Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface

The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.     

Turbulent Flow Around Fluid–Porous Interfaces Computed with a Diffusion-Jump Model for <Emphasis Type="Italic">k</Emphasis> and <Emphasis Type="Italic">ε</Emphasis> Transport Equations

Flow over vegetation and bottom of rivers can be characterized by some sort of porous structure of irregular surface through which a fluid permeates. Also, in engineering systems, one can have components that make use of a working fluid flowing over irregular layers of porous material. This article presents numerical solutions for such hybrid medium, considering here a channel partially filled with a flat porous layer saturated by a fluid flowing in turbulent regime. One unique set of transport equations is applied to both the regions. A diffusion-jump model for both the turbulent kinetic energy and its dissipation rate, across the interface, is presented and discussed upon. The discretization steps taken for numerically accommodating such model in the system of algebraic equations are presented. Numerical results show the effects of Reynolds number, porosity, and permeability on mean and turbulence fields. Results indicate that when negative values for the stress jump coefficient are applied, the peak of the turbulent kinetic energy distribution occurs at the macroscopic interface.     

Direct numerical simulation of a freely decaying turbulent interfacial flow

Whereas Large Eddy Simulation (LES) of single-phase flows is already widely used in the CFD world, even for industrial applications, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed data base from direct numerical simulation (DNS) of two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. This work is a first contribution in the study of the interface/turbulence interaction in the configuration where the interface is widely deformed and where both phases are resolved by DNS. To do this, the interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (HIT) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. Comparisons with existing theories built on wall-bounded or free-surface turbulence are carried out. To understand energy transfers between the interfacial energy and the turbulent one, PDFs of the droplet sizes distribution are calculated. An energy budget is carried out and turbulent statistics are performed including the distance to the interface as a parameter. A spectral analysis is achieved to highlight the energy transfer between turbulent scales of different sizes. The originality of this work is the study of the interface/turbulence interactions in the case of a widely deformed interface evolving in a turbulent flow.     

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

A qualitative assessment of the role of a viscosity depending on the third invariant of the rate-of-deformation tensor upon turbulent non-Newtonian flow

The numerical simulation of some non-Newtonian effects in wall and wall-free turbulent flows, such as drag reduction in pipe flows or the decrease in transverse normal Reynolds stresses, has been attempted in the past with a limited degree of success on the basis of modified wall functions applied to traditional turbulence models (k–ε), rather than through more realistic rheological constitutive equations. In this work, it is qualitatively shown that if the viscosity function of a generalised Newtonian fluid is assumed to depend on the third invariant of the rate of deformation tensor, there is an increase of the viscous diffusion terms, but especially, of the dissipation of turbulence kinetic energy by a factor equal to the Trouton ratio of the fluid, divided by the Trouton ratio of the solvent, thus indicating a possible way to improve rheological–turbulence modelling.     

A coupled boundary element–finite difference model of surface wave motion over a wall turbulent flow

An effective numerical technique is presented to model turbulent motion of a standing surface wave in a tank. The equations of motion for turbulent boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM–finite difference technique is used to model the wave motion and the corresponding boundary layer flow. A mixing‐length theory is used for turbulence modelling. The model results are in good agreement with previous physical and numerical experiments. Although the technique is presented for a standing surface wave, it can be easily applied to other free surface problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Combined action of anticonvection and thermocapillarity in two- and three-layer systemsAction simultanée d'anticonvection et de thermocapillarité dans des systèmes multi-couches

Anticonvection generated by the joint action of the external heating and heat sources (sinks) on the interface in the layers with finite thicknesses is studied. Anticonvective structures in fluid systems subject to the anticonvective instability only in the presence of heat sources (sinks) on the interface have been obtained. The nonlinear regimes of anticonvection in the system of three immiscible viscous fluids heated from above are investigated. The specific phenomena caused by direct and indirect interaction of anticonvective and thermocapillary mechanisms of instability are considered. In particular, different oscillatory configurations where anticonvection arises mainly near the upper interface and thermocapillary convection appears mainly near the lower interface, have been studied. To cite this article: I.B. Simanovskii, C. R. Mecanique 332 (2004).     

