Polymer Extrusion Cooling for the 21 Century

Polymer Extrusion Cooling for the 21st Century A white paper by: Wesley J. Sipe, Mechanical Systems Manager, GAI Consultants On Behalf Of: NOVATEC, Inc. Baltimore, MD USA

Considering all of the plastic produced and With these keys, required cooling times can used every day, it is surprising that very little be determined through the use of advanced is documented on the cooling process for computer models. continuous profiles of extruded shapes. The bulk of the cooling process is The challenge to this methodology is in accomplished through the application of obtaining accurate thermal conductivity and “rules of thumb” learned and used by heat capacity of polymer compounds for use cooling tank manufacturers, and through in predicting thermal response. Since there trial and error methods of individual are literally thousands of compounds that processors. In spite of the desirability of are used in polymer extrusion, this paper processors to minimize space and elapsed concentrates on only six commonly used: time required to effectively cool profiles, the  Polyethylene (PE) cooling process remains a “black art” as no  Polypropylene (PP) tools exist that will accurately predict the  Polycarbonate (PC) time response of cooling plastics with  Polystyrene (PS) liquids. This is remarkable in itself because the cooling puzzle can be solved through  Poly Vinyl Chloride (PVC) the simplification of the transient heat  Acrylonitrile Butadiene Styrene transfer equation for the materials involved. (ABS). Even more remarkable is that through the All of the analyses described in this paper use of powerful personal computers, the assume isotropic forms with temperature process can be modeled and a solution dependent properties. Since the extruder is derived through the use of finite difference a fairly good mixer and the material is methods. normally compounded prior to reaching the The keys to accurately predicting the throat of the extruder. This is a reasonable cooling response are: assumption.

1. Calculating the convection heat transfer coefficient from the plastic profile into the coolant The Cooling Process 2. Knowledge of the mechanical properties versus temperature of the The goal of the cooling process is to bring plastic the polymer from the molten state, leaving the die face, to a temperature that corresponds with the mechanical properties

required for post-processing (cutting and/or between the profile and the sprayed cooling packaging) that will not leave permanent water. By using enough force, the sprayed deformation of the final product. water can effectively decrease the boundary Manufacturers would ideally like to have this layer enough to enable increased cooling occur as soon as possible, and in the through a higher Δt, ergo increased heat shortest physical length attainable, for a transfer. It should be noted here that there given throughput of plastic. A third variable does exist a point of diminished returns that should be considered is the energy where increasing the force of the water (electricity) required for the cooling process spray yields very little increase in the rate of – this should be evaluated so that any cooling – at this point, increasing the spray cooling improvements do not add flows results in dramatically increased production costs that would not significantly energy costs per heat unit removed. affect the manufacturer’s ability to sell its product. Polymer Properties Effect on Cooling Times When plastic extrusion first came to popularity, cooling was accomplished by The principle material properties that affect blowing ambient air over the profile. Later, the cooling time are plastic thermal water immersion in a static bath was conductivity and specific heat (heat introduced and was followed by moving capacity). The thermal conductivity is a water – cooling, that increased the heat temperature dependent property that transfer coefficient with a corresponding defines how quickly heat can move through increase in manufacturing throughput. In a compound versus the temperature the 1990s, cooling rates were again difference within the compound. The increased by the use of high velocity spray thermal conductivity can be different for nozzles for forced convection cooling of the each compound with some having profile. Forced convection has become the properties that are directly proportional to state of the art as the energy required to temperature and some that are inversely move spray water is significantly less than proportional to temperature. Heat capacity that required to move an entire tank however, is the amount of heat that a contents of water. compound can hold and often is described as the amount of heat necessary to add or Forced convection cooling is the tradeoff remove from a compound to effect a between the energy required to spray the discrete change in temperature of that cooling water over the profile and the compound. increased benefit of the cold water “wiping away” the warm insulating water layer, For cooling plastic profiles, the thermal known as the boundary layer, next to the conductivity can be the limiting factor in profile. The boundary layer is created by determining the amount of time required for the heat transferred from the surface of the cooling. Since industry does not enhance hotter profile to the cooling water next to the (perhaps it should) the polymer properties to surface and tends to act as an insulator increase conduction, the time required to

