Development and validation of a model for the temperature distribution in the extrusion calibration stage

Habla, Florian; Fernandes, Célio; Maier, Maximilian; Densky, Lennart; Ferrás, Luís Jorge Lima; Rajkumar, Ananth; Carneiro, O. S.; Hinrichsen, Olaf; Nóbrega, J. M.

doi:10.1016/j.applthermaleng.2016.01.166

Cited by 19 publications

(28 citation statements)

References 15 publications

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“…The complete derivation of the governing equations needed to model the heat transfer between the calibrator and the profile was presented in a previous study . Therefore, only the most relevant details will be provided in this section.…”

Section: Numerical Modeling Codementioning

confidence: 99%

“…a. Hence, the equations used to model the contact resistance between the two phases are the following :

((), {\dot{bold-italicq}}_{p} - {\dot{bold-italicq}}_{c}) \cdot boldn = ((), k_{p} \nabla T_{∣ interface, normalp} - k_{c} \nabla T_{∣ interface, normalc}) \cdot boldn = 0

T_{∣ interface, normalp} - T_{∣ interface, normalc} = \frac{{\dot{bold-italicq}}_{c} \cdot boldn}{h},

where

\overset{q}{true}

indicates the interface heat flux; n is the interface normal vector pointing from the profile to the calibrator; and h is the interface heat transfer coefficient, which is the inverse of the contact resistance .…”

Section: Numerical Modeling Codementioning

confidence: 99%

“…In order to have one governing equation valid for all the domains, a new energy conservation equation was devised, Eq . 4 , using the conditional volume‐averaging technique ,

\nabla \cdot ((), U_{m} ρ_{m} c_{normalP, normalm} T_{m}) - k_{m} \nabla^{2} T_{m} = - \nabla \cdot ([], \frac{k_{normalm} \nabla α_{normalp} - α_{normalp} α_{normalc} ({\overset{k}{true}}^{p} - {\overset{k}{true}}^{c}) (\frac{1}{{\overset{false¯}{k}}^{p}} - \frac{1}{{\overset{false¯}{k}}^{c}}) h n}{h (\frac{α_{p}}{{\overset{false¯}{k}}^{p}} + \frac{α_{c}}{{\overset{false¯}{k}}^{c}}) + \nabla α_{normalp} \cdot n}) \nabla T_{m} \cdot boldn,

where T m is the mixture temperature; α p and α c are the computational cell volume fractions of polymer and calibrator, respectively; and the overbar denotes the conditional volume average of that quantity within the averaging volume . To obtain more details about this calculation procedure, the reader is advised to consult the work of Habla et al .…”

Section: Numerical Modeling Codementioning

confidence: 99%

“…4 , we first have the advection term and then the diffusion term, and on the right side, the term that accounts for the contact resistance at the interface is represented (see Ref. for details on the derivation of this term). Notice that, as expected, the latter term is not null just at the interface (where ∇ α p or α p α c are not null).…”

Section: Numerical Modeling Codementioning

confidence: 99%

“…The availability of open‐source codes can motivate extrusion companies to improve their design processes by integrating numerical modeling‐based approaches. With this is mind, a numerical code able to model the heat exchanges between the polymer and calibrator, which can handle complex geometry systems, was recently developed, by Habla et al , in the open‐source computational library OpenFOAM®. Verification of the code was undertaken, resorting to both analytical and numerical results of a benchmark case study , but the code was not experimentally assessed.…”

Section: Introductionmentioning

confidence: 99%

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Profile Extrusion: Experimental Assessment of a Numerical Code to Model the Temperature Evolution in the Cooling/Calibration Stage

Rajkumar¹,

Habla

Fernandes³

et al. 2019

Polymer Engineering & Sci

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Designing an industrial calibration system that ensures fast and uniform cooling of a complex extruded profile is always a difficult task. Numerical tools are a valuable aid for the design of these systems in order to achieve fast, low‐cost, and effective solutions. This work comprises the experimental validation of a numerical code, previously developed to support the design of profile extrusion calibration systems, using data collected from an industrial extrusion line. The referred numerical code was developed in the open‐source computational library, OpenFOAM, being able to predict the heat exchanges between the polymer and the calibrator during the profile extrusion cooling stage. The good agreement obtained between the numerical code predictions and the experimental measurements allowed us to confirm the code accuracy. Subsequently, and in order to demonstrate the usefulness of the numerical code, a numerical study was carried out based on an optimization algorithm aimed at improving the performance of the studied calibration system. As a result, the study led to the proposal of an alternative setup, which presents a simpler constructive solution and a better performance than the existing one. POLYM. ENG. SCI., 59:2367–2376, 2019. © 2019 Society of Plastics Engineers

