A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the single-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions. The project supported by the Special Funds for Major State Basic Research, China (G-1999-0222-08), and the Postdoctoral Science Foundation (2004036239) The English text was polished by Keren Wang     

EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.     

Turbulent flows in channels with injection. results of large eddy simulation and the two-equation turbulence model

Turbulent flows in channels with intense distributed injection are modeled using the large eddy method and the two-equation k-? turbulence model. The calculations are carried out for different velocities of injection from the channel walls. For a channel with one-sided injection the results of large eddy simulation are in good agreement with the measured data, whereas the calculations in accordance with the k-? model give a less convex cross-sectional velocity profile and an appreciable error in determining the surface friction coefficient on the impermeable wall and also have certain other shortcomings. In the case of two-sided injection, the results of the calculations by the large eddy method and the k-? model are in good agreement with one another and the data of physical experiments.     

Statistical models for predicting the effect of bidisperse particle collisions on particle velocities and stresses in homogeneous anisotropic turbulent flows

The purpose of this paper is to present and compare two statistical models for predicting the effect of collisions on particle velocities and stresses in bidisperse turbulent flows. These models start from a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a homogeneous anisotropic turbulent flow. The kinetic equation describes simultaneously particle–turbulence and particle–particle interactions. The paper is focused on deriving the collision terms in the governing equations of the PDF moments. One of the collision models is based on a Grad-like expansion for the PDF of the velocity distributions of two particles. The other model stems from a Grad-like expansion for the joint fluid–particle PDF. The validity of these models is explored by comparing with Lagrangian simulations of particle tracking in uniformly sheared and isotropic turbulent flows generated by LES. Notwithstanding the fact that the fluid turbulence may be isotropic, the particle velocity fluctuations are anisotropic due to the impact of gravitational settling. Comparisons of the model predictions and the numerical simulations show encouraging agreement.     

Prediction of aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate in aqueous suspension by population balance model

The aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate, a ceramic pigment, in aqueous suspension was predicted by a modified population balance model. In the model, the collision frequencies were selected to describe evolution of the particle size distribution of the suspension. The collision efficiency was estimated as a function of interaction potential between particles based on Derjaguin–Landau–Verwey–Overbeek theory. The population balance model was modified to predict the stable state of the aggregation by introducing the volume mean size of aggregate to stability ratio. In addition, aggregation of the particles in aqueous suspension in the presence of sodium dodecyl benzene sulfonate or potassium chloride was experimentally investigated. The predicted data (i.e., the final aggregate size, aggregation rate, and particle size distribution) were similar to the experimental results.     

Two-phase turbulence models for simulating dense gas–particle flows

The two-fluid model is widely adopted in simulations of dense gas–particle flows in engineering facilities. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas–particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas–particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-Θ and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle–particle collision using the transport equation model for the two-phase velocity correlation.     

基于颗粒湍流和颗粒碰撞相互作用规律的湍流模型的研究

颗粒湍流和颗粒碰撞的相互作用规律是两相流动中的核心问题。用颗粒湍流模型和颗粒碰撞的动力论模型叠加的方法在研究两相湍流流动方面取得了一定的成效,但是还有待改进。本文基于颗粒湍流形成大尺度脉动和颗粒间碰撞引起小尺度脉动的概念,从双流体模型出发,建立了两相流动的双尺度kp-pε两相湍流模型。利用该模型对下行床和突扩室内的气固...     

Investigation of Particle Deposition Characteristics in Vicinity of Laidback Fan-shaped Film Cooling Holes

To design efficient film cooling systems and mitigate particulate deposition, it is very important to know the influences of the design parameters of film cooling holes on particulate deposition. However, most previous research focused on round film cooling holes. Particle deposition characteristics near shaped film cooling holes need to be studied further. In the present study, numerical computations were carried out to simulate the particle deposition behavior on gas turbine disk samples with laidback fan-shaped film cooling holes by using CFD-DPM (Computational fluid dynamics-discrete particle method). The critical velocities for particle sticking and detachment were determined by EI-Batsh model. Compared with round holes, shaped holes mitigate the particle-wall collision for small particles (d_p≤2μm, ρ_p=990kg/m ³), but promote particle-wall collision for large particles (d_p≥4μm, ρ_p=990kg/m ³). Adding the lateral and forward expansion angle can both cause the decrease of particle deposition efficiency, however, the effect of lateral expansion angle on particle deposition is more active.     

Understanding and Modelling Turbulence Over and Inside Porous Media

To understand turbulence over porous media, a series of PIV measurements were carried out in porous-walled channel flows. The porous walls were made of three types of foamed ceramics which had the same porosity but different permeability. For turbulence inside porous media, LES studies of fully developed flows in three different model porous media were performed. Referring to these databases, a multi-scale k ? ε four equation eddy viscosity model for turbulence around and/or inside porous media was developed. Through the comparison to the experimental results, the proposed model was validated with satisfactory accuracy.     

