Accessible Requires Authentication Published by De Gruyter September 15, 2021

Using Symbolic Regression Models to Predict the Pressure Loss of Non-Newtonian Polymer-Melt Flows through Melt-Filtration Systems with Woven Screens

S. Pachner, W. Roland, M. Aigner, C. Marschik, U. Stritzinger and J. Miethlinger


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.

Wolfgang Roland, Johannes Kepler University Linz, Institute of Polymer Extrusion and Compounding,Altenberger Str. 69, 4040 Linz, Austria


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).


(42)  Subfunctions for Πp,zSquare Eq. 38: A1=a3+a4ea6n+a7PD,
(43) A2=a8(ea9n+a10n+a11PD),
(44) A3=a25ea26PDPD,
(45) A4=(a21n+a22PD)(a23n+a24PD),
(46) A5=ea14n+a15+ea16n+a17PDa18+ea19PD+a20PD,
(47) A6=a27n2(a28+a29ea30n+a31PD+ea32na33+log(PD)).

Subfunctions for ΠP,zDutch Eq. 39.

(48) B1=b18A+b3+b15eb16nb17A+b4eb6n,
(49) B2=b11eb12A+b13D+b14n+b7eb8A+b9D+b10n,
(50) B3=b22D+b19eb20n(A+b21D)2,
(51) B4=b52n+eb54nb53(b55A+n),
(52) B5=b46(eb47A+b48D+b49n+b50D+b51n)2,
(54) B6=b23b24D2+B7,
(55) B7=b25eb26nb27Ab31A+eb28 A+b29D+b30n+b32D+b33n,
(56) B8=b34(b44A+b45n)2,
(57) B9=b35Ab39A+eb36A+b37D+b38n+b40D,
(58) B10=(eb41A+b42D+b43n)2.



screen diameter


mesh width or mesh opening


number of wires per inch


wire diameter


initial pressure drop of woven screen



mass flow rate


shear rate


melt density


power-law exponent


consistency index


diameter of the warp wire


pitch in warp direction


diameter of the weft wire


pitch in weft direction

x, y, z

spatial coordinates


velocity vector

vx, vy, vz

velocity components


viscous stress tensor


rate-of-deformation tensor


undisturbed velocity


screen-specific volume flow rate


screen-specific mass flow rate


volume flow rate


overall screening surface


characteristic surface of the elementary cell

ξ, ψ, μ

dimensionless coordinates

vx, vy, vz

dimensionless velocity components


dimensionless volume flow rate


dimensionless pressure gradient


dimensionless shear rate


dimensionless viscosity


Reynolds number for power-law fluid-based flows


dimensionless pitch-to-diameter ratio


dimensionless pitch ratio


dimensionless overlapping ratio


dimensionless diameter ratio


pressure loss


dimensionless pressure gradient (square woven screens)

A1 – A6

subfunctions (square woven)

a1 – a33

constants (square woven)


dimensionless pressure gradient (Dutch weave screens)

B1 – B10

subfunctions (Dutch weave)

b1 – a54

constants (Dutch weave)


coefficient of determination


mean absolute error


mean relative error


maximum relative error


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Received: 2020-08-13
Accepted: 2021-02-16
Published Online: 2021-09-15
Published in Print: 2021-09-27

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