Indirect Surface Transpiration Concept

This is one of the most common and oldest methods for aerodynamic shape inverse design. Like any iterative technique, it requires an initial guess for the aerodynamic shape Then, using an in – viscid flow-field analysis code with desired surface tangential velocity components enforced will result in non-zero values of the surface normal velocity component. The objective is then to find a configuration that has zero velocity components normal to the final body surface. The comput­ed normal velocity components. v#. are therefore used to modify the shape of the initially guessed configuration using a surface transpiration analogy. The new surface shape is predicted by treat­ing the old surface as porous, hence fictitiously injecting the mass (p vn) normal to the onginal surface so rival the new surface becomes an updated stream surface. The local surface displace­ments. Дп, can be obtained from mass conservation equations for the quasi two-dimensional sec­tions (stream tubes) of the flow-field bounded by the two consecutive cross sections of the body surface, the onginal surface shape, and the updated surface shape displaced locally by Дл j 149]- (153J. Starting from a stagnation line where Дп,.^** 0.0 and Дл,.| «0.0. separate updating of

the pressure surface and the suction surface can be readily performed by solving for Діц* and Дп, j+t from a Ы-diagona! system. With the classical transpiration concept, normal surface veloc­ities can be computed using any potential flow solver including a highly economical surface pan­el flow (I52J. (I53J analysis code Figure 72. The indirect surface transpiration method works quite satisfactory in conjunction with Euler and even Navicr-Stokes equations barring any shock waves or flow separation A drawback of this approach is that during the repetitive surface up­dating using this method, the updated surfaces develop a progressively increasing degree of os­cillation. This can be eliminated by periodically smoothing the updated surfaces with a least – squares surface fitting algorithm.

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