Particle-laden Pipe Flow Research Articles

Prediction of particle-laden pipe flows using deep neural network models

An accurate and fast prediction of particle-laden flow fields is of particular relevance for a wide variety of industrial applications. The motivation for this research is to evaluate the applicability of deep learning methods for providing statistical properties of the carrier and dispersed phases in a particle-laden vertical pipe flow. Deep neural network (DNN) models are trained for different dependent variables using 756 high-fidelity datasets acquired from point-particle large-eddy simulations for different values of Stokes number, St, bulk particle volume fraction, Φ¯v, and wall roughness, Δγ, for the range St=10−500, Φ¯v=5×10−5−10−3, and Δγ=1°−6°. The considered parameter space corresponds to the inertia-dominated regime and covers a large extent of the typical conditions in powder-based laser metal deposition. We find that the DNN models capture the nonlinear dynamics of the system and recreate the statistical properties of the particle-laden pipe flow. However, DNN predictions of the particle statistics are of higher accuracy compared to the fluid statistics, which is attributed to the highly non-monotonic dependence of the fluid statistics on the control parameters. Owing to significantly decreased time-to-solution, the trained DNN models are promising as surrogate models to expedite model development and design process of various industrial applications.

Effects of Large Particles in Pipe Flow at Low and Moderate Reynolds Numbers

AbstractThe presence of solid particles in a Newtonian liquid flow will affect the properties of the flow. For small particles these effects are fairly well understood and models, for example for the pressure drop in particle laden pipe flows have been present for a long time. However, the behavior of liquids laden with large particles are less well understood. In the present study, large particles of spherical shape are considered. By large is here meant particles that are of the same size as the large scale length scales of the flow and larger. The effect of particles volume fraction on parameters such as pressure drop and velocity distribution in the pipe flow is investigated. The sizes of the particles are 17 % and 40 % of the pipe diameter and the volume fraction is varied between 5 % and 20 %.

The dominant mechanisms for each regime of secondary flows in horizontal particle-laden pipe flows

Numerical simulations have been conducted to identify the dominant mechanism responsible for driving secondary flow motions in horizontal particle-laden pipe flows, based on an analysis of the forces acting on each phase. A four-way coupling Euler–Lagrangian approach was employed, using direct numerical simulations for the gas phase and Lagrangian particle tracking to account for the drag, gravitational and lift forces, together with the interactions that occur for both particle–wall and inter-particle collisions. The four different flow regimes, which had been identified previously as depending on various combinations of flow parameters and are characterised by the secondary flow structures of both the fluid and particle phases, were identified via varying the mass loading alone from $\varPhi _m=0.4$ to $\varPhi _m=1.8$ . The distribution of the divergence of Reynolds stresses was used to help characterise the classes of the secondary fluid flow. This shows that secondary fluid flows of both the first and second kinds can either exist separately or co-exist in such flows. The forces exerted on the fluid phase by the pressure gradient and fluid–particle interactions were examined qualitatively and quantitatively to identify their contribution to the secondary fluid flow motions. A similar study was also applied to the drag, lift and gravitational forces exerted on the particle phase for the secondary particle flow motions. These were found to explain the secondary flows of both the fluid and particle phases with regard to both the flow direction and magnitude, together with the interaction between the two phases.

Onset of turbulence in particle-laden pipe flows

We propose a scaling law for the onset of turbulence in pipe flow of neutrally buoyant suspensions. This scaling law, based on a large set of experimental data, relates the amplitude of the particle-induced perturbations ($\epsilon$) to the critical suspension Reynolds number, $Re_{s,c}$. Here $\epsilon$ is a function of the particle-to-pipe diameter ratio and the volume fraction of the suspended particles, $\epsilon = (d/D)^{1/2} \phi^{1/6}$. $Re_{s,c}$ is found to scale as $\epsilon^{-1}$. Furthermore, the perturbation amplitude allows a distinction between classical, intermediate and particle-induced transition.

