Asymptotic Modeling Framework for Fiber-Flow Interactions in a Two-Way Coupling

Cibis, Thomas Martin; Marheineke, Nicole; Wegener, Raimund

doi:10.1007/978-3-319-05365-3_15

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…The implicitly given solution expressions result in Volterra integral equations of second kind for the surface values of polymer mass fraction and temperature with singular integration kernel, which can be solved quickly by the product integration method. This efficiency allows the realization of two-way coupled fiber and airflow simulations by the help of momentum (drag), heat and mass exchange models according to the principle that action equals reaction [8,7], similar as in the study on glass wool manufacturing [3]. The numerical results show that our reduced dry spinning model is a very good approximation of the underlying three-dimensional model while saving a huge amount of computation time.…”

Section: Introductionmentioning

confidence: 76%

“…The two-way-coupling is based on a homogenization concept and done in the given framework by the help of respective momentum, heat and mass exchange models (drag forces as well as heat and mass sources) that obey the principle that action equals reaction, cf. [8,7].…”

Section: Iterative Coupling Of Fiber and Airflow Computationsmentioning

confidence: 99%

“…In this context the numerical cell-averaging can be interpreted as homogenization strategy for the exchange models that is necessary to avoid the occurrence of singularities and the failure of the two-way-coupling. For details we refer to [8] for the two-way-coupling within an asymptotic modeling framework, to [7] for the homogenization and to [3] for the algorithmic procedure.…”

Section: 4mentioning

confidence: 99%

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An efficient numerical framework for fiber spinning scenarios with evaporation effects in airflows

Wieland

Arne

Feßler

et al. 2019

Journal of Computational Physics

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In many spinning processes, as for example in dry spinning, solvent evaporates out of the spun jets and leads to thinning and solidification of the produced fibers. Such production processes are significantly driven by the interaction of the fibers with the surrounding airflow. Faced with industrial applications producing up to several hundred fibers simultaneously, the direct numerical simulation of the three-dimensional multiphase, multiscale problem is computationally extremely demanding and thus in general not possible. In this paper, we hence propose a dimensionally reduced, efficiently evaluable fiber model that enables the realization of fiberair interactions in a two-way coupling with airflow computations. For viscous dry spinning of an uni-axial two-phase flow, we deduce one-dimensional equations for fiber velocity and stress from cross-sectional averaging and combine them with two-dimensional advection-diffusion equations for polymer mass fraction and temperature revealing the radial effects that are observably present in experiments. For the numerical treatment of the resulting parametric boundary value problem composed of one-dimensional ordinary differential equations and two-dimensional partial differential equations we develop an iterative coupling algorithm. Thereby, the solution of the advection-diffusion equations is implicitly given in terms of Green's functions and leads for the surface values to Volterra integral equations of second kind with singular kernel, which we can solve very efficiently by the product integration method. For the ordinary differential equations a suitable collocation-continuation procedure is presented. Compared with the referential solution of a three-dimensional setting, the numerical results are very convincing. They provide a good approximation while drastically reducing the computational time. This efficiency allows the twoway coupled simulation of industrial dry spinning in airflows for which we present results for the first time in literature.

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Section: Introductionmentioning

confidence: 76%

Section: Iterative Coupling Of Fiber and Airflow Computationsmentioning

confidence: 99%

Section: 4mentioning

confidence: 99%

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An efficient numerical framework for fiber spinning scenarios with evaporation effects in airflows

Wieland

Arne

Feßler

et al. 2019

Journal of Computational Physics

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“…The exchange models are constructed in such a way, that the principle of action equaling reaction is fulfilled, cf. [5,6]. The two-way fiber-air-interaction is realized by a weak coupling algorithm which iterates between fiber computations and airflow simulations.…”

Section: Coupling Proceduresmentioning

confidence: 99%

Industrial dry spinning processes: algorithmic for a two-phase fiber model in airflows

et al. 2020

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The dry spinning of fibers can be described by three-dimensional multi-phase flow models that contain key effects like solvent evaporation and fiber-air interaction. Since the direct numerical simulation of the three-dimensional models is in general not possible, dimensionally reduced models are deduced. We recently developed a one-two-dimensional fiber model and presented a problem-tailored numerical solution strategy in Wieland et al. (J Comput Phys 384:326-348, 2019). However, in view of industrial setups with multiple fibers spun simultaneously the numerical schemes must be accelerated to achieve feasible simulation times. The bottleneck builds the computation of the radial concentration and temperature profiles as well as their cross-sectionally averaged values. In this paper we address this issue and develop efficient numerical algorithms. MSC: 34B08; 68U20; 35Q79; 45D05; 76-XX

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