Search results

The purpose of this study is to investigate the accuracy and applicability of the Flowfield Dependent Variation (FDV) method for large-eddy simulations (LES) of decaying isotropic turbulence.

In an earlier paper, the FDV method was successfully demonstrated for simulations of laminar flows with speeds varying from low subsonic to high supersonic Mach numbers. In the current study, the FDV method, implemented in a finite element framework, is used to perform LESs of decaying isotropic turbulence. The FDV method is fundamentally derived from the Lax–Wendroff Scheme (LWS) by replacing the explicit time derivatives in LWS with a weighted combination of explicit and implicit time derivatives. The increased implicitness and the inherent numerical dissipation of FDV contribute to the scheme’s numerical stability and monotonicity. Understanding the role of numerical dissipation that is inherent to the FDV method is essential for the maturation of FDV into a robust scheme for LES of turbulent flows. Accordingly, three types of LES of decaying isotropic turbulence were performed. The first two types of LES utilized explicit subgrid scale (SGS) models, namely, the constant-coefficient Smagorinsky and dynamic Smagorinsky models. In the third, no explicit SGS model was employed; instead, the numerical dissipation inherent to FDV was used to emulate the role played by explicit SGS models. Such an approach is commonly known as Implicit LES (ILES). A new formulation was also developed for quantifying the FDV numerical viscosity that principally arises from the convective terms of the filtered Navier–Stokes equations.

The temporal variation of the turbulent kinetic energy and enstrophy and the energy spectra are presented and analyzed. At all grid resolutions, the temporal profiles of kinetic energy showed good agreement with t^(−1.43) theoretical scaling in the fully developed turbulent flow regime, where t represents time. The energy spectra also showed reasonable agreement with the Kolmogorov’s k^(−5/3) power law in the inertial subrange, with the spectra moving closer to the Kolmogorov scaling at higher-grid resolutions. The intrinsic numerical viscosity and the dissipation rate of the FDV scheme are quantified, both in physical and spectral spaces, and compared with those of the two SGS LES runs. Furthermore, at a finite number of flow realizations, the numerical viscosities of FDV and of the Streamline Upwind/Petrov–Galerkin (SUPG) finite element method are compared. In the initial stages of turbulence development, all three LES cases have similar viscosities. But, once the turbulence is fully developed, implicit LES is less dissipative compared to the two SGS LES runs. It was also observed that the SUPG method is significantly more dissipative than the three LES approaches.

Just as any computational method, the limitations are based on the available computational resources.

Solving problems involving turbulent flows is by far the biggest challenge facing engineers and scientists in the twenty-first century, this is the road that the authors have embarked upon in this paper and the road ahead of is very long.

Understanding turbulence is a very lofty goal and a challenging one as well; however, if the authors succeed, the rewards are limitless.

The derivation of an explicit expression for the numerical viscosity tensor of FDV is an important contribution of this study, and is a crucial step forward in elucidating the fundamental properties of the FDV method. The comparison of viscosities for the three LES cases and the SUPG method has important implications for the application of ILES approach for turbulent flow simulations.

A number of finite element formulations involving discontinuous weighting functions have been tested against analytic solutions for a steady scalar convection—diffusion problem at intermediate Peclet number, with a ‘hard’ downstream boundary condition. The emphasis is on extending these methods to isoparametric bilinear and biquadratic elements. In order to do this a procedure is given for the exact calculation of shape function Laplacians. Having confirmed the success of the Brooks—Hughes streamline upwind Petrov—Galerkin (SUPG) method for isoparametric bilinear elements, formulations for biquadratic elements are examined. Galerkin least squares offers little advantage over SUPG in the test problem. The generalized Galerkin method of Donea et al. gave excellent results, but because of concern over the possibility of cross‐streamline artificial diffusion in some cases, a strictly streamline formulation incorporating the optimal parameters of Donea et al. is proposed. This gave excellent results on a sufficiently refined mesh.

The purpose of this paper is to simulate two macrosegregation benchmarks with a newly developed stabilized finite element algorithm based on a semi-implicit pressure correction scheme.

