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In many spinning processes, as for example in dry spinning, solventevaporates out of the spun jets and leads to thinning and solidification of theproduced fibers. Such production processes are significantly driven by theinteraction of the fibers with the surrounding airflow. Faced with industrialapplications producing up to several hundred fibers simultaneously, the directnumerical simulation of the three-dimensional multiphase, multiscale problem iscomputationally extremely demanding and thus in general not possible. In thispaper, we hence propose a dimensionally reduced, efficiently evaluable fibermodel that enables the realization of fiber-air interactions in a two-waycoupling with airflow computations. For viscous dry spinning of an uni-axialtwo-phase flow, we deduce one-dimensional equations for fiber velocity andstress from cross-sectional averaging and combine them with two-dimensionaladvection-diffusion equations for polymer mass fraction and temperaturerevealing the radial effects that are observably present in experiments. Forthe numerical treatment of the resulting parametric boundary value problemcomposed of one-dimensional ordinary differential equations and two-dimensionalpartial differential equations we develop an iterative coupling algorithm.Thereby, the solution of the advection-diffusion equations is implicitly givenin terms of Green's functions and leads for the surface values to Volterraintegral equations of second kind with singular kernel, which we can solve veryefficiently by the product integration method. For the ordinary differentialequations a suitable collocation-continuation procedure is presented. Comparedwith the referential solution of a three-dimensional setting, the numericalresults are very convincing. They provide a good approximation whiledrastically reducing the computational time.

An Efficient Numerical Framework for Fiber Spinning Scenarios with Evaporation Effects in Airflows