基于k-ε模型模拟平衡态大气边界层的比较研究

平衡态大气边界层的准确模拟是计算风工程领域的基础性难题,也是研究热点问题之一。该文首先对近年来国内外针对这一问题的理论研究成果按入流边界条件、湍流模型参数、附加源项模型以及壁面函数模型等四个方面进行了全面梳理和系统总结,并建议了一组新的标准k-ε模型湍流模型参数和通用壁面函数模型表达式。接着,采用计算流体动力学方法,建立简单边界层流动数值风洞模型,按照以上四种类别采用递进的方法对这些理论成果进行了详细的数值模拟验证和比较分析。结果表明:基于湍动能k方程解析解的入流边界条件并不必然会生成平衡态边界层,它和湍动能剖面的数学模型表达形式关系很大;除入流湍流边界条件外,湍流模型参数取值及壁面函数对平衡态大气边界层的模拟亦有较大影响,而增加源项并不能有效改善速度和湍动能剖面在整个流域范围的自保持性。该文对这一类问题的研究具有一定参考价值。     

Turbulent biomagnetic fluid flow in a rectangular channel under the action of a localized magnetic field

The fundamental problem of the turbulent flow of a biomagnetic fluid (blood) between two parallel plates under the action of a localized magnetic field is studied. The blood is considered to be an electrically conducting, incompressible and Newtonian fluid and its flow is steady, two-dimensional and turbulent. The turbulent flow is described by the Reynolds averaged Navier–Stokes (RANS) equations. For the numerical solution of the problem under consideration, which is described by a coupled and non-linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is used. For the eddy-kinematic viscosity, the low Reynolds number k–ε turbulence model is adopted. The solution of the problem, for different values of the dimensionless parameter entering into it, is obtained by developing and applying an efficient numerical technique based on finite differences scheme. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the localized magnetic field, appreciable influences the turbulent flow field. A comparison is also made with the corresponding laminar flow, indicating that the influence of the magnetic field decreases in the presence of turbulence.     

超临界二氧化碳微细管内冷却换热研究

对超临界二氧化碳在微细竖直圆管内冷却条件下的对流换热进行了数值模拟研究,分析了不同管径、进口雷诺数及不同的热流率对超临界二氧化碳对流换热的影响,考察管内局部流体温度、湍动能、湍流雷诺数的变化。湍流模型采用低雷诺数YS模型。研究表明,在临界温度区域比较大的截面,超临界二氧化碳局部传热系数达到最大值,同时管内传热受湍流雷诺数影响较大。     

Nonstationary Nonlinear Phenomena on the Charged Surface of Liquid Hydrogen

Investigations of nonlinear phenomena on the charged surface of liquid hydrogen are reviewed. It is demonstrated that excitation of the surface by a low frequency AC electric field results in the formation of capillary waves in the high-frequency domain, and that the latter exhibit turbulence. The quasi-adiabatic decay of this capillary turbulence has been studied both experimentally and theoretically. It is shown that the processes of formation and decay of the turbulence are both controlled by the same relaxation mechanisms. For spectrally narrow pumping, the application of an additional low-frequency driving force causes a decrease of wave amplitude in the high-frequency domain of the turbulent spectrum and correspondingly decreases the width of the inertial range of energy transfer.      

Combined three‐dimensional lattice Boltzmann method and discrete element method for modelling fluid–particle interactions with experimental assessment

A general algorithmic framework is established in this paper for numerical simulations of three‐dimensional fluid–particle interaction problems with a large number of moving particles in turbulent flows using a combined lattice Boltzmann method (LBM) and discrete element method (DEM). In this approach, the fluid field is solved by the extended three‐dimensional LBM with the incorporation of the Smagorinsky turbulence model, while particle interactions are modelled by the DEM. The hydrodynamic interactions between fluid and particles are realized through the extension of an existing two‐dimensional fluid–particle hydrodynamic interaction scheme. The main computational aspects comprise the lattice Boltzmann formulation for the solution of fluid flows, the incorporation of a large eddy simulation‐based turbulence model within the framework of the three‐dimensional LBM for turbulent flows, the moving boundary condition for hydrodynamic interactions between fluid and moving particles, and the discrete element modelling of particle‐particle interactions. To assess the solution accuracy of the proposed approach, a much simplified laboratory model of vacuum dredging systems for mineral recovery is employed. The numerical results are compared with the experimental data available. It shows that the overall correspondence between numerical results and experimental measurements is good and thus indicates, to a certain extent, the solution accuracy of the proposed methodology. Copyright © 2009 John Wiley & Sons, Ltd.     

