NUMERICAL MODELLING OF THREE-DIMENSIONAL FLY-ASH FLOW IN POWER UTILITY BOILERS

A two-fluid Eulerian model in combination with a particle–wall collision model and generalized Eulerian boundary conditions for the particulate phase is employed to predict complex three- dimensional fly-ash flows which often cause severe erosion to boiler tubes located in power utility boilers. Mean momentum and mass conservation equations are solved for each phase using a finite volume scheme with two-way coupling and a modified renormalization group (RNG)-based k –ϵ turbulence model. Comparison of predicted particle concentration with measured data is made and excellent agreement is obtained. The detailed character of the particulate velocity field and concentration just downstream of the 180° bend shows a marked dependence on the Stokes number not previously reported. © 1997 by John Wiley & Sons, Ltd.     

CFD simulation of particle suspension in a stirred tank

Particle suspension characteristics are predicted computationally in a stirred tank driven by a Smith turbine. In order to verify the hydrodynamic model and numerical method, the predicted power number and flow pattern are compared with designed values and simulated results from the literature, respectively. The effects of particle density, particle diameter, liquid viscosity and initial solid loading on particle suspension behavior are investigated by using the Eulerian–Eulerian two-fluid model and the standard k–? turbulence model. The results indicate that solid concentration distribution depends on the flow field in the stirred tank. Higher particle density or larger particle size results in less homogenous distribution of solid particles in the tank. Increasing initial solid loading has an adverse impact on the homogeneous suspension of solid particles in a low-viscosity liquid, whilst more uniform particle distribution is found in a high-viscosity liquid.     

A Lagrangian–Eulerian model of particle dispersion in a turbulent plane mixing layer

A Lagrangian–Eulerian model for the dispersion of solid particles in a two‐dimensional, incompressible, turbulent flow is reported and validated. Prediction of the continuous phase is done by solving an Eulerian model using a control‐volume finite element method (CVFEM). A Lagrangian model is also applied, using a Runge–Kutta method to obtain the particle trajectories. The effect of fluid turbulence upon particle dispersion is taken into consideration through a simple stochastic approach. Validation tests are performed by comparing predictions for both phases in a particle‐laden, plane mixing layer airflow with corresponding measurements formerly reported by other authors. Even though some limitations are detected in the calculation of particle dispersion, on the whole the validation results are rather successful. Copyright © 2002 John Wiley & Sons, Ltd.     

Thermo-mechanical modeling of turbulent heat transfer in gas–solid flows including particle collisions

A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas–solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k_θ–τ_θ equations, in addition to the hydrodynamic k–τ transport, and accounts for the particle–particle and particle–wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.     

Prediction of turbulent gas–solids flow in curved ducts using the Eulerian–Lagrangian method

The flow of particulate two‐phase flow mixtures occur in several components of solid fuel combustion systems, such as the pressurised fluidised bed combustors (PFBC) and suspension‐fired coal boilers. A detailed understanding of the mixture characteristics in the conveying component can aid in refining and optimising its design. In this study, the flow of an isothermal, dilute two‐phase particulate mixture has been examined in a high curvature duct, which can be representative of that transporting the gas–solid mixture from the hot clean‐up section to the gas turbine combustor in a PFBC plant. The numerical study has been approached by utilising the Eulerian–Lagrangian methodology for describing the characteristics of the fluid and particulate phases. By assuming that the mixture is dilute and the particles are spherical, the governing particle momentum equations have been solved with appropriately prescribed boundary conditions. Turbulence effects on the particle dispersion were represented by a statistical model that accounts for both the turbulent eddy lifetime and the particle transit time scales. For the turbulent flow condition examined it was observed that mixtures with small particle diameters had low interphase slip velocities and low impaction probability with the pipe walls. Increasing the particle diameters (>50 μm) resulted in higher interphase slip velocities and, as expected, their impaction probability with the pipe walls was significantly increased. The particle dispersion is significant for the smaller sizes, whereas the larger particles are relatively insensitive to the gas turbulence. The main particle impaction region, and locations most prone to erosion damage, is estimated to be within an outer duct length of two to six times the duct diameter, when the duct radius of curvature to the duct diameter ratio is equal to unity. Copyright © 1999 John Wiley & Sons, Ltd.     

Lagrangian particle dispersion in turbulent flow over a wall mounted obstacle

Large-eddy simulations (LES) of particle-laden turbulent flows are presented in order to investigate the effects of particle response time on the dispersion patterns of a space developing flow with an obstruction, where solid particles are injected inside the wake of an obstacle [Vincont, J.Y., Simoens, S., Ayrault M., Wallace, J.M., 2000. Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and downstream of an obstacle. J. Fluid Mech. 424, 127–167]. The numerical method is based on a fully explicit fractional step approach and finite-differences on Cartesian grids, using the immersed boundary method (IBM) to represent the existence of solid obstacles. Two different turbulence models have been tested, the classical Smagorinsky turbulence model and the filtered structure function model. The dispersed phase was modelled either by an Eulerian approach or a Lagrangian particle tracking scheme of solid particles with Stokes numbers in the range St = 0–25, assuming one-way coupling between the two phases. A very good agreement was observed between the Lagrangian and Eulerian approaches. The effect of particle size was found to significantly differentiate the dispersion pattern for the inhomogeneous flow over the obstacle. Although in homogeneous flows like particle-laden turbulent channels near-wall particle clustering increases monotonically with particle size, for the examined flow over an obstacle, preferential concentration effects were stronger only for an intermediate range of Stokes numbers.     

