Numerical analysis of a corrected Smagorinsky model

The classical Smagorinsky model's solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity. This model has recently been corrected to incorporate this flow and still be well-posed. Herein we first develop some basic properties of the corrected model. Next, we perform a complete numerical analysis of two algorithms for its approximation. They are tested and proven to be effective.     

Low and moderate Reynolds number transient flow simulations using space filtered Navier-Stokes equations

In this study, low and moderate Reynolds number flow problems in the laminar range are solved numerically with grids that do not resolve all the significant scales of motion. Spatial averaging or filtering of the Navier-Stokes equations and Taylor series approximations to the filtered advective terms are used in order to account for the effects of the unresolved or subgrid scales on the resolved scales. Numerical experiments with a transient 2-D lid driven cavity flow problem, using a penalty method Galerkin finite element code, show that this approach enhances the momentum transfer properties of the numerical solution, eliminates 2Δx type oscillations, and enables the use of coarser grids. The significance and order of the terms that describe the interaction between the resolved and the subgrid scales is studied and the success of the series approximations to these terms is demonstrated. © 1994 John Wiley & Sons, Inc.     

Large Scale Oscillations in the Continuous Casting Process

Long-term oscillations of the flow in a continuous casting tundish are investigated numerically and experimentally. The numerical model is based on the Reynolds averaged Navier-Stokes equations (URANS). A comparison between numerical results and experimental data from a water model is presented. Frequencies due to long-term oscillations are resolved in the simulation. These frequencies are in satisfactory agreement with the experimental results of LDA measurements. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow models and numerical schemes for single/two-phase transient flow in one dimension

In the two-phase flow field, a traditional mathematical model for simulating the transition of severe slugging flow presents a challenge when liquid slugs completely block pipelines. Accordingly, an advanced and practical slug model that is derived from a mixture model associated with a slip closure is essential to solving the problem in cooperation with the two-fluid model. The model can offset numerical instability that arises from the discontinuous function of the friction factor across the transition from one flow pattern to the other. Two numerical schemes, the non-iterative and the iterative, are developed, and the proposed schemes can stably predict the transient problems under the Courant–Friedrichs–Lewy (CFL) condition for semi-implicit/implicit schemes. In the present work, pressure transients produced by a complex phenomenon, named water hammer effect, are captured using the single-phase flow model in one-dimension to verify the applicability of the numerical schemes and the friction factor model. At last, the analysis of the two-phase transient flow in a pipeline-riser system indicates that the significant advantage of the present schemes is the robustness that the numerical prediction of the severe slugging behaviour is accurate and stable.     

Up-scaled Dynamical Model of the Human Vocal Folds

Flow and volume flow measurements are carried out through a driven 3:1 up–scaled glottis model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical solution of transonic and subsonic flow of compressible inviscid and viscous fluid

The work presents two numerical solutions of compressible flows problems with high and very low Mach numbers. Both problems are numerically solved by finite volume method and the explicit MacCormack scheme using a grid of quadrilateral cells. Moved grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian–Eulerian method. In the first case, inviscid transonic flow through cascade DCA 8% is presented and the numerical results are compared to experimental data. The second case, numerical solution of unsteady viscous flow in the channel for upstream Mach number M_∞=0.012 and frequency of the wall motions 100 Hz is presented. The unsteady case can represent a simplified model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds to the human vocal tract. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows

The current research aims at deriving a one-dimensional numerical model for describing highly transient mixed flows. In particular, this paper focuses on the development and assessment of a unified numerical scheme adapted to describe free-surface flow, pressurized flow and mixed flow (characterized by the simultaneous occurrence of free-surface and pressurized flows). The methodology includes three steps. First, the authors derived a unified mathematical model based on the Preissmann slot model. Second, a first-order explicit finite volume Godunov-type scheme is used to solve the set of equations. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The key results of the paper are the development of an original negative Preissmann slot for simulating sub-atmospheric pressurized flow and the derivation of an exact Riemann solver for the Saint-Venant equations coupled with the Preissmann slot.     

