연구발표초록 ( 분리기술 ) : 용융방사와 연신에 의한 미세다공성 Polypropylene 중공사막

권영돈,장태석,김재진 (정),김은영 (정) ( Young Don Kwon,Tae Seok Jang,Jae Jin Kim,Un Young Kim ) 한국화학공학회 1990 춘계학술발표회 Vol.- No.-

tensor-logarothmic formulation에 의한 점탄성 유체 유동의 수치해석

권영돈 한국고분자학회 2006 한국고분자학회 학술대회 연구논문 초록집 Vol.2006 No.4

Supercritical bifurcation to periodic melt fracture as the 1st transition to 2D elastic flow instability

권영돈 한국유변학회 2020 Korea-Australia rheology journal Vol.32 No.4

This study, employing a numerical approximation, computationally describes 2D melt fracture as elastic instability in the flow along and outside a straight channel. In the preceding research (Kwon, 2018, Numerical modeling of two-dimensional melt fracture instability in viscoelastic flow, J. Fluid Mech. 855, 595-615) several types of unique instability and corresponding bifurcations such as subcritical and chaotic transitions have been illustrated with possible mechanism presumed. However, the 1st bifurcation from stable steady to unstable periodic state could not be accurately characterized even though its existence was proven evident. The analysis herein aims at verification of this 1st transition to temporally (and also spatially) periodic instability, utilizing the same numerical technique with attentive control of flow condition. As a result of scrutinizing the solutions, the steady elastic flow described by the Leonov rheological model passes through supercritical Hopf bifurcation at the Deborah number of 10.42 and then transforms to the state of the 1st weak periodic instability. It has also been confirmed that near this bifurcation point it takes extremely long to completely develop into either steady state (in the stable case) or periodic instability, which obstructed immediate characterization of the transition in the previous work.

Convergence limit in numerical modeling of steady contraction viscoelastic flow and time-dependent behavior near the limit

권영돈,한정현 한국유변학회 2010 Korea-Australia rheology journal Vol.22 No.4

In the framework of finite element analysis we numerically analyze both the steady and transient 4:1 contraction creeping viscoelastic flow. In the analysis of steady solutions, there exists upper limit of available numerical solutions in contraction flow of the Leonov fluid, and it is free from the frustrating mesh dependence when we incorporate the tensor-logarithmic formulation (Fattal and Kupferman, 2004). With the time dependent flow modeling with pressure difference imposed slightly below the steady limit, the 1st and 2nd order conventional approximation schemes have demonstrated fluctuating solution without approaching the steady state. From the result, we conclude that the existence of upper limit for convergent steady solution may imply flow transition to highly elastic time-fluctuating field without steady asymptotic. However definite conclusion certainly requires further investigation and devising some methodology for its proof.

揖翠軒의 生涯와 詩世界

權永돈,Kwon, Yeong Don 한국외국어대학교 1987 우리어문학연구 Vol.1 No.1

룡비어천가(龍飛御天歌)의 찬자(撰者)와 가사용어(歌詞用語) 문제(問題)

권영돈 한국어문교육연구회 1980 어문연구(語文硏究) Vol.8 No.1-2

Finite element analysis of planar 4:1 contraction flow with the tensor-logarithmic formulation of differential constitutive equations

권영돈 한국유변학회 2004 Korea-Australia rheology journal Vol.16 No.4

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the logarithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative procedure for deriving the tensor-logarithmic representation of the differential constitutive equations and provide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the mathematical stability criteria perhaps play an important role on the choice and development of the suitable constitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

Finite element analysis of viscoelastic flows in a domain with geometric singularities

권영돈,Sungho Yoon 한국유변학회 2005 Korea-Australia rheology journal Vol.17 No.3

This work presents results of finite element analysis of isothermal incompressible creeping viscoelastic flows with the tensor-logarithmic formulation of the Leonov model especially for the planar geometry with singular corners in the domain. In the case of 4:1 contraction flow, for all 5 meshes we have obtained solutions over the Deborah number of 100, even though there exists slight decrease of convergence limit as the mesh becomes finer. From this analysis, singular behavior of the corner vortex has been clearly seen and proper interpolation of variables in terms of the logarithmic transformation is demonstrated. Solutions of 4:1:4 contraction/expansion flow are also presented, where there exists 2 singular corners. 5 different types spatial resolutions are also employed, in which convergent solutions are obtained over the Deborah number of 10. Although the convergence limit is rather low in comparison with the result of the contraction flow, the results presented herein seem to be the only numerical outcome available for this flow type. As the flow rate increases, the upstream vortex increases, but the downstream vortex decreases in their size. In addition, peculiar deflection of the streamlines near the exit corner has been found. When the spatial resolution is fine enough and the Deborah number is high, small lip vortex just before the exit corner has been observed. It seems to occur due to abrupt expansion of the elastic liquid through the constriction exit that accompanies sudden relaxation of elastic deformation.

Numerical analysis of viscoelastic flows in a channel obstructed by an asymmetric array of obstacles

권영돈 한국유변학회 2006 Korea-Australia rheology journal Vol.18 No.3

This study presents results on the numerical simulation of Newtonian and non-Newtonian flow in a channel obstructed by an asymmetric array of obstacles for clarifying the descriptive ability of current non-Newtonian constitutive equations. Jones and Walters (1989) have performed the corresponding experiment that clearly demonstrates the characteristic difference among the flow patterns of the various liquids. In order to appropriately account for flow properties, the Navier-Stokes, the Carreau viscous and the Leonov equations are employed for Newtonian, shear thinning and extension hardening liquids, respectively. Making use of the tensor-logarithmic formulation of the Leonov model in the computational scheme, we have obtained stable solutions up to relatively high Deborah numbers. The peculiar characteristics of the non-Newtonian liquids such as shear thinning and extension hardening seem to be properly illustrated by the flow modeling. In our opinion, the results show the possibility of current constitutive modeling to appropriately describe non-Newtonian flow phenomena at least qualitatively, even though the model parameters specified for the current computation do not precisely represent material characteristics.

단순전단유동에서 Doi-Edwards 모델의 불안정성

권영돈 한국유변학회 1998 Korea-Australia rheology journal Vol.10 No.3

본 연구에서 Doi-Edwards 점탄성 조성방정식의 Hadamard 안정성 분석을 행하였 다. Hadamard 안정성은 방정식의 탄성 성질과 연관되는 특성으로 파장이 짧고 진동수가 큰 파동에 의한 외란 하에서 식의 안정성을 의미한다. 먼저 안정성을 위한 일반 3차원 조건을 수립하고 단순한 1차원과 2차원 외란하에서 필요조건을 구하였다. Doi-Edwards 이론을 따 르는 물질의 단순전단유동을 고려함에 의하여 순간 전단변형률이 1.8786을 넘어설 때 파장 이 짧고 진동수가 큰 외란에 의하여 불안정성이 나타남이 증명되었다. 이 안정성의 임계치 는 실제 고분자공정 뿐 아니라 실험실에서도 쉽게 도달할수 있는 값으로 이와 같은 불안정 유동은 mi-crophase separation과 같은 물리적 현상과는 관련이 있다는 증거가 없으므로 조 성방정식 자체가 지니는 수학적 모순점에 기인한 것이라 할수 있다.