Study of the Spectral Difference Numerical Dissipation for Turbulent Flows Using Unstructured Grids

In this paper, the numerical dissipation properties of the Spectral Difference (SD) method are studied in the context of vortex dominated flows and wall-bounded turbulence, using uniform and distorted grids. First, the validity of using the SD numerical dissipation as the only source of subgrid dissipation (the so-called Implicit-LES approach) is assessed on regular grids using various polynomial degrees (namely, p = 3, p = 4, p = 5) for the Taylor-Green vortex flow configuration at R e = 5 000. It is shown that the levels of numerical dissipation greatly depend on the order of accuracy chosen and, in turn, lead to an incorrect estimation of the viscous dissipation levels. The influence of grid distortion on the numerical dissipation is then assessed in the context of finite Reynolds number freely-decaying and wall-bounded turbulence. Tests involving different amplitudes of distortion show that highly skewed grids lead to the presence of small-scale, noisy structures, emphasizing the need of explicit subgrid modeling or regularization procedures when considering coarse, high-order SD computations on unstructured grids. Under-resolved, high-order computations of the turbulent channel flow at R e _τ = 1000 using highly-skewed grids are considered as well and present a qualitatively similar agreement to results obtained on a regular grid.     

Studies on gas turbulence and particle fluctuation in dense gas-particle flows

Particle fluctuation and gas turbulence in dense gas-particle flows are less studied due to complexity of the phenomena. In the present study, simulations of gas turbulent flows passing over a single particle are carried out first by using RANS modeling with a Reynolds stress equation turbulence model and sufficiently fine grids, and then by using LES. The turbulence enhancement by the particle wake effect is studied under various particle sizes and relative gas velocities, and the turbulence enhancement is found proportional to the particle diameter and the square of velocity. Based on the above results, a turbulence enhancement model for the particle-wake effect is proposed and is incorporated as a sub-model into a comprehensive two-phase flow model, which is then used to simulate dilute gas-particle flows in a horizontal channel. The simulation results show that the predicted gas turbulence by using the present model accounting for the particle wake effect is obviously in better agreement with the experimental results than the prediction given by the model not accounting for the wake effect. Finally, the proposed model is incorporated into another two-phase flow model to simulate dense gasparticle flows in a downer. The results show that the particle wake effect not only enhances the gas turbulence, but also amplifies the particle fluctuation.     

Application of the γ-Reθ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 10⁵) was simulated using the Navier-Stokes equations and the γ-Re_θ transition model coupled with the SST k ? ω turbulence model (hereinafter abbreviated as γ-Re_θ model). Considering the effect of free-stream turbulence intensity decay, the SST k ? ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k ? ω turbulence model is coupled with the γ-Re_θ transition model (hereinafter abbreviated as γ-Re_θ-SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ-Re_θ-SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ-Re_θ-SR model, and the three flow states were analyzed. It was found that compared with the SST k ? ω turbulence model, the γ-Re_θ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ-Re_θ model, for relatively high inlet turbulence intensities, the γ-Re_θ-SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ-Re_θ-SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.     

Numerical Study of Turbulent Channel Flow over Surfaces with Variable Spanwise Heterogeneities: Topographically-driven Secondary Flows Affect Outer-layer Similarity of Turbulent Length Scales

Wall-bounded turbulent flows over surfaces with spanwise heterogeneous surface roughness – that is, spanwise-adjacent patches of relatively high and low roughness – exhibit mean flow phenomena entirely different to what would otherwise exist in the absence of spanwise heterogeneity. In the outer layer, mean counter-rotating rolls occupy the depth of the flow, and are positioned such that “upwelling” and “downwelling” occurs above the low and high roughness, respectively. It has been comprehensively shown that these secondary flows are Prandtl’s secondary flow of the second kind (Anderson et al., J. Fluid Mech. 768, 316–347 2015). This behaviour indicates that spanwise spacing, s _y , between adjacent patches of high and low roughness is, itself, a problem parameter; in this study, we have systematically assessed how s _y affects turbulence structure in high Reynolds number channel flows via two-point correlations. “High roughness” is imposed with streamwise-aligned pyramid elements with height, h, selected to be ≈ 5% of the channel half height, H. For \(s_{y}/H \gtrsim 1\), we find that the aforementioned domain-scale mean circulations exist and the surface may be regarded as a topography. For s _y /H ? 0.2, turbulence statistics show characteristics very similar to a homogeneous roughness and thus the surface may be regarded as a roughness. For 0.2 ? s _y /H ? 2, the spatial extent of the counter-rotating rolls is controlled by proximity to adjacent rows, and we define such surfaces as being intermediate. We refer to such surfaces as intermediate state.     

