Fiber spinning process may involve high take-up velocity. It is not unusual that
drag force originating from the air surrounding the free boundary of the fiber
becomes significant with respect to the take-up force. When simulating fiber
spinning process with a 2D axisymmetric model, it is possible to include the drag
force into the calculation. From the point of view of modeling, the vector of drag
force density is given as:
(15–21) |
In the equation above, and
are independent parameters, while
and
are the local Reynolds number and the density of the surrounding
gas, and
is the magnitude of the local velocity on the surface of the
fiber. The quantity
denotes a unit vector parallel to the local velocity. The Reynolds
number
is evaluated on the basis of the local fiber radius
, the magnitude
of the fiber velocity, and the kinematic viscosity
of the surrounding gas. The density
of the gas is evaluated from the law of perfect gases, that
involves the mole mass
of the gas, the local pressure
, the universal thermodynamic molar gas constant
and the absolute temperature. For the temperature, reference
temperature
and offset temperature
can be defined as well.
From the point of view of the physics, the relationship indicates that the intensity of the drag force increases with the density of the surrounding gas and with its velocity as well. The quadratic dependence of the drag force is affected by the local Reynolds number.