Table 4 Dimensionless numbers for one representative fiber (cf. Fig. 1) in the industrial dry spinning setup assuming the airflow without fibers (first step in the fiber-airflow coupling). Note that some dimensionless numbers might vary during the simulation due to the fiber-airflow interaction (cf. Table 1)
From: Industrial dry spinning processes: algorithmic for a two-phase fiber model in airflows
Dimensionless numbers | ||
|---|---|---|
Description | Symbol | Value |
Slenderness | ε | 1.23⋅10−5 |
Reynolds | Re | 1.79⋅103 |
Froude | Fr | 7.07⋅10−1 |
Drawing | Dr | 2.00 |
Mass Peclet | \(\mathrm{Pe}_{c}\) | 4.16⋅106 |
Temperature Peclet | \(\mathrm{Pe}_{T}\) | 2.73⋅103 |
Mass Stanton | \(\mathrm{St}_{c}\) | 3.76⋅10−4 |
Temperature Stanton | \(\mathrm{St}_{T}\) | 5.88⋅10−5 |
Air drag associated | \(\mathrm{A}_{\star }\) | 1.14⋅102 |
Air-fiber Reynolds | \(\mathrm{Re}_{\star }\) | 2.15⋅101 |
Nusselt | \(\mathrm{Nu}_{\star }\) | 1.33 |
Prandtl | \(\mathrm{Pr}_{\star }\) | 7.44⋅10−1 |
Sherwood | \(\mathrm{Sh}_{\star }\) | 6.59 |
Schmidt | \(\mathrm{Sc}_{\star }\) | 1.15 |