Evolution properties of partially coherent four-petal Gaussian beams in oceanic turbulence

Based on the extended Huygens–Fresnel integral formula, the analytical expressions for partially coherent four-petal Gaussian beam propagating in oceanic turbulence are derived, and the influences of coherence length, beam order N and the parameters of oceanic turbulence (the rate of dissipation of turbulent kinetic energy per unit mass of fluid, the rate of dissipation of mean square temperature and the relative strength of temperature and salinity fluctuations) on average intensity properties are investigated using numerical examples in detail. The results show that the beam with the higher beam order N or coherence length will lose its initial four-petal profiles slower. It is also indicated that the beam will evolve into a Gauss-like beam more rapidly with increasing oceanic turbulence strength. The results have the potential application in underwater laser communication using a partially coherent four-petal Gaussian beam.     

Numerical simulation of a two-dimensional turbulent wall jet in an external stream

Turbulent wall jets possess a region with negative production of turbulent kinetic energy between the points of maximum velocity and vanishing shear stress. This characteristic feature cannot be shown with many turbulence models. The use of an extended expression for the primary turbulent shear stress together with a k–? or an algebraic Reynolds stress model results in a model which can show this physical property. Computed results obtained with this concept are compared with measurements and results obtained with the standard k–? model and a full Reynolds stress closure. It is shown that the computed results with the present and the Reynolds stress model are of similar quality. However, the Reynolds stress solution is more costly in computing time.     

Turbulence modulation by large ellipsoidal particles: concentration effects

We use laboratory measurements to study how suspended ellipsoidal particles affect the velocity statistics of a turbulent flow. The ellipsoids have size, time, and velocity scales corresponding to the inertial subrange of the turbulence and are nearly neutrally buoyant. These characteristics make them likely candidates for two-way interactions with the fluid (i.e., they influence the flow and are influenced by it). We vary the volume fraction of suspended ellipsoids and observe the effects on one- and two-point velocity statistics in the fluid phase. Measurements at two different heights indicate that particle buoyancy (0.5 % denser than the ambient fluid) significantly changes volume fraction. We see that particles’ effect on turbulent kinetic energy is a non-monotonic function of the volume fraction. We also find that particles’ presence causes a redistribution of velocity variance from large scales to small scales within the inertial subrange, i.e., the slope of power spectra is flatter than in the single-phase case.     

On diffusion theory in turbulence

The Fokker-Planck equation for the probability density of fluid particle position in inhomogeneous unsteady turbulent flow is derived. The equation is obtained starting from the general kinematic relationship between velocity and displacement of a fluid particle and applying exact asymptotic analysis. For (almost) incompressible flow the equation reduces to the convection diffusion equation and the equation pertaining to the scalar gradient hypothesis. In this way the connection is established with eddy diffusivity models, widely used in numerical codes of computational fluid dynamics. It is further shown that within the accuracy of the approximation scheme of the diffusion limit, diffusion constants can equally be based on coarse-grained Lagrangian statistics as defined by Kolmogorov or on Eulerian statistics in a frame that moves with the mean Eulerian velocity as proposed by Burgers. The results presented for diffusion theory are the leading terms of asymptotic expansions. Truncated terms are higher-order spatial derivatives of the probability density or of the scalar mean value with coefficients based on cumulants higher than second order of fluid velocities and their derivatives. The magnitude of these terms has been assessed by employing scaling rules of turbulent flows in pipes and channels, turbulent boundary layers, turbulent jets, wakes and mixing layers, grid turbulence, convective layers and canopy turbulence. It reveals that a true diffusion limit does not exist. Although truncated terms can be of limited magnitude, a limit process by which these terms become vanishingly small and by which the diffusion approximation would become exact does not occur for any of the cases of turbulent flow considered. Applying the concepts of diffusion theory resorts to employing approximate methods of analysis.     