Ultrasound imaging velocimetry in particle-laden flows: counteracting attenuation with correlation averaging

Ultrasound imaging velocimetry (UIV) refers to the technique wherein ultrasound images are analysed with 2D cross-correlation techniques developed originally in the framework of particle image velocimetry. Applying UIV to opaque, particle-laden multiphase flows have long been considered to be an attractive prospect. In this study, we demonstrate how fundamental differences in acoustical imaging, as compared to optical imaging, manifest themselves in the 2D cross-correlation analysis. A chief point of departure from conventional particle image velocimetry is the strong variation in the intensity profile of the acoustic wavefield, primarily caused by the attenuation of ultrasonic waves in particle-laden flows. Attenuation necessitates using a larger ensemble of correlation planes to obtain satisfactory time-averaged velocity profiles. For a given combination of imaging and flow conditions, attenuation sets upper limits on volume fraction, penetration depth, as well as temporal resolutions that may be accessed confidently. This behaviour is demonstrated in two experimental datasets and is also supported by a modified cross-correlation theory. The modification is brought about by incorporating a lumped model of ultrasonic backscattering in suspensions into existing spatial cross-correlation analysis. The two experimental datasets correspond to two distinct particle-laden pipe flows: (1) a neutrally buoyant non-Brownian suspension in a laboratory-scale flow facility, wherein particle sizes are comparable to the ultrasonic wavelength and (2) a non-Newtonian slurry in an industrial-scale flow facility, wherein particle sizes are much smaller than the ultrasonic wavelength. We illustrate how and to what extent correlation averaging can counteract the adversity caused by attenuation. The work herein offers a template for one to evaluate the performance of UIV in particle-laden flows.Graphical abstract

The influence of the coefficient of restitution on flow regimes within horizontal particle-laden pipe flows

Numerical simulations of the particle-laden gas–solid flow in horizontal circular pipes have been used to identify the role of particle collision coefficients in flow regimes within it. A four-way coupling Euler–Lagrangian approach was employed, using direct numerical simulations of the gas phase and Lagrangian particle tracking to account for the drag, gravitational and lift forces, together with particle–wall and inter-particle interactions. The influences on the flow of the mass loading ratio (Φm) and of the coefficients of restitution for collisions both between particles and the wall (ep−w) and between particles (ep−p) are assessed by examining the fluid and particle velocities, particle concentration distribution, turbulence kinetic energy, static pressure, inter-phase transferred momentum, and the secondary flow motions of both the fluid and particle phases. Three dominant flow regimes that include three sub-regimes based on their secondary flow patterns are identified, the transition between which depends on the combination of Φm, ep−w, and ep−p. Additionally, the quantitative dependence of these transitions on these three parameters is also reported for a series of Stokes and Froude numbers.

Flow regimes within horizontal particle-laden pipe flows

This study presents numerical simulations for particle-laden gas–solid flows in horizontal circular pipes to identify the key flow regimes as a function of the main dimensionless parameters. A Euler–Lagrangian approach is employed, using direct numerical simulations (DNS) coupled with a Lagrangian particle tracking (LPT) method, to consider the drag, gravitational and lift forces on particles, as well as the effect of inter-particle collisions. The influence of the Stokes number (Sk), mass loading ratio (Φm) and Froude number (Fr) on critical flow regimes is assessed to identify conditions under which gravity bias becomes either negligible or dominant with regard to fluid characteristics and particle statistics. Three different regimes of the flow behaviour are identified, depending on the combination of these dimensionless parameters. These flow regimes are described and their dependence on these three parameters (Sk, Φm and Fr) is reported, including the significance of gravity in generating a bias on distributions of the flow statistics.

