Vertical Turbulent Channel Flow Research Articles

Improved modelling of interfacial terms in the second-moment closure for particle-laden flows based on interface-resolved simulation data

Correlations for the interfacial terms in the fluid dissipation rate equation and Reynolds stress equations are established for particle-laden flows, based on data from the interfaced-resolved direct numerical simulations of particle sedimentation in a periodic domain at a density ratio ranging from 0.01 to 1000, a particle concentration ranging from 2.3 % to 30.2 % and a particle Reynolds number below 250. The correlations for the mean drag and the pseudo-turbulent kinetic energy are also reported, which are used for the modelling of the interfacial term in the fluid dissipation rate equation. The interfacial term correlations obtained are then incorporated in the Reynolds stress model (RSM) (i.e. second-moment closure) for the simulation of vertical turbulent channel flows laden with the finite-size particles at relatively low particle volume fractions. The results show that the RSM with new interfacial term correlations can quantitatively predict particle-induced turbulence enhancement or suppression in vertical channel flows.

Dynamics of particle-laden turbulent Couette flow: Turbulence modulation by inertial particles

In particle-laden turbulent flows, it is established that the turbulence in the carrier fluid phase gets affected by the dispersed particle phase for volume fractions above 10−4. Hence, reverse coupling or two-way coupling becomes relevant in that volume fraction regime. Due to their greater inertia, larger particles change either the mean flow or the intensity of fluid-phase fluctuations. In a recent study [Muramulla et al., “Disruption of turbulence due to particle loading in a dilute gas–particle suspension,” J. Fluid Mech. 889, A28 (2020)], a discontinuous decrease of turbulence intensity is observed in a vertical particle-laden turbulent channel flow for a critical volume fraction O(10−3) for particles with varying Stokes numbers (St) in the range of 1−420 based on the fluid-integral time scales. The collapse of turbulent intensity is found out to be the result of a “catastrophic reduction of turbulent energy production rate.” Mechanistically, a turbulent Couette flow differs from a pressure-driven channel flow in many ways, such as fluid-phase mean-velocity profile and turbulent coherent structures. In the particle-laden Couette flow, particles are treated as neutrally buoyant. Therefore, it is worth investigating the mechanism of turbulence modulation by inertial particles in the particle-laden turbulent Couette flow. In this article, the turbulence modulation in the fluid phase in the presence of inertial particles is investigated using two-way coupled direct numerical simulations of a particle-laden sheared turbulent suspension. The particle volume fraction (ϕ) is varied from 1.75×10−4 to 1.05×10−3 and the Reynolds number based on the half-channel width (δ) and the wall velocity (U) (Reδ) is 750. The particles are of high inertia with St∼367 based on a fluid integral timescale represented by δ/U. A discontinuous decrease in turbulence intensity and Reynolds stress is observed beyond a critical volume fraction ϕcr∼7.875×10−4. The drastic reduction of shear production of turbulence leads to the collapse of fluid-phase turbulence. The stepwise particle injection and stepwise removal study confirm the role of critical volume loading in the discontinuous transition. Additionally, the effect of the nature of particle–particle and particle–wall collisions has been investigated. It is observed that the inelastic collisions increase the ϕcr marginally although the nature of turbulence modulation remains similar. The explicit role of the inter-particle collisions has also been investigated by switching off the particle–particle collisions. In this case, ϕcr increases more than in the case of an inelastic collision. The turbulence modulation carries the signatures of transition from sheared turbulence to particle-driven fluid fluctuation at higher volume loading.

Drag model from interface-resolved simulations of particle sedimentation in a periodic domain and vertical turbulent channel flows

A drag correlation is established for laminar particle-laden flows, based on data from the interfaced-resolved direct numerical simulations (IR-DNS) of particle sedimentation in a periodic domain at density ratio ranging from 2 to 1000, particle concentration ranging from 0.59 % to 14.16 %, and particle Reynolds number below 132. Our drag decreases slightly with increasing density ratio when the other parameters are fixed. The drag correlation is then corrected to account for the turbulence effect by introducing the relative turbulent kinetic energy, from the IR-DNS data of the upward turbulent channel flows laden with the particles larger than the Kolmogorov length scale at relatively low particle volume fractions. A drift velocity model is developed to obtain the effective slip velocity from the interphase mean velocity difference for the vertical turbulent channel flow by considering the effects of particle inertia, particle concentration distribution and large-scale streamwise vortices.