cool a defined profile is largely governed by the actual temperature of the polymer the size, thickness and general mass of the compound. This means that as heat moves profile and the thermal conductivity of the from one location to another within the compound, which incidentally, is usually low profile, these properties will vary. The for polymers as they make good thermal variability of these properties needs to be insulators. accounted for in the calculation for cooling or serious inaccuracies in predicting cooling Heat capacity (specific heat) defines the times will result. The ultimate means of amount of energy needed to change the accounting for this is a time-marching finite temperature of a polymer. It can expressed difference methodology. In other words, the in heat rate per unit time per unit profile cross section is divided into many temperature. Since there is no clearly small elements where the properties are defined melting temperature for polymers, “constant” for a given slice of time. The we will address the latent and sensible temperature is calculated across these transfer lumped in together as heat elements for each time step and tabulated capacity. to closely approximate the temperature What this leaves us with, from a practical profile of the polymer at any given moment. standpoint, is that the heat within the Here again is another tradeoff; this one extruded compound needs to be lowered to being in computing power versus the time the maximum allowable temperature of the required to run the simulation. With today’s profile for post processing. We can begin to personal computing power these accurately predict how to accomplish the simulations are quite precise with minimum cooling time possible knowing the: reasonable calculation times. Each simulation takes between 3 to 30 minutes to  Maximum thermal conductivity rate produce the profile’s temperature versus  Specific heat of the compound time response to a cooling scenario.  Starting temperature  Required temperature after cooling Solving the Temperature vs. Time Problem This information, coupled with the amount of energy expended to achieve the minimum The computer simulation is set up by cooling time, can be adjusted accordingly to selecting the polymer, its shape and maximize the process from a business thickness and the initial starting (Die) standpoint. temperature. To perform the simulation, the profile is sprayed with a virtual spray of Simulation of the Cooling System’s water that promotes a heat transfer Effect on the Profile coefficient on the surface of the profile. This To add to the complexity of the calculation coefficient, together with the temperature of of cooling, it must be remembered that both the cooling water predicts the surface of the primary considerations, heat capacity convection heat transfer of the profile. It is and thermal conductivity, are dependent on a time dependent prediction as the amount

of heat transferred at any given moment is system. Without this calculation, the subject to the Δt between the cooling water amount of unknowns to this process and the surface of the profile which is previously caused safety factor after safety continuously changing. The computer factor to be added to the process – adding simulation calculates the local temperature unnecessary capital expense to the marching through the cross section of the downstream tank and operating expense to extruded profile taking into account the local the cooling process for the producer. This polymer properties at that temperature. The calculation predicts the performance of the simulation performs this calculation for each cooling tank without extensive empirical time period that is requested. The highest testing. final allowable temperature is located where the profile is the thickest (the center for a Future Work solid profile). This is the critical temperature The precision of this calculation could lead to understand because post processing of to some overconfidence in the accuracy of the profile out of the cooling tank needs to the results of these calculations. There are have a maximum allowable temperature to several areas where the accuracy can prevent poor profile ends or other heat suffer, especially if trying to extrapolate the related permanent deformation of the results to polymer compounds that were not profile. considered in the development of the For a constant profile speed through the calculation – “average” compounds were cooling tank, the time also represents a used in the development of the model from linear position in the cooling tank. Hence which mechanical properties versus for a requested final temperature, there is a temperature were ascertained. If the tank length that is associated with the polymer compound to be used has amount of time the profile requires to be additional components or additives, the cooled. We have been able to fit a curve for properties could vary and introduce error standard profiles and polymers that we can into the solution. predict the final temperature of the inside of Opportunities for application of this model to the profile versus time. For example, if the additional profiles would be to model the producer knows that they need the polymer internal foaming process. The present to be at 130°F to prevent post processing model uses a homogenous mixture across deformation, we can predict the amount of the cross section. To accomplish this, the time needed to cool a specific product and profile would need to be radially segmented maximum throughput in pounds per hour into solid layers, and foamed layers that a certain length of tank can support. (probably lower in thermal conductivity, but There needs to be no additional length or also lower in density and mass), the “safety factor” because the process is different material properties of these foamed completely calculated. This can create layers would have to be tested and input significant confidence in the throughput that into the perspective layers for the model. can be supported by a given cooling The finite difference calculation would

require more processing time, but not submerging and moving the profile through necessarily more computing power. a tank of water. Spraying maintains the minimum thermal boundary layer (resulting Conclusion in maximum heat transfer) while only moving a fraction of a full tank of water over We know that polymer properties of density, thermal conductivity and heat capacity vary the profile. This process, using the finite significantly with the temperature of the difference equations and thermal / polymer as it cools and hence must be mechanical properties, has been analyzed and developed for several common profiles accounted for in any cooling calculation. Today’s computers are able to calculate the and compounds and your Novatec transient temperature profile for plastic as it representative can assist you in your cools and these results have been extrusion cooling application system sizing. The sizing program available will eliminate assembled into a final temperature vs. time equation for a given profile. Using this, it the need for multiple safety factors and a has been demonstrated that Forced close approximation to the actual physical system performance by accounting for Convection (Spray) Cooling has the benefit of high velocities of cold water applied to the polymer compound properties variation with profile resulting in increased throughput and temperature. lower operating costs compared to