沉浸邊界法於移動邊界之數值分析

Numerical simulations of the immersed boundary formulation for flow with moving boundary

廖川傑(Chuan-Jie Liao)

指導教授 ： 林昭安

國立清華大學/工學院/動力機械工程學系/碩士(2007年)

https://doi.org/10.6843/NTHU.2007.00204

摘要

Abstract
In the present study, a new immersed boundary technique is proposed for the simulation of two-dimensional viscous incompressible flow interacting with moving solid boundary. The numerical integration is based on a second-order fraction step method under the staggered grid spatial framework. Base on the direct momentum forcing on the Cartesian grid, a “Solid-body-forcing” procedure is used to keep a suitable velocity field in the solid domain. Five different test problems are simulated using the present technique (flows over an asymmetrically placed in a channel, in-line oscillating cylinder and transverse oscillation cylinder in a free stream, in-line oscillating cylinder in a fluid at rest, two cylinders moving with respect to each other). Two forcing strategies, including extrapolation (Scheme 1) and interpolation (Scheme 2) are used in the stationary boundary problems and get good results. However, the two forcing strategies can not predict the flow field adequately for moving boundary problems. It can be observed that server oscillations of the predicted lift and drag coefficients occur when using the interpolation or extrapolation procedures. In order to quantify oscillations, “Fourier Series Expansion” was used to analyze the predicted lift and drag coefficients. It provides a criterion to judge the difference between Fourier series forms and original ones. A “Solid-body-forcing” procedure can modify the velocity field inside the boundary when it moves, and satisfying result can be observed when the forcing strategy is using a combination of interpolation and Solid-body-forcing procedure. Besides, a simple interaction between two cylinders with different paths can also be predicted by the present method, indicating the usability of the present method for various moving solid boundary.

關鍵字

沉浸邊界法

並列摘要

Abstract
In the present study, a new immersed boundary technique is proposed for the simulation of two-dimensional viscous incompressible flow interacting with moving solid boundary. The numerical integration is based on a second-order fraction step method under the staggered grid spatial framework. Base on the direct momentum forcing on the Cartesian grid, a “Solid-body-forcing” procedure is used to keep a suitable velocity field in the solid domain. Five different test problems are simulated using the present technique (flows over an asymmetrically placed in a channel, in-line oscillating cylinder and transverse oscillation cylinder in a free stream, in-line oscillating cylinder in a fluid at rest, two cylinders moving with respect to each other). Two forcing strategies, including extrapolation (Scheme 1) and interpolation (Scheme 2) are used in the stationary boundary problems and get good results. However, the two forcing strategies can not predict the flow field adequately for moving boundary problems. It can be observed that server oscillations of the predicted lift and drag coefficients occur when using the interpolation or extrapolation procedures. In order to quantify oscillations, “Fourier Series Expansion” was used to analyze the predicted lift and drag coefficients. It provides a criterion to judge the difference between Fourier series forms and original ones. A “Solid-body-forcing” procedure can modify the velocity field inside the boundary when it moves, and satisfying result can be observed when the forcing strategy is using a combination of interpolation and Solid-body-forcing procedure. Besides, a simple interaction between two cylinders with different paths can also be predicted by the present method, indicating the usability of the present method for various moving solid boundary.

並列關鍵字

Immersed boundary method ； moving rigid boundary ； Solid-body-forcing ； in-line oscillating ； transverse oscillating

參考文獻

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