Micro-swimmers in vertical turbulent channel flows

The behavior of micro-organisms in fluid flows, with a rich spectrum of dynamics, has been long an intriguing problem. Despite the wide presence of micro-swimmers in nature, only recently has their motility in turbulence been explored by simulation and experimental approaches. In this work, we study the effect of active swimming on motile micro-organisms in vertical turbulent channel flows by direct numerical simulations. The micro-swimmers are elongated and modeled as inertia-less prolate spheroids which are also subjected to gravity induced settling. The swimmers show a non-uniform distribution in the wall-normal direction and preferential orientation in mean flow direction. Particles with a predominant swimming velocity accumulate near the solid walls, regardless of the flow direction. This differs from the case of settling non-motile particles where flow direction changes the location of particle accumulation. The underlying mechanisms are explained by the wall-normal transport process including particle–fluid slip velocity and local clustering. The mean slip velocity makes the swimmer drift towards the wall relative to the local fluid, while the local fluid carries the swimmers away from the wall. Particle distribution reaches a stable state as the two mechanisms balance each other. In terms of orientation for prolate spheroids, swimming has been shown to increase a tendency that particles align with the streamwise direction. This suggests that swimming plays an important role in orientation, motion and accumulation of micro-organisms in wall turbulence. Our discovery may contribute to further understanding of the behavior of many aquatic creatures including algae and oyster larvae in natural environment and industrial bioreactors.

Interface-resolved direct numerical simulations of the interactions between spheroidal particles and upward vertical turbulent channel flows

The interactions between finite-size spheroidal particles and upward turbulent flows in a vertical channel are numerically simulated with a direct-forcing fictitious domain method at two particle settling coefficients $u_{s}$ (the ratio of the particle Stokes free-fall velocity to the bulk velocity) of 0.1 and 0.3, a bulk Reynolds number of 2873, a ratio of the particle equivalent diameter to the channel width of 0.05, a particle volume fraction of 2.36 % and particle aspect ratios of $1/3$ , 1 and 2. Our results show that the flow friction is largest for the case of a sphere, and smallest for the oblate case when the particle sedimentation effect is weak ( $u_{s}=0.1$ ), whereas the flow friction is smallest for the case of a sphere, and largest for the oblate case when the particle sedimentation effect is moderately strong ( $u_{s}=0.3$ ). The reason for the lower flow friction of the spherical particles is that the large-scale vortices are more strongly attenuated by the spherical particles than by the non-spherical particles in the case of $u_{s}=0.3$ . The settling particles tend to migrate towards the channel centre due to the Saffman effect, and the migration is strongest for the spherical particles. The non-spherical particles tend to align their long axes with the streamwise direction in the near-wall region, and perpendicular to the streamwise direction in the bulk region due to the significant settling effect.

Near-Wall heat transfer of solid particles in particle-laden turbulent flows

Abstract The focus of this study is on the near-wall thermal interaction of micro-particles in a vertical turbulent channel flow. Three mechanisms for the heat transfer of solid particles and the wall, when the distance between the particles and wall is less than half of the particle's radius, have been considered. The first two mechanisms are the solid-solid (Qss) and the solid-fluid-solid (Qsfsc) heat transfer of wall-colliding particles. The time of collision and the contact area are calculated based on the elastic Hertzian contact equations. The third mechanism is the solid-fluid-solid (Qsfsp) heat transfer for particles that do not hit the wall but move closely parallel to the wall. Mathematical models for these three mechanisms are implemented into an Eulerian-Lagrangian direct numerical simulation (DNS) solver for a particle Stokes number of St = 192, and a constant particle mass loading of φm= 0.54. Comparing these three mechanisms, it is shown that the heat transfer rate via the third mechanism (Qsfsp) is significantly larger than the ones of the two other mechanisms (Qss, Qsfsc). This can be contributed to the fact that some of the near wall particles stay in the laminar sublayer for a large time interval and by moving parallel to the wall they have enough time to have direct thermal interaction with the wall. The overall heat transfer rate of particle-laden flow, however, is almost unaffected by the inclusion of these thermal interactions at this mass loading and particle Stokes number. The only effect of including these near-wall particle interactions is to slightly decrease the slope of the temperature profile, the convective heat transfer, and the fluid-particle temperature difference at the near wall region.