Slow gas motions and the negative drag of a strongly heated spherical particle

In the slow flows of a strongly and nonuniformly heated gas, in the continuum regime (Kn → 0) thermal stresses may be present. The theory of slow nonisothermal continuum gas flows with account for thermal stresses was developed in 1969–1974. The action of the thermal stresses on the gas results in certain paradoxical effects, including the reversal of the direction of the force exerted on a spherical particle in Stokes flow. The propulsion force effect is manifested at large but finite temperature differences between the particle and the gas. This study is devoted to the thermal-stress effect on the drag of a strongly heated spherical particle traveling slowly in a gas for small Knudsen numbers (M ～ Kn → 0), small but finite Reynolds numbers (Re ≤ 1), a linear temperature dependence of the transport coefficients µ ∝ T, and large but finite temperature differences ((T _w ? T _∞ )/T _M8 ～ 1). Two different systems of equations are solved numerically: the simplified Navier-Stokes equations and the modified Navier-Stokes equations with account for the thermal stresses.     

Simulation of Receptivity and Induced Transition From Discrete Roughness Elements

Simulations have been carried out to predict the receptivity and growth of crossflow vortices created by Discrete Roughness Elements (DREs) The final transition to turbulence has also been examined, including the effect of DRE spacing and freestream turbulence. Measurements by Hunt and Saric (2011) of perturbation mode shape at various locations were used to validate the code in particular for the receptivity region. The WALE sub-grid stress (SGS) model was adopted for application to transitional flows, since it allows the SGS viscosity to vanish in laminar regions and in the innermost region of the boundary layer when transition begins. Simulations were carried out for two spanwise wavelengths: λ= 12mm (critical) and λ= 6mm (control) and for roughness heights (k) from 12 μm to 42 μm. The base flow considered was an ASU (67)-0315 aerofoil with 45 ⁰ sweep at -2.9 ⁰ incidence and with onset flow at a chord-based Reynolds number Re _c= 2.4x10 ⁶. For λ= 12mm results showed, in accord with the experimental data, that the disturbance amplitude growth rate was linear for k = 12 μm and 24 μm, but the growth rate was decreased for k = 36 μm Receptivity to λ= 6mm roughness showed equally good agreement with experiments, indicating that this mode disappeared after a short distance to be replaced by a critical wavelength mode. Analysis of the development of modal disturbance amplitudes with downstream distance showed regions of linear, non-linear, saturation, and secondary instability behaviour. Examination of breakdown to turbulence revealed two possible routes: the first was 2D-like transition (probably Tollmien-Schlichting waves even in the presence of crossflow vortices) when transition occurred beyond the pressure minimum; the second was a classical crossflow vortex secondary instability, leading to the formation of a turbulent wedge.     

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU _w ≡ 2U _w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity u _τ , and h is the half-height of the channel. This leads to a one-parameter family of one-dimensional flows of varying Reynolds number Re ≡ U _w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of two each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend’s hypothesis of universal behavior for the velocity and shear stress, when they are normalized with u _τ and h; on the other hand universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford’s conjectures, suggesting that at least in this idealized flow turbulence theory is successful like it was for the classical logarithmic law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, that again does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.     

Numerical prediction of particle slip velocity in turbulence by CFD-DEM simulation

Turbulent environment improves the flotation recovery of fine particles by promoting the particle–bubble collision rate, which directly depends on the particle slip velocity. However, the existing slip velocity models are not applicable to fine particles in turbulence. The mechanism of turbulence characteristics and particle properties on the slip velocity of fine particles in turbulence was unclear. In this study, a coupled ANSYS FLUENT and EDEM based on computational fluid dynamics (CFD) and discrete element method (DEM) were used to simulate the slip velocity of fine particles in the approximately homogenous isotropic turbulence, which was excited by the grid. The reliability of the used CFD-DEM simulation method was validated against the slip velocity measured by the particle image velocimetry (PIV) experiments. In particular, the effects of the particle shapes, particle densities, and turbulence intensities on the slip velocity have been investigated with this numerical method. Numerical results show that particle shapes have no significant effect on fine particles between 37 and 225 μm. The slip velocity of the spherical particles increases with the turbulence intensity and particle density. Based on the simulated data, a model which has a correlation coefficient of 0.95 is built by using nonlinear fitting.     

