Numerical simulation data for assessment of particle-laden turbulent flow models

This paper presents a collection of numerical simulation data which provides a reference for the assessment of various statistical/stochastic models in incompressible homogeneous particle-laden turbulent flows. Four different homogeneous flow configurations are studied, namely, homogeneous shear flow, homogeneous plane strain flow, homogeneous axisymmetric expansion and contraction. An Eulerian-Lagrangian formulation is used for the two-phase flow simulation. A Fourier pseudospectral method is used for the solution of the Eulerian carrier-phase equations without resorting to any turbulence model. The Lagrangian equations for the dispersed phase are integrated using a modified Stokes drag. For the shear flow, both monodispersed and polydispersed particles have been considered. In this paper, only the results that are relevant for assessment of various statistical models for both the fluid and dispersed phases are presented.     

采用欧拉和拉格朗日混合模型对浓相颗粒流的研究

论述了一种组合了欧拉／欧拉和欧拉／拉格朗日方法的研究浓相气固流的新数值模拟。模型用基于Chapman-Enskog浓相气体理论的微元流体动理学方法计及了欧拉坐标系中的颗粒间相互作用。该模型在计算拉格朗日坐标系中颗粒湍流扩散时采取颗粒随机分布模型。用该模型得出的计算结果与已发表的实验结果进行了比较,能较好地吻合。图7参12     

SIMULATION OF EROSION BY THE DILUTE PARTICULATE FLOW IMPACT

In this study, the effects of turbulence intensity, temperature, particle sizes, and impinging velocity on erosion by particle impact are demonstrated numerically. Underlying turbulent flow on an Eulerian frame is described by the Reynolds averaged Navier - Stokes equations with an Renormalization Group Theory (RNG) k-epsilon turbulence model. The particle trajectories and particle - wall interactions are evaluated by a Lagrangian approach. An erosion model considering material weight removal from surfaces is used to predict erosive wear. Computational validation against measured data is performed on a one-phase and two-phase impinging jet. Numerical comparisons reveal that the current study provides better predictive capability for erosion than the previous works.     

Heat transfer in particulate flows with Direct Numerical Simulation (DNS)

A Direct Numerical Simulation (DNS) method has been developed to solve the heat transfer equations for the computation of thermal convection in particulate flows. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. The numerical methods developed in this paper have been validated extensively by comparing the present simulation results with those obtained by others.     

气粒两相平面湍射流拟序结构的大涡模拟

采用Eulerian/Lagrangian方法,对空间发展的气粒两相平面湍射流的非定常流动过程进行了数值模拟。以Re数为13000的平面不可压缩湍射流流动为例,气相场采用大涡模拟（large-eddy simulaiton,LES）技术,直接求解大尺度涡运动的Navier-Stokes方程,小尺度涡采用标准Smagorinsky亚格子模式模拟。为了示踪两相射流中气相的运动,同时球 解了标志物的浓度输运方程。颗粒相的运动用Lagrangian方法直接求解。大涡模拟结果表明,在平面射流的过渡区及充分发展区存在丰富的拟序结构及其相互作用。对于稀疏两相射流,不同Stokes数的颗粒运动规律和浓度分布取决于颗粒惯性和气相拟序结构的共同作用。对于Stokes数小于10的两相射流,颗粒相的瞬时浓度场分布与拟序结构密切相关,研究颗粒相的扩散应当考虑拟序结构的影响。     

Thermal stochastic collision model in turbulent gas–solid pipe flows

New thermal stochastic particle collision model in gas–solid flow in a riser is developed. The simulation is based on four-way coupling of phases considering inter-particle collision and heat transfer. It is shown that the limitation of excessive computational time in Eulerian–Lagrangian simulation of gas–solid flows for the high loading ratios is eliminated by using the stochastic particle collision model. The simulation results demonstrate that the predictions of the developed thermal stochastic particle collision modem are in good agreement with those obtained by the direct particle collision model and the available experimental data. The new stochastic modeling is used and nearly dense gas–solid flow is simulated for high loading ratios up to eight and the results are presented and discussed.     