A fictitious domain method for particulate flows of arbitrary density ratio

In this paper, our previous direct-forcing fictitious domain method is modified for particle-laden flows of arbitrary density ratio. The instability of original scheme for low density ratio is circumvented by a simple modification in the particle motion equations, with the key idea of increasing the coefficient of particle inertial term. Three schemes are proposed, which are shown to be equally accurate. The modified DF/FD method is extensively validated with various tests, and it is shown that the accuracy of our method is comparable to previous methods. In addition, our method is applied to the direct numerical simulations of the motion of finite-size particles (or bubbles) in a vertical turbulent channel flow of the density ratio 0.001. Our results indicate that the effects of particle-fluid density ratio on turbulent channel flow are negligibly small when the density ratio is smaller than unity and the gravity effect is not considered. The fluid Reynolds shear stress and the wall friction are enhanced in upflow where the particles are aggregated near the wall, whereas they are reduced in downflow where the particles move towards the channel center.

Inertial particle velocity and distribution in vertical turbulent channel flow: A numerical and experimental comparison

This study is concerned with the statistics of vertical turbulent channel flow laden with inertial particles for two different volume concentrations (ΦV=3×10−6 and ΦV=5×10−5) at a Stokes number of St+=58.6 based on viscous units. Two independent direct numerical simulation models utilizing the point-particle approach are compared to recent experimental measurements, where all relevant nondimensional parameters are directly matched. While both numerical models are built on the same general approach, details of the implementations are different, particularly regarding how two-way coupling is represented. At low volume loading, both numerical models are in general agreement with the experimental measurements, with certain exceptions near the walls for the wall-normal particle velocity fluctuations. At high loading, these discrepancies are increased, and it is found that particle clustering is overpredicted in the simulations as compared to the experimental observations. Potential reasons for the discrepancies are discussed. As this study is among the first to perform one-to-one comparisons of particle-laden flow statistics between numerical models and experiments, it suggests that continued efforts are required to reconcile differences between the observed behavior and numerical predictions.

Settling tracer spheroids in vertical turbulent channel flows

The motion of particles settling in turbulence is an intriguing problem, which is relevant to an in-depth understanding of planktons in marine flows or the design of photobioreactors. This work studies the motion, orientation and distribution of inertia-less spheroidal particles settling in vertical channel flows by direct numerical simulations. We show that, compared to spherical tracers, the settling velocity of spheroidal tracers is enhanced due to preferential orientation and local clustering (not due to particle inertia, in the present case). Prolate spheroids tend to align their symmetry axes in the direction of gravity while oblate ones align perpendicular to it. Both kinds of particles attain a larger slip velocity in the direction of gravity and, therefore, settle faster. We also show that particles sample preferentially regions of high fluid velocity in downward flow and regions of low fluid velocity in upward flow. Such preferential sampling, which also contributes to the enhancement of settling, is the result of clustering. Besides, tracer particles are observed to accumulate in the channel center in downward flow and near the wall in upward flow: We show that tracer transport in the wall-normal direction is controlled by the particle-to-fluid slip velocity and by clustering. The slip velocity dominates the transport initially, but tracers increasingly cluster in regions with opposite flow direction as they accumulate either in the channel center or near the wall. Clustering appears to be associate with the coherent structures that characterize wall turbulence, and tracer distribution in the wall-normal direction is found to reach a steady state when the two qualitatively different mechanisms balance each other.

On the transition between turbulence regimes in particle-laden channel flows

Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e. drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

On wall-normal motions of inertial spheroids in vertical turbulent channel flows

Dynamics of inertial non-spherical particles in upward and downward turbulent channel flows are investigated. Oblate (disk-like) and prolate (rod-like) spheroids are considered in a Lagrangian point-particle approach in which the turbulence field is obtained by direct numerical simulations. Fluid and particle statistics are conditionally sampled with the view to distinguish between particles moving toward or away from the channel walls. Outward-moving particles tend to locate more in lower-speed streamwise fluid streaks than inward-moving particles. For highly inertial spheroids, these tendencies are differently affected by gravity in upward and downward flows. The gravity force is therefore believed to influence turbophoresis. The tendency of oblate and prolate spheroids to orient parallel with and normal to the spanwise direction near the walls is stronger for outward- than for inward-moving particles. These distinctions are ascribed to the wall-normal force on the spheroids from the surrounding fluid. In the absence of gravity, heavy spheroids in the channel center align randomly with the almost isotropic fluid vorticity. Gravity is seen to have a de-isotropization effect on the particles’ orientation in the inertial frame.

