Negative Pressures in Modelling Rotating Polymer Processing Machinery Are Meaningless, But They Are Telling Something

Abstract

In the technical literature, some authors have reported calculation of negative pressures in simulations of twin screw extrusion and other types of processing, without giving any explanations. In the majority publicationst here is no mention of such meaningless results, even though theoretical considerations indicate that negative pressures could be obtained in the expansionr egion of drag flows through narrow nonparallel surfaces. The meaningless negative pressures are due to the application of single fluid theory to flow regions where bubbles would form, when the pressure drops below the vapor pressure of the liquid. This has been known for a long time from the study of lubrication bearings and related cavitation phenomena. It is argued that the boundary conditions should be carefully chosen for avoiding results in numerical simulations, which can never be reconciled with experimental pressure data. 1I ntroductionRotating polymer processing machinery frequently involves melt flow between two non-parallel surfaces. The melt is usually dragged and compressed towards an arrow gap and then it expands. As aresult of the drag flow in the non-parallel narrow gap, the pressure reaches am aximum in the compression region and then aminimum in the expansion region. Modelling is usually carried out with the help of the lubrication approximation or with fully 3D momentum equations for creeping (inertialess, viscous) flow. If the baseline pressure at both ends of the compression-expansion flow field is zero, then negative pressures will be calculated in the expansion region. Figure 1shows positive and negative pressure development between two co-rotating cylinders. In the counter-rotating case, both compression and expansion are higher than in the co-rotating case and consequently the positive and negative pressures calculated are higher, as shown in Fig. 2. Of course, negative pressures are meaningless. However, with so many machines operating at or near ambient pressure, boundary conditions at or close to zero values are quite realistic and so these negative results should occur quite frequently in modelling. It is argued in this paper that these negative pressures are telling researchers important information about their modeled environment. 2R eviewing Modelling ResultsThe authors have carried out an extensive literature search regarding the calculation and reporting of negative pressures in flow simulations of twin screw extruders and other types of rotating polymer processing equipment. In the vast majority of publications there is never any mention that negative pressures were ever calculated when solving the conservation of mass and momentum equations. It is not clear whether this was due to the fortuitous occurrence of high baseline pressures or convenient choices of boundary conditions. Most papers ignore negative pressure results even though the mathematical descriptions suggest such possibilities. These studies usually confine their discussions to the negative and positive pressure gradients and the implications ...

A composite model for an intermeshing counter‐rotating twin‐screw extruder and its experimental verification

“…Negative pressures observed in modeling do not exist in reality. This issue has been recently discussed in the literature .…”

The Role of Calender Gap in Barrel and Screw Wear in Counterrotating Twin Screw Extruders

“…As both screws rotate, the material is dragged towards the nip region, where the pressure rises to a maximum value just upstream of the minimum gap. Right after the minimum gap, the numerical simulation shows that the pressure drops to rather large negative values, which are meaningless [ 38 ]. Negative pressures have appeared in a number of published simulations [ 39 , 40 , 41 , 42 ] of flow in polymer processing machinery.…”

Computer modeling for polymer processing co-rotating twin screw extrusion – nonconventional screw configurations

“…Gradient ciśnienia jest ujemny, a jego wartość również określa wielkość przepływu ciśnieniowego. Interesującą dyskusję wyników modelowania przepływów ślimakowych przedstawiono ostatnio w [19], wskazując na często błędne interpretacje wyników i brak zrozumienia kinematycznej istoty przepływów ślimakowych.…”