Turbulent Velocity Fluctuations Research Articles

Deposition fraction of ellipsoidal fibers in a model of human nasal cavity for laminar and turbulent flows

In this study, the deposition fraction of ellipsoidal fibers in a realistic model of a human nasal cavity was evaluated for laminar and turbulent airflow conditions. The mean flow field was simulated by solving the discretized continuity and Navier-Stokes equations using the ANSYS-Fluent software. For ellipsoidal particle trajectory analysis, several user defined functions (UDFs) were developed and coupled to the ANSYS-Fluent discrete phase model (DPM). The presented formulation accounted for the coupled translation and rotational motions of ellipsoidal fibers and included the stochastic modeling of turbulence velocity and velocity gradient fluctuations. Particular attention was given to the proper modeling of turbulence fluctuation fields especially in the near wall region for accurate evaluation of fiber deposition rate. The predicted fiber deposition fractions in the nasal passage were compared with the available experimental and numerical results for both laminar and turbulent flows and good agreement was observed.

Experimental study on dependence of streak breakdown on disturbance nature

Instability and breakdown of a low-speed streak initially forced by disturbances with a frequency-spectrum similar to that of wall turbulence were examined experimentally. A single low-speed streak was generated using a small piece of screen set normal to a boundary-layer plate, and disturbances made by two loudspeakers were introduced through two small holes. Turbulent velocity fluctuations with various spanwise coherences were used as driving signals to two loudspeakers to see how strongly the streak breakdown depended on the nature of disturbances. Signals were deduced at two spanwise locations with distance Δz+= 24–149 in the buffer region of a turbulent boundary layer by using a pair of hot-wires. The correlation coefficient Ct of the two turbulent signals ranged from −0.11 to 0.56. Both sinuous and varicose modes were excited but the former became dominant downstream in all cases. Development of the disturbance excited was compared to those for anti-symmetric (Ct=−1) and symmetric (Ct=1) excitations with the same turbulent spectrum. The comparison showed that the magnitude of the sinuous instability mode excited was dependent on the initial disturbances, but not strongly for −1≤Ct≤0. That is, in terms of the rms value of velocity fluctuations, the magnitude of the sinuous instability mode for the initial disturbance with Ct∼0 was about 75% of that in the case of anti-symmetric forcing. Even for Ct∼+0.56, the magnitude of the sinuous mode excited was as large as 50% of that in the anti-symmetric case.

Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence

Direct numerical simulation of open-channel flow over a bed of spheres arranged in a regular pattern has been carried out at bulk Reynolds number and roughness Reynolds number (based on sphere diameter) of approximately 6900 and 120, respectively, for which the flow regime is fully rough. The open-channel height was approximately 5.5 times the diameter of the spheres. Extending the results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, pp. 441–474) for an open-channel flow in the transitionally rough regime, the present purpose is to show how the flow structure changes as the fully rough regime is attained and, for the first time, to enable a direct comparison with experimental observations. Different statistical tools were used to investigate the flow field in the roughness sublayer and in the logarithmic region. The results indicate that, in the vicinity of the roughness elements, the average flow field is affected both by Reynolds number effects and by the geometrical features of the roughness, while at larger wall distances this is not the case, and roughness concepts can be applied. Thus, the roughness function is computed which in the present set-up can be expected to depend on the relative submergence. The flow–roughness interaction occurs mostly in the region above the virtual origin of the velocity profile, and the effect of form-induced velocity fluctuations is maximum at the level of sphere crests. In particular, the root mean square of fluctuations about the streamwise component of the average velocity field reflects the geometry of the spheres in the roughness sublayer and attains a maximum value just above the roughness elements. The latter is significantly weakened and shifted towards larger wall distances as compared to the transitionally rough regime or the case of a smooth wall. The spanwise length scale of turbulent velocity fluctuations in the vicinity of the sphere crests shows the same dependence on the distance from the wall as that observed over a smooth wall, and both vary with Reynolds number in a similar fashion. Moreover, the hydrodynamic force and torque experienced by the roughness elements are investigated and the footprint left by vortex structures on the stress acting on the sphere surface is observed. Finally, the possibility either to adopt an analogy between the hydrodynamic forces associated with the interaction of turbulent structures with a flat smooth wall or with the surface of the spheres is also discussed, distinguishing the skin-friction from the form-drag contributions both in the transitionally rough and in the fully rough regimes.