入流滑移条件对两相射流特性影响的大涡模拟研究

研究了入流滑移条件对空间发展的气粒两相平面湍射流的非定常流动特性的影响。以Re数13000的平面不可压缩湍射流流动为例,气相场用Euler方法求解,通过大涡模拟(large-eddy　simulation,LES),直接求解大尺度涡运动的Navier-Stokes方程,小尺度涡用标准Smagorinsky亚格子模式模拟。颗粒相的运动用Lagrangian方法直接求解。在不同入流滑移条件下(U     

MODELING OF DENSELY LOADED TWO-PHASE FLOWS

A mathematical model for densely loaded particle-laden flows is proposed to account for particle collisions and particle-turbulence interaction. The coupled conservation equations are based on a Eulerian scheme for the gas and a stochastic Lagrangian technique for the particles. The model was validated against the experimental data of densely loaded particle-laden jet flows. The comparison between the computational results and measurements suggested that both turbulence modulation and particle collisions are important and should be considered in an accurate analysis of dense two-phase flows.     

Numerical and experimental investigations on gas–particle flow behaviors of the Opposed Multi-Burner Gasifier

Numerical and experimental study on the gas–particle flow field has been carried out in the large Opposed Multi-Burner (OMB) Gasifier (I.D. 1.0 m) at high temperature and pressure. A 3D numerical model based on the Eulerian–Lagrangian model is used to simulate the gas–particle flow behaviors. The gas phase is treated as continuous phase with an Eulerian method while the Lagrangian method is applied to trace of the particles, and the interaction between gas and particles is considered. The behavior of slag/ash particle collision and its effects on particle dispersion are presented. The simulations are validated by available experimental data. The results showed that material residence time increased with the straight section height above the burner, and the deposition flux increased with the inlet velocity. The axis profiles of particle concentrations at high temperature and pressure have the similar characteristic shapes to those at ambient pressure and temperature. And the highest turbulence intensity and collision flame are converged around the centre of impingement zone. Though the inter-particle collision led to the phenomenon of particle agglomeration, the holistic distribution of particle concentration was reasonable. Finally, the effect of operating pressure and particles Stokes number were studied.     

Combination of the fictitious domain method and the sharp interface method for direct numerical simulation of particulate flows with heat transfer

In this paper, the fictitious domain (FD) method and the sharp interface (SI) method are combined for the direct numerical simulations of particulate flows with heat transfer in three dimensions. The flow field and the motion of particles are solved with the FD method. The temperature field is solved in both fluid and solid media with the SI method. The accuracy of the proposed FD/SI method is validated via two problems: the natural convection in a two- dimensional cavity with fixed solid particles, and the flow over a cold sphere. The method is then applied to the natural convection in a three dimensional cavity with a fixed sphere, the motion of a spherical particle in a non-isothermal fluid, and the rising of spherical catalyst particles in an enclosure. The effects of the thermal conductivity ratio are examined in the first and third problems, respectively, and the significant effects of the thermal expansion coefficient ratio on the particle motion are demonstrated in the second problem.     

Numerical investigation of erosion on a staggered tube bank by particle laden flows with immersed boundary method

In the present paper, particle-laden flows past 10 × 11 staggered stainless steel tube banks in a duct and the caused erosion are investigated using point-particle Eulerian–Lagrangian method. The continuous gas flow field is obtained through direct numerical simulation. The coupling between fluid and the embedded tubes is handled through the multi-direct forcing immersed boundary method. Four types of coal ash particles with Stokes numbers 0.01, 0.1, 1.0, 10.0, are considered. The collision and erosion characteristics on the tubes located in the middle of the duct are analyzed in detail. It has been found that the global tube erosion of the first tube increases with the increment of the particle size, but particles with an intermediate Stokes number of 1.0 cause the most erosion to the other downstream tubes due to preferential accumulation effect. Results predict much more erosion to the second row of tubes in staggered tube banks than the first row of tubes. Global erosion to the tubes near the wall is much larger than the corresponding ones located in the center, especially far downstream. The maximum local tube erosion occurs within certain angle regions around the tubes, where more attention needs to be paid to prevent erosion.     