Numerical simulation of the filling behavior of a Non-Newtonian Fluid

A numerical model for free surface flows of non-newtonian liquids which are injected into a cavity is presented. These flows are regarded as a basic model of injection molding. Model experiments of the injection process are performed with a water-based gel. The flow equations are integrated according to the finite-volume-method. The volume of fluid method (VoF) is employed in order to describe the free surface flow of two incompressible phases, the phase interface is resolved by the method of geometric reconstruction. The Herschel-Bulkley model is used in order to describe shear-thinning behavior of the molding material and the effects of a yielding point. Different patterns of the filling flow depending on the injection parameters are evident in the experiment and the simulation. They are characterized and arranged with respect to the similarity parameters of the flow. Again, the results of the simulation are found to agree well with the experimental observations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semi‐implicit schemes for transient Navier–Stokes equations and eddy viscosity models

This study presents two computational schemes for the numerical approximation of solutions to eddy viscosity models as well as transient Navier–Stokes equations. The eddy viscosity model is one example of a class of Large Eddy Simulation models, which are used to simulate turbulent flow. The first approximation scheme is a first order single step method that treats the nonlinear term using a semi‐implicit discretization. The second scheme employs a two step approach that applies a Crank–Nicolson method for the nonlinear term while also retaining the semi‐implicit treatment used in the first scheme. A finite element approximation is used in the spatial discretization of the partial differential equations. The convergence analysis for both schemes is discussed in detail, and numerical results are given for two test problems one of which is the two dimensional flow around a cylinder. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

A corrected smoothed particle hydrodynamics method for solving transient viscoelastic fluid flows

In this work, a corrected smoothed particle hydrodynamics (CSPH) method is proposed and extended to the numerical simulation of transient viscoelastic fluid flows due to that its approximation accuracy in solving the Navier–Stokes equations is higher than that of the smoothed particle hydrodynamics (SPH) method, especially near the boundary of the domain. The CSPH approach comes with the idea of combining the SPH approximation for the interior particles with the modified smoothed particle hydrodynamics (MSPH) method for the exterior particles, this is because that the later method has higher accuracy than the SPH method although it also needs more computational cost. In order to show the validity of CSPH method to simulate unsteady viscoelastic flows problems, the planar shear flow problems, including transient Poiseuille, Couette flow and transient combined Poiseuille and Couette flow for the Oldroyd-B fluid are solved and compared with the analytical and SPH results. Subsequently, the general viscoelastic fluid based on the eXtended Pom–Pom (XPP) model is numerically investigated and the viscoelastic free surface phenomena of impacting drop are simulated by the CSPH for its extended application and the purpose of illustrating the ability of the proposed method. The numerical results are presented and compared with available solutions, which shows a very good agreement. All the numerical results show the higher accuracy and better stability of the CSPH than the SPH, especially for larger Weissenberg numbers.     

Modelling free surfaces in oscillating pipe flows

An oscillating pipe flow with a free surface is investigated numerically and experimentally. The pipe diameter is 12mm. Due to this small diameter capillary forces play an important role. Therefore special attention has to be paid to the flow field near the free surface. The numerical model is based on the fundamental flow equations. The free surface is resolved according to the volume-of-fluid method. The model equations are solved on a moving grid. In the experiment, pictures of the flow field are taken near the free surface. The effects occuring near the interface will be presented here. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixing in low rate flows

By means of a single transport equation, solutions to a numerical model of the mixing of two fluids through a porous region are obtained. The flow rates are low and constant and the fluids are separated upstream by an impermeable barrier. The region over which the mixing takes place is finite. Both steady state and transient solutions are evaluated and the results indicate that diffusive mixing occurs around the barrier against the flow.     

Incompressible flows in elastic domains: an immersed boundary method approach

This study illustrates how the immersed boundary method may be applied to perform the numerical simulation of incompressible flows in two-dimensional domains bounded by elastic boundaries. It presents the basic intermediate steps involved in the derivation of a solution methodology, from a scientific motivation to the numerical results, which can be applied for both steady and transient problems, even when the boundaries have an arbitrary shape. Its motivation, briefly presented, was borne in a bioengineering problem: the numerical simulation of the performance of ventricular assist devices. The mathematical model is composed by the Navier–Stokes equations, where the forcing term contains singular forces which arise from the elastic stresses acting on the boundaries. The incompressibility constraint is modified to introduce the inflow and outflow conditions into the problem through the use of sources and sinks. The methodology is applied to simulate two problems: the steady flow between two parallel plates, for which the exact solution is known and can be used to validate the approach, and the periodic flow in a winding channel, a transient problem in a non-trivial domain.     