Reactor modelling assessment for urea-SNCR applications

PurposeThis work aims to investigate the effects of neglecting, modelling or partly resolving turbulent fluctuations of velocity, temperature and concentrations on the predicted turbulence-chemistry interaction in urea-selective non-catalytic reduction (SNCR) systems.Design/methodology/approachNumerical predictions of the NO conversion efficiency in an industrial urea-SNCR system are compared to experimental data. Reactor models of varying complexity are assessed, ranging from one-dimensional ideal reactor models to state-of-the-art computational fluid dynamics simulations based on the detached-eddy simulation (DES) approach. The models use the same reaction mechanism but differ in the degree to which they resolve the turbulent fluctuations of the gas phase. A methodology for handling of unknown experimental data with regard to providing adequate boundary conditions is also proposed.FindingsOne-dimensional reactor models may be useful for a first quick assessment of urea-SNCR system performance. It is critical to account for heat losses, if present, due to the significant sensitivity of the overall process to temperature. The most comprehensive DES setup evaluated is associated with approximately two orders of magnitude higher computational cost than the conventional Reynolds-averaged Navier–Stokes-based simulations. For studies that require a large number of simulations (e.g. optimizations or handling of incomplete experimental data), the less costly approaches may be favored with a tolerable loss of accuracy.Originality/valueNovel numerical and experimental results are presented to elucidate the role of turbulent fluctuations on the performance of a complex, turbulent, reacting multiphase flow.

Coupled mesoscale‐LES modeling of a diurnal cycle during the CWEX‐13 field campaign: From weather to boundary‐layer eddies

AbstractMultiscale modeling of a diurnal cycle of real‐world conditions is presented for the first time, validated using data from the CWEX‐13 field experiment. Dynamical downscaling from synoptic‐scale down to resolved three‐dimensional eddies in the atmospheric boundary layer (ABL) was performed, spanning 4 orders of magnitude in horizontal grid resolution: from 111 km down to 8.2 m (30 m) in stable (convective) conditions. Computationally efficient mesoscale‐to‐microscale transition was made possible by the generalized cell perturbation method with time‐varying parameters derived from mesoscale forcing conditions, which substantially reduced the fetch to achieve fully developed turbulence. In addition, careful design of the simulations was made to inhibit the presence of under‐resolved convection at convection‐resolving mesoscale resolution and to ensure proper turbulence representation in stably‐stratified conditions. Comparison to in situ wind‐profiling lidar and near‐surface sonic anemometer measurements demonstrated the ability to reproduce the ABL structure throughout the entire diurnal cycle with a high degree of fidelity. The multiscale simulations exhibit realistic atmospheric features such as convective rolls and global intermittency. Also, the diurnal evolution of turbulence was accurately simulated, with probability density functions of resolved turbulent velocity fluctuations nearly identical to the lidar measurements. Explicit representation of turbulence in the stably‐stratified ABL was found to provide the right balance with larger scales, resulting in the development of intra‐hour variability as observed by the wind lidar; this variability was not captured by the mesoscale model. Moreover, multiscale simulations improved mean ABL characteristics such as horizontal velocity, vertical wind shear, and turbulence.

The Effects of Magnetic Fields on the Dynamics of Radiation Pressure–dominated Massive Star Envelopes

