On the use of Csanady’s formulae in a turbulent gas–solid channel flow

The paper examines the use of expressions proposed by Csanady to predict the influence of the crossing trajectory and continuity effects on the decorrelation time scales of the fluid along solid particle trajectories in horizontal and downward vertical channel flows. The model is evaluated using data provided by a direct numerical simulation (DNS) of the carrier phase combined with a Lagrangian simulation of discrete particle (LS). Two particle relaxation times and two values of the gravity acceleration are considered. The results show the possibility of using Csanady’s expressions in a turbulent channel flow provided that the spatial and temporal correlations anisotropy is included in the model. As in isotropic homogeneous turbulence, a decrease of the decorrelation time scales is found to be more important in the directions perpendicular to the mean relative velocity.     

Characteristics of turbulence transport for momentum and heat in particle-laden turbulent vertical channel flows

The dynamic and thermal performance of particle-laden turbulent flow is investigated via direction numerical simulation combined with the Lagrangian point-particle tracking under the condition of two-way coupling, with a focus on the contributions of particle feedback effect to momentum and heat transfer of turbulence. We take into account the effects of particles on flow drag and Nusselt number and explore the possibility of drag reduction in con-junction with heat transfer enhancement in particle-laden turbulent flows.The effects of particles on momentum and heat transfer are analyzed,and the possibility of drag reduc-tion in conjunction with heat transfer enhancement for the prototypical case of particle-laden turbulent channel flows is addressed.We present results of turbulence modification and heat transfer in turbulent particle-laden channel flow,which shows the heat transfer reduction when large inertial parti-cles with low specific heat capacity are added to the flow. However,we also found an enhancement of the heat transfer and a small reduction of the flow drag when particles with high specific heat capacity are involved.The present results show that particles,which are active agents,interact not only with the velocity field,but also the temperature field and can cause a dissimilarity in momentum and heat transport.This demonstrates that the possibility to increase heat transfer and suppress friction drag can be achieved with addition of par-ticles with different thermal properties.     

Spectral-based simulations of particle-laden turbulent flows

In this paper, we discuss the application of spectral-based methods to simulation of particle-laden turbulent flows. The primary focus of the article is on the past and ongoing works by the authors. The particles are tracked in Lagrangian framework, while direct numerical simulation (DNS) or large-eddy simulation (LES) is used to describe the carrier-phase flow field. Two different spectral methods are considered, namely Fourier pseudo-spectral method and Chebyshev multidomain spectral method. The pseudo-spectral method is used for the simulation of homogeneous turbulence. DNS of both incompressible and compressible flows with one- and two-way couplings are reported. For LES of particle-laden flows, two new models, developed by the authors, account for the effect of sub-grid fluctuations on the dispersed phase. The Chebyshev multidomain method is employed for the works on inhomogeneous flows. A number of canonical flows are discussed, including flow past a square cylinder, channel flow and flow over backward-facing step. Ongoing research on particle-laden LES of inhomogeneous flows is briefly reported.     

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.     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

On the role of the lateral lift force in poly-dispersed bubbly flows

An extensive experimental database comprising air–water as well as steam-water upwards vertical pipe flows for a pressure up to 6.5 MPa was used to investigate the effect of the lateral lift force on turbulent poly-dispersed flows with medium or high gas volume fraction. It was clearly shown that the lift force plays an important role also in such flows. Several effects such as bubble coalescence and breakup as well as fast rising large bubbles which push small bubbles towards the pipe wall superpose the effect of the lift force but can be separated from this effect. The critical bubble diameter, at which the lift force changes its sign, predicted by using Tomiyama’s correlation agrees well with experimental data obtained for turbulent air–water and steam-water flows with medium and high void fraction and a broad spectrum of bubbles sizes. The values for this critical bubble diameter are confirmed by the experimental data within the frame of the uncertainty of the data. Consequences of the action of the lateral lift force on flow structures in different flow situations are discussed. From the investigations it can be concluded that the lift force including the bubble size dependent change of its sign should be considered in a proper numerical 2D or 3D-simulation on flows in which bubbles in the range of several millimeters are present.     

