potential flow past a body by conformally mapping it to a unit circle. Similar approaches were used by McFadden (1979) and Garabedian & McFadden (1982) for two-and three-dimensional compressible flow. An alternative formulation of the potential flow design problem is to convert the specified pressure distribution into a corresponding surface speed that can be integrated to obtain the surface potential.…”

Section: Introductionmentioning

confidence: 97%

Optimum plane diffusers in laminar flow

Çlabuk

Modi

1992

J. Fluid Mech.

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The problem of determining the profile of a plane diffuser (of given upstream width and length) that provides the maximum static pressure rise is solved. Two-dimensional, incompressible, laminar flow governed by the steady-state Navier-Stokes equations is assumed through the diffuser. Recent advances in computational resources and algorithms have made it possible to solve the ‘direct’ problem of determining such a flow through a body of known geometry. In this paper, a set of ‘adjoint’ equations is obtained, the solution to which permits the calculation of the direction and relative magnitude of change in the diffuser profile that leads to a higher pressure rise. The direct as well as the adjoint set of partial differential equations are obtained for Dirichlet-type inflow and outflow conditions. Repeatedly modifying the diffuser geometry with each solution to these two sets of equations with the above boundary conditions would in principle lead to a diffuser with the maximum static pressure rise, also called the optimum diffuser. The optimality condition, that the shear stress all along the wall must vanish for the optimum diffuser, is also recovered from the analysis. It is postulated that the adjoint set of equations continues to hold even if the computationally inconvenient Dirichlet-type outflow boundary condition is replaced by Neumann-type conditions. It is shown that numerical solutions obtained in this fashion do satisfy the optimality condition.

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Section: Introductionmentioning

confidence: 97%

Optimum plane diffusers in laminar flow

Çlabuk

Modi

1992

J. Fluid Mech.

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“…The flexible membrane method, which is an iterative mathematically based inverse design technique, was initially introduced by Garabedian and McFadden [30,31] as GM method. Then, Malone et al [32][33][34] developed this method to the MGM (Malone-Garabedian-McFadden) method.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm

et al. 2021

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The upgraded elastic surface algorithm (UESA) is a physical inverse design method that was recently developed for a compressor cascade with double-circular-arc blades. In this method, the blade walls are modeled as elastic Timoshenko beams that smoothly deform because of the difference between the target and current pressure distributions. Nevertheless, the UESA is completely unstable for a compressor cascade with an intense normal shock, which causes a divergence due to the high pressure difference near the shock and the displacement of shock during the geometry corrections. In this study, the UESA was stabilized for the inverse design of a compressor cascade with normal shock, with no geometrical filtration. In the new version of this method, a distribution for the elastic modulus along the Timoshenko beam was chosen to increase its stiffness near the normal shock and to control the high deformations and oscillations in this region. Furthermore, to prevent surface oscillations, nodes need to be constrained to move perpendicularly to the chord line. With these modifications, the instability and oscillation were removed through the shape modification process. Two design cases were examined to evaluate the method for a transonic cascade with normal shock. The method was also capable of finding a physical pressure distribution that was nearest to the target one.

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“…It allows the recovery of smooth profiles that generate flows containing shock waves, and it has been used to design improved blade sections for propellers (Taverna, 1983). A related method for three-dimensional design was devised by Garabedian and McFadden (1982). In their scheme the steady potential flow solution is obtained by solving an artificial time-dependent equation, and the surface is treated as a free boundary.…”

Section: Automatic Design Optimizationmentioning

confidence: 99%