Abstract We use three-dimensional radiation magnetohydrodynamic simulations to study the effects of magnetic fields on the energy transport and structure of radiation pressure–dominated main sequence massive star envelopes at the region of the iron opacity peak. We focus on the regime where the local thermal timescale is shorter than the dynamical timescale, corresponding to inefficient convective energy transport. We begin with initially weak magnetic fields relative to the thermal pressure, from 100 to 1000 G in differing geometries. The unstable density inversion amplifies the magnetic field, increasing the magnetic energy density to values close to equipartition with the turbulent kinetic energy density. By providing pressure support, the magnetic field’s presence significantly increases the density fluctuations in the turbulent envelope, thereby enhancing the radiative energy transport by allowing photons to diffuse out through low-density regions. Magnetic buoyancy brings small-scale magnetic fields to the photosphere and increases the vertical energy transport, with the energy advection velocity proportional to the Alfvén velocity, although in all cases we study, photon diffusion still dominates the energy transport. The increased radiative and advective energy transport causes the stellar envelope to shrink by several scale heights. We also find larger turbulent velocity fluctuations compared with the purely hydrodynamic case, reaching at the stellar photosphere. The photosphere also shows vertical oscillations with similar averaged velocities and periods of a few hours. The increased turbulent velocity and oscillations will have strong impacts on the line broadening and periodic signals in massive stars.

Assessment of Algebraic Flame Surface Density Closures in the Context of Large Eddy Simulations of Head-On Quenching of Turbulent Premixed Flames

ABSTRACTThe applicability of algebraic large eddy simulation (LES) closures of flame surface density (FSD) for head-on quenching of premixed turbulent flames by an isothermal inert wall has been assessed using 3D direct numerical simulations (DNS) data for different values of root-mean-square turbulent velocity fluctuation, Damköhler and Karlovitz numbers. An algebraic FSD closure, which has been reported to perform relatively satisfactorily among several available models, has been considered for this analysis alongside a model, which has recently been used for LES of flame-wall interaction. The applicability of previously proposed near-wall damping factors for flame surface wrinkling and consumption rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations has also been assessed for LES based on the current a-priori DNS analysis. It has been found that existing models considered for this analysis do not predict the near-wall behavior of the FSD accurately for all cases considered here. Furthermore, the widely used expression (where and are the unburned gas density and the laminar burning velocity, respectively) has been found to overpredict the combined reaction rate and molecular diffusion term in the near-wall region but the agreement between these terms gets better away from the wall. However, does not sufficiently capture the local behavior of the density-weighted surface filtered displacement speed so the correlation coefficient between and the combined reaction rate and molecular diffusion term remains much smaller than unity. It has been found that the damping factors proposed for RANS are not suitable for LES, and they severely damp the near-wall magnitudes of FSD and the combined reaction rate and molecular diffusion term and lead to significant under-predictions. Based on this a-priori analyses new near-wall modifications to the generalized FSD and the combined reaction and molecular diffusion term have been proposed in the context of LES, which have been found to capture both qualitative and quantitative trends obtained from DNS data.

Combined CFD-Stochastic Analysis of an Active Fluidic Injection System for Jet Noise Reduction

In the framework of DANTE project (Development of Aero-Vibroacoustics Numerical and Technical Expertise), funded under the Italian Aerospace Research Program (PRORA), the prediction and reduction of noise from subsonic jets through the reconstruction of turbulent fields from Reynolds Averaged Navier Stokes (RANS) calculations are addressed. This approach, known as Stochastic Noise Generation and Radiation (SNGR), reconstructs the turbulent velocity fluctuations by RANS fields and calculates the source terms of Vortex Sound acoustic analogy. In the first part of this work, numerical and experimental jet-noise test cases have been reproduced by means RANS simulations and with different turbulence models in order to validate the approach for its subsequent use as a design tool. The noise spectra, predicted with SNGR, are in good agreement with both the experimental data and the results of Large-Eddy Simulations (LES). In the last part of this work, an active fluid injection technique, based on extractions from turbine and injections of high-pressure gas into the main stream of exhausts, has been proposed and finally assessed with the aim of reducing the jet-noise through the mixing and breaking of the turbulent eddies. Some tests have been carried out in order to set the best design parameters in terms of mass flow rate and injection velocity and to design the system functionalities. The SNGR method is, therefore, suitable to be used for the early design phase of jet-noise reduction technologies and a right combination of the fluid injection design parameters allows for a reduction of the jet-noise to 3.5 dB, as compared to the baseline case without injections.