Ultrasonic particle volume fraction profiling: an evaluation of empirical approaches

We discuss empirical techniques to extract quantitative particle volume fraction profiles in particle-laden flows using an ultrasound transducer. A key step involves probing several uniform suspensions with varying bulk volume fractions from which two key volume fraction dependent calibration parameters are identified: the peak backscatter amplitude (acoustic energy backscattered by the initial layer of the suspension) and the amplitude attenuation rate (rate at which the acoustic energy decays with depth owing to scattering losses). These properties can then be used to reconstruct spatially varying particle volume fraction profiles. Such an empirical approach allows circumventing detailed theoretical models which characterize the interaction between ultrasound and suspensions, which are not universally applicable. We assess the reconstruction techniques via synthetic volume fraction profiles and a known particle-laden suspension immobilized in a gel. While qualitative trends can be easily picked up, the following factors compromise the quantitative accuracy: (1) initial reconstruction errors made in the near-wall regions can propagate and grow along the reconstruction direction, (2) multiple scattering can create artefacts which may affect the reconstruction, and (3) the accuracy of the reconstruction is very sensitive to the goodness of the calibration. Despite these issues, application of the technique to particle-laden pipe flows shows the presence of a core with reduced particle volume fractions in laminar flows, whose prominence reduces as the flow becomes turbulent. This observation is associated with inertia-induced radial migration of particles away from the pipe axis and is observed in flows with bulk volume fractions as high as 0.08. Even transitional flows with low levels of intermittency are not devoid of this depleted core. In conclusion, ultrasonic particle volume fraction profiling can play a key complementary role to ultrasound-based velocimetry in studying the internal features of particle-laden flows.Graphic abstract

Particle trajectories in pipe flow considering particle–wall collisions

Particle–wall collision behaviors have strong effects on confined particle-laden pipe flows, which are important in pneumatic conveying and pulverized coal combustion. In this paper, a numerical simulation of a pipe flow was conducted to analyze the effects of different initial conditions and particle–wall collision model parameters. The results show that a realistic collision model with coefficients provided by experiments can predict accurate particle exit velocity distributions. The effects of the initial motion of the particles diminish at the exit as long as the pipe length and the number of wall collisions are sufficient, and larger particles require the length to be longer. A simplified collision model with an arbitrary constant restitution coefficient e and a friction coefficient f leads to inaccurate results of the particle exit velocity probability density function, and using constant coefficients from data of a single collision angle will make the model ineffective. It is better to apply a normal distribution for e and a constant f if available collision data are limited, which gets reasonably accurate statistical results despite small distribution deviations.

An instability mechanism for particulate pipe flow

We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J. Fluid Mech., vol. 13 (01), 1962, pp. 120–128). We extend previous analysis in a channel (Klinkenberg et al., Phys. Fluids, vol. 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol. 47 (3), 2012, pp. 351–363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

Particle-Laden Pipe Flows at High Volume Fractions Show Transition Without Puffs

Using ultrasound imaging velocimetry, we are able to present unique insight in transitional particle-laden flows. Together with a Moody diagram of time-averaged properties, we demonstrate that the laminar-turbulent transition behavior at high volume fractions is distinct from the single-phase case and cases with low volume fractions. For low volume fractions, a sharp transition is found with the presence of turbulent puffs, similar to the single-phase case. Seemingly, particles in this regime trigger subcritical transition. For high volume fractions a smooth transition is discovered without turbulent puffs in the transition regime. For this regime, particles cause a supercritical transition.

Eulerian-Eulerian modelling of particle-laden two-phase flow

When typical fluid RMS velocities scale with the terminal velocities of inertial particles, turbulent particle-laden pipe flows exhibit special features. Recent experiments have shown that the taking of Eulerian averages requires special measures in such flows. An existing Eulerian numerical method has been adapted in order to accommodate for these special features. The effects of flow direction (upward or downward) and mean concentration (in the range 5.0×10−6 to 3.2×10−5) on radial particle distribution and on the mean axial velocities of both particles and fluid are investigated. Inertial particles have a Stokes number equal to 2.3, based on the particle relaxation time and viscous scales; Reynolds number is 10,300, based on the bulk velocity and the pipe diameter. To get agreement between experimental findings and model predictions, a lift force term had to be included; core peaking in up-flow and wall peaking in down-flow result from it. The difference of mean particle and fluid Eulerian velocities is found to decrease towards zero near the wall in both up-flow and down-flow. This feature required inclusion of a modified drag component in the particle axial momentum equation of the Eulerian model.

