Abstract
When selecting a melt-filtration system, the initial pressure drop is a critical parameter. We used heuristic optimization algorithms to develop general analytical equations for estimating the dimensionless pressure loss of square and Dutch woven screens in polymer processing and recycling. We present a mathematical description – without the need for further numerical methods – of the dimensionless pressure loss of non-Newtonian polymer melt-flows through woven screens. Applying the theory of similarity, we first simplified, and then transformed into dimensionless form, the governing equations. By varying the characteristic independent dimensionless influencing parameters, we created a comprehensive parameter set. For each design point, the nonlinear governing equations were solved numerically. We subsequently applied symbolic regression based on genetic programming to develop models for the dimensionless pressure drop. Finally, we validated our models against experiments using both virgin and slightly contaminated in-house and post-industrial recycling materials. Our regression models predict the experimental data accurately, yielding a mean relative error of MRE = 13.7%. Our modeling approach, the accuracy of which we have proven, allows fast and stable prediction of the initial pressure drop of polymer-melt flows through square woven and Dutch weave screens, rendering further numerical simulations unnecessary.
Acknowledgements
This work was supported by Erema Engineering Recycling Maschinen und Anlagen Ges.m.b.H and funded by the Austrian Research Promotion Agency (FFG; project number: 867202) and by the Austrian Science Fund (FWF; project number: P 29545-N34).
Appendix
Subfunctions for ΠP,zDutch Eq. 39.
Nomenclature
- DScreen
screen diameter
- MW
mesh width or mesh opening
- MN
number of wires per inch
- dW
wire diameter
- ΔPScreen
initial pressure drop of woven screen
- η
viscosity
- ṁ
mass flow rate
- γ
shear rate
- ρ
melt density
- n
power-law exponent
- K
consistency index
- DK
diameter of the warp wire
- PK
pitch in warp direction
- DS
diameter of the weft wire
- PS
pitch in weft direction
- x, y, z
spatial coordinates
- v
velocity vector
- vx, vy, vz
velocity components
- τ
viscous stress tensor
- D
rate-of-deformation tensor
- vref
undisturbed velocity
- ⟇cell
screen-specific volume flow rate
- ṁcell
screen-specific mass flow rate
- ⟇total
volume flow rate
- AScreen
overall screening surface
- ACell
characteristic surface of the elementary cell
- ξ, ψ, μ
dimensionless coordinates
- vx, vy, vz
dimensionless velocity components
- ΠV
dimensionless volume flow rate
- ΠP,i
dimensionless pressure gradient
- γ
dimensionless shear rate
- η
dimensionless viscosity
- Repl
Reynolds number for power-law fluid-based flows
- PD
dimensionless pitch-to-diameter ratio
- A
dimensionless pitch ratio
- α
dimensionless overlapping ratio
- D
dimensionless diameter ratio
- dpz
pressure loss
- ΠP,zSquare
dimensionless pressure gradient (square woven screens)
- A1 – A6
subfunctions (square woven)
- a1 – a33
constants (square woven)
- ΠP,zDutch
dimensionless pressure gradient (Dutch weave screens)
- B1 – B10
subfunctions (Dutch weave)
- b1 – a54
constants (Dutch weave)
- R2
coefficient of determination
- MAE
mean absolute error
- MRE
mean relative error
- REmax
maximum relative error
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