Experimental study of stratified jet by simultaneous measurements of velocity and density fields

Stratified flows with small density difference commonly exist in geophysical and engineering applications, which often involve interaction of turbulence and buoyancy effect. A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system is developed to measure the velocity and density fields in a dense jet discharged horizontally into a tank filled with light fluid. The illumination of PIV particles and excitation of PLIF dye are achieved by a dual-head pulsed Nd:YAG laser and two CCD cameras with a set of optical filters. The procedure for matching refractive indexes of two fluids and calibration of the combined system are presented, as well as a quantitative analysis of the measurement uncertainties. The flow structures and mixing dynamics within the central vertical plane are studied by examining the averaged parameters, turbulent kinetic energy budget, and modeling of momentum flux and buoyancy flux. At downstream, profiles of velocity and density display strong asymmetry with respect to its center. This is attributed to the fact that stable stratification reduces mixing and unstable stratification enhances mixing. In stable stratification region, most of turbulence production is consumed by mean-flow convection, whereas in unstable stratification region, turbulence production is nearly balanced by viscous dissipation. Experimental data also indicate that at downstream locations, mixing length model performs better in mixing zone of stable stratification regions, whereas in other regions, eddy viscosity/diffusivity models with static model coefficients represent effectively momentum and buoyancy flux terms. The measured turbulent Prandtl number displays strong spatial variation in the stratified jet.     

稳定分层湍流中逆梯度输运的关联分析研究

本文采用关联分析方法研究了稳定温度分层湍流中的结构特性、输运特性,以及热量、动量逆梯度输运现象的尺度效应及其参数演化．首先采用大涡模拟方法对稳定分层湍流中的结构特性和输运特性进行了分析,将逆梯度输运发生的时间尺度作为已知条件,结合关联量分析方法在波数空间中的解析解,对逆梯度输运现象的尺度效应进行了分析研究．结果发现,稳定分层强度较大的流动中发生垂向热量及动量逆梯度输运现象,发生的结构尺度与关联分析所发现垂向热量、动量逆梯度输运的波数形成了呼应．随着分层强度增加,热量、动量的输运强度均受抑制,与逆梯度输运关联的流场结构尺度减小,同样的效应也发生在流场结构向下游演化的过程中．     

Time evolution of structures in rotating and stratified turbulence

Rotating and stably stratified turbulence exhibit not only significant anisotropies but also dynamics, which are qualitatively different from purely rotating or stratified turbulence. Furthermore, the different time scales due to rotation, stratification and the turbulence one open up a wide field of possibilities for the temporal evolution of rotating and stratified turbulence.We analyze results from DNS with different parameters α = f/N by visualizing iso-enstrophy surfaces, the temporal evolution of velocity correlation length scales and angular energy spectra.We retrieve standard results, such as a large anisotropy for small scales in rotating turbulence and a large anisotropy for intermediate scales in the vortex mode of stratified turbulence. Furthermore, at large times we find qualitatively different phenomena for cases α = 10 and α = 0.1 such as modified cascades due to the existence of potential energy or small scale vorticity production respectively.     

分层流体中栅格湍流的特性

本文考察了分层流体中栅格湍流衰减和演化过程的细节,通过对空间场的信息二维图象处理,获得了湍流动能、耗散率、功率谱及多种湍流尺度等主要湍流特征量。结果显示层结加速了湍流垂直动能的衰减,而水平动能的衰减几乎很少受影响。流场各特征量与前人结果也符合得较好。     

Turbulence structure in a diabatically heated forest canopy composed of fractal Pythagoras trees

We investigate the turbulent flow through a heterogeneous forest canopy by high-resolution numerical modeling. For this purpose, a novel approach to model individual trees is implemented in our large-eddy simulation (LES). A group of sixteen fractal Pythagoras trees is placed in the computational domain and the tree elements are numerically treated as immersed boundaries. Our objective is to resolve the multiscale flow response starting at the diameter of individual tree elements up to the depth of the atmospheric surface layer. A reference run, conducted for the forest flow under neutral thermal stratification, produces physically meaningful turbulence statistics. Our numerical results agree quantitatively with data obtained from former field-scale LESs and wind tunnel experiments. Furthermore, the numerical simulations resolve vortex shedding behind individual branches and trunks as well as the integral response of the turbulent flow through the heterogeneous forest canopy. A focus is the investigation of the turbulence structure of the flow under stable thermal stratification and in response to the heating of the fractal tree crowns. For the stratified flows, statistical quantities, e.g. turbulent kinetic energy and vorticity, are presented and the turbulent exchange processes of momentum and heat are considered in detail. The onset and formation of coherent structures such as elevated shear layers above the diabatically heated forest canopy are analyzed. For the stably stratified flow, temperature ramps above the forest canopy were simulated in agreement with previous observations. Thermally driven vortices with a typical diameter of the canopy height were simulated when the tree crowns were diabatically heated. The impact of the coherent flow structures on the heat flux is investigated.     

Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

The direct numerical simulation(DNS) of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed.The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers(P r = 0.71,1.5,and 3.0) and a shear Reynolds number(Reτ = 180).Some typical thermal statistics,including normalized mean temperature and their fluctuations,turbulent heat fluxes,Nusselt number and so on,are analyzed.The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number.Two reasons can explain this.First,the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases,and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field.Second,the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number,and the thermal feedback of the particles to turbulence becomes weak.     

Nusselt number and friction factor in thermally stratified turbulent channel flow under Non-Oberbeck–Boussinesq conditions

In stably stratified turbulence, computations under Oberbeck–Boussinesq (OB) hypothesis of temperature-independent fluid properties may lead to inaccurate representation of the flow field and to wrong estimates of momentum/heat transfer coefficients. This is clearly assessed here comparing direct numerical simulations of stratified turbulence under OB conditions to simulations under NOB (Non-Oberbeck–Boussinesq) conditions of temperature-dependent fluid viscosity and thermal expansion coefficient. Compared to the OB case, NOB conditions may induce local flow relaminarization with significant variations (up to 30%) of heat and momentum transfer coefficients. Together with DNS results, we propose a phenomenological model (based on turbulent bursts) for heat transfer prediction in stratified turbulence under OB and NOB conditions. Implications of NOB assumptions on mixing efficiency (i.e. flux Richardson number Ri_f) and turbulent Prandtl number (Pr_t) are also discussed. These results are of specific importance in RANS modelling, where the condition Pr_t = 1 is usually assumed (Reynolds analogy). Although this assumption is valid in some situations (i.e. boundary layer, pipe flow) there is uncertainty about its validity for stably-stratified turbulence. We demonstrate that this assumption is inaccurate when NOB effects become significant.     

Steady turbulent flow and heat transfer downstream of a sudden enlargement in a pipe of circular cross-section

Stream-line and temperature contours, and the corresponding fluxes at the walls, are computed by numerical solution of the elliptic transport equations of vorticity, enthalpy and turbulence energy, together with auxiliary relations comprising a turbulence model similar to that of Prandtl [19]. The length-scale distribution is determined empirically in order to ensure that the recirculation region has the right length, and the maximum of the wall heat flux occurs at the right place, but the other empirical inputs have values which are determined from quite different experiments. — Agreement between predictions and experimental data of Krall and Sparrow [13] is good. In particular, the correct exponent is predicted for the Stanton number ? Reynolds number law. This exponent is uninfluenced by the length-scale distribution. — For practical use, it is argued, the Prandtl turbulence model needs to be replaced by one embodying two differential equations for turbulence quantities.     

Turbulence Budgets in Buoyancy-affected Vertical Backward-facing Step Flow at Low Prandtl Number

The paper investigates buoyancy impact on the vertical flow over a backward-facing step at low Prandtl number by Direct Numerical Simulation. In particular, the very low Prandtl number of liquid sodium, 0.0088, is considered in the regime of mixed convection, i.e. for Richardson numbers below unity. The effects of buoyancy on mean flow, heat transfer and turbulence are assessed. Buoyancy is found to attenuate recirculation and, consequently, increase heat transfer. Turbulence is decreased in the attached boundary layer for moderate buoyancy impact but surpasses the levels found in forced convection at the largest Richardson number investigated. Beyond the mean flow and second moments, the budgets of turbulent kinetic energy, Reynolds shear stress, temperature variance, and turbulent heat flux components are studied and related to the alterations in the mean field quantities. Due to scale separation, production and dissipation nearly balance for temperature variance while this is not the case for turbulent kinetic energy. Similar findings for the turbulent heat fluxes show that the correlation between temperature and pressure gradient is the most important contribution to the budget aside from production and dissipation. In addition to the physical insight into this flow, the data presented may be used for the validation and improvement of turbulence models for liquid metal flows.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

