비압축성 유동 해석을 위한 입자법 수치 시뮬레이션 기술 개발

이병혁,박종천,류민철,김용수,김영훈 한국해양공학회 2007 韓國海洋工學會誌 Vol.21 No.4

A particle method recognized as one of gridless methods has been developed to investigate incompressible viscous flow. The method is more feasible and effective than conventional grid methods for solving the flow field with complicated boundary shapes or multiple bodies. The method is consists of particle interaction models representing pressure gradient, diffusion, incompressibility and the boundary conditions. In the present study, the models in case of various simulation condition were checked with the analytic solution, and applied to the two-dimensional Poiseuille flow in order to validate the developed method.1. 서 론 종래 연속체의 수치 시뮬레이션 기술로는 격자계를 이용하는 방법이 널리 사용되어 왔다. 하지만 복잡한 형상에 대해서는 격자 생성에 많은 어려움과 방대한 시간이 소요되며 연속적으로 계면(Interface)이 크게 변형하는 문제에는 격자 생성에 대해 다양한 연구가 불가피하다. 한편 입자를 사용하는 SPH법(Monaghan, 1988), PIC법(Harlow, 1988), PIC법의 계량인 FLIP 법(Brackbill and Ruppel, 1986; Brackbill et al., 1988), MPS법(Koshizuka et al., 1995) 등은 격자생성의 복잡한 작업이 불필요하여 격자가 꼬이는 등의 위상관계를 고려할 필요가 없고, 계면이 크게 변형되는 문제에도 적용될 수 있는 장점을 가지고 있다. 특히 비선형성 자유표면 유동의 수치 시뮬레이션의 경우에 있어서 입자를 이용한 수치 시뮬레이션 방법은 격자를 이용한 해석 방법보다 복잡한 형상의 물리 현상을 해석할 수 있는 가능성을 가지고 있다. 또한 입자를 이용한 수치 시뮬레이션 방법은 이류항(Convection term)의 계산을 입자의 완전한 라그란지안(Lagrangian) 접근에 의해 입자의 이동으로 계산함으로서 오일러(Eulerian) 방법에서 심각하게 유발되는 수치 확산(Numerical diffusion)을 줄일 수 있다.

A pre-conditioned implicit direct forcing based immersed boundary method for incompressible viscous flows

Park, Hyunwook,Pan, Xiaomin,Lee, Changhoon,Choi, Jung-Il Elsevier 2016 Journal of computational physics Vol.314 No.-

<P><B>Abstract</B></P> <P>A novel immersed boundary (IB) method based on an implicit direct forcing (IDF) scheme is developed for incompressible viscous flows. The key idea for the present IDF method is to use a block LU decomposition technique in momentum equations with Taylor series expansion to construct the implicit IB forcing in a recurrence form, which imposes more accurate no-slip boundary conditions on the IB surface. To accelerate the IB forcing convergence during the iterative procedure, a pre-conditioner matrix is introduced in the recurrence formulation of the IB forcing. A Jacobi-type parameter is determined in the pre-conditioner matrix by minimizing the Frobenius norm of the matrix function representing the difference between the IB forcing solution matrix and the pre-conditioner matrix. In addition, the pre-conditioning parameter is restricted due to the numerical stability in the recurrence formulation. Consequently, the present pre-conditioned IDF (PIDF) enables accurate calculation of the IB forcing within a few iterations. We perform numerical simulations of two-dimensional flows around a circular cylinder and three-dimensional flows around a sphere for low and moderate Reynolds numbers. The result shows that PIDF yields a better imposition of no-slip boundary conditions on the IB surfaces for low Reynolds number with a fairly larger time step than IB methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the IB forcing. Finally, we demonstrate the robustness of the present PIDF scheme by numerical simulations of flow around a circular array of cylinders, flows around a falling sphere, and two sedimenting spheres in gravity.</P>

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.

A NOTE ON THE UNSTEADY FLOW OF DUSTY VISCOUS FLUID BETWEEN TWO PARALLEL PLATES

AJADI, SURAJU OLUSEGUN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1

We study the isothermal flow of a dusty viscous incompressible conducting fluid between two types of boundary motions- oscillatory and non-oscillatory, under the influence of gravitational force. Within the frame work of some physically realistic approximations and suitable boundary conditions, closed form solutions were obtained for the velocity profiles and the skin friction of the particulate flow. These results show that for a constant pressure gradient, only the velocity profile of the fluid and the skin friction are unaffected by gravity, while magnetic field is seen to affect both the fluid, particle velocities and the skin friction. Thus, our results are extension of previous results in literature, and graphical demonstration of some these solutions have been presented.