Vortices for computing: the engines of turbulence simulation

Vortices have been described as the “sinews of turbulence”. They are also, increasingly, the computational engines driving numerical simulations of turbulence. In this paper, I review some recent advances in vortex-based numerical methods for simulating high Reynolds number turbulent flows. I focus on coherent vortex simulation, where nonlinear wavelet filtering is used to identify and track the few high energy multiscale vortices that dominate the flow dynamics. This filtering drastically reduces the computational complexity for high Reynolds number simulations, e.g. by a factor of 1000 for fluid–structure interaction calculations (Kevlahan and Vasilyevvon in SIAM J Sci Comput 26(6):1894–1915, 2005). It also has the advantage of decomposing the flow into two physically important components: coherent vortices and background noise. In addition to its computational efficiency, this decomposition provides a way of directly estimating how space and space–time intermittency scales with Reynolds number, Re ^α . Comparing α to its non-intermittent values gives a realistic Reynolds number upper bound for adaptive direct numerical simulation of turbulent flows. This direct measure of intermittency also guides the development of new mathematical theories for the structure of high Reynolds number turbulence.     

A numerical experiment on the interaction between a film and a turbulent jet

This work is focused on the study of the impingement of a turbulent plane jet on a moving film. A computational fluid dynamics code has been used to simulate the interaction between the turbulent plane jet and the moving film. Since the problem of coupling between turbulence and free surface flow is poorly understood and experiments in this problem are difficult to carry out, this new numerical tool has been designed to give insight into global and local parameters of the free surface flow. To cite this article: D. Lacanette et al., C. R. Mecanique 333 (2005).     

A hybrid Lagrangian–Eulerian particle‐level set method for numerical simulations of two‐fluid turbulent flows

A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd.     

Experiments on entrainment in an annulus with and without velocity gradient across the density interface

The entrainment process in a two layer density stratified fluid column was studied experimentally by imposing external shear stress on one or both layers. The experiments have been conducted in an annular tank containing two water layers of different salt concentration and the shear stress was applied by means of rotating screens. The following quantities were measured: the screen velocity (which was kept constant during each experiment), the stress at the upper screen, and vertical profiles of circumferential velocity and density at different radial locations. When equal stress was imposed at the surface of the upper layer and at the bottom of the lower layer, entrainment took place from the two sides of the density interface at equal rate so that the interface was stationary in the central position between the two screens and there was no velocity gradient across the interface. The dependence of the entrainment coefficient on Richardson number obtained in these experiments was similar in form to that obtained in the shear-free experiments with an oscillating grid (e.g. Nokes 1988). When a shear stress was applied at the upper surface only, the upper layer depth increased with time and a velocity gradient existed at the interface. The influence of the interfacial velocity gradient on the entrainment rate was studied by comparing the rates obtained with and without this velocity gradient. The entrainment rates were approximately the same for high values of the Richardson number while at low Richardson number the entrainment rate was much larger when a velocity gradient existed across the interface. The main results of this work are as follows:

1. Despite the curved geometry of the annular system, the dependence of the entrainment coefficient on Richardson number for shear-free interface experiments was found to be similar in form to that obtained for oscillating grid experiments.
2. The entrainment across the interface is due to turbulent energy generated at some distance from the interface by an external source (i.e. shear stress induced by a screen) and due to turbulence produced locally at the interface by a velocity gradient. The relative contribution of each turbulence source to the total entrainment was found to depend on the stability of the interface.

     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of near-wall turbulence enhancement on the mechanisms of particle deposition

The modification of deposition mechanisms of small particles in wall turbulence due to enhanced near-wall fluctuations is presented. The direct numerical simulation database of turbulent air flow over a water surface populated by gravity-capillary waves of small wave slope was used to mimic the enhancement in fluctuation intensity. Lagrangian tracking of particles is performed under the assumption of one-way coupling between the particles and the flow. Two sets of particles have been considered with inertial response times of 5 and 15, respectively, normalized using the friction velocity at the air–water interface and the kinematic viscosity of air. Compared to wall-bounded flow, the particle deposition rates on the interface were found to be considerably higher; specifically for the low-inertia particles, an eightfold increase was observed. The deposition rate for particles of higher inertia increased by only 60%. The correlation characterizing particle deposition rates for wall-bounded flows, where the deposition rate is proportional to the square of the particle response time, was found to be invalid for the flow with enhanced near-wall turbulence. Comparison with experimental results on particle deposition onto rough walls showed better correlation. Depositing particles were divided into free-flight and diffusional deposition populations. Since the primary effect of the interfacial waves is to increase the turbulence intensity in the near-interface region with high particle concentration, a remarkable increase in diffusional deposition is observed. As in wall-bounded flows, diffusional deposition is seen to be the dominant mechanism of deposition. The free-flight mechanism, where particles acquire velocities high enough to travel directly to the interface, remains unaffected by enhanced near-wall velocity fluctuations.     