Appraisal of energy recovering sub-grid scale models for large-eddy simulation of turbulent dispersed flows

Current capabilities of Large-Eddy Simulation (LES) in Eulerian–Lagrangian studies of dispersed flows are limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. These effects should be taken into account in order to reproduce accurately the physics of particle dispersion since the LES cut-off filter removes both energy and flow structures from the turbulent flow field. In this paper, we examine the possibility of including explicitly SGS effects by incorporating ad hoc closure models in the Lagrangian equations of particle motion. Specifically, we consider candidate models based on fractal interpolation and approximate deconvolution techniques. Results show that, even when closure models are able to recover the fraction of SGS turbulent kinetic energy for the fluid velocity field (not resolved in LES), prediction of local segregation and, in turn, of near-wall accumulation may still be inaccurate. This failure indicates that reconstructing the correct amount of fluid and particle velocity fluctuations is not enough to reproduce the effect of SGS turbulence on particle near-wall accumulation.     

Exact Analysis of Non-Linear Fractionalized Jeffrey Fluid. A Novel Approach of Atangana-Baleanu Fractional Model

It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation. Therefore, this article aims to investigate the viscous dissipation (VD) effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane. Based on the Atangana-Baleanu operator, the fractional model is developed from the fractional constitutive equations. VD is responsible for the non-linear behavior in the problem. Upon taking the Laplace and Fourier sine transforms, exact expressions have been obtained for momentum and energy equations. The influence of relative parameters on fluid flow and temperature distribution is shown graphically. As special cases, and for the sake of correctness, the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained. It is interesting to note that fractional parameter α provides more than one line as compared to the classical model. This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model. It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer.     

Similarity without diffusion: shear turbulent layer damped by buoyancy

The evolution of a turbulent layer generated by velocity shear between two half-spaces of fluid and suppressed by a stable density difference is studied. Initially the layer expands, then shrinks to a point in finite time. By the end of the expansion stage the turbulent diffusion decays to a small value compared to the shear and buoyancy inputs in the turbulent energy balance. During the shrinking stage the diffusion decays even further by comparison. It is shown that at this stage the profiles of the turbulent energy, velocity and buoyancy become virtually self-similar. The differences between this case and the more usual types of self-similarity, where diffusion plays significant role, are discussed.     

Effect of atmospheric spectrum models on scintillation in moderate turbulence

Experimental studies have shown that a ‘bump’ occurs in the atmospheric spectrum just prior to turbulence cell dissipation. In weak optical turbulence, this bump affects calculated scintillation. The purpose of this study was to determine if a simpler non-bump atmospheric power spectrum can be used to model scintillation for plane waves and spherical waves in moderate to strong optical turbulence regimes. Scintillation expressions were developed from an ‘effective’ von Karman spectrum using an approach similar to that used by Andrews et al. in developing expressions from an effective modified (bump) spectrum. The effective spectrum extends the Rytov approximation into all optical turbulence regimes using filter functions to eliminate mid-range turbulent cell size effects to the scintillation index. Filter cutoffs were established by matching to known weak and saturated scintillation results. The resulting new expressions track those derived from the effective bump spectrum fairly closely. In extremely strong turbulence, differences are minimal.     

Surface Oscillations of an Electromagnetically Levitated Droplet

The natural oscillation frequency of freely suspended liquid droplets can be related to the surface tension of the material, and the decay of oscillations to the liquid viscosity. However, the fluid flow inside the droplet must be laminar to measure viscosity with existing correlations; otherwise the damping of the oscillations is dominated by turbulent dissipation. Because no experimental method has yet been developed to visualize flow in electromagnetically levitated oscillating metal droplets, mathematical modeling can assist in predicting whether or not turbulence occurs, and under what processing conditions. In this paper, three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k−ɛ turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem when the interior flow is turbulent. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to available experimental results.     

