  In melt-blowing processes mico- and nanofibers are produced by the extrusion
of polymeric jets into a directed, turbulent high-speed airflow. Up to now the
physical mechanism for the drastic jet thinning is not fully understood, since
in the existing literature the numerically computed/predicted fiber thickness
differs several orders of magnitude from those experimentally measured. Recent
works suggest that this discrepancy might arise from the neglect of the
turbulent aerodynamic fluctuations in the simulations. In this paper we confirm
this suggestion numerically. Due to the complexity of the process direct
numerical simulations of the multiscale-multiphase problem are not possible.
Hence, we develop a numerical framework for a growing fiber in turbulent air
that makes the simulation of industrial setups feasible. For this purpose we
employ an asymptotic viscoelastic model for the fiber. The turbulent effects
are taken into account by a stochastic aerodynamic force model where the
underlying velocity fluctuations are reconstructed from a $k$-$\epsilon$
turbulence description of the airflow. Our numerical results show the
significance of the turbulence on the jet thinning and give fiber diameters of
realistic order of magnitude.
