Analysis of turbulent diffusion in the temperature variance dissipation rate equation

Results of a new direct numerical simulation (DNS) for the Rayleigh‐Bénard convection at Prandtl number Pr = 0.025 and Rayleigh number Ra = 100,000 are used to analyse the turbulent diffusion term in the transport equation for the temperature variance dissipation rate. These DNS results are also used to investigate the performance of statistical models for this turbulent diffusion term. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

扩散速度与组元的质量守恒方程*

在混合物流动中,某组元i的质量迁移速度(绝对速度)等于对流速度(牵连速度)与扩散速度(相对速度)之和.扩散速度——以及扩散系数——依对流速度取法之不同而不同.     

Bifurcation to Mean Flows in Convection

Convection with a strip plate in the middle is studied in this paper. Simultaneous instability of two convection modes of different vertical structures with a same horizontal wave number is possible in this system. It is found that the interaction of these two modes generates mean flows similar to those observed by Krishnamurti and Howard [9] in a turbulent convection experiment. Coupled nonlinear equations are derived for the amplitudes of the two modes. Traveling wave solutions and more complicated time-dependent solutions are also found near the onset of convection.     

Computation of the turbulent friction resistance of polymer solutions in pipes

We construct a nonlayer and a three-layer model for the effect of lowering of hydrodynamic resistance by polymer additives. When the nonlayer model is used for various pipe diameters, the results of the theory and experiments show satisfactory agreement and describe well the scale effect of the turbulent flows of polymer solutions. The three-layer model can be used to compute the resistance of turbulent flows with polymer additives, including the case of limiting reduction of hydrodynamic resistance. Two figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 137–142.     

Unstable Thermocapillary Flow at a Gas-Liquid Phase Boundary

We present results of thermocapillary experiments in the vicinity of a bubble under a heated wall. Thermocapillary convection is a flow along the interface of two fluids, which is caused by local gradients of the surface tensions σ. The aim of the present work is to study this flow phenomenon at higher Marangoni-numbers Mg. At sufficiently high values of Mg the flow exhibits oscillatory fluid motion and eventually becomes turbulent. For the detection of the flow velocity and temperature field, we applied a PIV method and a modified differential interferometer. In order to separate buoyancy effects from thermocapillary convection, we chose an experimental setup, where a bubble is positioned in a liquid matrix under a heated wall. We could observe various regimes of Marangoni flow, from steady flow over regular oscillating up to highly irregular oscillating flows at Mg up to 63,000. However, we also found unexpected stable flow regions and additional evaporation processes. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust heteroclinic cycles

Summary One phenomenon in the dynamics of differential equations which does not typically occur in systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust for symmetry-preserving perturbations and stable. Cycles have been observed in a number of simulations and experiments, for example in rotating convection between two plates and for turbulent flows in a boundary layer. Theoretically the existence of robust cycles has been proved in the unfoldings of some low codimension bifurcations and in the context of forced symmetry breaking from a larger to a smaller symmetry group. In this article we review the theoretical and the applied research on robust cycles.     

对流扩散方程在成品油顺序输送混油分析中的应用

本文研究了对流与扩散对成品油顺序输送混油过程的影响;推导了紊流条件下,描述混油过程的对流占优的扩散方程;将该方程分解为纯对流方程和纯扩散方程,分别应用特征线法和差分法求解,数值计算结果和实际操作经验相符,能很好地解释混油的形成和发展.     

On dispersion of settling particles from an elevated source in an open-channel flow

Longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a rough-bed surface is investigated numerically when the settling particles are released from an elevated continuous line-source. A combined scheme of central and four-point upwind differences is used to solve the steady turbulent convection–diffusion equation and the alternating direction implicit (ADI) method is adopted for the unsteady equation. It is shown how the mixing of settling particles is influenced by the ‘log-wake law’ velocity and the corresponding eddy diffusivity when the initial distribution of concentration is regarded as a line-source. The concentration profiles for the steady-state conditions agree well with the existing experimental data and some other numerical results when the settling velocity is zero. The behaviours of iso-concentration lines in the vertical plane for different releasing heights are studied in terms of the relative importance of convection, eddy diffusion and settling velocity.     

Simulation of turbulent thermal convection in complicated domains

To simulate turbulent flows in complicated enclosed three-dimensional domains a fast finite-volume high-order method is developed. In principle, the method is based on the Chorin–Temam scheme. The Poisson solver, which is applied to compute the pressure, uses the separation of variables together with capacitance matrix technique. The developed numerical method generally allows to use hexahedral computational meshes, which are non-equidistant in all three directions and non-regular in any two directions. The method was successfully used in three-dimensional Direct Numerical Simulations of turbulent high-Rayleigh-number thermal convection in cylindrical and parallelepiped domains with obstacles.     

On the nature of turbulence in Rayleigh-Benard convection

In the present paper, we suggest a numerical method for the analysis of the motion of a viscous incompressible fluid under the passage to the turbulent mode in Rayleigh-Benard convection. We show that one possible scenario of the onset of turbulence in the problem is given by a subharmonic cascade of bifurcations of stable two-dimensional tori.     

