2023-03-25T05:42:19Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00023512
2023-01-16T04:13:17Z
312:313:314
Shape optimization of flow field improving hydrodynamic stability
Nakazawa, Takashi
69768
Azegami, Hideyuki
69769
Shape optimization
Fluid dynamics
Hydrodynamic stability
This paper presents a solution of a shape optimization problem of a flow field for delaying transition from a laminar flow to a turbulent flow. Mapping from an initial domain to a new domain is chosen as the design variable. Main problems are defined by the stationary Navier–Stokes problem and an eigenvalue problem assuming a linear disturbance on the solution of the stationary Navier–Stokes problem. The maximum value of the real part of the eigenvalue is used as an objective cost function. The shape derivative of the cost function is defined as the Fréchet derivative of the cost function with respect to arbitrary variation of the design variable, which denotes the domain variation, and is evaluated using the Lagrange multiplier method. To obtain a numerical solution, we use an iterative algorithm based on the H1 gradient method using the finite element method. To confirm the validity of the solution, a numerical example for two-dimensional Poiseuille flow with a sudden expansion is presented. Results reveal that a critical Reynolds number increases by the iteration of reshaping.
journal article
Springer
2016-02
application/pdf
Japan Journal of Industrial and Applied Mathematics
1
33
167
181
http://doi.org/10.1007/s13160-015-0201-9
http://hdl.handle.net/2237/25704
0916-7005
https://nagoya.repo.nii.ac.jp/record/23512/files/JJIAM_Nakazawa.pdf
eng
https://doi.org/10.1007/s13160-015-0201-9
The final publication is available at Springer via http://doi.org/10.1007/s13160-015-0201-9