A streamline-upwind/Petrov–Galerkin (SUPG) stabilized finite element algorithm is developed for the coupled conservation equations of mass, momentum, energy and species. A semi-implicit pressure correction method combined with SUPG stabilization technique is proposed to solve the convection flow during solidification. An analytically derived enthalpy method is adopted to solve the energy conservation equation. The nonlinearities of the energy and species equations are tackled by Newton–Raphson method. Two macrosegregation benchmarks considering the solidification of an Al-4.5 per cent Cu alloy and a Sn-10 per cent Pb alloy are simulated.

A very good agreement is achieved by comparison with the classical finite volume method and a novel meshless method for the Al-4.5 per cent Cu alloy solidification benchmark. Moreover, a unique reference numerical solution has been obtained. Besides, it is demonstrated that the stabilized finite element algorithm can capture the flow instability and channel segregation during solidification of the Sn-10 per cent Pb alloy.

A semi-implicit pressure correction method combined with SUPG stabilization technique is adopted to develop robust stabilized finite element algorithm for the macrosegregation model. A new enthalpy formulation for heat transfer problems with phase change is derived analytically.

An original finite element scheme for advection‐diffusion‐reaction problems is presented. The new method, called spotted Petrov‐Galerkin (SPG), is a quadratic Petrov‐Galerkin (PG) formulation developed for the solution of equations where either reaction (associated to zero‐order derivatives of the unknown) and/or advection (proportional to first‐order derivatives) dominates on diffusion (associated to second‐order derivatives). The addressed issues are turbulence and advective‐reactive features in modelling turbomachinery flows.

The present work addresses the definition of a new PG stabilization scheme for the reactive flow limit, formulated on a quadratic finite element space of approximation. We advocate the use of a higher order stabilized formulation that guarantees the best compromise between solution stability and accuracy. The formulation is first presented for linear scalar one‐dimensional advective‐diffusive‐reactive problems and then extended to quadrangular Q2 elements.

The proposed advective‐diffusive‐reactive PG formulation improves the solution accuracy with respect to a standard streamline driven stabilization schemes, e.g. the streamline upwind or Galerkin, in that it properly accounts for the boundary layer region flow phenomena in presence of non‐equilibrium effects.

The numerical method here proposed has been designed for second‐order quadrangular finite‐elements. In particular, the Reynolds‐Averaged Navier‐Stokes equations with a non‐linear turbulence closure have been modelled using the stable mixed element pair Q2‐Q1.

This paper investigated the predicting capabilities of a finite element method stabilized formulation developed for the purpose of solving advection‐reaction‐diffusion problems. The new method, called SPG, demonstrates its suitability in solving the typical equations of turbulence eddy viscosity models.

In this paper we consider several aspects related to the application of the pseudo‐concentration techniques to the simulation of mould filling processes. We discuss, in particular, the smoothing of the front when finite elements with interior nodes are employed and the evacuation of air through the introduction of temporary free wall nodes. The basic numerical techniques to solve the incompressible Navier—Stokes equations are also briefly described. The main features of the numerical model are the use of div‐stable velocity—pressure interpolations with discontinuous pressures, the elimination of the pressure via an iterative penalty formulation, the use of the SUPG approach to deal with convection‐dominated problems and the temporal integration using the generalized trapezoidal rule. At the end of the paper we present some numerical results obtained for a two‐dimensional test problem showing the ability of the method to capture complicated flow patterns.

The purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and finite element method (FEM) in dealing with turbulent flows are compared.

The stabilization scheme, the streamline-upwind/Petrov-Galerkin stabilization is coupled with stabilized pressure gradient projection in the fractional step framework. The Reynolds-averaged Navier-Stokes equations with standard k-epsilon model are selected to solve turbulent flows based on S-FEM and FEM. Standard wall functions are applied to predict boundary layer profiles.

This paper explores a completely new application of S-FEM on turbulent flows. The adopted stabilization scheme presents a good performance on stabilizing the flows, especially for very high Reynolds numbers flows. An advantage of S-FEM is found in applying wall functions comparing with FEM. The differences between S-FEM and FEM have been investigated.

The research in this work is limited to the two-dimensional incompressible turbulent flow.