Particle statistics in a gas–solid coaxial strongly swirling flow: A direct numerical simulation

A direct numerical simulation of a strongly coaxial swirling particle-laden flow is conducted with reference to a previous experiment. The carrier phase is simulated as a coaxial swirling flow through a short nozzle injecting into a large container. The particle phase is carried by the primary jet, and simulated in the Lagrangian approach. The drag force, slip-shear force and slip-rotation force experienced by particles are calculated. A partial validation of the results is followed. The results are analyzed in Eulerian approach focusing on the statistical behavior of particle motion. The relative importance of the drag, slip-shear and slip-rotation forces under different Stokes numbers is indicated quantitatively. The particle velocity profiles, fluctuations, Reynolds stress, and turbulence intensity are demonstrated and analyzed respectively. An important “choke” behavior for large particles within the mainstream is found and interpreted. Additionally, the patterns of particle distribution and the helical structures of particle motion under different Stokes numbers are demonstrated qualitatively and analyzed quantitatively.     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.     

Effect of thermophoresis and other parameters on the particle deposition on a tilted surface

In this study a modified version of v2-f turbulence model (φ-α), is applied to simulate a non-isothermal air-flow. The φ-α model and a two-phase Eulerian approach complement each other to predict the rate of particle deposition on a tilted surface. The φ-α model can accurately calculate the normal fluctuations, which mainly represent the non-isotropic nature of turbulence regime near the wall. The Eulerian model was modified considering the most important mechanism in the particle deposition rate when compared to the experimental data. The model performance is examined by comparing the rate of particle deposition on a vertical surface with the experimental data in a turbulent channel flow available in the literature. The effects of lift force, turbophoretic force, thermophoreric force, electrostatic force, gravitational force and Brownian/turbulent diffusion were examined on the particle deposition rate. The results show that, using the φ-α model predicts the rate of deposition with reasonable accuracy. The results of modified particle model are in good agreement with the experimental data. This study highlights the paramount effect of thermophoretic force on the particle deposition rate and clearly shows that when the temperature difference exceeds a certain limit, the electrostatic force has insignificant effect on the particle deposition rate. Furthermore, it is indicated that even at small temperature differences, the effect of tilt angle on the particle deposition rate for intermediate-size particles is negligible.     

A hybrid Lagrangian–Eulerian particle‐level set method for numerical simulations of two‐fluid turbulent flows

A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical study on turbulence modulation in gas–particle flows

A mathematical model is proposed based on the Eulerian/Lagrangian approach to account for both the particle crossing trajectory effect and the extra turbulence production due to particle wake effects. The resulting model, together with existing models from the literature, is applied to two different particle-laden flow configurations, namely a vertical pipe flow and axisymmetric downward jet flow. The results show that the proposed model is able to provide improved predictions of the experimental results.     

Analysis of erosion behaviour in a turbocharger radial turbine

An analysis of the erosion behaviour of a turbocharger radial turbine is presented. The solution domain includes both sides of the radial turbine scroll with double intake and the rotor channel. In the analysis a dilute gas-particle flow assumption is employed. The gas turbulence is defined by the k-ε model. In solving the gas phase equation, the computer code Harwell-FLOW3D is employed, which is based on a finite volume formulation using non-orthogonal body-fitted structured gridding and a pressure correction method. The particle phase is described by a Lagrangian approach, while particle paths are computed deterministically, neglecting the turbulent dispersion. For the computation of particle trajectories the code PTRACK is employed, which has been developed at ABB. Computations are carried out for several particle size classes. The results show that particles are thrown back into the scroll by the rotor at high rates. This seems to be the main source of erosion effects in the scroll. It has been observed that particles are unequally distributed between the scroll sides on their re-entry, resulting in greater erosion on one of the scroll sides. The maximum erosion along the scroll is found to be likely to occur near the scroll end.     

Computation of particle dispersion in turbulent liquid flows using an efficient Lagrangian trajectory model

The dispersion of solid particles in a turbulent liquid flow impinging on a centrebody through an axisymmetric sudden expansion was investigated numerically using a Eulerian–Lagrangian model. Detailed experimental measurements at the inlet were used to specify the inlet conditions for two-phase flow computations. The anisotropy of liquid turbulence was accounted for using a second-moment Reynold stress transport model. A recently developed stochastic–probabilistic model was used to enhance the computational efficiency of Lagrangian trajectory computations. Numerical results of the stochastic–probabilistic model using 650 particle trajectories were compared with those of the conventional stochastic discrete-delta-function model using 18 000 particle trajectories. In addition, results of the two models were compared with experimental measurements. © 1998 John Wiley & Sons, Ltd.     

