An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k_SGS, containing a production term proportional to the square root of k_SGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k_SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k_SGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k_SGS transport equation. In the MTS model, the SGS turbulence energy, k_es, estimated by filtering the instantaneous flow field is used. Since the k_es approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional k_SGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.     

A scaling analysis for point–particle approaches to turbulent multiphase flows

Simple dimensional arguments are used in establishing three different regimes of particle time scale, where explicit expression for particle Reynolds number and Stokes number are obtained as a function of nondimensional particle size (d/η)$(d/\eta )$ and density ratio. From a comparative analysis of the different computational approaches available for turbulent multiphase flows it is argued that the point–particle approach is uniquely suited to address turbulent multiphase flows where the Stokes number, defined as the ratio of particle time scale to Kolmogorov time scale (_τp/_τk)$({\tau }_p/{\tau }_k)$, is greater than 1. The Stokes number estimate has been used to establish parameter range where point–particle approach is ideally suited. The point–particle approach can be extended to handle “finite-sized” particles whose diameter approach that of the smallest resolved eddies. However, new challenges arise in the implementation of Lagrangian–Eulerian coupling between the particles and the carrier phase. An approach where the inter-phase momentum and energy coupling can be separated into a deterministic and a stochastic contribution has been suggested.     

A modular RANS approach for modelling laminar–turbulent transition in turbomachinery flows

In this study we propose a laminar–turbulent transition model, which considers the effects of the various instability modes that exist in turbomachinery flows. This model is based on a K–ω–γ three-equation eddy-viscosity concept with K representing the fluctuating kinetic energy, ω the specific dissipation rate and γ the intermittency factor. As usual, the local mechanics by which the freestream disturbances penetrate into the laminar boundary layer, namely convection and viscous diffusion, are described by the transport equations. However, as a novel feature, the non-local effects due to pressure diffusion are additionally represented by an elliptic formulation. Such an approach allows the present model to respond accurately to freestream turbulence intensity properly and to predict both long and short bubble lengths well. The success in its application to a 3-D cascade indicates that the mixed-mode transition scenario indeed benefits from such a modular prediction approach, which embodies current conceptual understanding of the transition process.     

Euler–Euler large eddy simulations for dispersed turbulent bubbly flows

In this paper we present detailed Euler–Euler Large Eddy Simulations (LES) of dispersed bubbly flow in a rectangular bubble column. The motivation of this study is to investigate the potential of this approach for the prediction of bubbly flows, in terms of mean quantities. The physical models describing the momentum exchange between the phases including drag, lift and wall force were chosen according to previous experiences of the authors. Experimental data, Euler–Lagrange LES and unsteady Euler–Euler Reynolds-Averaged Navier–Stokes results are used for comparison. It is found that the present model combination provides good agreement with experimental data for the mean flow and liquid velocity fluctuations. The energy spectrum obtained from the resolved velocity of the Euler–Euler LES is presented as well.     

A compressible two-layer model for transient gas–liquid flows in pipes

This work is dedicated to the modeling of gas–liquid flows in pipes. As a first step, a new two-layer model is proposed to deal with the stratified regime. The starting point is the isentropic Euler set of equations for each phase where the classical hydrostatic assumption is made for the liquid. The main difference with the models issued from the classical literature is that the liquid as well as the gas is assumed compressible. In that framework, an averaging process results in a five-equation system where the hydrostatic constraint has been used to define the interfacial pressure. Closure laws for the interfacial velocity and source terms such as mass and momentum transfer are provided following an entropy inequality. The resulting model is hyperbolic with non-conservative terms. Therefore, regarding the homogeneous part of the system, the definition and uniqueness of jump conditions is studied carefully and acquired. The nature of characteristic fields and the corresponding Riemann invariants are also detailed. Thus, one may build analytical solutions for the Riemann problem. In addition, positivity is obtained for heights and densities. The overall derivation deals with gas–liquid flows through rectangular channels, circular pipes with variable cross section and includes vapor–liquid flows.     

A priori study for the modelling of velocity–interface correlations in the stratified air–water flows

This work concerns the modelling of stratified two-phase turbulent flows with interfaces. We consider an equation for an intermittency function $\alpha (\mathbf{x}\text{,}t)$ which denotes the probability of finding an interface at a given time t and a given point $\mathbf{x}$. In Wacławczyk and Oberlack (2011) a model for the unclosed terms in this equation was proposed. Here, we investigate the performance of this model by a priori tests, and finally, based on the a priori data discuss its possible modification and improvements.     

A k–ℓ turbulence closure sensitized to non-simple shear flows

This paper introduces a two-equation turbulence model sensitized to deviations from simple shear flows. The closure is topography-parameter-free and is based on solving transport equations for the turbulence kinetic energy (k) and the turbulence length-scale (?). Brief model derivation details are given and test cases are presented to compare the model's performance to other closures and to experimental data. The flow examples demonstrate the advantage of the k–? model in non-simple shear flows.     