Mixed convection turbulent film condensation on a sphere

The present paper reports a research on condensation heat transfer of an isothermal sphere with an external flow of vapor. The high tangential velocity of the vapor flow is determined from potential flow theory. The transition criterion of the onset turbulence has been given in the local film Reynolds number (Re_Γ). An eddy diffusivity model along with an expression by [H. Kato, N.N. Shiwaki, M. Hirota, On the turbulent heat transfer by free convection from a vertical plate, Int. J. Heat Mass Transfer, 11(1968) 1117–1125] is used to model turbulence. And the local liquid–vapor interfacial shear which occurs for high velocity vapor flow across a sphere surface is defined by the Colburn analogy. The paper then presents analytical analysis for the local dimensionless film thickness and heat transfer characteristics for the film condensation. And a comparison with those generated by previous theoretical of laminar condensation is discussed. The comparison shows the heat transfer coefficient of turbulent film condensation is higher than laminar film condensation under the high vapor velocity.     

Existence and positivity of a system k-ε with a production term of the Rayleigh-Taylor type

In this paper, we study a modelization of the turbulence which allows us to have a control on the positivity of the kinetic turbulence energy k and the dissipation growth rate of the energy ε. We use for that purpose the maximum principle on a new system modelling the turbulence, written on the variables θ and φ first introduced by Lewandowski (θ = k/ε, φ = ε²/k³).Estimates on θ and φ are given for a turbulent system with a Rayleigh-Taylor type term under a hypothesis of low compressibility of the mean flow, which is more general than the hypothesis of Lewandowski.In a second part, we study a simpler convection diffusion system (the diffusion is a constant) in which there is still the Rayleigh-Taylor term. We show that the presence of this term gives greater solutions of the k, ε system, hence proving that these terms are turbulent kinetic energy production terms.     

Limits on the Transport of Heat and Momentum by Turbulent Convection with Large-Scale Flow

Under certain conditions, high-Rayleigh-number convection in a horizontal layer exhibits an organized pattern of large-scale flow superposed on an irregular structure of turbulent plumes. Bounds on the heat and momentum fluxes in such a flow, which provide upper estimates of the possible level of the large-scale flow, are presented.     

On the stabilizing effect of convection in three‐dimensional incompressible flows

We investigate the stabilizing effect of convection in three‐dimensional incompressible Euler and Navier‐Stokes equations. The convection term is the main source of nonlinearity for these equations. It is often considered destabilizing although it conserves energy due to the incompressibility condition. In this paper, we show that the convection term together with the incompressibility condition actually has a surprising stabilizing effect. We demonstrate this by constructing a new three‐dimensional model that is derived for axisymmetric flows with swirl using a set of new variables. This model preserves almost all the properties of the full three‐dimensional Euler or Navier‐Stokes equations except for the convection term, which is neglected in our model. If we added the convection term back to our model, we would recover the full Navier‐Stokes equations. We will present numerical evidence that seems to support that the three‐dimensional model may develop a potential finite time singularity. We will also analyze the mechanism that leads to these singular events in the new three‐dimensional model and how the convection term in the full Euler and Navier‐Stokes equations destroys such a mechanism, thus preventing the singularity from forming in a finite time. © 2008 Wiley Periodicals, Inc.     

From Disorder to Order August 2000

Recently the "turbulent sublayer" was explored using a shear flow idealization akin to L. N. Howard's study of turbulent thermal convection [ 2 ]. There, the growing diffusive layers were studied to determine when they became unstable. Here, that work is extended to the first transitions of Couette and Poiseuille parallel flow. The merging boundary layers of the presumed flows pose a linear nonautonomous problem of following the time dependent first Lyapunov vector. As in Blasius flow, the first results emerge from perturbation theory, with corrections for streamwise evolution of the velocity profiles. The estimated critical Reynolds numbers for [back] transition from disorder to the laminar state are within 15% of the observations.     

Numerical analysis of two ensemble eddy viscosity numerical regularizations of fluid motion

This report analyzes an efficient ensemble regularization algorithm for under‐resolved and convection dominated flows (including ones at higher Reynolds numbers). Computing an ensemble simultaneously allows each realization to access ensemble data. This allows use of means and fluctuations in regularizations used for each realization. The combined approach of ensemble time stepping and ensemble regularizations allows direct calculation of the turbulent viscosity coefficient and gives an unconditionally stable algorithm. It also suggests reconsidering an old but not as well‐developed definition of the mixing length. This mixing length vanishes at solid walls without van Driest damping, increases stability, and improves flow predictions in our preliminary tests. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 630–651, 2015     

A stochastic method to account for the ambient turbulence in Lagrangian Vortex computations

This paper describes a detailed implementation of the Synthetic Eddy Method (SEM) initially presented in Jarrin et al. (2006) applied to the Lagrangian Vortex simulation. While the treatment of turbulent diffusion is already extensively covered in scientific literature, this is one of the first attempts to represent ambient turbulence in a fully Lagrangian framework. This implementation is well suited to the integration of PSE (Particle Strength Exchange) or DVM (Diffusion Velocity Method), often used to account for molecular and turbulent diffusion in Lagrangian simulations. The adaptation and implementation of the SEM into a Lagrangian method using the PSE diffusion model is presented, and the turbulent velocity fields produced by this method are then analysed. In this adaptation, SEM turbulent structures are simply advected, without stretching or diffusion of their own, over the flow domain. This implementation proves its ability to produce turbulent velocity fields in accordance with any desired turbulent flow parameters. As the SEM is a purely mathematical and stochastic model, turbulent spectra and turbulent length scales are also investigated. With the addition of variation in the turbulent structures sizes, a satisfying representation of turbulent spectra is recovered, and a linear relation is obtained between the turbulent structures sizes and the Taylor macroscale. Lastly, the model is applied to the computation of a tidal turbine wake for different ambient turbulence levels, demonstrating the ability of this new implementation to emulate experimentally observed tendencies.