Experimental investigations on liquid metal MHD turbulent flows through a circular pipe with a conductive wall

Experimental results on a liquid metal magnetohydrodynamic (MHD) turbulent flow through a circular conductive pipe subject to a uniform transversal magnetic field are summarized in this paper. The results of the MHD turbulent velocity distributions inside the conductive pipe are obtained. The velocity profiles along the center line of the middle cross section of the pipe are given. There are no big velocity jets in the Robert layers. The velocity distribution agrees well with the numerical simulation result. The transient turbulent velocity of one point in above mentioned line changing with times are measured in the experiment, it is found that the transient velocity varies dramatically compared to the average velocity at high Reynolds number (Re). The strong magnetic field suppresses the turbulent velocity fluctuation. The velocity profiles varying with the different Reynolds numbers at the same Hartmann number (Ha) are also presented in this paper. It is shown that the velocity in the center fluid area decreases with the Reynolds numbers increasing. The Reynolds stresses at different Reynolds numbers and Hartmann numbers are also derived from experimental data. The Reynolds stresses decrease with the increasing of Hartmann numbers. The map of laminar-turbulent transition for MHD circular conductive pipe flows at high Reynolds and Hartmann numbers are also presented. A different fluid instability from the theoretical prediction in Refs. Lielausis (1975) and Moresco et al. (2004) is observed and the transition condition is Re/Ha>20.

Large eddy simulation of piloted pulverised coal combustion using extended flamelet/progress variable model

An extended flamelet/progress variable (EFPV) model for simulating pulverised coal combustion (PCC) in the context of large eddy simulation (LES) is proposed, in which devolatilisation, char surface reaction and radiation are all taken into account. The pulverised coal particles are tracked in the Lagrangian framework with various sub-models and the sub-grid scale (SGS) effects of turbulent velocity and scalar fluctuations on the coal particles are modelled by the velocity-scalar joint filtered density function (VSJFDF) model. The presented model is then evaluated by LES of an experimental piloted coal jet flame and comparing the numerical results with the experimental data and the results from the eddy break up (EBU) model. Detailed quantitative comparisons are carried out. It is found that the proposed model performs much better than the EBU model on radial velocity and species concentrations predictions. Comparing against the adiabatic counterpart, we find that the predicted temperature is evidently lowered and agrees well with the experimental data if the conditional sampling method is adopted.

Turbulent-convective block for the ASTRA transport code

A physical model for the enhanced transport code is presented, which explicitly takes into account the contribution of turbulent convection to the processes of particle and heat transport in the hot core of the tokamak plasma. The model is based on the specially developed CONTRA-A turbulent block, while an adapted version of the existing ASTRA transport code is used as a transport envelope. The CONTRA-A turbulent block, based on the adiabatically reduced quasi-2D magnetohydrodynamic equations, calculates the generation and self-consistent evolution of low-frequency turbulence, including the spatiotemporal structure of turbulent fluctuations of the plasma velocity, density, and temperatures of electrons and ions. Using the obtained data on fluctuations, the CONTRA-A block calculates the turbulent-convective particle and heat fluxes and transfers them to the modified ASTRA code, which computes the evolution of quasi-equilibrium plasma parameters. To illustrate the capabilities of the enhanced transport model, the results of simulations of turbulent plasma evolution in two discharge scenarios with nonstationary auxiliary plasma heating in the T-10 and T-15MD tokamaks are presented.

Boundary layers at a dynamic interface: Air‐sea exchange of heat and mass

AbstractExchange of mass or heat across a turbulent liquid‐gas interface is a problem of critical interest, especially in air‐sea transfer of natural and anthropogenic gases involved in the study of climate. The goal in this research area is to determine the gas flux from air to sea or vice versa. For sparingly soluble nonreactive gases, this is controlled by liquid phase turbulent velocity fluctuations that act on the thin species concentration boundary layer on the liquid side of the interface. If the fluctuations in surface‐normal velocity and gas concentration are known, then it is possible to determine the turbulent contribution to the gas flux. However, there is no suitable fundamental direct approach in the general case where neither nor can be easily measured. A new approach is presented to deduce key aspects about the near‐surface turbulent motions from measurements that can be taken by an infrared (IR) camera. An equation is derived with inputs being the surface temperature and heat flux, and a solution method developed for the surface‐normal strain experienced over time by boundary layers at the interface. Because the thermal and concentration boundary layers experience the same near‐surface fluid motions, the solution for the surface‐normal strain determines the gas flux or gas transfer velocity. Examples illustrate the approach in the cases of complete surface renewal, partial surface renewal, and insolation. The prospects for use of the approach in flows characterized by sheared interfaces or rapid boundary layer straining are explored.

