Direct difference methods have been used to solve the simultaneous non-linear partial differential equations formelt spinning without recourse to linearisation or perturbation approximation.The stability of each diffe...Direct difference methods have been used to solve the simultaneous non-linear partial differential equations formelt spinning without recourse to linearisation or perturbation approximation.The stability of each difference schemes wasstudied by error analysis using the Taylor series,and by comparison of the results obtained from numerical simulation withthe logical value in melt spinning.It is found that computation with 19 digit long double precision has significantlysimplified the stability problem of difference equations.Using this method,the precise critical draw ratio of draw resonancein an isothermal and uniform tension spinning of Newtonian fluids can be obtained in between 20.218 and 21.219,a figureconsistent with 20.218 which was obtained by a linear perturbation approximation method by Kase and Denn.It thus haspaved the way to computation of full information for unsteady melt spinning processes using the difference method.展开更多
A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw ...A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.展开更多
文摘Direct difference methods have been used to solve the simultaneous non-linear partial differential equations formelt spinning without recourse to linearisation or perturbation approximation.The stability of each difference schemes wasstudied by error analysis using the Taylor series,and by comparison of the results obtained from numerical simulation withthe logical value in melt spinning.It is found that computation with 19 digit long double precision has significantlysimplified the stability problem of difference equations.Using this method,the precise critical draw ratio of draw resonancein an isothermal and uniform tension spinning of Newtonian fluids can be obtained in between 20.218 and 21.219,a figureconsistent with 20.218 which was obtained by a linear perturbation approximation method by Kase and Denn.It thus haspaved the way to computation of full information for unsteady melt spinning processes using the difference method.
文摘A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.
