Two-phase micro- and macro-time scales in particle-laden turbulent channel flows

The micro-and macro-time scales in two-phaseturbulent channel flows are investigated using the direct numerical simulation and the Lagrangian particle trajectorymethods for the fluid-and the particle-phases,respectively.Lagrangian and Eulerian time scales of both phases are calculated using velocity correlation functions.Due to flowanisotropy,micro-time scales are not the same with the theoretical estimations in large Reynolds number(isotropic) turbulence.Lagrangian macro-time scales of particle-phaseand of fluid-phase seen by particles are both dependent onparticle Stokes number.The fluid-phase Lagrangian integral time scales increase with distance from the wall,longerthan those time scales seen by particles.The Eulerian integral macro-time scales increase in near-wall regions but decrease in out-layer regions.The moving Eulerian time scalesare also investigated and compared with Lagrangian integraltime scales,and in good agreement with previous measurements and numerical predictions.For the fluid particles themicro Eulerian time scales are longer than the Lagrangianones in the near wall regions,while away from the walls themicro Lagrangian time scales are longer.The Lagrangianintegral time scales are longer than the Eulerian ones.Theresults are useful for further understanding two-phase flowphysics and especially for constructing accurate predictionmodels of inertial particle dispersion.     

Effect of coarse particles on the heat transfer in a particle-laden turbulent boundary layer

The temperature distribution in particle-laden turbulent flow, in a flume, was investigated both by DNS and experimentally. Simulations were performed at Re=171 and Pr=5.4 in order to study the interaction between the particle motion and flow turbulence. Two-way coupling was used to obtain various turbulence statistics, the grid resolution was sufficiently fine to resolve all essential turbulent scales. The effect of particle diameter on momentum, heat transfer and particle deposition was considered. The details of particle-turbulence interaction depend on the particle Stokes number and the particle Reynolds number.

The spatial structures of instantaneous flow and temperature fields were visualized. Low frequency small oscillations of deposited particles were observed. It was found that these small deviations from the initial position, caused strong changes in the instantaneous temperature field near the particle.

The experiments provided details of the temperature field on the heated wall close to the particle. In the front of the particle, a sharp increase in heat transfer coefficient was observed. The experimental results agree well with the computational predictions.     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force

A formulation of the skin-friction drag related to the Reynolds shear stress in a turbulent channel flow is derived. A direct numerical simulation (DNS) of the turbulent control is performed by imposing the spatially oscillating spanwise Lorentz force. Under the action of the Lorentz force with several proper control parameters, only the periodically well-organized streamwise vortices are finally observed in the near-wall region. The Reynolds shear stress decreases dramatically, especially in the near-wall area, resulting in a drag reduction.     

Direct numerical simulation of particle interaction with ejections in turbulent channel flows

Direct numerical simulations (DNS) of incompressible turbulent channel flows coupled with Lagrangian particle tracking are performed to study the characteristics of ejections that surround solid particles. The behavior of particles in dilute turbulent channel flows, without particle collisions and without feedback of particles on the carrier fluid, is studied using high Reynolds number DNS (Re = 12,500). The results show that particles moving away from the wall are surrounded by ejections, confirming previous studies on this issue. A threshold value separating ejections with only upward moving particles is established. When normalized by the square root of the Stokes number and the square of the friction velocity, the threshold profiles follow the same qualitative trends, for all the parameters tested in this study, in the range of the experiments. When compared to suspension thresholds proposed by other studies in the Shields diagram, our simulations predict a much larger value because of the measure used to characterize the fluid and the criterion chosen to decide whether particles are influenced by the surrounding fluid. However, for intermediate particle Reynolds numbers, the threshold proposed here is in fair agreement with the theoretical criterion proposed by Bagnold (1966) [Bagnold, R., 1966. Geological Survey Professional Paper, vol. 422-1]. Nevertheless, further studies will be conducted to understand the normalization of the threshold.     

湍流横掠固定颗粒的全尺度直接数值模拟

气固两相流模拟中,当固相尺度接近或大于Kolmogorov尺度时,普通的点源模型将不再适用,固体相的体积效应和表面效应将对流体相产生显著的影响。通过采用直接数值模拟方法,结合内嵌边界方法对湍流中不同湍流强度流体横掠大于Kolmogorov尺度的固相颗粒进行了全尺度模拟,讨论分析了在两种湍流度下方形颗粒对湍流的调制影响以及颗粒的受力情况。     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Velocity and temperature dissimilarity in fully developed turbulent channel and plane Couette flows

The natural dissimilarity or decorrelation of stream-wise velocity and temperature fluctuations in fully developed turbulent channel and plane Couette flows was studied using direct numerical simulation (DNS). For both of the flow configurations, a Reynolds number of about 150 was used based on the friction velocity and half the distance between walls. Buoyancy effects were neglected, and only results with a molecular Prandtl number, Pr, equal to 1 are presented. The boundary conditions for the thermal field were a uniform source of energy in the domain and isothermal wall temperature for the channel and Couette flow, respectively. The importance of those events responsible for wall-normal turbulent fluxes in the generation of axial velocity and temperature dissimilarity was examined using conditional probability. It was found that the dissimilarity in the whole domain was higher in Couette than in channel flow. It was also found that for wall-normal turbulent fluxes (momentum and heat), the averaged dissimilarity in the whole domain was slightly more correlated with those events in the second or fourth quadrant, according to the quadrant analysis technique. For channel flow, the importance of both kinds of events was similar, while for Couette flow there was a predominance in the generation of dissimilarity by those events in the fourth quadrant. Also, for both flow configurations and throughout the wall-normal direction, it was found that in the buffer region there was a predominance of events in the fourth quadrant associated with dissimilarity for both wall-normal turbulent fluxes. In the frequency domain, the distribution of energy showed that there was a high-frequency shift experienced from the wall towards the centerline by the temperature spectrum with regards to the axial velocity spectrum, for which the action of the fluctuations of the wall-normal velocity was the main cause. In the central region of the flow, on the other hand, there was a global convergence of all spectra towards the pressure spectrum, with this convergence lower for Couette flow. Finally, it is shown that the dissimilarity in developed conditions is caused by the greater correlation existing for the temperature fluctuation with the instantaneous axial pressure gradient than for the velocity fluctuation with the instantaneous axial pressure gradient.     