Application of Lattice-Boltzmann Method for Analysing Detachment of Micron-Sized Particles from Carrier Particles in Turbulent Flows

Numerical calculations based on the Lattice-Boltzmann method were performed for a particle cluster consisting of a large spherical carrier particle covered with hundreds of small spherical drug particles. This cluster, fixed in space within a cubic computational domain, was exposed to turbulent plug airflow with predefined intensity. Such a situation is found in dry powder inhalers where carrier particles blended with fine drug powder are dispersed in a highly turbulent flow with the objective of detaching the drug powder for pulmonary delivery. Turbulence was generated by a digital filtering technique applied to the inflow velocity boundary condition. This technique was first validated by analysing the turbulence intensity at 15 fluid nodes along the stream-wise direction of the computational domain. The size ratio between the drug and carrier particle was 5 μ m/100 μ m, and the coverage degree of the carrier by the small particles was 50%, which is a typical value for carrier particle blending. The range of carrier particle Reynolds numbers considered was between 80 and 200, typical values found in inhaler devices. Exemplarily, at Re = 200 turbulence intensity was varied from 0.3% to 9.0%. The systematic increase of the mean flow (i.e. 80 < Re <200) resulted in varying turbulence intensities from 20 to 9%. These simulations provided the temporal evolution of the fluid dynamic forces on the drug particles in dependence of their angular position on the carrier in order to estimate the possibility of drug particle detachment. For turbulent conditions (i.e. Re = 200 and I = 9.0%) the maximum fluid forces on the drug particles were found to be about 10-times larger than found in laminar flow. The fluctuations in the forces were found to be higher than the flow velocity fluctuations due to the modification of the boundary layer around the cluster and instabilities triggered by the turbulent flow. There are three possibilities for detaching the drug powder, namely, through lift-off and sliding or rolling. Lift-off was found to be of minor importance due to the observed small normal fluid forces even at Re = 200 and I = 9.0%. The probability of sliding and rolling detachment in dependence of the angular position was estimated based on measured adhesion properties, i.e. van der Waals force, adhesion surface energy and friction coefficient. The remarkable rise of detachment probability for both effects due to the action of turbulence is an important finding of this study. In accordance with laminar flow, rolling detachment occurs before sliding, however in turbulent conditions over the entire carrier particle. The present studies improve the understanding of drug particle detachment from carrier particles in an inhaler device. The results will be the basis for developing Lagrangian detachment models that eventually should allow the optimisation of dry powder inhalators through computational fluid dynamics.     

Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

A scale-similarity model of a two-point two-time Lagrangian velocity correlation(LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows(HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80, 066313(2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity V. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values(R_λ = 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity.Moreover, the dispersion velocity V normalized by the Kolmogorov velocity V_η≡η/τ_η in which η and τ_η are the Kolmogorov space and time scales, respectively, scales with the Reynolds number R_λ as V/V_η∝ R_λ~(1.39) obtained from the numerical data.     

Reynolds-Averaged,Scale-Adaptive and Large-Eddy Simulations of Premixed Bluff-Body Combustion Using the Eddy Dissipation Concept

A lean premixed propane/air bluff-body stabilized flame (Volvo test rig) is calculated using the Scale-Adaptive Simulation turbulence model (SAS) and Large-Eddy simulations (LES) as well as the conventional Reynolds-averaged approach (RAS). RAS and SAS are closed by the standard k-?? and the k-ω Shear Stress Transport (SST) turbulence models, respectively. The conventional Smagorinsky and the k-equation sub-grid scales models are used for the LES closure. Effects of the sub-grid scalar flux modeling using the classical gradient hypothesis and Clark’s tensor diffusivity closures both for the inert and reactive LES flows are discussed. The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction. It assumes that molecular mixing and the subsequent combustion occur in the ’fine structures’ (smaller dissipative eddies, which are close to the Kolmogorov scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the ’fine structures’ are evaluated using different turbulence models (RAS, SAS and LES). The finite-rate chemical kinetics is taken into account by treating the ’fine structures’ as constant pressure and adiabatic homogeneous reactors, calculated as a system of ordinary-differential equations (ODEs) described by a Perfectly Stirred Reactor (PSR) concept. Several further enhancements to model the PSRs are proposed, including a new Livermore Solver (LSODA) for integrating stiff ODEs and a new correction to calculate the PSR time scales. All models have been implemented as a stand-alone application \(\text {edcPisoFoam}\) based on the OpenFOAM technology. Additionally, several RAS calculations were performed using the Turbulence Flame Speed Closure model in Ansys Fluent to assess effects of the heat losses by modeling the conjugate heat transfer between the bluff-body and the reactive flow. Effects of the turbulence Schmidt number on RAS results are discussed as well. Numerical results are compared with available experimental data. Reasonable consistency between experimental data and numerical results provided by RAS, SAS and LES is observed. In general, there is satisfactory agreement between present LES-EDC simulations, numerical results by other authors and measurements without any major modification to the EDC closure constants, which gives a quite reasonable indication on the adequacy and accuracy of the method and its further application for turbulent premixed combustion simulations.