Closure proposals for the tracking of turbulence-agitated gas–liquid interfaces in stratified flows

The present work focuses on the formulation of new modelling approaches to ensemble-averaged equation for the interface tracking in stratified two-phase flow regime with separated gas and liquid layers. The model aims to represent the influence of the unresolved part of the surface. The modelling constants have been estimated based on the k–? model and the empirical observations of Brocchini and Peregrine (2001a) for the air–water flows. The new modelling proposal was implemented numerically for the 1D case. Results of the simulations are presented in the paper.     

A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows (USM- model), combining the unified second-order moment two-phase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM- model is also better than the k--kp- model and the k--kp-p- model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.The project supported by the Special Funds for Major State Basic Research of China (G-1999-0222-08), the National Natural Science Foundation of China (50376004), and Ph.D. Program Foundation, Ministry of Education of China (20030007028)     

Time–space characteristics of stratified shear layer from UVP measurements

The stratified shear layer flow pattern involves a fresh water layer flowing over a salted water one. The instabilities arising due to velocity gradients are mainly convective and thus evolve in time and space during their downstream propagation. This work was carried out within the framework of a study on the interaction between fresh water and seawater in the estuaries of rivers, where the main part of the physicochemical and biological phenomena occurs under the control of hydrodynamic conditions. The spatio-temporal velocity profile measurement by the ultrasonic Doppler method is well adapted to the stability analysis of such flows. It allows a comparison between the experimental wave properties and the theoretical results given by a linear temporal approach extended to the spatial point of view.     

Velocity–pressure correlation measurements in complex free shear flows

Simultaneous measurements of fluctuating velocity and pressure were performed in various turbulent free shear flows including a turbulent mixing layer and the wing-tip vortex trailing from a NACA0012 half-wing. Two different methods for fluctuating static pressure measurement were considered: a direct method using a miniature Pitot tube and an indirect method where static pressure was calculated from total pressure. The pressure obtained by either of these methods was correlated with the velocity measured by an X-type hot-wire probe. The results from these two techniques agreed with each other in the turbulent mixing layer. In the wing-tip vortex case, however, some discrepancies were found, although overall characteristics of the pressure-related statistics were adequately captured by both methods.     

From stratified wakes to rotor–stator flows by an SVV–LES method

We extend a large-eddy simulation (LES) methodology, based on using the spectral vanishing viscosity (SVV) method to stabilize spectral collocation approximations, from the Cartesian to the cylindrical geometry. The capabilities of the SVV–LES approach are illustrated for two very different physical problems: (1) the influence of thermal stratification on the wake of a cylinder, and (2) the instabilities that develop in transitional and fully turbulent rotor–stator flows.     

A reaction–diffusion model for competing languages

The extinction of many of the world’s minority languages is of great concern as language death can lead to the irrevocable loss of cultural information. This often occurs through a process of language shift, where individuals switch from speaking one language to a different, more dominant, language. To prevent the loss of language, it is necessary to determine whether language loss is inevitable or if languages can coexist. We address this question by constructing a nonlinear system of reaction–diffusion equations to model the spread of two competing languages, u and v, which vary temporally and spatially. Language u is assumed to confer a relative status advantage to its speakers, thus individuals may convert from language v to language u. The four constant system equilibria are found. Instability and stability conditions are found for each equilibrium. We conclude that the coexistence of both languages u and v is globally stable, subject to certain constraints on the growth rate of each language and the initial values of both u and v.     

Relation of entropy generation to wall ‘laws’ for turbulent flows

For non-dimensional pressure gradients sufficiently low and Reynolds numbers sufficiently high for the constant shear stress approximation to be valid at the first node of a turbulent wall layer computation, relationships for entropy generation rates are applied to popular wall ‘laws’. The resulting observations lead to a simple approach for evaluating the entropy generation rate per unit area in a computational fluid dynamics calculation for situations which satisfy this approximation.     

A thermo-viscoelastic–viscoplastic–viscodamage constitutive model for asphaltic materials

A temperature-dependent viscodamage model is proposed and coupled to the temperature-dependent Schapery’s nonlinear viscoelasticity and the temperature-dependent Perzyna’s viscoplasticity constitutive model presented in Abu Al-Rub et al., 2009, Huang et al., in press in order to model the nonlinear constitutive behavior of asphalt mixes. The thermo-viscodamage model is formulated to be a function of temperature, total effective strain, and the damage driving force which is expressed in terms of the stress invariants of the effective stress in the undamaged configuration. This expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth. A systematic procedure for obtaining the thermo-viscodamage model parameters using creep test data at different stress levels and different temperatures is presented. The recursive-iterative and radial return algorithms are used for the numerical implementation of the nonlinear viscoelasticity and viscoplasticity models, respectively, whereas the viscodamage model is implemented using the effective (undamaged) configuration concept. Numerical algorithms are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The model is then calibrated and verified by comparing the model predictions with experimental data that include creep-recovery, creep, and uniaxial constant strain rate tests over a range of temperatures, stress levels, and strain rates. It is shown that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions.     

A void–crack nucleation model for ductile metals

A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.