Pulsating Turbulent Flow of Gas in a Round Pipe

An analysis is performed of the presently available results of experimental and prediction studies into pulsating turbulent flow of liquid in a narrow pipe under conditions when the compressibility is apparent. It is demonstrated that the simulation of such flows in the general case may be performed only numerically, using a model of turbulence that adequately includes the effect of oscillation on turbulent transfer. Use is made of a model of turbulence whose validity is proved by comparing the calculation and experimental results for a wide range of flows. Calculations are performed for a pulsating flow of gas in pipes with isothermal and adiabatic walls, acoustically closed at the outlet, in the frequency range corresponding to the first resonance harmonic. The predicted variations of the heat flux to the wall and of the hydraulic drag, averaged over the oscillation period, as functions of the process parameters such as the Reynolds number of the mean flow and the dimensionless oscillation frequency are discussed.     

Modélisation semi-empirique des écoulements et des transferts dans un milieu poreux en régime turbulentSemi-empirical modeling of turbulent fluid flow and heat transfer in porus media

The model allows the prediction of turbulent fluid flow and heating transfers inside a stack of obstacles, which is considered as a porous media. The heat transfer intensity between fluid and particles is related to the local values of velocity and turbulence intensity. The turbulent kinetic energy is predicted by a transport equation inspired from literature, which can also be used for two-dimensional flow patterns. Model parameters were experimentally identified for a stack of spheres with a void fraction of 34%. Laser anemometer measurements were performed upstream the from stack. Heat transfer coefficients were measured at different positions in the stack and for different flow rates. The standard error between measured and predicted coefficients is 5%.     

Numerical modeling of heat exchange and turbulent flow of fluid within tubes at supercritical pressure

Modes of normal and degraded (with peaks of wall temperature) heat transfer are computed for the turbulent flow of carbon dioxide within a circular tube at supercritical pressure. Computation is based on a set of motion, continuity, and energy equations written under the approximation of a narrow channel. The turbulence model uses the Prandtl formula for the turbulent viscosity. The relationship for the travel length takes into account the effect of variation in the fluid properties and thermal acceleration through the tube section. Computation results for variation in the wall temperature along the tube fit the experimental data. An explanation is given for causes of the appearance of the peak on the wall temperature distribution along the tube in the area, where the fluid temperature is close to the pseudocritical temperature.     

Two-point,two-time analysis of the decay of turbulence in the presence of a magnetic field

A two-point, two-time approach is attempted for the final period of decay of turbulence in an external, homogeneous magnetic field. Two-point, two-time correlation and spectral equations are obtained by considering the equations of fluid and electrodynamics for two points in a turbulent fluid at two different times. Solutions, corresponding to any given initial distribution, are obtained by assuming that the turbulence is weak enough for second-order truncation approximations to be applicable. The analysis shows that pronounced axisymmetric properties are developed in this case, turbulence elements with small extensions in the direction of the field and with large time separations being damped relatively rapidly under normal physical conditions. In its final period, the decay is governed by both periodic and non-periodic motions.     

Effect of anisotropy on intensity fluctuations in oceanic turbulence

For an optical spherical wave propagating in an oceanic turbulent medium, the effect of anisotropy on the received intensity fluctuations is investigated. For different anisotropy factors, the variations of the scintillation index vs. the ratio that determines the relative strength of temperature and salinity in the index fluctuations, the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, viscosity, link length and the wavelength are plotted. It is found that, for all the oceanic turbulence and the link parameters of interest, as the medium becomes more anisotropic, the intensity of the optical spherical wave fluctuates less. It is concluded that the performance of an optical wireless communication systems (OWCS) operating in anisotropic oceanic turbulence is better than the performance of OWCS operating in isotropic oceanic turbulence.