Prolate spheroidal particles’ behavior in a vertical wall-bounded turbulent flow

Direct numerical simulations (DNSs) have been performed to examine the inertia, shape, and gravity field effects on the dynamics of ellipsoidal particles within a vertical turbulent channel flow. To investigate the effects induced by the particle inertia and shape, computations have been conducted for three aspect ratios and two response times. The influence of gravity has been examined through a comparison with DNS data provided in earlier studies without gravity. The originality of this study is that the prediction of the hydrodynamic force and pitching torque acting on the non-spherical particles has been carried out with recent expressions valid outside the Stokes flow regime. With the data extracted from the DNS, a statistical analysis of the particle spatial distribution, orientation, and translational and angular velocities is carried out. Results show that the presence of a significant mean relative velocity between the dispersed and continuous phases greatly modifies the dynamics of non-spherical particles. Without gravity, the dynamics of ellipsoids is close to that of spheres, whereas it becomes strongly dependent on the particle shape with gravity.

Modeling and simulation of particle–wall adhesion of aerosol particles in particle-laden turbulent flows

The present study is concerned with the development of a computational model for predicting particle–wall adhesion (deposition) of aerosol particles in turbulent particle-laden flows. Particularly, the standard hard-sphere model is extended to include the adhesion during sticking or sliding particle–wall collisions. For both impact types the deposition condition of a particle on bounding walls is determined. The strategy of the proposed model is based on the momentum-based agglomeration model by Breuer and Almohammed (2015). The main advantage of the proposed model compared to the state-of-the-art in the literature is that the adhesive impulse is determined more reasonably taking the time intervals of the compression and the restitution phase into account. Furthermore, if the deposition condition is not satisfied, the treatment of the particle motion after the impact including adhesion depends on the particle–wall type (sticking or sliding). To examine the effect of the particle–wall adhesion, the developed model is first evaluated using simple test cases including oblique particle–wall collisions with friction. In the second step, the performance of the adhesion model is validated based on a horizontal turbulent channel flow against existing experimental data of Kvasnak et al. (1993) and numerical results by Fan and Ahmadi (1993)based on an energy-based deposition model. The predictions of the present model agree very well with the experiments and the numerical results chosen for the validation study as well as the empirical relation by Wood (1981). Third, the adhesion model is employed to investigate the influence of different simulation parameters (normal restitution coefficient for particle–wall collisions and particle diameter) on the particle–wall adhesion and deposition process in a vertical turbulent channel flow laden with a huge number of primary particles. The results show that the inclusion of the adhesion significantly reduces the number of particle–wall collisions, whereas the number of particle–particle collisions is only slightly reduced. Furthermore, the number of deposited particles is higher for small particles than for large particles, since the adhesive impulse is inversely proportional to the diameter of the primary particles. The proposed adhesion model is developed and tested in the context of large-eddy simulation, but it can also be applied in DNS or RANS predictions.

Direct Numerical Simulations of spherical bubbles in vertical turbulent channel flow. Influence of bubble size and bidispersity

The paper presents two Direct Numerical Simulations of bubble swarms in a vertical turbulent channel flow and is intended as a complement to the companion paper, Santarelli and Fröhlich (2015). Both swarms addressed here are composed of spherical bubbles in contaminated fluid with a void fraction of 2.14%, as for the reference case in the companion paper. The first simulation reported is done for a monodisperse swarm of larger bubbles while in the second case a bidisperse swarm is considered. The influence of the bubble size and of the bidispersity is investigated by means of flow visualizations and quantitative statistical analysis. Due to the higher Reynolds number, the behavior of the larger bubbles differs from the one of the small bubbles and this impacts the turbulence of the carrier phase. The results show that for the parameter range considered both swarms induce elongated flow structures in the streamwise direction and that the liquid turbulence is enhanced by the bubbles, as quantified by the budget of the turbulence kinetic energy. In both cases the tendency of bubbles to align horizontally is confirmed while the analysis of mixed pairs in the bidisperse swarm allows elucidating the complex interaction of bubbles of different size.

Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel

This paper analyses the turbulent kinetic energy budget for bubble swarms in a turbulent channel flow configuration with realistic density difference. The data employed result from Euler–Lagrange Direct Numerical Simulations of vertical turbulent channel flow laden with finite-size bubbles and enable the individual evaluation of each term of the budget equation. Two monodisperse swarms are addressed with the same bubble diameter but with different total void fraction. For the parameter range investigated bubbles enhance the liquid turbulence, and this is quantified in the terms of the budget. The turbulence enhancement is generated by the interfacial term which is balanced by the dissipation term in the core region. In the near-wall region, also the production term and the transport term contribute to the budget in a significant manner. Furthermore, the local turbulence modification induced by the bubbles is investigated by means of the transport equation of the local instantaneous kinetic energy and its contributions. Finally, existing closures for the modelling of the interfacial term are assessed and an improvement of these closures is proposed. The data provided may constitute a reference for model development in the framework of Euler–Euler approaches to bubbly flows.