Experiments on the spreading of shear-free turbulence under the influence of confinement and rotation

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Günther (Fluid Dyn Res 33:453–476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

Air flow aerodynamic on a wall-mounted hemisphere for various turbulent boundary layers

Air flow field around a surface-mounted hemisphere of a fixed height for two different turbulent boundary layers (thin and thick) are investigated experimentally and numerically. Flow measurements are performed in a wind tunnel using hot-wire anemometer and streamwise component of velocity fluctuation are calculated using a special developed program of the hardware system. Mean surface pressure coefficients and velocity field for the same hemisphere are determined by the numerical simulation. Turbulent flow field and intensity are measured for two types of boundary layers and compared at various sections in both streamwise and spanwise directions. Numerical scheme based on finite volume and SIMPLE algorithm is used to treat pressure and velocity coupling. Studies are performed for Reynolds number, Re_H = 32,000. Based on the numerical simulation using RNG k–ε turbulence model, flow pathlines, separation region and recirculation area are determined for the two types of turbulent boundary layer flows and complex flow field and recirculation regions are identified and presented graphically.     

Corrélations de vitesse lagrangienne et échelle intégrale temporelle en simulation des grandes échellesLagrangian velocity correlations and timescales by a large-eddy simulation

Velocity correlations and Lagrangian timescales are studied numerically by means of a direct numerical simulation (DNS) and a large-eddy simulation (LES) coupled with a subgrid Lagrangian stochastic model, in the case of a homogeneous and isotropic turbulence. A Langevin model is used to determine the subgrid component of the velocity of fluid particles. Numerical results of Lagrangian velocity correlations and timescales are presented. These quantities play an important role in turbulent mixing and scalar dispersion. To cite this article: G. Wei et al., C. R. Mecanique 334 (2006).     

Finite element methods for a class of continuum models for immiscible flows with moving contact lines

In this paper, we present a finite element method for two‐phase incompressible flows with moving contact lines. We use a sharp interface Navier–Stokes model for the bulk phase fluid dynamics. Surface tension forces, including Marangoni forces and viscous interfacial effects, are modeled. For describing the moving contact lines, we consider a class of continuum models that contains several special cases known from the literature. For the whole model, describing bulk fluid dynamics, surface tension forces, and contact line forces, we derive a variational formulation and a corresponding energy estimate. For handling the evolving interface numerically, the level‐set technique is applied. The discontinuous pressure is accurately approximated by using a stabilized extended finite element space. We apply a Nitsche technique to weakly impose the Navier slip conditions on the solid wall. A unified approach for discretization of the (different types of) surface tension forces and contact line forces is introduced. Results of numerical experiments are presented, which illustrate the performance of the solver. Copyright © 2016 John Wiley & Sons, Ltd.     

Correlations for modeling transitional boundary layers under influences of freestream turbulence and pressure gradient

This paper presents mathematical expressions for two significant parameters which control the onset location and length of transition in the γ–Re_θ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. In: ERCOFTAC International Symposium on Engineering Turbulence Modelling and Measurements]. The expressions are formulated and calibrated by means of numerical experiments for predicting transitional boundary layers under the influences of freestream turbulence and pressure gradient. It was also found that the correlation for transition momentum thickness Reynolds number needs only to be expressed in terms of local turbulence intensity, so that the more complex form that includes pressure gradient effects is unnecessary. Transitional boundary layers on a flat plate both with and without pressure gradients are employed to assess the performance of these two expressions for predicting the transition. The results show that the proposed expressions can work well with the model of Menter et al. (2005).