CFD models comparative study on nanofluids subcooled flow boiling in a vertical pipe

The effects of subcooled flow boiling of nanofluids (Al₂O₃/water and Cu/water) through a vertical heated pipe are investigated numerically considering a number real flow factors such as uneven particle distributions and particle deposition on the wall surface. The results from the Eulerian–Eulerian two-phase model (liquid/nanofluid–gas) and those of the Eulerian–Lagrangian three-phase model (liquid–gas particles) are compared in detail. For the heat transfer coefficient prediction, the latter model gives about 6% error, whereas the Eulerian–Eulerian model gives about 12% error when it is compared with Chen’s correlation. The uneven distribution of nanoparticles concentrations, i.e., lower near the tube wall and higher at the pipe center, is well predicted by the Eulerian–Lagrangian model. On top that, for the first time, the changes on heating surface wettability induced by nanoparticles deposition is included via user define functions.     

Time response characteristics of microcapsulated liquid-crystal particles

Microcapsulated liquid-crystal particles are widely used as temperature sensors in the field of heat transfer engineering. Conventionally, these particles are painted on a surface of a heated plate for temperature measurements. The temperature is measured by tracing the color changes of the microcapsulated liquid-crystal particle through the color digital image processing technique. Recently, these particles are often suspended in thermal fluid flows as temperature tracers of the flows. For the use of a microcapsulated liquid-crystal particle itself as a temperature sensor in the suspending method, the heat capacity of the capsule covering the liquid crystal should be regarded as an important factor in predicting the time response of the microcapsulated liquid-crystal particle which is directly injected into a thermal fluid flow. The heat capacity of the liquid crystal and the capsule can produce a delayed time response for the temperature change of the outside fluids and eventually produce erroneous measurement data. Without a new temperature sensor smaller than the particle, it is very difficult to measure the time response of the microcapsulated liquid-crystal particle since the particles move with the working thermal fluid in different flow conditions. Therefore, a numerical simulation for the time response of the particle is made and its usable limit is discussed in detail for the measurement of turbulent thermal flows. Responses for a temperature step change, fluctuating temperature changes, and the thermal inertia of the working fluid temperature are considered. The response time of the microcapsulated liquid-crystal particle has been evaluated to be as much as 150 ms time delay for a step change of the working fluid temperature, which means the physical properties of the particle itself must be considered for outside temperature changes. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 390–398, 1998     

Gas–solid turbulent flow and heat transfer with collision effect in a vertical pipe

A turbulent gas–solid suspension upward flow in a vertical pipe is simulated numerically using Eulerian–Lagrangian approach. Particle–particle and particle–wall collisions are simulated based on deterministic approach. The influence of particle collisions on the particle concentration, mean temperature and fluctuating velocities are investigated. Numerical results are presented for different values of loading ratios. The profiles of particle concentration, mean velocity and temperature are shown to be flatter by considering inter-particle collisions, while this effect on the gas mean velocity and temperature is not significant. It is demonstrated that the effect of inter-particle collisions have a dramatic influence on the particle fluctuation velocity. It is shown that the profiles of particle concentration and particle velocity are flattened due to inter-particle collisions and this effect becomes more pronounced with increasing loading ratio. Also, the attenuation of turbulence by inter-particle collisions in the core region of the pipe is increased by increasing loading ratio.     

Heat transfer in a turbulent particle-laden channel flow

The objective of this paper is twofold: (i) to present and analyze particle temperature statistics in turbulent non-isothermal fully-developed turbulent gas–solid channel flow for a large range of particle inertia in order to better understand particle heat transfer mechanisms; (ii) to examine the performance of a recent Probability Density Function (PDF) model provided by Zaichik et al. (2011) [1]. In order to achieve such objectives, a Direct Numerical Simulation (DNS) coupled with a Lagrangian Particle Tracking (LPT) was used to collect fluid and particle temperature statistics after particles reach a statistically stationary regime. A non-monotonic behavior of particle temperature statistics is observed as inertia increases. The competition between different mechanisms (filtering inertia effect, preferential concentration, production of fluctuating quantities induced by the presence of the mean velocity and/or mean temperature gradients) are responsible for such a behavior. This competition is investigated from the exact transport equations of particle temperature statistical moments, fluid statistics conditionally-averaged at particle location, and instantaneous particle distribution in the flow field. Using these data, the accuracy of a PDF model is also assessed in the second part. From this assessment, it is seen that, despite the assumptions made, the model leads to a satisfactory prediction of most of the particle temperature statistics for not too high particle inertia.     