On pressure and thermal flux in gas-mixture flows and in two-phase flows

To begin with, two different definitions of pressure, thermal flux, etc. in the diffusion model and two-fluid model are given. Then the physical interpretations of the pressure and the thermal flux are provided by introducing the momentum and energy fluxes,M and ε, through a surface dS in the flow field. The quantities defined in the diffusion model are suggested when the motion of the mixture is studied as a whole, while the quantities defined in the two-fluid model are suggested when the motion of individual species is studied. The collision pressure and thermal flux in dense gas-mixtures are also discussed in detail, i.e. their origin, their expressions in the momentum and energy equations, and their distinctions from the normal partial pressure and thermal flux. A gas-particle flow can be treated as a flow of dense gas-mixtures. The long-standing controversy whether the “inertial coupling term” should exist in the momentum equation can be clarified by the two different definitions of pressure.     

A film boiling model for cryogenic chilldown at low mass flux inside a horizontal pipeline

A film boiling heat transfer model is developed for cryogenic chilldown at low mass flux inside a horizontal pipeline. It incorporates the stratified flow structure and is based on conservation principles of mass, momentum, and energy. Simplifying assumptions lead to an expression for the local film boiling heat transfer coefficient which varies with the azimuthal angle. The efficacy of the model is assessed by comparing the predicted wall temperature histories with those measured at several azimuthal positions and various mass fluxes. Good agreement is observed at low flux, G = 13–54 kg/m² s.     

Scale properties of turbulent transport and coherent structure in stably stratified flows

The empirical mode decomposition (EMD) is used to study the scale properties of turbulent transport and coherent structures based on velocity and temperature time series in stably stratified turbulence. The analysis is focused on the scale properties of intermittency and coherent structures in different modes and the contributions of energy-contained coherent structures to turbulent scalar counter-gradient transport (CGT). It is inferred that the velocity intermittency is scattered to more modes with the development of the stratified flow, and the intermittency is enhanced by the vertical stratification, especially in small scales. The anisotropy of the field is presented due to different time scales of coherent structures of streamwise and vertical velocities. There is global counter-gradient heat transport close to the turbulence-generated grid, and there is local counter-gradient heat transport at certain modes in different positions. Coherent structures play a principal role in the turbulent vertical transport of temperature.     

稳定分层流动中湍流特性的研究综述

本文总结了近60 年来分层流动中湍流特性研究的成果. 主要从两个方面进行了综述:(1) 分层流动中湍流场的演变和混合. 在这方面主要分析稳定分层对湍流混合和湍流结构的影响, 以及混合层内湍流结构的特性和混合层的演化规律. (2) 分层流动中湍流的扩散和输运. 动量和标量的逆梯度输运特性是分层湍流研究的一个重要方向;分析分层对湍流扩散的影响. 并指出了一些值得今后进一步研究的方向.     

Agglomeration of inertial particles in a random rotating symmetric straining flow

This paper is concerned with the development and validation of a simple Lagrangian model for particle agglomeration in a turbulent flow involving the collision of particles in a sequence of correlated straining and vortical structures which simulate the Kolmogorov small scales of motion of the turbulence responsible for particle pair dispersion and collision. In this particular study we consider the collision rate of monodisperse spherical particles in a symmetric (pure) straining flow which is randomly rotated to create an isotropic flow. The model is similar to the classical model of Saffman and Turner (S&T) (1956) for the collision (agglomeration) of tracer particles suspended in a turbulent flow. However unlike S&T, the straining flow is not frozen in time persisting only for timescales ∼Kolmogorov timescale. Furthermore, we consider the collision of inertial particles as well as tracer particles, and study their behavior not only at the collision boundary but also in its vicinity. In the simulation, particles are injected continuously at the boundaries of the straining flow, the size of the straining region being typical of the Kolmogorov length scale η_K of the turbulence. For steady state conditions, we calculate the flux of particles colliding with a test particle at the centre of the straining flow and consider its dependence on the inertia of the colliding particles (characterized by the particle Stokes number, St). The model replicates the segregation and accumulation observed in DNS and in particular the maximum segregation for St ∼ 1 (where St is the ratio of the particle response time to the Kolmogorov timescale). We also calculate the contributions of the various turbulent forces in the momentum balance equation for satellite particles and show for instance that for small Stokes number, there is a balance between turbulent diffusion and turbophoresis (gradient of kinetic stresses) which in turn is responsible for the build-up of concentration at the collision boundary. As found in previous studies, for the case of inertialess tracer particles, the collision rate turns out to be significantly smaller than the S&T prediction due to a lowering of the concentration at the collision boundary compared to the fully mixed value. The increase in collision rate for St ∼ 0.5 is shown to be a combination of particle segregation (build-up of concentration near the collision boundary) and the decorrelation of the relative velocity between the local fluid and a colliding particle. The difference from the S&T value for the agglomeration kernel is shown to be a consequence of the choice of perfectly absorbing boundary conditions at collision and the influence of the time scale of the turbulence (eddy lifetime). We draw the analogy between turbulent agglomeration and particle deposition in a fully developed turbulent boundary layer.     