Accounting for finite-size effects in simulations of disperse particle-laden flows

A numerical formulation for Eulerian–Lagrangian simulations of particle-laden flows in complex geometries is developed. The formulation accounts for the finite-size of the dispersed phase. Similar to the commonly used point-particle formulation, the dispersed particles are treated as point-sources, and the forces acting on the particles are modeled through drag and lift correlations. In addition to the inter-phase momentum exchange, the presence of particles affects the fluid phase continuity and momentum equations through the displaced fluid volume. Three flow configurations are considered in order to study the effect of finite particle size on the overall flowfield: (a) gravitational settling, (b) fluidization by a gaseous jet, and (c) fluidization by lift in a channel. The finite-size formulation is compared to point-particle representations, which do not account for the effect of finite-size. It is shown that the fluid displaced by the particles plays an important role in predicting the correct behavior of particle motion. The results suggest that the standard point-particle approach should be modified to account for finite particle size, in simulations of particle-laden flows.     

On an attempt to simplify the Quartapelle–Napolitano approach to computation of hydrodynamic forces in open flows

In this paper we are interested in the Quartapelle–Napolitano approach to calculation of forces in viscous incompressible flows in exterior domains. We study the possibility of deriving a simpler formulation of this approach which might lead to a more convenient expression for the hydrodynamic force, but conclude that such a simplification is, within the family of approaches considered, impossible. This shows that the original Quartapelle–Napolitano formula is in fact “optimal” within this class of approaches.     

On the role of the smallest scales of a passive scalar field in a near-wall turbulent flow

Role of the smallest diffusive scales of a passive scalar field in the near-wall turbulent flow was examined with pseudo-spectral numerical simulations. Temperature fields were analyzed at friction Reynolds number Re _τ=171 and at Prandtl numbers, Pr=1 and Pr=5.4. Results of direct numerical simulations (DNS) were compared with the under-resolved simulations where the velocity field was still resolved with the DNS accuracy, while a coarser grid was used to describe the temperature fields. Since the smallest temperature scales remained unresolved in these simulations, an appropriate spectral turbulent thermal diffusivity was applied to avoid pile-up at the higher wave numbers. In spite of coarser numerical grids, the temperature fields are still highly correlated with the DNS results, including instantaneous temperature fields. Results point to practically negligible role of the diffusive temperature scales on the macroscopic behavior of the turbulent heat transfer.     

On calculation of hydrodynamic forces for steady flows in unbounded domains

This note addresses the question why the “impulse formula”, often employed to compute hydrodynamic forces in vortex-dominated time-dependent flows, is not applicable to steady flows in unbounded domains. By analyzing the asymptotic structure of steady and unsteady flow solutions in unbounded domains, it is demonstrated that one assumption made in the derivation of the impulse formula is in fact not satisfied in the steady case. This result also highlights the special character of steady flows in unbounded domains.     

PIV measurement of particle motion in spiral gas–solid two-phase flow

With a concise review on some basic and novel algorithms and methods for the techniques of particle-imaging velocimetry (PIV), the paper reports an application of the PIV techniques to the investigation of particle motion in a gas–solid two-phase spiral flow in a horizontal tube. Axial velocities of the transported particles are obtained. Some important features of particle motion governing high transportation efficiency of the spiral flow are revealed by investigating probability density distribution of particle locations in a pipe cross-section.     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

Large Eddy Simulations of turbulent particle-laden channel flow

This paper scrutinises the Large Eddy Simulation (LES) approach to simulate the behaviour of inter-acting particles in a turbulent channel flow. A series of simulations that are fully (four-way), two-way and one-way coupled are performed in order to investigate the importance of the individual physical phenomena occurring in particle-laden flows. Moreover, the soft sphere and hard sphere models, which describe the interaction between colliding particles, are compared with each other and the drawbacks and advantages of each algorithm are discussed. Different models to describe the sub-grid scale stresses with LES are compared. Finally, simulations accounting for the rough walls of the channel are compared to simulations with smooth walls. The results of the simulations are discussed with the aid of the experimental data of Kussin J. and Sommerfeld M., 2002, Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness, Exp. in Fluids, 33, pp. 143–159 of Reynolds number 42,000 based on the full channel height. The simulations are carried out in a three-dimensional domain of 0.175 m × 0.035 m  × 0.035 m where the direction of gravity is perpendicular to the flow. The simulation results demonstrate that rough walls and inter-particle collisions have an important effect in redistributing the particles across the channel, even for very dilute flows. A new roughness model is proposed which takes into account the fact that a collision in the soft sphere model is fully resolved and it is shown that the new model is in very good agreement with the available experimental data.     