层流管流入口压力突然升高引起的水力瞬变的理论分析

研究了层流状态下管道入口压力突然升高引起的水力瞬变过程,建立了瞬态压力分布的偏微分方程和初边值条件,用分离变量法求得了压力的理论解．根据压力和流量间的约束关系,得到了关于流量的偏微分方程和初边值条件,用分离变量求得了瞬变过程流量分布理论解．最后,用特征线法(MOC)对该问题进行了数值求解,理论解和数值解吻合很好．     

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

Coupled fluid-solid thermal interaction modeling for efficient transient simulation of biphasic water-steam energy systems

This paper proposes a fluid-solid coupled finite element formulation for the transient simulation of water-steam energy systems with phase change due to boiling and condensation. As it is commonly assumed in the study of thermal systems, the transient effects considered are exclusively originated by heat transfer processes. A homogeneous mixture model is adopted for the analysis of biphasic flow, resulting in a nonlinear transient advection-diffusion-reaction energy equation and an integral form for mass conservation in the fluid, coupled to the linear transient heat conduction equation for the solid. The conservation equations are approximated applying a stabilized Petrov-Galerkin FEM formulation, providing a set of coupled nonlinear equations for mass and energy conservation. This numerical model, combined with experimental heat transfer coefficients, provides a comprehensive simulation tool for the coupled analysis of boiling and condensation processes. For the treatment of enthalpy discontinuities traveling with the flow, a novel explicit-implicit time integration method based on Crank-Nicolson scheme is proposed, analyzing its accuracy and stability properties. To reduce problem size and enhance numerical efficiency, a modal superposition method with balanced truncation is applied to the solid equations. Finally, different example problems are solved to demonstrate the capabilities, flexibility and accuracy of the proposed formulation.     

Dynamic properties of wing panels made of composite materials

The dynamic characteristics of an elastic wing panel made of composite material are investigated in relation to the transient processes in a gas flow. The problem is solved using the geometrically nonlinear equations of shallow orthotropic shells and the numerical methods of linearized nonsteady aerodynamics. The displacements are determined by a finite-difference method and the aerodynamic load intensity by means of a model of a thin lifting surface. The numerical results are presented in the form of graphs reflecting the laws of deformation of the middle surface of the panel and pressure distribution and their development with time. Curves characterizing the motion of individual points in relation to the parameters reflecting the anisotropic properties of the panel are also constructed.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 662–669, July–August, 1974.     

幂律流体在分形介质中不定常椭圆渗流

以椭圆渗流模型为基础,得到了分形油藏中,垂直裂缝井的幂律型非牛顿流体的定常渗流的压力分布公式和产量公式;并用数值差分的方法研究了分形油藏中,垂直裂缝井的不定常渗流,分析了分形参数对不定常压力的影响;同时从平均质量守恒方程出发,得到了相应的不定常渗流的近似解析解。分析表明:用椭圆渗流模型研究垂直裂缝井的渗流,大大简化了渗流问题的复杂性。     

Numerical modelling of free surface flows in metallurgical vessels

A numerical model for simulating the transient behaviour of multi-fluid problems defined in 2D rectangular and cylindrical geometries is presented. The model uses a piecewise linear volume tracking scheme, and maintains sharp interfaces and captures fine-scale flow phenomena such as fragmentation and coalescence. The numerical model was applied to four problems of pyrometallurgical relevance – entrainment of matte in the flow of slag during skimming operations, splash resulting from a drop impinging on a bath, bubble rise in a liquid bath, and top-submerged gas injection. The numerical predictions are in good agreement with the published experimental results. The simulation of top-submerged gas injection showed, in detail, the phenomena of bubble formation, bubble rise, and splash drop formation and recoalescence with the bath. Data useful for engineering purposes such as pressure traces and time-averaged flow fields were obtained, allowing assessment of splash behaviour for given gas injection conditions. The numerical model has been shown to be versatile in being able to adapt to a wide range of multi-phase flow problems.     

Flow-induced anisotropic viscosity in short fiber reinforced polymers

The commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh-Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth-order fiber orientation tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)