Experimental Investigation of Film-Cooling Effectiveness of a Highly Loaded Turbine Blade Under Steady and Periodic Unsteady Flow Conditions

This paper describes the experimental investigations of film-cooling effectiveness on a highly loaded low-pressure turbine blade under steady and unsteady wake flow conditions. The cascade facility in Turbomachinery Performance and Flow Research Lab (TPFL) at the Texas A&M University was used to simulate the periodic flow condition inside gas turbine engines. Moving wakes, originated from upstream stator blades, are simulated inside the cascade facility by moving rods in front of the blades. The flow coefficient is maintained at 0.8 and the incoming wakes have a reduced frequency of 3.18. A total of 617 holes on the blade are distributed along 13 different rows. Six rows cover the suction side, six other rows cover the pressure side, and one last row feeds the leading edge. Each row has a twin row on the other side of the blade with exact same number of holes and arrangement (except for leading edge). They both are connected to the same cavity. Coolant is injected from either sides of the blade through cavities to form a uniform distribution along the span of the blade. Film-cooling effectiveness under periodic unsteady flow condition was studied using pressure-sensitive paint. Experiments were performed at Reynolds number of 150,000 and blowing ratio of one, based on equal mass flux distribution. Experimental investigations were performed to determine the effect of flow separation and pressure gradient on film-cooling effectiveness. Moreover, the effect of impinging wakes on the overall film coverage of blade surfaces was studied. It was found that heat transfer coefficient (HTC) and film-cooling effectiveness (FCE) in majority of regions behave in opposite ways. This can be justified from turbulence intensity and velocity fluctuation point of view. Also, unsteady wakes imposed on top of film injection have opposite effects on suction and pressure side of the blade. This is more clearly seen in region near leading edge.

Large eddy simulation of turbulent attached cavitating flow with special emphasis on large scale structures of the hydrofoil wake and turbulence-cavitation interactions

In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simulation (LES) method coupled with a homogeneous cavitation model. The predicted lift coefficient and the cavity volume show a distinctly quasi-periodic process with cavitation shedding and the results agree fairly well with the available experimental data. The present simulation accurately captures the main features of the unsteady cavitation transient behavior including the attached cavity growth, the sheet/cloud cavitation transition and the cloud cavitation collapse. The vortex shedding structure from a hydrofoil cavitating wake is identified by the criterion, which implies that the large scale structures might slide and roll down along the suction side of the hydrofoil while being further developed at the downstream. Further analysis demonstrates that the turbulence level of the flow is clearly related to the cavitation and the turbulence velocity fluctuation is much influenced by the cavity shedding.

High sampling-rate measurement of turbulence velocity fluctuations in Mach 1.8 Laval jet using interferometric Rayleigh scattering**Project supported by the National Natural Science Foundation of China (Grant No. 11272337).

Interferometric Rayleigh scattering diagnostic technique for the time-resolved measurement of flow velocity is studied. Theoretically, this systematic velocity-measured accuracy can reach up to 1.23 m/s. Measurement accuracy is then evaluated by comparing with hot wire anemometry results. Moreover, the distributions of velocity and turbulence intensity in a supersonic free jet from a Laval nozzle with a Mach number of 1.8 are also obtained quantitatively. The sampling rate in this measurement is determined to be approximately 10 kHz.

