Calibrator modelling in the simulation of extrusion process

Technical rubber or polymer profiles are often extruded while dragging them into a water bath. However, complex or heavy profiles may require additional guiding tools. For example, geometrically complex profiles, such as PVC-window frames, require the use of calibrators for satisfying severe geometric requirements, while heavy rubber profiles, such as D-shape fenders or tire treads, require a conveying belt mainly for being able to achieve the process. Within the context of numerical simulation of extrusion flows, such a guiding tool brings an additional downstream constraint to the kinematic equation which dictates the shape of the extrudate surface. In the present paper, we propose a simple engineering approach for modelling a conveyor belt used in rubber tire tread extrusion, and we apply it to the simulation of the extrusion flow for a 3D non-symmetric profile of a viscoelastic material.

15 - Numerical simulation of flow processes in composites manufacturing

Analysis of recent research and publications. It is known that the presence near the body of another body or a solid wall in a flow can significantly change both the overall flow pattern and the aerodynamic characteristics of bodies in a group. Studies of the interaction of bodies in the flow are conducted for a long time. In [6], the results of a study of changes in the overall flow pattern and the form of interaction of vortices behind tandem-arranged circular cylinders are presented. Further, experimental studies of the flow around a group consisting of two cylinders were aimed at classifying flow patterns depending on the position of the group in the flow, the distance between the cylinders and the Reynolds number [1, 2, 9]. A rather complete identification and classification of the pattern of flow was performed in [6, 7]. Studies on the classification and analysis of flow patterns are still being conducted [1]. Studies on the classification of patterns of the flow around group of spheres are currently performed mainly with the help of numerical simulation. In [3, 4, 5], simulation of the flow around spheres on the side-by-side position was performed. In [8], the classification of typical patterns of the flow around two spheres (Re = 300) with considering of different positions of the spheres relative to the flow direction was made. The authors of [8] describe nine typical patterns of the flow around two spheres in analogy with the patterns of the flow of the two cylinders.The purpose of the study. The main goal of this work is study the mutual influence of two bodies in a flow of a viscous incompressible fluid and a change in the flow structure with a change in the position of the bodies in the group relative to the incoming flow. Also, the aim of the work was to study the influence of the mutual arrangement of bodies in a group on the non-stationary and time-averaged aerodynamic characteristics of bodies in a group.Modeling of the flow around groups of cylinders and spheres. Numerical simulation of the flow around the group of cylinders was carried out with the values of the angle θ = 0°, 15°, 30°, 45°, 60°, 75°, 90° and the gap between the cylinders h = 0.2D, 0.4D, 0.6D, 0.8D, 1.0D, 2.0D, 3.0D, 4.0D, 5.0D. The flow parameters was corresponded to the flow around a circular cylinder at Re = 80 and 1.66 105. Eight patterns (regimes) of flow around a group of two cylinders at Re = 80 were found. Regimes 1 and 2 are steady state flows. In regime 1, the drag coefficient is Cx2 <0, and for regime 2, Cx2> 0. Regimes 3-8 are unsteady flows. Regime 8 is an aperiodic change in Cx, Cy. Regimes 3 - 7 are periodic, characterized by different values of the coefficients Cx, Cy, as well as those oscillations of Cx and Cy that occur in phase or antiphase. Simulation of the turbulent flow around a group of two cylinders took place at the tandem and the side-by-side positions at distances between cylinders centers 1.435D and 3.7D.Similarly, in this work, was performed the parametric study of the flow around two spheres for Reynolds number 750 with the distances between the centers of the spheres along axis Δx = 0.0, 1.0, 2.0, 3.0 and Δy = 0.0, 1.0, 2.0, 3.0. The drag and lift coefficients were obtained, as well as the patterns of flow around two spheres were analyzed.Conclusions. Depending on the position of the group relative to the flow, the average drag coefficient of the cylinders and spheres in the group can be both smaller and larger than the drag coefficient of a single body with the same parameters of the free flow. With a tandem arrangement, the second cylinder has a stabilizing effect and with a decrease in the gap of less than three diameters, the flow becomes steady state. For all cases with staggered arrangement of spheres the symmetry restoration of vortex structures is observed. In the case of the tandem arrangement of spheres, the separation of loop-shaped vortex structures is realized as in the case of a flow around a single sphere.

Physical experiments allow to obtain maximum information on a studied process at minimal cost, ensuring its higher accuracy comparing with data, obtained by mathematical simulation and avoiding risks, which can occur at industrial testing of new technological modes. Results of studies of deformation in the process of pipes production by extrusion presented. The studies were accomplished at laboratory test units, developed by specialists of the laboratory of drawing and extrusion of JSC “RusNITI”. One of the basic problems at pipes production by extrusion is ensuring minimal possible wall non-uniform thickness. It was noted that the relation between plunger die moving speeds during sleeve pressing-out and immediate pipe extrusion has a significant effect on pipe wall non-uniform thickness. Computer simulation of the pipe extrusion process, accomplished by application QForm program shown that minimal values of wall non-uniform thickness corresponded to relation abovementioned speeds as 0.5–0.8. To check the data, a physical simulation of extrusion process of lead cylinder samples, having outside diameter of 18.94 mm and wall thickness 5.19–5.32 mm was accomplished. For the extrusion, a universal servohydraulic system of dynamic test Shimadzu Servopulser was used. Within the physical experiment a dependence was established between pipe wall non-uniform thickness on relation between speeds of pressing-out and extrusion. The revealed regularity was confirmed during pilot production of a pipe lot at the 55 MN force extrusion line. Another physical simulation of extrusion of 10.0×2.0 mm pipe-samples made of C1 grade lead was accomplished with one- and twothread helical ribbing of internal surface. For its accomplishment an experimental module was designed and manufactured. It was established that rotation speed of the extrusion mandrel had no significant effect on extrusion force. Metallographic studies shown that the extrusion mandrel rotation speed contributes to considerable increase of pipes surface hardness and obtaining finer grain comparing with the classic extrusion method. The technical ability of pipes production with internal helical ribbing by hot extrusion method was confirmed. The results of the study became a base for elaboration of a technology of pipes production at Volzhsky pipe plant according to ТУ 14-3Р-157–2018 “Steel seamless hot-extruded pipes with helical ribbing of internal surface for steam boilers”. Results of physical simulation of pipe drawing process at self-adjusting mandrel with application of lubricant materials of various viscosity. The data obtained were used for elaboration of a technology for production of cold-deformed pipes with internal diameter of 6.0–12.0 mm at Sinarsky pipe plant.

