가동물체형 구조물 해석을 위한 Simplified Immersed Boundary법의 개발

이광호(Kwang-Ho Lee),김도삼(Do-Sam Kim) 한국해안해양공학회 2021 한국해안해양공학회 논문집 Vol.33 No.3

고정된 격자시스템에서 임의형상의 불투과 경계를 갖는 물체와 유체와 연성해석이 가능한 IB(Immersed Boundary)법이 개발 된 이후로 다양한 CFD 모델에서 IB법의 활용이 증가하고 있다. 기존의 IB법의 대부분은 구조물의 경계면에서 산정되는 유체력으로부터 수치적으로 경계조건을 만족시키는 directing-forcing법이나 구조물 내부에 가상셀을 위치시켜 보간을 통해 경계조건을 만족시키는 ghost-cell법들로 알고리즘이 복잡하다. 본 연구에서는 고정된 격자시스템에서 가동물체형 구조물 해석이 가능함과 더불어 3차원으로의 확장도 용이한 SIB(Simplified Immersed Boundary)법을 제안하였다. 본 연구에서 제안한 SIB법은 각 상(phase)의 밀도함수가 국소질량의 중심과 함께 이동하는 것으로 가정한 단일유체모델(one-field model for immiscible two-phase fluid)을 기초로 하였다. 또한 이동하는 고체상태의 구조물을 취급하기 위해 고체의 밀도함수를 이용한 체적가중평균법을 적용하고, 수치확산을 방지하기 위해 이류계산에는 CIP법을 적용하였다. 제안된 SIB법의 해석성능을 검토하기 위해 자유수면으로 낙하하는 물체에 대한 수치모의를 수행하였다. 수치해석결과는 자유수면으로 낙하하는 물체를 양호하게 재현하였다. Since the IB (Immersed Boundary) method, which can perform coupling analysis with objects and fluids having an impermeable boundary of arbitrary shape on a fixed grid system, has been developed, the IB method in various CFD models is increasing. The representative IB methods are the directing-forcing method and the ghost cell method. The directing-forcing type method numerically satisfies the boundary condition from the fluid force calculated at the boundary surface of the structure, and the ghost-cell type method is a computational method that satisfies the boundary condition through interpolation by placing a virtual cell inside the obstacle. These IB methods have a disadvantage in that the computational algorithm is complex. In this study, the simplified immersed boundary (SIB) method enables the analysis of temporary structures on a fixed grid system and is easy to expand to three proposed dimensions. The SIB method proposed in this study is based on a one-field model for immiscible two-phase fluid that assumes that the density function of each phase moves with the center of local mass. In addition, the volume-weighted average method using the density function of the solid was applied to handle moving solid structures, and the CIP method was applied to the advection calculation to prevent numerical diffusion. To examine the analysis performance of the proposed SIB method, a numerical simulation was performed on an object falling to the free water surface. The numerical analysis result reproduced the object falling to the free water surface well.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Sung Wan Son,하만영,윤현식,Hae Kwon Jeong,S. Balachandar 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.2

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

COMPARISON OF NUMERICAL METHODS FOR TERNARY FLUID FLOWS

SEUNGGYU LEE,DARAE JEONG,YONGHO CHOI,JUNSEOK KIM 한국산업응용수학회 2016 Journal of the Korean Society for Industrial and A Vol.20 No.1

This paper reviews and compares three different methods for modeling incompressible and immiscible ternary fluid flows: the immersed boundary, level set, and phase-field methods. The immersed boundary method represents the moving interface by tracking the Lagrangian particles. In the level set method, an interface is defined implicitly by using the signed distance function, and its evolution is governed by a transport equation. In the phase-field method, the advective Cahn–Hilliard equation is used as the evolution equation, and its order parameter also implicitly defines an interface. Each method has its merits and demerits. We perform the several simulations under different conditions to examine the merits and demerits of each method. Based on the results, we determine the most suitable method depending on the specific modeling needs of different situations.

Immersed Boundary-Finite Difference Lattice Boltzmann Method using the Feedback Forcing Scheme to Simulate the Incompressible Flows

김래성,양휘주,하만영,Zhe-Zhu Xu,Hong Xiao,류성기 한국정밀공학회 2016 International Journal of Precision Engineering and Vol.17 No.8

In this study, the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using the feedback momentum forcing scheme is proposed and implemented to simulate 2-D incompressible flows. IB-FBLBM incorporates the immersed boundary method (IBM) into the finite difference lattice Boltzmann method (FDLBM) devised to alleviate shortcomings by using the uniform Cartesian grid of the standard lattice Boltzmann method (LBM). In order to obtain numerical stability while combining IBM with FDLBM, this method utilizes feedback momentum forcing scheme and equilibrium velocity approach to take into account the change of momentum induced by a body force on the immersed boundaries. This approach has the advantages of being simple and easy to implement, and does not require modification of the original governing equations. In order to confirm the applicability and validation of IB-FDLBM, the lid-driven cavity flow with a circular cylinder, the external steady flows around a circular cylinder and external steady flows around a circular cylinder near a plane wall are simulated with a range of Reynolds numbers. The current numerical results are consistent with those of existing researches.