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Section: Numerical Modeling Codementioning

confidence: 99%

“…a. Hence, the equations used to model the contact resistance between the two phases are the following :

((), {\dot{bold-italicq}}_{p} - {\dot{bold-italicq}}_{c}) \cdot boldn = ((), k_{p} \nabla T_{∣ interface, normalp} - k_{c} \nabla T_{∣ interface, normalc}) \cdot boldn = 0

T_{∣ interface, normalp} - T_{∣ interface, normalc} = \frac{{\dot{bold-italicq}}_{c} \cdot boldn}{h},

where

\overset{q}{true}

Section: Numerical Modeling Codementioning

confidence: 99%

“…In order to have one governing equation valid for all the domains, a new energy conservation equation was devised, Eq . 4 , using the conditional volume‐averaging technique ,

\nabla \cdot ((), U_{m} ρ_{m} c_{normalP, normalm} T_{m}) - k_{m} \nabla^{2} T_{m} = - \nabla \cdot ([], \frac{k_{normalm} \nabla α_{normalp} - α_{normalp} α_{normalc} ({\overset{k}{true}}^{p} - {\overset{k}{true}}^{c}) (\frac{1}{{\overset{false¯}{k}}^{p}} - \frac{1}{{\overset{false¯}{k}}^{c}}) h n}{h (\frac{α_{p}}{{\overset{false¯}{k}}^{p}} + \frac{α_{c}}{{\overset{false¯}{k}}^{c}}) + \nabla α_{normalp} \cdot n}) \nabla T_{m} \cdot boldn,

Section: Numerical Modeling Codementioning

confidence: 99%

Section: Numerical Modeling Codementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Profile Extrusion: Experimental Assessment of a Numerical Code to Model the Temperature Evolution in the Cooling/Calibration Stage

Rajkumar¹,

Habla

Fernandes³

et al. 2019

Polymer Engineering & Sci

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High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

Costa

Nóbrega

Clain

et al. 2021

Numerical Meth Engineering

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The computational modeling has become an indispensable tool to support the engineering design and control of many industrial processes. In polymer processing applications, the simulation of conjugate heat transfer phenomena is critical as rigorous temperature control is necessary to ensure that the produced parts meet the required specifications. In this article, a high-order accurate finite volume method is proposed to improve the numerical accuracy and the computational efficiency of conjugate heat transfer simulations with application in polymer processing. Anisotropic meshes are investigated to significantly reduce the number of unknowns in convection-dominated problems where the higher temperature variations occur perpendicularly to curved boundaries and interfaces. The reconstruction for off-site data method based on polynomial reconstructions is employed to fulfill the prescribed boundary and interface conditions solely using polygonal meshes to avoid the limitations of curved mesh approaches. A code verification benchmark based on manufactured solutions proves that the proposed method provides a fourth-order of convergence and is computationally more cost-effective than the classical second-order of convergence. Moreover, meshes with higher aspect ratios improve the calculation efficiency but suffer from a small accuracy penalty due to conditioning deterioration. Comparison with the classical finite volume discretization techniques, widely implemented in commercial and open-source software packages, is also provided. The applicability and performance of the proposed method are further supported with a practical case study for the sheet extrusion cooling stage. K E Y W O R D Sanisotropic polygonal meshes, conjugate heat transfer problems, curved boundaries and interfaces, high-order accurate finite volume method, OpenFOAM® software, polymer processing applications 1146

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New Process Concepts: Composites Processing

Gomes

Pais

2020

Advanced Structured Materials

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Development and validation of a model for the temperature distribution in the extrusion calibration stage

Cited by 19 publications

References 15 publications

Profile Extrusion: Experimental Assessment of a Numerical Code to Model the Temperature Evolution in the Cooling/Calibration Stage

Profile Extrusion: Experimental Assessment of a Numerical Code to Model the Temperature Evolution in the Cooling/Calibration Stage

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

New Process Concepts: Composites Processing

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