×

Considerations on shape identification for flow channel including a rotational body. (English) Zbl 1458.76034

Summary: In this paper, we describe the shape identification of a channel in incompressible viscous flow considering a rotational body. The purpose of this study is to obtain an optimal shape that will closely approach the target velocity in the target regions. The incompressible Navier Stokes equations are employed as the governing equations, and the adjoint variable method is applied to obtain the sensitivity for the optimal shape. The traction method is used to control the numerical oscillations of sensitivity for the shape update. Shape identification analysis is carried out using computed flow velocities in the target regions of target shape.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] O. Pironneau, On optimum profiles in Stokes flow, J. Fluid Mech., 59, 117-128 (1973) · Zbl 0274.76022
[2] H. Azegami, Solution to domain optimization problems (in Japanese), Trans. Jpn. Soc. Mech. Eng., Series A, 60, 1479-1486 (1994)
[3] E. Katamine; H. Azegami, Solution to viscose flow field domain optimization problems (Approach by the traction method) (in Japanese), Trans. Jpn. Soc. Mech. Eng., Series B, 60, 3859-3866 (1994)
[4] E. Katamine; H. Azegami, Domain optimization analysis of potential flow field (in Japanese), Trans. Jpn. Soc. Mech. Eng., Series B, 61, 103-108 (1995)
[5] E. Katamine; N. Nishihashi; H. Azegami, Shape optimization of steady-state viscous flow fields for drag minimization and lift maximization (in Japanese), Trans. Jpn. Soc. Mech. Eng., Series B, 74, 2426-2434 (2008)
[6] Y. Kiriyama; E. Katamine; H. Azegami, Shape optimisation problem for stability of Navier-Stokes flow field, Int. J. Comput. Fluid Dyn., 32, 68-87 (2018) · Zbl 07474457
[7] T. Kurahashi; Y. Ozeki; E. Katamine, Shape optimization analysis considering a rotational body in a flow field based on the adjoint variable and the finite element methods, J. Fluid Sci. Tech., 14, 1-13 (2019)
[8] XXXX. XXXX, Mitsubishi Electric Corporation (in Japanese), Jour. Jpn. Soc. Mech. Eng., 122, 38-39 (2019)
[9] M. Behr; T. Tezduyar, The shear-slip mesh update method, Comput. Methods Appl. Mech. Engrg., 174, 261-274 (1999) · Zbl 0959.76037
[10] K. Ootsuka and T. Takaishi, Finite Element Analysis using Mathematical Programming Language FreeFEM++ (in Japanese), Kyoritsu Shuppan Co., Ltd., Tokyo, 2014.
[11] I. Imai, Fluid Dynamics (First part) (in Japanese), Shokabo Co., Ltd., Tokyo, 1973.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.