The numerical simulation of a flow through a duct requires an externally specified forcing that makes the fluid flow against viscous friction. To this end, it is customary to enforce a constant value for either the flow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct flow before and after a geometrical modification that induces a change of the viscous drag, both approaches lead to a change of the power input across the comparison. Similarly, when carrying out direct numerical simulation or large-eddy simulation of unsteady turbulent flows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of flow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with defining a new power-related Reynolds number, whose velocity scale is the bulk flow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata–Iwamoto–Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of naturally including the required control power. The implementation of the CPI approach is then exemplified in the standard case of a plane turbulent channel flow, and then further applied to a flow control case, where a spanwise-oscillating wall is used for skin-friction drag reduction. For this low-Reynolds-number flow, using 90 % of the available power for the pumping system and the remaining 10 % for the control system is found to be the optimum share that yields the largest increase of the flow rate above the reference case where 100 % of the power goes to the pump.

The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated, they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip-clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-ε turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.

The paper is concerned with the experimental and numerical simulations of the viscous flows in 3D planar cylindrical bifurcations and in a bypass configuration. The main goal of the study is to investigate the influence of the angle between the main and secondary branches of the bifurcation on the flow pattern and the wall stresses distributions. Numerical simulations of the flows in a bypass are also performed. The flow rate distribution between the branches in the presence of a stenosis is determined, as function of the Reynolds number. The results are expected to give value information about the functioning of cardiovascular bifurcation and bypass configuration in the pre-stenosis and stenosis regimes.

Numerical simulation of a turbulent flow of air with dispersed particles through a cyclonic separator is presented. Because of a high streamline curvature in the separator it is difficult to simulate the flow by using the conventional turbulent models. In this work the curvature correction term was included into the k – ω – SST turbulence model implemented in the OpenFOAM® software. Experimental data and results of numerical simulation by the commercial ANSYS Fluent® solver for a turbulent flow in a U-duct were used to validate the model. The numerical simulation of the flow in the cyclonic separator demonstrates that the implemented turbulence model successfully predicts the cyclonic separator efficiency.

Semi-automatic rezone-algorithm for the simulation of 2D-axisymmetric extrusion processes with FEM

This numerical study was conducted to investigate the flow properties in a model scramjet configuration of the experiment in the T4 shock tunnel. In most numerical simulations of flows in shock tunnels, the inflow conditions in the test section are determined by assuming the thermal equilibrium of the gas. To define the inflow conditions in the test section, the numerical simulation of the nozzle flow with the given nozzle reservoir conditions from the experiment is conducted by a thermochemical nonequilibrium computational fluid dynamics (CFD) solver. Both two-dimensional (2D) and three-dimensional (3D) numerical simulations of the flow in a model scramjet were conducted without fuel injection. Simulations were performed for two types of inflow conditions: one for thermochemical nonequilibrium states obtained from the present nozzle simulation and the other for the data available using the thermal equilibrium and chemical nonequilibrium assumptions. The four results demonstrate the significance of the modelling approach for choosing between 2D or 3D, and thermal equilibrium or nonequilibrium.

The extrusion of large or heavy technical rubber profiles is usually assisted by a conveying device. Such a device can be a conveyor belt or a series of rollers, and its use is necessary mainly for being able to achieve the process. Within the context of numerical simulation of extrusion flows, a conveying device brings additional downstream constraints to the flow governing equations. In the present paper, we propose a simple engineering approach for modelling a roller conveyor used in rubber tire tread extrusion, and we apply it to the extrusion simulation of a flat tire tread profile as typically encountered in the tire manufacturing industry.

Two explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free surface water flow. Two numerical simulations of flow with different hydraulic characteristics were performed - the first one for the extreme flow of the dam-break type and the second one for the simplified flood wave propagation problem. The computational results are compared to each other and to arbitrary solutions.

In this work a numerical method for the simulation of extrusion processes with modeling of microstructure is presented. Extensive testing was done to provide a basis for the verification of simulation results. Circular rods of AA6005A were extruded by backward and forward extrusion with different extrusion ratios, billet temperatures and product velocities. The extruded rods were cooled either by water or at air to distinguish between dynamic and static recrystallization. Temperature and strain-rate dependent yield stresses were determined from hot compression tests. Special friction tests on cylindrical specimens under high hydrostatic stresses at high temperatures have been performed and the parameters of a friction model were identified from the experiments. The recrystallized volume fraction and grain sizes in the extruded rods were analyzed by means of optical micrographs. The obtained results were used to determine the parameters of a recrystallization model which was implemented in the FE code HyperXtrude. The transferability of the numerical model was checked by simulating forward extrusion tests using the model parameters obtained from backward extrusion tests.

Advanced Dynamic & Crash Simulation of Lightweight Profiles for Design of Roadside Infrastructure

Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an “advection” step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.