Dissipation rate correction methods

Dissipation rates of the turbulent kinetic energy and of the scalar variance are underestimated when the measurement resolution of the small scales of a turbulent flow field are insufficient. Results are presented of experiments conducted in a salt-stratified water tunnel (Schmidt number ∼700). Dissipation rates are determined to be underestimated, and thus correction techniques based on velocity structure functions and mixed-moment functions are proposed. Dissipation rates in laboratory experiments of shear-free, grid-generated turbulence are determined from balance calculations of the kinetic energy and scalar variance evolution equations. Comparisons between the structure function and balance estimates of dissipation show that the corrections are O(1) for the kinetic energy dissipation rate, and are O(100) for the scalar variance dissipation rate. This difference is due to the lack of resolution down to the Batchelor scales that is required for a high Schmidt number flow. Simple correction functions based on microscale Reynolds numbers are developed for both turbulent kinetic energy and scalar variance dissipation rates. Application of the technique to the results of laboratory experiments of density stratified turbulence, sheared turbulence, and sheared density stratified turbulence yields successful corrections. It is also demonstrated that the Karman–Howarth equality (and the analogous Yaglom equation) that relates second and third-order structure functions to dissipation rates is valid for both unstrained (decaying grid-generated turbulence) and density stratified and sheared turbulence at least up to the magnitudes of strains of the current experiments Nt∼10, St∼10, respectively. This is helpful for it allows the use of these equations in the analysis of turbulence even when the large scale background profiles of velocity and scalar are unknown.     

Prandtl number effects in MRT lattice Boltzmann models for shocked and unshocked compressible fluids

This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids, but also for the unshocked compressible fluids. To make the model work for unshocked compressible fluids, a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system. The unnecessity of the modification for systems under strong shock is analyzed. The model is validated by some well-known benchmark tests, including thermal Couette flow, Riemann problem. The first system is unshocked and the latter is shocked. In both systems, the Prandtl number effects are checked. Satisfying agreements are obtained between new model results and analytical ones.     

A K-ε TWO-EQUATION TURBULENCE MODEL FOR THE SOLID-LIQUID TWO-PHASE FLOWS

A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and ε equations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.     

Pr数对湍流被动标量输运的影响

采用直接数值模拟的方法,研究分子Pг数对湍流被动标量输运的影响,并提供充分的证据证明,湍流Pг数明显依赖于分子Pг数.在算例中,湍流雷诺平均PгT数与分子Pг数的倒数呈线性关系;湍流亚格子Pгt数与分子Pг数的关系较为复杂,在分子Pг数为1附近时,湍流亚格子Pгt数出现极小值.     

Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer

An analysis is carried out to study the momentum, mass and heat transfer characteristics on the flow of visco-elastic fluid (Walter's liquid-B model) past a stretching sheet in the presence of a transverse magnetic field.In heat transfer, two cases are considered:

1.

The sheet with prescribed surface temperature (PST case); and

2.

The sheet with prescribed wall heat flux (PHF case).

The solution of equations of momentum, mass and heat transfer are obtained analytically. Emphasis has been laid to study the effects of various parameters like magnetic parameter Mn, visco-elastic parameter k₁, Schmidt number Sc, and Prandtl number Pr on flow, heat and mass transfer characteristics.