Effects of High-Order Slip/Jump,Thermal Creep,and Variable Thermophysical Properties on Natural Convection in Microchannels With Constant Wall Heat Fluxes

Natural convection gaseous slip flows in open-ended vertical parallel-plate microchannels with symmetric wall heat fluxes are numerically investigated. A second-order model, including thermal creep effects, is considered for velocity slip and temperature jump boundary conditions with variable thermophysical properties. Simulations are performed for wide range of Rayleigh numbers from 5 × 10^{? 6} to 5 × 10^{? 3} in the continuum to slip flow regime. The developing and fully developed solutions are examined by solving the Navier–Stokes and energy equations using a control volume technique. It is found that the second-order effects reduce the temperature jump and the slip velocity, whereas thermal creep strongly increases the slip velocity in both developing and fully developed regions. Moreover, the rarefaction effects increase the flow and heat transfer rates considerably, while decreasing the maximum gas temperature and friction coefficient as compared to the continuum limit. It was also shown that the axial temperature variations of the gas layer adjacent to the wall in the modeling of the thermal creep are of paramount importance and neglecting these variations, which is common in literature, leads to unphysical velocity and temperature distributions.     

Direct numerical simulation of thermal conductivity of nanofluids: The effect of temperature two-way coupling and coagulation of particles

An Eulerian–Lagrangian based direct numerical simulations (DNS) model was developed to investigate the effective thermal conductivity of nanofluids. A two-way coupling term to resolve the temperature interactions between the solid particles and fluid field was considered. The model also considered various forces acting on the nanoparticles. Cu/water nanofluids with 100 nm particles and Al₂O₃/water nanofluids with 80 nm particles were simulated at different volume fractions and the effective thermal conductivity of nanofluids was calculated. The present results suggest that the particle conductivity and forces acting on nanoparticle are necessary while predicting the effective thermal conductivity of nanofluids.     

Radiative heat transfer by flowing multiphase medium-part I. An analysis on heat transfer of laminar flow between parallel flat plates

The multiphase flow of gaseous suspensions of fine particles furnishes high heat transfer characteristics at high and/or extremely high temperatures and at high heat fluxes due to the radiative transfer from heat source to suspensions. The phaseshift of particulate medium improves the overall heat transfer remarkably and from the practical viewpoint there exists important relevance pertinent to the industrial applications.

It is worth having a closer look at the behaviors of the suspensions and the heat transfer mechanism in flowing multiphase media so that the discussions are held concerning the foregoing media in some details.

An analysis is carried out on the laminar flow between parallel plates by taking into account of thermal radiation and the results illustrate the temperature profiles of fluid and dispersed phase, respectively, and the heat transfer characteristics for the wide ranges of dimensionless parameters such as conduction y, and radiation interaction parameter, loading ratio of particles, optical depth of duct, heat transfer between the two phases and so forth. Reference to the temperature profiles reveals the facts that while the temperature gradient in the vicinity of the heating surface increases due to the presence of particulate phase, the cupmixing mean temperature is raised appreciably by thermal radiation through the dispersed medium. In consequence, the contributions of suspensions on heat transfer are drastic, particularly in high temperature cases. Alternatively the correlations between the foregoing dimensionless parameters are also examined in current study.     

Numerical study on fluid flow and heat transfer in the thin liquid film involving a hydraulic jump

The fluid flow and heat transfer in a thin liquid film are investigated numerically. The flow is assumed to be two-dimensional laminar, and surface tension effects at the exit are considered. The most important characteristic of this flow is the existence of a hydraulic jump through which the flow undergoes a very sharp and discontinuous change. In the present study, a simplified model of a free liquid jet impinging on a plane is considered. An arbitrary Lagrangian–Eulerian (ALE) method is used to describe the moving free boundary, and the fractional step method (FSM) based on the streamline upwind Petrov–Galerkin (SUPG) finite element method is used for the time-marching iterative solution. The numerical results obtained by solving the unsteady full Navier–Stokes equations are presented for plane and radial flows with constant wall temperature. © 1999 Scripta Technica, Heat Trans Asian Res, 28(1): 18–33, 1999