Multi-array/multi-location synthetic jet을 이용한 박리 제어

김상훈(Sang Hoon Kim),김종암(Chongam Kim) 한국항공우주학회 2006 韓國航空宇宙學會誌 Vol.34 No.8

고받음각의 NACA23012익형에 대하여 synthetic jet을 이용하여 박리 제어를 수행하였다. 단일 synthetic jet을 이용하여 익형에 발생하는 앞전 박리를 효과적으로 지연시킬 수 있고, 또한 실속 특성을 개선 할 수 있음을 확인하였다. 그때 발생하는 비정상 유동 특성을 파악하였다. 또한, 현실적으로 구현 가능한 jet 속도를 얻기 위하여 multi-array synthetic jet의 특성을 파악하였다. 그리고 단일 위치에 장착된 synthetic jet을 이용하여 박리를 제어 하였을 경우 익형 윗면에 발생하는 작은 와동을 제거하기 위하여, multi-location synthetic jet을 이용하였다. 작은 와동을 제거 하고 안정적인 유동을 확보하기 위하여, 높은 진동수의 synthetic jet을 이용하여 국부적으로 효과적인 박리 제어를 통한 익형 주변의 유동의 전체적 특성을 안정화 시킬 수 있음을 확인하였다. Multi-location synthetic jet의 phase 변화를 이용하여 multi-array/multi-location synthetic jet의 성능 및 특성을 향상 시킬 수 있음을 확인하였다. Separation control has been performed using the multi-array/multi-location synthetic jet on NACA23012 at high angle of attack. The flow control using single synthetic jet shows that stall characteristics can be substantially improved with delayed separation point. Theses results show the characteristic of unsteady flow of single synthetic jet. Beside, we researched on multi-array synthetic jet to obtain applicable synthetic jet velocity. Multi-location synthetic jet is proposed to eliminate small vortex on suction surface of airfoil. With the results, we concluded that the flow around airfoil is stable by high frequency synthetic jet with elimination of small vortex and confirmation of stable flow. Moreover, performance of multi-array/multi-location synthetic jet can be improved by changing phase angle of multi-location synthetic jet.

Numerical simulations of impact flows with incompressible smoothed particle hydrodynamics

Abdelraheem M. Aly,이상욱 대한기계학회 2014 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.28 No.6

A 2D incompressible smoothed particle hydrodynamics (SPH) method is implemented to simulate the impact flows associated withcomplex free surface. In the incompressible SPH framework, pressure Poisson equation (PPE) based on the projection method is solvedusing a semi-implicit scheme to evaluate the correct pressure distribution. In this procedure, the PPE comprises the divergence-free velocitycondition and density-invariance condition with a relaxation parameter. To test the accuracy and efficiency of the proposed incompressibleSPH method, it was applied to several sample problems with largely distorted free surface, including 2D dam-break over horizontaland inclined planes with different inclination angles, as well as the water entry of a circular cylinder into a tank. We mainly focusedon the time history of impact pressure on various positions of the solid boundary and temporal evolution of free surface profiles. The results showed reasonably good agreement with experimental data. However, further improvement is needed for extremely highimpact flow.

대각행렬화된 근사 인수분해 기법을 이용한 3차원 비압축성 점성 흐름 해석

백중철(Paik Joongcheol) 대한토목학회 2011 대한토목학회논문집 B Vol.31 No.3B

비압축성 점성 흐름을 수치해석하기 위한 효율적인 대각행렬화된 근사 인수분해(DAF) 알고리즘을 개발하였다. 압력에 근거한 인공압축성(AC) 기법을 이용하여 3차원 정상 비압축성 Navier-Stokes 방정식을 계산한다. AC 형태로 변형된 지배방정식은 2차 정확도의 유한차분법을 이용하여 공간에 대해서 이산화하였다. 이산화된 방정식계를 2차 정확도로 분할하기 위해서 본 연구에서 개발한 DAF 기법을 적용한다. 이 연구의 목적은 이 DAF 기법의 계산상 효율성을 검토하는 것이다. 만곡부를 갖는 사각형 덕트에서 완전히 발달한 층류 흐름과 발달하는 층류흐름 그리고 공동에서의 층류흐름에 대한 DAF 기법의 해석결과를 잘 알려진 4단계 Runge-Kutta(RK4)기법에 의한 해석해와 상대적으로 비교평가 하였다. 공간에 대해서 동일한 이산화기법을 이용하므로 동일한 격자상에서 계산된 DAF기법과 RK4기법의 해는 근본적으로 통일한 반면에, 이들 두 기법의 계산상 효율성은 확연히 다른 것으로 나타났다. 본 연구에서 개발된 DAF기법은 적용한 모든 흐름 문제에 대해서 RK4기법에 비해 최소 2배 이상 적은 계산 시간만을 필요로 하는 것으로 나타났다. 이러한 DAF 기법의 계산상 효율성은 계산용량의 추가나 프로그래밍의 추가적인 복잡함이 없이 확보된다. An efficient diagonalized approximate factorization algorithm (OAF) is developed for the solution of three-dimensional incompressible viscous flows. The pressure-based, artificial compressibility (AC) method is used for calculating steady incompressible Navier-Stokes equations. The AC form of the governing equations is discretized in space using a second-order-accurate finite volume method. The present DAF method is applied to derive a second-order accurate splitting of the discrete system of equations. The primary objective of this study is to investigate the computational efficiency of the present DAF method. The solutions of the DAF method are evaluated relative to those of well-known four-stage Runge-Kutta (RK4) method for fully developed and developing laminar flows in curved square ducts and a laminar flow in a cavity. While converged solutions obtained by DAF and RK4 methods on the same computational meshes are essentially identical because of employing the same discrete schemes in space, both algorithms shows significant discrepancy in the computing efficiency. The results reveal that the DAF method requires substantially at least two times less computational time than RK4 to solve all applied flow fields. The increase in computational efficiency of the DAF methods is achieved with no increase in computational resources and coding complexity.