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.     

Flow patterns and heat transfer in vertical upward air–water flow with surfactant

Flow patterns, the pressure drag reduction and the heat transfer in a vertical upward air–water flow with the surfactant having negligible environmental impact were studied experimentally in a tube of 2.5 cm in diameter. Visual observations showed that gas bubbles in the air–water solution with surfactant are smaller in size but much larger in number than in pure air–water mixture, at the all flow regimes. The transition lines in the flow regime map for the solution of air–water mixture with surfactant of the 300 ppm concentration are mainly consistent with the experimental data obtained in clear air–water mixture. An additive of surfactant to two-phase flow reduces the total pressure drop and decrease heat transfer, especially in the churn flow regime.     

Self-consistency and the use of correlated stochastic separated flow models for prediction of particle-laden flows

Computational fluid dynamics (CFD) is being used increasingly in the design and analysis of particle-laden flows. A significant challenge of this work is in correctly predicting the interaction of the fluid turbulence with the particulate phase. Typically, Lagrangian tracking is used to calculate the particle trajectories with stochastic treatments used to provide an instantaneous turbulent flow field. The stochastic calculations are based on the mean velocities and turbulence quantities calculated by the CFD solver. The current work examines the correlated stochastic separated flow (SSF) model used to synthesize the instantaneous fluid velocity field. Two functional forms of the Eulerian spatial correlation are considered: exponential, and Frenkiel with loop parameter m equal to unity. It is well known that the use of a Frenkiel function is incorrect due to the Markovian nature of the model. Nonetheless, a literature review indicates that the Frenkiel function is still being used in the CFD community. In order to illustrate the implications of this, numerical predictions are compared to Taylor's analytical result for fluid particle dispersion in homogeneous isotropic turbulence. Excellent predictions are obtained with the exponential correlation and recommendations on timestep requirements are made. In contrast, predictions from the Frenkiel model are in poor agreement with Taylor's solution. This poor agreement results from an inconsistency between the effective correlation of fluid velocities arising from the model and the original intended correlation.     

Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls

Interest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo-spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant-property, turbulent fluid in a two-dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions. Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half-height of 180 or 2800 based on channel half-height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two-point velocity correlations are given. Deficiencies are that the calculation requires many hours on a fast computer with a large high-speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.     

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.     

DNS of a spatially developing turbulent boundary layer with passive scalar transport

A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier–Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U_∞ and momentum thickness θ is Re_θ=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors’ knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.     

DNS of heat transfer in turbulent and transitional channel flow obstructed by rectangular prisms

Direct numerical simulation (DNS) of heat transfer in a channel flow obstructed by rectangular prisms has been performed for Re_τ = 80–20, where Re_τ is based on the friction velocity, the channel half width and the kinematic viscosity. The molecular Prandtl number is set to be 0.71. The flow remains unsteady down to Re_τ = 40 owing to the disturbance induced by the prism. For Re_τ = 30 and 20, the flow results in a steady laminar flow. In the vicinity of the prism, the three-dimensional complex vortices are generated and heat transfer is enhanced. The Reynolds number effect on the time-averaged vortex structure and the local Nusselt number are investigated. The mechanism of the heat transfer enhancement is discussed. In addition, the mean flow parameters such as the friction factor and the Nusselt number are examined in comparison with existing DNS and experimental data.     

Mechanism of drag reduction by spanwise oscillating Lorentz force in turbulent channel flow

Numerical simulations and experimental research are both carried out to investigate the controlled effect of spanwise oscillating Lorentz force on a turbulent channel flow. The variations of the streaks and the skin friction drag are obtained through the PIV system and the drag measurement system, respectively. The flow field in the near-wall region is shown through direct numerical simulations utilizing spectral method. The experimental results are consistent with the numerical simulation results qualitatively, and both the results indicate that the streaks are tilted into the spanwise direction and the drag reduction utilizing spanwise oscillating Lorentz forces can be realized. The numerical simulation results reveal more detail of the drag reduction mechanism which can be explained, since the spanwise vorticity generated from the interaction between the induced Stokes layer and intrinsic turbulent flow in the near-wall region can make the longitudinal vortices tilt and oscillate, and leads to turbulence suppression and drag reduction.     

The comparison of two approaches to numerical modelling of gas-particles turbulent flow and heat transfer in a pipe

The comparison of two theoretical approaches for the numerical investigation of turbulent gas–solid flows with heat transfer in a pipe are presented in this paper. The first approach is based on Eulerian–Eulerian modelling of investigated phenomena, the second one is formulated within the framework of the Eulerian–Lagrangian approach. The verification of numerical models under consideration. Their testing against available experimental data show good prognostic properties of the elaborated theoretical tool for research activities to study new physical fundamentals of turbulent gas-suspended particles flows in pipes and channels.