On the capability of the curvilinear immersed boundary method in predicting near-wall turbulence of turbulent channel flows

The immersed boundary method has been widely used for simulating flows over complex geometries.However, its accuracy in predicting the statistics of near-wall turbulence has not been fully tested. In this work, we evaluate the capability of the curvilinear immersed boundary(CURVIB) method in predicting near-wall velocity and pressure fluctuations in turbulent channel flows. Simulation results show that quantities including the time-averaged streamwise velocity, the rms(root-mean-square) of velocity fluctuations, the rms of vorticity fluctuations, the shear stresses, and the correlation coefficients of u and v computed from the CURVIB simulations are in good agreement with those from the body-fitted simulations. More importantly, it is found that the time-averaged pressure, the rms and wavenumber-frequency spectra of pressure fluctuations computed using the CURVIB method agree well with the body-fitted results.     

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.     

On the nature of the organized structures in turbulent near-wall flows

A physical mechanism of onset of large-scale organized structures in turbulent flows along a plane wall which are the cause of intensification of turbulent fluctuations is formulated. The structures take the form of high-speed and low-speed streaks caused by streamwise vortices, i.e., motions in the plane of the transverse cross-section. The streamwise vortices are excited as a result of instability under the action of the anisotropy of the normal components of the Reynolds stress tensor. A model for describing these vortices that gives characteristics in qualitative and quantitative agreement with the experimental data is proposed. In particular, the most probable and mean distances between neighboring vortices are correctly reproduced. The theory makes it possible to explain certain methods of turbulent flow control for the purpose of drag reduction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–30, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00602).     

Sidewall flow stability in the MHD channel flows

The velocity distribution between two sidewalls is M-shaped for the MHD channel, flows with rectangular cross section and thin conducting walls in a strong transverse magnetic field. Assume that the dimensionless numbersR _m ?1,M, N? 1, and σ* and that the distance between two perpendicular walls is very long in comparison with the distance between two sidewalls. First, the equation for steady flow is established, and the solution of M-shaped velocity distribution is given. Then, an equation for stability of small disturbances is derived based on the velocity distribution obtained. Finally, it is proved that the stability equation for sidewall flow can be transformed into the famous Orr-Sommerfeld equation, in addition, the following theorems are also proved, namely, the analogy theorem, the generalized Rayleigh's theorem, the generalized Fjørtoft's theorem and the generalized Joseph's theorems.     

On the relationship between drag and vertical velocity fluctuations in flow over riblets and liquid infused surfaces

Direct numerical simulations (DNS) of flow over triangular and rectangular riblets in a wide range of size and Reynolds number have been carried out. The flow within the grooves is directly resolved by exploiting the immersed-boundary method. It is found that the drag reduction property is primarily associated with the capability of inhibiting vertical velocity fluctuations at the plane of the crests, as in liquid-infused surfaces (LIS) devices. This is mimicked in DNS through artificial suppression of the vertical velocity component, which yields large drag decrease, proportionate to the riblets size. A parametrization of the drag reduction effect in terms of the vertical velocity variance is found to be quite successful in accounting for variation of the controlling parameters. A Moody-like friction diagram is thus introduced which incorporates the effect of slip velocity and a single, geometry-dependent parameter. Reduced drag-reduction efficiency of LIS-like riblets is found as compared to cases with artificially imposed slip velocity. Last, we find that simple wall models of riblets and LIS-like devices are unlikely to provide accurate prediction of the flow phenomenon, and direct resolution of flow within the grooves in necessary.     

Numerical simulation and experimental validation of gas–solid flow in the riser of a dense fluidized bed reactor

Gas–solid flow in the riser of a dense fluidized bed using Geldart B particles (sand), at high gas velocity (7.6–15.5 m/s) and with comparatively high solid flux (140–333.8 kg/m² s), was investigated experimentally and simulated by computational fluid dynamics (CFD), both two- and three-dimensional and using the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd and EMMS drag models. The results predicted by EMMS drag model showed the best agreement with experimental results. Calculated axial solids hold-up profiles, in particular, are well consistent with experimental data. The flow structure in the riser was well represented by the CFD results, which also indicated the cause of cluster formation. Complex hydrodynamical behaviors of particle cluster were observed. The relative motion between gas and solid phases and axial heterogeneity in the three subzones of the riser were also investigated, and were found to be consistent with predicted flow structure. The model could well depict the difference between the two exit configurations used, viz., semi-bend smooth exit and T-shaped abrupt exit. The numerical results indicate that the proposed EMMS method gives better agreement with the experimental results as compared with the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd models. As a result, the proposed drag force model can be used as an efficient approach for the dense gas–solid two-phase flow.