A Hybrid Ale Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

The present work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two dimensional beam finite element is presented, based on the Absolute Nodal Coordinate Formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as the case of (continuously) distributed mass.

Non-Isothermal Free-Surface Viscous Flow of Polymer Melts in Pipe Extrusion Using an Open-Source Interface Tracking Finite Volume Method

Polymer extrudate swelling is a rheological phenomenon that occurs after polymer melt flow emerges at the die exit of extrusion equipment due to molecular stress relaxations and flow redistributions. Specifically, with the growing demand for large scale and high productivity, polymer pipes have recently been produced by extrusion. This study reports the development of a new incompressible non-isothermal finite volume method, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation, to compute the viscous flow of polymer melts obeying the Herschel–Bulkley constitutive equation. The Papanastasiou-regularized version of the constitutive equation is employed. The influence of the temperature on the rheological behavior of the material is controlled by the Williams–Landel–Ferry (WLF) function. The new method is validated by comparing the extrudate swell ratio obtained for Bingham and Herschel–Bulkley flows (shear-thinning and shear-thickening) with reference data found in the scientific literature. Additionally, the essential flow characteristics including yield-stress, inertia and non-isothermal effects were investigated.

Dynamic Modeling and Experimental Verification of A Cable-Driven Continuum Manipulator With Cable-Constrained Synchronous Rotating Mechanisms

The cable-driven segmented manipulator with cable-constrained synchronous rotating mechanisms (CCSRM) is a new type of continuum manipulator, which has large stiffness and less motors, and thus exhibits excellent comprehensive performance. This paper presents a dynamic modeling method for this type of manipulator to analyze the friction and deformation of the cables on the dynamical behaviors of the system. First, the driving cables are modeled based on the ALE formulation, the strategies for detecting stick-slip transitions are proposed by using a trial-and-error algorithm, and the stiff problems of the dynamic equations are released by a model smoothing method. Second, the dynamic modeling method for rigid links is presented by using quaternion parameters. Third, the connecting cables are modeled by torsional spring-dampers and the frictions between the connecting cables and the conduits are considered based on a modified Coulomb friction model. Finally, the numerical results are presented and verified by comparing with experiment results. The study shows that the friction and cable deformation play an important role in the dynamical behaviors of the manipulator. Due to these two factors, the constant curvature bending of the segments does not remain.

Transient Cavitation and Friction-Induced Heating Effects of Diesel Fuel during the Needle Valve Early Opening Stages for Discharge Pressures up to 450 MPa

An investigation of the fuel heating, vapor formation, and cavitation erosion location patterns inside a five-hole common rail diesel fuel injector, occurring during the early opening period of the needle valve (from 2 μm to 80 μm), discharging at pressures of up to 450 MPa, is presented. Numerical simulations were performed using the explicit density-based solver of the compressible Navier–Stokes (NS) and energy conservation equations. The flow solver was combined with tabulated property data for a four-component diesel fuel surrogate, derived from the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS), which allowed for a significant amount of the fuel’s physical and transport properties to be quantified. The Wall Adapting Local Eddy viscosity (WALE) Large Eddy Simulation (LES) model was used to resolve sub-grid scale turbulence, while a cell-based mesh deformation arbitrary Lagrangian–Eulerian (ALE) formulation was used for modelling the injector’s needle valve movement. Friction-induced heating was found to increase significantly when decreasing the pressure. At the same time, the Joule–Thomson cooling effect was calculated for up to 25 degrees K for the local fuel temperature drop relative to the fuel’s feed temperature. The extreme injection pressures induced fuel jet velocities in the order of 1100 m/s, affecting the formation of coherent vortical flow structures into the nozzle’s sac volume.

ALE formulation for thermomechanical inelastic material models applied to tire forming and curing simulations

Forming of tires during production is a challenging process for Lagrangian solid mechanics due to large changes in the geometry and material properties of the rubber layers. This paper extends the Arbitrary Lagrangian–Eulerian (ALE) formulation to thermomechanical inelastic material models with special consideration of rubber. The ALE approach based on tracking the material and spatial meshes is used, and an operator-split is employed which splits up the solution within a time step into a mesh smoothing step, a history remapping step and a Lagrangian step. Mesh distortion is reduced in the smoothing step by solving a boundary value problem. History variables are subsequently remapped to the new mesh with a particle tracking scheme. Within the Lagrangian steps, a fully coupled thermomechanical problem is solved. An advanced two-phase rubber model is incorporated into the ALE approach, which can describe green rubber, cured rubber and the transition process. Several numerical examples demonstrate the superior behavior of the developed formulation in comparison to purely Lagrangian finite elements.

A reconstructed discontinuous Galerkin method for compressible flows on moving curved grids

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and invalid elements near moving boundaries.

A Reconstructed Discontinuous Galerkin Method for Compressible Flows on Moving Curved Grids

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and elements near moving boundaries.

A Useful Manufacturing Guide for Rotary Piercing Seamless Pipe by ALE Method

The development of numerical simulations is potentially useful in predicting the most suitable manufacturing processes and ultimately improving product quality. Seamless pipes are manufactured by a rotary piercing process in which round billets (workpiece) are fed between two rolls and pierced by a stationary plug. During this process, the material undergoes severe deformation which renders it impractical to be modelled and analysed with conventional finite element methods. In this paper, three-dimensional numerical simulations of the piercing process are performed with an arbitrary Lagrangian–Eulerian (ALE) formulation in LS-DYNA software. Details about the material model as well as the elements’ formulations are elaborated here, and mesh sensitivity analysis was performed. The results of the numerical simulations are in good agreement with experimental data found in the literature and the validity of the analysis method is confirmed. The effects of varying workpiece velocity, process temperature, and wall thickness on the maximum stress levels of the product material/pipes are investigated by performing simulations of sixty scenarios. Three-dimensional surface plots are generated which can be utilized to predict the maximum stress value at any given combination of the three parameters.