Analysis of unsteady gas–liquid flows in a rectangular tank: Comparison of Euler–Eulerian and Euler–Lagrangian simulations

We study the dynamics of gas–liquid flows experimentally and computationally in a rectangular bubble column where the gas source is introduced at the corner. The flow in this reactor is complex and inherently unsteady in nature. The two-dimensional liquid phase velocity field is calculated by an Eulerian approach solving the unsteady Reynolds Averaged Navier Stokes equations. The conservation equations are closed using a two parameter turbulence model. The two-way coupling was accounted for by adding source terms in the conservation equations of the continuous phase to take into account the interaction with the dispersed phase. Bubble tracking is achieved through a Lagrangian approach. Here the equations of motion are solved taking into account the drag, pressure, buoyancy and gravity forces. The time-averaged flows along with the variables which characterize turbulence are analyzed for a wide range of gas flow-rates using Euler–Lagrangian simulations. These simulation predictions are validated with Euler–Eulerian simulations where the gas-phase distribution is captured as a void fraction and PIV experiments. The motion of bubbles induces turbulence in the flow. The applicability of two parameter models for turbulence like the standard k–ε model on time-averaged flow properties is addressed. From the results of the time averaged velocity field, turbulence intensity, turbulent viscosity and gas hold-up profiles, it is concluded that the Euler–Lagrangian model is applicable at lower gas flow-rates. The Euler–Eulerian approach was found to be valid at lower as well as higher gas flow-rates.     

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.     

SPH computation of plunging waves using a 2‐D sub‐particle scale (SPS) turbulence model

The paper presents a 2‐D large eddy simulation (LES) modelling approach to investigate the properties of the plunging waves. The numerical model is based on the smoothed particle hydrodynamics (SPH) method. SPH is a mesh‐free Lagrangian particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The Smagorinsky model is used as the turbulence model due to its simplicity and effectiveness. The proposed 2‐D SPH–LES model is applied to a cnoidal wave breaking and plunging over a mild slope. The computations are in good agreement with the documented data. Especially the computed turbulence quantities under the breaking waves agree better with the experiments as compared with the numerical results obtained by using the k–ε model. The sensitivity analyses of the SPH–LES computations indicate that both the turbulence model and the spatial resolution play an important role in the model predictions and the contributions from the sub‐particle scale (SPS) turbulence decrease with the particle size refinement. Copyright © 2006 John Wiley & Sons, Ltd.     

Assessment of variants of the k–ϵ turbulence model for engine flow applications

This paper is concerned with simulation of the mean flow and turbulence evolution in a model engine and comparison of the behaviour of certain important turbulence parameters, namely the intensity, length scale and dissipation time scale, as predicted by three variants of the k–? model developed for application to strongly compressible flows. The predictions pertain to the axisymmetric, disc-chamber, four-stroke, Imperial College model engine operating at 200 rpm and compression ratios of 3·5 and 6·7. The paper analyses the predicted variations of these parameters during the induction, compression and expansion strokes and identifies the versions that produce the most consistent and physically plausible variations. The significance, to the turbulence evolution, of the ratio of the turbulence dissipation time scale to the time scale of compression/expansion is also discussed. It is concluded that on these grounds the Morel–Mansour and El Tahry versions are, and the Watkins version is not, suitable for engine applications.     

Numerical simulation of turbulent flow through series stenoses

The flow fields in the neighbourhoods of series vascular stenoses are studied numerically for the Reynolds numbers from 100 to 4000, diameter constriction ratios of 0.2–0.6 and spacing ratios of 1, 2, 3, 4 and ∞. In this study, it has been further verified that in the laminar flow region, the numerical predictions by k–ω turbulence model matched those by the laminar‐flow modelling very well. This suggests that the k–ω turbulence model is capable of the prediction of the laminar flow as well as the prediction of the turbulent stenotic flow with good accuracy. The extent of the spreading of the recirculation region from the first stenosis and its effects on the flow field downstream of the second stenosis depend on the stenosis spacing ratio, constriction ratio and the Reynolds number. For c₁ = 0.5 with c₂ ≤ c₁, the peak value of wall vorticity generated by the second stenosis is always less than that generated by the first stenosis. However, the maximum centreline velocity and turbulence intensity at the second stenosis are higher than those at the first stenosis. In contrast, for c₁ = 0.5 with c₂ = 0.6, the maximum values at the second stenosis are much higher than those at the first stenosis whether for centreline velocity and turbulence intensity or for wall vorticity. The peak values of the wall vorticity and the centreline disturbance intensity both grow up with the Reynolds number increasing. The present study shows that the more stenoses can result in a lower critical Reynolds number that means an earlier occurrence of turbulence for the stenotic flows. Copyright © 2003 John Wiley & Sons, Ltd.