균일 사 염색을 위한 최적 Spindle 형상 설계에 관한 연구

강민성(Min-Sung Kang),김재형(Jae-Hyung Kim),노석홍(Seok-Hong Noh),김용대(Young-Dae Kim),김희동(Heuy-Dong Kim) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.10

In the field of yarn dyeing, the most generally employed method is a type of package dyeing which uses a package cheeses stacked on a spindle made of a perforated tube. Spindles up to now, have been designed without considering the characteristics of dyeing liquid, focusing only on the geometric configuration which cause many problems such as lack of level dyeing. To improve the level dyeing and find the appropriate spindle configuration for the most effective dyeing process, this study examines the spindle flow-field in detail, using a computational method. Flow characteristics inside the spindle have been investigated with varying in porosity, porous diameter and the velocity of the flow. The results show that the total pressure of the flow through the spindle is used to overcome body force. The characteristics of the flow from the porous spindle could also be observed. Based on the results from this study, an effective spindle configuration for level-dyeing has been proposed.

비압축성 자유표면 유동에서 갇힌 기체의 등엔트로피 및 등온과정에 따른 공기 완충 효과 변화

신상묵(Sangmook Shin) 한국전산유체공학회 2019 한국전산유체공학회지 Vol.24 No.3

A developed code is applied to simulate the air cushion effects caused by isentropic and isothermal processes of entrapped air in incompressible free surface flows. The code uses a pressure-based method for the unified conservation laws of incompressible and compressible fluids. To calculate a pressure field, including compressible entrapped gas region, a pressure Poisson equation is solved for the whole domain. The effects of gas compressibility are reflected in the source terms of the pressure Poisson equation. The oscillations of water column in a closed tube are simulated, which are caused by compression and expansion of air on both sides of the water column. A good agreement is achieved for comparison of computed time history of pressure at the end of the closed tube with other reported result. In the isentropic process, the period of the oscillation becomes shorter and the amplitude becomes bigger. It is shown that the variations in the period and the amplitude can be readily explained based on analogy of a spring-mass system. As the initial velocity of the water column increases, the non-linearity of pressure oscillation becomes more noticeable. However, the variations in oscillation characteristics according to the processes of air remain unchanged. The developed code is applied to compare the air cushion effects caused by isentropic and isothermal processes of entrapped air in broken dam flows. Similar tendencies are observed for variations in period and amplitude of pressure oscillations, according to the assumptions on density-pressure relationship of entrapped air in broken dam flows.

익형에서의 synthetic jet을 이용한 박리제어 mechanism

김상훈(S.H. Kim),김우레(W. Kim),홍우람(W. Hong),김종암(C. Kim) 한국전산유체공학회 2007 한국전산유체공학회 학술대회논문집 Vol.2007 No.-

Separation control has been performed using synthetic jets airfoil at high angle of attack. Computed results demonstrated that stall characteristics and control surface performance could be substantially improved by resizing separation vortices. It was observed that the actual flow control mechanism and flow structure is fundamentally different depending on the range of synthetic jet frequency. For low frequency range, small vortices due to synthetic jet penetrated to the large leading edge separation vortex, and as a result, the size of the leading edge vortex was remarkably reduced. For high frequency range, however, small vortex did not grow up enough to penetrate into the leading edge separation vortex. Instead, synthetic jet firmly attached the local flow and influenced the circulation of the virtual airfoil shape which is the combined shape of the main airfoil with the separation vortex. Theses results show the characteristic of unsteady flow of single synthetic jet. Beside, we researched on multi-array synthetic jet to obtain applicable synthetic jet velocity. Multi-location synthetic jet is proposed to eliminate small vortex on suction surface of airfoil. With the results, we concluded that the flow around airfoil is stable by high frequency synthetic jet with elimination of small vortex and confirmation of stable flow. Moreover, performance of multi-array/multi-location synthetic jet can be improved by changing phase angle of multi-location synthetic jet.