The verification and validation of a new combination are conducted by several numerical examples. The new combination could be used to deal with more complicated turbulent flows.

The applications of the new combination to study basic and complex turbulent flow are also presented, which demonstrates its potential to solve more turbulent flows in nature and engineering.

This work carries out a great extension of S-FEM in simulations of fluid dynamics. The new combination is verified to be very effective in handling turbulent flows. The performances of S-FEM and FEM on turbulent flows were analyzed by several numerical examples. Superior results were found compared with existing results and experiments. Meanwhile, S-FEM has an advantage of accuracy in predicting boundary layer profile.

The purpose of this paper is to present a finite element approximation of the low Mach number equations coupled with radiative equations to account for radiative heat transfer. For high-temperature flows this coupling can have strong effects on the temperature and velocity fields.

The basic numerical formulation has been proposed in previous works. It is based on the variational multiscale (VMS) concept in which the unknowns of the problem are divided into resolved and subgrid parts which are modeled to consider their effect into the former. The aim of the present paper is to extend this modeling to the case in which the low Mach number equations are coupled with radiation, also introducing the concept of subgrid scales for the radiation equations.

As in the non-radiative case, an important improvement in the accuracy of the numerical scheme is observed when the nonlinear effects of the subgrid scales are taken into account. Besides it is possible to show global conservation of thermal energy.

The original contribution of the work is the proposal of keeping the VMS splitting into the nonlinear coupling between the low Mach number and the radiative transport equations, its numerical evaluation and the description of its properties.

A finite element model has been developed for the 3D simulation of the sintering of a single track during a selective laser sintering process (SLS). The model takes into account both the thermal and the sintering phenomena involved in the process. Owing to the continuous movement of the laser beam the model takes also into account the transient nature of the problem. This is transformed into a pseudo‐static one through a transformation of the coordinates system of the equations. Nevertheless, this transformation introduces a convective term into the heat equations that produces instabilities in the solution. These instabilities have been solved by using a stream upwind Petrov Galerkin (SUPG) strategy together with a shock capturing scheme. Finally, a fixed point strategy is used for the solution of the analysis. The model has been tested through the solution of some examples.

The purpose of this study is to propose an isogeometric analysis (IGA) approach for solving the Reynolds equation in textured piston ring cylinder liner (PRCL) contacts.

The texture region is accurately and conveniently expressed by non-uniform rational B-splines (NURBS) besides hydrodynamic pressure and the oil film density ratio is represented in this mathematical form. A quadratic programming method combined with a Lagrange multiplier method is developed to address the cavitation issue.

The comparison with the results solved by an analytical method has verified the effectiveness of the proposed approach. In the study of the PRCL contact with two-dimensional circular dimple textures, the solution of the IGA approach shows high smoothness and accuracy, and it well satisfies the complementarity condition in the case of cavitation presence.

This paper proposes an IGA approach for solving the Reynolds equation in textured PRCL contacts. Its novelty is reflected in three aspects. First, NURBS functions are simultaneously used to express the solution domain, texture shape, hydrodynamic pressure and oil density ratio. Second, the streamline upwind/Petrov–Galerkin method is adopted to create a weak form for the Reynolds equation that takes the oil density ratio as a first-order unknown variable. Third, a quadratic programming approach is developed to impose the complementarity conditions between the hydrodynamic pressure and the oil density ratio.

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and improving performances of the final products. This paper aims to present a numerical strategy for the simulation of dispersed-phase evolution for immiscible polymer blends in injection molding.

First, the dispersed-phase modeling is discussed in detail. Then the Maffettone–Minale model, affine deformation model, breakup model and coalescence statistical model are chosen for the dispersed-phase evolution. A general coupled model of microscopic morphological evolution and macroscopic flow field is constructed. Besides, a stable finite element simulation strategy based on pressure-stabilizing/Petrov–Galerkin/streamline-upwind/Petrov–Galerkin method is adopted for both scales.

Finally, the simulation results are compared and evaluated with the experimental data, suggesting the reliability of the presented numerical strategy.

The coupled modeling of dispersed-phase and complex flow field during injection molding and the tracing and simulation of droplet evolution during the whole process can be achieved.