가상 경계 방법

김정우(J. Kim) 한국전산유체공학회 2013 한국전산유체공학회 학술대회논문집 Vol.2013 No.5

It is known that immersed boundary methods have the ability to handle complex geometries. A new immersed-boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source/sink as well as a momentum forcing. Both momentum forcing and mass source/sink are applied on the body surface or inside the body to satisfy the no-slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary. Also, a heat source/sink is applied to satisfy the thermal conditions such as the iso-thermal and iso-heat flux conditions. To verify the accuracy of the present immersed boundary method, some numerical simulations would be shown. Finally, in this talk, based on the authors personal research experience, some perspectives of immersed boundary methods would be presented.

가상경계-격자 볼츠만 방법을 이용한 유동장내 나노/마이크로 입자에 작용하는 힘의 해석

조홍주,이세영 대한의용생체공학회 2022 의공학회지 Vol.43 No.1

Immersed boundary-Lattice Boltzmann Method (IB-LBM) is used for the analysis of flow over the circular cylinder in the concept of fluid-structure interaction analysis (FSI). Recently, IB-LBM has shown the enormous pos- sibility for the application of various biomedical engineering fields, such as the movement of a human body or the behavior of the blood cells and/or particle-based drug delivery system in blood vessels. In order for the numerical analysis of the interaction between fluid and solid object, immersed boundary method and lattice Boltzmann method are coupled to analyze the flow over a cylinder for low Reynolds laminar flow (Re=10, 20, 40 and 100) with Zhu- He boundary condition at the boundary. With the developed IB-LBM, the flow around the cylinder in the uniform flow is analyzed for the laminar flow and the drag and lift coefficients and recirculation length are compared to the previous results.

SIMPLE Algorithm기반의 비압축성 Navier-Stokes Solver를 이용한 Immersed Boundary Method의 적용

김건홍(G.H. Kim),박승오(S.O. Park) 한국전산유체공학회 2012 한국전산유체공학회지 Vol.17 No.1

Immersed boundary method(IBM) is a numerical scheme proposed to simulate flow field around complex objectives using simple Cartesian grid system. In the previous studies, the IBM has mostly been implemented to fractional step method based Navier-Stokes solvers. In this study, we implement the IBM to an incompressible Navier-Stokes solver which uses SIMPLE algorithm. The weight coefficients of the bi-linear and quadratic interpolation equations were formulated by using only geometric information of boundary to reconstruct velocities near IB. Flow around 2D circular cylinder at Re=40 and 100 was solved by using these formulations. It was found that the pressure buildup was not observed even when the bi-linear interpolation was adopted. The use of quadratic interpolation made the predicted aerodynamic forces in good agreement with those of previous studies. For an analysis of moving boundary, we smulated an oscillating circular cylinder with Re=100 and KC(Keulegan-Carpenter) number of 5. The predicted flow fields were compared with experimental data and they also showed good agreements.

An immersed boundary method for simulating dynamic and thermal flows with moving rigid boundary

Chuan-Chieh Liao,Chao-An Lin 한국전산유체공학회 2014 한국전산유체공학회 학술대회논문집 Vol.2014 No.10

In the present study, dynamic and thermal fields with moving rigid boundary are investigated by using an immersed-boundary method. This is achieved via direct momentum and energy forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes, and issue involving the influence of the solid-body forcing is addressed. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L1-norm in time and the L2-norm in space. 3-D simulation of a heated sphere settling under gravity in a static fluid is adopted to examine the validity of the present technique. All computed results are in generally good agreement with experimental measurements. This indicates the capability of the present simple implementation in solving complex-geometry flow problems.

Improvement of mass source/sink for an immersed boundary method

Huang, Wei-Xi,Sung, Hyung Jin John Wiley Sons, Ltd. 2007 International journal for numerical methods in flu Vol.53 No.11

<P>An improved immersed boundary method using a mass source/sink as well as momentum forcing is developed for simulating flows over or inside complex geometries. The present method is based on the Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. A more accurate formulation of the mass source/sink is derived by considering mass conservation of the virtual cells in the fluid crossed by the immersed boundary. Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are used to validate the proposed formulation. The results indicate that the accuracy near the immersed boundary is improved by introducing the accurate mass source/sink. Copyright © 2006 John Wiley & Sons, Ltd.</P>

이상 유동에서의 유체-구조 연성해석을 위한 Direct Forcing/Ficititious Domain-Level Set Method

전충호(Chung Ho Jeon),윤현식(Hyun-Sik Yoon),정재환(JaeHwan Jung) 한국해양공학회 2011 韓國海洋工學會誌 Vol.25 No.4

In the present paper, a direct forcing/fictitious domain (DF/FD) level set method is proposed to simulate the FSI (fluid-solid interaction) in two-phase flow. The main idea is to combine the direct-forcing/fictitious domain (DF/FD) method with the level set method in the Cartesian coordinates. The DF/FD method is a non-Lagrange-multiplier version of a distributed Lagrange multiplier/fictitious domain (DLM/FD) method. This method does not sacrifice the accuracy and robustness by employing a discrete δ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, easy implementation, and utilization of the original governing equation without modification. Simulations of various water-entry problems have been conducted to validate the capability and accuracy of the present method in solving the FSI in two-phase flow. Consequently, the present results are found to be in good agreement with those of previous studies.