Effect of different removal conditions on the growth and removal of inclusions in the molten steel in a two-strand tundish

In the current study, mathematical models were developed to predict the concentration, size distribution of inclusions in a two-strand tundish. The effect of the floating velocity, the velocity of the molten steel, and the turbulent fluctuation velocity on the removal of inclusions at the interface between the molten steel and slag was also studied. Meanwhile, the composition, amount, and size of inclusions in the steel were detected and the content of the total oxygen was obtained from the industrial trial. The calculated results were well validated by the measured ones. The strong stirring energy was greatly beneficial to the collision and growth of inclusions in the molten steel. When only considering the floating velocity, the removal fraction of inclusions was 23.4%. Furthermore, the contribution of the velocity of the molten steel and the turbulent fluctuation velocity to the removal fraction of inclusions at the top surface in the tundish was 23.2% and 14.5%, respectively. Finally, the mathematical model only considering the floating velocity can accurately predict the growth and removal of inclusions in the tundish.

Probability Distribution of Turbulent Velocity Fluctuations in a Patchy Vegetated Open Channel

The probability density function (PDF) for the stream wise velocity fluctuations was obtained for various cross sections in a patchy vegetated open channel. The pdf obtained for all the cross sections appeared to be qualitatively Gaussian, hence adequate to predict the extreme values arising from coherent structures of the patchy vegetated open channel for two experimental conditions. Relative to gravel bed, it is shown that the vegetation stem density produces asymmetric velocity fluctuations over the vegetated bed due to more distortion of large scale flow structures. At the boundary region however, the pdf is negatively skewed in experiment two relative to experiment one. This asymmetry is attributed to the enhanced lateral transport of momentum at the boundary region.

Turbulent boundary layer response to the introduction of stable stratification

The response of an initially neutral rough-wall turbulent boundary layer to a change in wall temperature is investigated experimentally. The change causes a localized peak in stable stratification that diffuses and moves away from the wall with downstream distance. The streamwise and wall-normal components of turbulent velocity fluctuations are damped at similar rates, even though the stratification only directly impacts the wall-normal component. The Reynolds shear profiles reveal the growth of an internal layer that scales approximately with the bulk Brunt–Väisälä frequency.

Statistical Analysis of the Reaction Progress Variable and Mixture Fraction Gradients in Flames Propagating into Droplet Mist: A Direct Numerical Simulation Analysis

ABSTRACTThe statistics of reaction progress variable, , and mixture fraction, , and their gradients (i.e., and ) in flames propagating in droplet mist, where the fuel was supplied in the form of monodisperse droplets, have been analyzed for different values of turbulent velocity fluctuations (), droplet equivalence ratios (, and droplet diameters ( based on three-dimensional direct numerical simulations (DNS) in a canonical configuration under decaying turbulence. The combustion process in the gaseous phase has been found to take place predominantly in fuel-lean mode, even for . The probability of finding fuel-lean mixture increases with increasing initial droplet diameter due to slower evaporation of larger droplets. It has been shown that the joint probability density function (i.e., joint PDF) of and (i.e., ), cannot be approximated in terms of discrete delta functions throughout the flame brush for the cases considered here. Furthermore, the magnitude of cannot be adequately approximated by the product of marginal PDFs of , and variable, (i.e., ). The statistical properties of the Favre probability density functions (Favre-PDFs) of the mixture fraction, , and oxidizer-based reaction progress variable, , have been analyzed at several locations across the flame brush and a -function distribution has been found to capture the Favre-PDFs of and obtained from the DNS data. Furthermore, a log-normal distribution has been shown to capture the qualitative behaviors of the PDFs of the gradient of the mixture fraction and the gradient of the reaction progress variable, and , respectively, but discrepancies between the log-normal distribution and the DNS data were observed at the tails of PDFs. In addition, the interrelation between and was examined in terms of the PDFs of the cosine of the angle between them (i.e., and it was observed that most droplet cases exhibited much greater likelihood of positive values of than negative values. Finally, the joint PDF of and , , has been compared with that of P( (i.e., assuming statistical independence of and ) and a good level of agreement has been obtained. The bivariate log-normal distribution has been considered both assuming correlation between and and assuming no correlation for the purpose of modeling , and the variant with no correlation has been found to be more successful in capturing qualitative behavior of although quantitative discrepancies have been observed due to inaccuracies involved in parameterizing P( and P(by log-normal distributions.

Reduced particle settling speed in turbulence

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).