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RISS 인기검색어
- 검색키워드
- 저자 : Kwon Youngdon (검색결과 18 건)
- 무료
- 기관 내 무료
- 유료
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Kwon, Youngdon The Korean Society of Rheology 1999 Korea-Australia rheology journal Vol.11 No.3
This study presents 1-dimensional simple model for sheet casting or rectangular fiber spinning process. In order to achieve this goal, we introduce the concept of force flux balance at the die exit, which assigns for the extensional flow outside the die the initial condition containing the information of shear flow history inside the die. With the Leonov constitutive equation that predicts non-vanishing second normal stress difference in shear flow, we are able to describe the anisotropic swelling behavior of the extrudate at least qualitatively. In other words, the negative value of the second normal stress difference causes thickness swelling much higher than width of extrudate. This result implies the importance of choosing the rheological model in the analysis of polymer processing operations, since the constitutive equation with the vanishing second normal stress difference is shown to exhibit the characteristic of isotropic swelling, that is, the thickness swell ratio always equal to the ratio in width direction.
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Kwon Youngdon The Korean Society of Rheology 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.
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Mathematical Properties of the Differential Pom-Pom Model
Kwon, Youngdon The Polymer Society of Korea 2001 Korea polymer journal Vol.9 No.3
Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for the simplified differential version of these constitutive equations. It is proved that they are globally Hadamard stable except for the case of maximum constant backbone stretch (λ = q) with arm withdrawal s$\_$c/ neglected, as long as the orientation tensor remains positive definite or the smooth strain history in the now is previously given. However this model is dissipative unstable, since the steady shear How curves exhibit non-monotonic dependence on shear rate. This type of instability corresponds to the nonlinear instability in simple shear flow under finite amplitude disturbances. Additionally in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady now curves, the constitutive equations will possibly violate the positive definiteness of the orientation tensor and thus become Hadamard unstable.
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Recent results on the analysis of viscoelastic constitutive equations
Kwon, Youngdon The Korean Society of Rheology 2002 Korea-Australia rheology journal Vol.14 No.1
Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.
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Numerical modelling of two-dimensional melt fracture instability in viscoelastic flow
Cambridge University Press 2018 Journal of fluid mechanics Vol.855 No.-
<P>Computationally modelling the two-dimensional (2-D) Poiseuille flow along and outside a straight channel with a differential viscoelastic constitutive equation, we demonstrate unstable dynamics involving bifurcations from steady flow to periodic melt fracture (sharkskin instability) and its further transition regime to a chaotic state. The numerical simulation first exposes transition from steady flow to a weak instability of periodic fluctuation, and in the middle of this periodic limit cycle (in the course of increasing flow intensity) a unique bifurcation into the second steady state is manifested. Then, a subcritical (Hopf) transition restoring this stable flow to stronger periodic instability follows, which results from the high stress along the streamlines of finite curvature with small vortices near the die lip. Its succeeding chaotic transition at higher levels of flow elasticity that induces gross melt fracture, seems to take a period doubling as well as quasiperiodic route. By simple geometrical modification of the die exit, we, as well, illustrate reduction or complete removal of sharkskin and melt fractures. The result as a matter of fact suggests convincing evidence of the possible cause of the sharkskin instability and it is thought that this fluid dynamic transition has to be taken into account for the complete description of melt fracture. The competition between nonlinear dynamic transition and other possible origins such as wall slip will ultimately determine the onset of the sharkskin and melt fractures. Therefore, the current study conceivably provides a robust methodology to portray every possible type of melt fracture if combined with an appropriate mechanism that also results in flow instability.</P>
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Jaewook Lee,Youngdon Kwon,A. I. Leonov 한국유변학회 2008 Korea-Australia rheology journal Vol.20 No.2
A theoretical model was developed to describe the flow behavior of a filled polymer in the packing stage of reaction injection molding and predict the residual stress distribution of thin injection-molded parts. The model predictions were compared with experiments performed for phenol-formaldehyde resin filled with wood dust and cured by urotropine. The packing stage of reaction injection molding process presents a typical example of complex non-isothermal flow combined with chemical reaction. It is shown that the time evolution of pressure distribution along the mold cavity that determines the residual stress in the final product can be described by a single 1D partial differential equation (PDE) if the rheological behavior of reacting liquid is simplistically described by the power-law approach with some approximations made for describing cure reaction and non-isothermality. In the formulation, the dimensionless time variable is defined in such a way that it includes all necessary information on the cure reaction history. Employing the routine separation of variables made possible to obtain the analytical solution for the nonlinear PDE under specific initial condition. It is shown that direct numerical solution of the PDE exactly coincides with the analytical solution. With the use of the power-law approximation that describes highly shear thinning behavior, the theoretical calculations significantly deviate from the experimental data. Bearing in mind that in the packing stage the flow is extremely slow, we employed in our theory the Newtonian law for flow of reacting liquid and described well enough the experimental data on evolution of pressure.
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