Direct Numerical Simulations of spherical bubbles in vertical turbulent channel flow

The paper presents results of Direct Numerical Simulations of bubbles rising in a vertical channel flow configuration for a dilute and for a denser swarm. The bubbles, considered as spherical objects, are simulated by means of an Immersed Boundary Method and the channel dimensions are chosen in order to address large-scale flow features. The interaction between the bubbles and the fluid phase is investigated with instantaneous flow visualizations and a detailed statistical analysis for both phases addressing single-point statistics, two-point correlation functions and pair correlation functions. Elongated flow structures in the streamwise direction induced by the bubbles are found in both cases but are somewhat larger and present a higher turbulence level in the denser swarm. For the chosen parameter range turbulence enhancement due to the bubbles is observed. The small-scale interaction of bubbles is investigated yielding different results for the two cases: in the dilute swarm, the aspiration mechanism of a trailing bubble yields a preferential vertical alignment while in the denser swarm, a pressure-related mechanism dominates due to the smaller bubble distance yielding a preferential horizontal alignment. The results reported here provide detailed and reference data for model development and validation.

Large eddy simulation of turbulent particle-laden channel flow considering turbulence modulation by particles

Large Eddy Simulation of vertical turbulent channel flow laden with particles are performed. The number of particles is chosen very large and the volume fraction of particles is high enough for consideration of two-way coupling. This means that the particles are influenced by fluid and vice versa. The inter-particle collisions are neglected. The Euler-Lagrange method is adopted, which means that the fluid is considered to be continuum (Euler approach) and for each individual particle is solved Lagrangian equation of motion. Particles are considered to be spherical. The simulations are performed for different volume fractions of particles in the channel. The results are compared to the single-phase channel flow in order to investigate the effect of the particles on the turbulence statistics of the carrier phase

Using RANS turbulence models and Lagrangian approach to predict particle deposition in turbulent channel flows

This study investigates the capability and accuracy of three Reynolds-Averaged Navier–Stokes (RANS) turbulence models, i.e. a Reynolds stress model (RSM), a RNG k-ε model, and an SST k-ω model in the prediction of particle deposition in vertical and horizontal turbulent channel flows. The particle movement was simulated using a Lagrangian-based discrete random walk (DRW) model. The performances of the three RANS turbulence models with and without near-wall turbulence corrections were evaluated. A new modification method for turbulence kinetic energy was proposed for the RNG k-ε model and the SST k-ω model. The results were compared with previous experimental data, empirical equation as well as simulation outcomes. It is found that the isotropic SST k-ω model and the RSM model can successfully predict the transition from the diffusion region to the inertia-moderated region. The RNG k-ε model with near-wall modifications can also reflect the V-shape deposition curve although without modifications it greatly over-predicts the deposition velocity and shows an almost straight deposition line. For all of the three turbulence models, application of near-wall corrections is able to improve the simulation results to different extents.

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.

Large-Eddy Simulation of Heavy-Particle Transport in Turbulent Channel Flow

Large-eddy simulations are carried out for a particle-laden vertical turbulent channel flow at Reynolds number of 180 based on friction velocity and channel half-width. To minimize the numerical and aliasing errors, a fourth-order compact finite-volume method in space and a fourth-order Runge-Kutta method in time along with a dynamic Smagorinsky model with explicit filter-grid size ratio 2 have been used to solve the filtered equations of the carrier flow. Heavy, small particle motion is governed by drag, gravitational, and Saffman lift forces in the Lagrangian frame. These particle equations are integrated in time using a second-order Adams-Bashforth method. The effect of subgrid-scale (SGS) fluctuations on particle statistics has been studied using two models available in the literature, with and without considering SGS velocity temporal correlation. In addition, a new model is implemented in this work to account for the anisotropy of flow. The results show that in the near-wall region the effect of SGS fluctuations on particle statistics is considerable, especially for small particle size of the order of 1μ m. The fluctuation levels of the wall-normal and spanwise directions of 1 − μ m lycopodium particle velocity are influenced strongly by SGS fluctuations and they are accentuated when the SGS effects are considered. The results for the 1 − μ m lycopodium particle show that the new model, which accounts for SGS anisotropy and Lagrangian temporal correlations of SGS fluctuations, yields improved results for particle turbulent intensity, especially in the near-wall region, when compared with other models. The effect of Saffman lift force on particle turbulent intensity is increased by increasing particle Reynolds number, especially in the wall-normal and spanwise directions.