Lagrangian velocity and acceleration statistics of fluid and inertial particles measured in pipe flow with 3D particle tracking velocimetry

Three-dimensional particle tracking velocimetry (3D-PTV) has been applied to particle-laden pipe flow at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. The volume fraction of the inertial particles was equal to 1.4×10−5. Lagrangian velocity and acceleration statistics were determined both for tracers and for inertial particles with Stokes number equal to 2.3, based on the particle relaxation time and the viscous time scale. The decay of Lagrangian velocity and acceleration correlation functions was measured both for the fluid and for the dispersed phase at various radial positions. The decay of Lagrangian velocity correlations is faster for inertial particles than for flow tracers, whereas the decay of Lagrangian acceleration correlations is about 25% slower for inertial particles than for flow tracers. Further differences between inertial and tracer particles are found in velocity fluctuations evaluated for both positive and negative time lags. The asymmetry in time of velocity cross-correlations is more pronounced for inertial particles. Quadrant analysis revealed another difference still near the wall: ejection and sweep events are less frequent for inertial particles than for tracers.

Turbulent stresses and particle break-up criteria in particle-laden pipe flows

Three-dimensional particle tracking velocimetry (3D-PTV) is applied to particle-laden pipe flows at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. The effects of flow direction (upward or downward) and mean concentration (in the range 0.5×10−5–3.2×10−5) on the production of turbulence are assessed for inertial particles with a Stokes number equal to 2.3, based on the particle relaxation time and viscous scales. The turbulence production and the Kolmogorov constant, both measured for particle laden flows in upflow and downflow, allowed for the derivation of a break-up criterion as a function of the radial coordinate. This criterion predicts the maximum possible particle size before break-up may occur. It is shown that the maximum particle size is bigger at the pipe centerline than in the near-wall zone by more than a factor of 5. Flow direction affects the particle concentration profile, with wall peaking in downflow and core peaking in upflow. This affects both the residence time and the maximum particle size, the latter by 7%.

Euler–Lagrange simulation of gas–solid pipe flow with smooth and rough wall boundary conditions

Numerical simulation of upward turbulent particle-laden pipe flow is performed with the intention to reveal the influence of surface roughness on the velocity statistics of the particle phase. A rough wall collision model, which models the surface as being sinusoidal, is proposed to account for the wall boundary condition ranging for smooth surfaces to very rough surfaces. This model accounts for the entire range of possible surface roughness found in pipes and industrial pneumatic equipment from smooth plastic pipes over machined steel pipes to cast iron surfaces. The model is based on a geometric interpretation of the wall collision process where the particle restitution coefficient is based on the data presented by Sommerfeld and Huber [1]. Simulations are performed using the Eulerian–Lagrangian methodology for the dilute one-way coupling regime. Results are reported for 3 different sizes of glass spheres: 50μm, 200μm and 550μm and evaluated using the data by Mathisen et al. [2]. The results reveal the dependence of the particle concentration, particle mean and particle RMS velocity profiles on the surface roughness. Significant differences can be seen for the particle RMS velocity profiles as the mean motion changes from motion mainly in the axial direction for the smooth surface condition to bouncing motion between the pipe sides for the fully rough surface condition.

A mathematical model of turbulence modulation in particle-laden pipe flows

This investigation is concerned with developing a model of the processes involved in turbulence modulation by relatively large particles in dilute gas–solid turbulent flows. The mathematical model, which focuses on two-way coupling, has been developed based on the work of Lightstone and Hodgson (Turbulence modulation in gas–particle flows: a comparison of selected models, “Can. J. Chem. Eng.” 82, 2004, 209–219) to account for both enhancements and reductions in turbulent kinetic energy as well as the particle crossing trajectory effect. The underlying formulation scheme employs an Eulerian–Lagrangian reference frame, i.e. the carrier phase is considered as a continuum system, while the trajectories of individual particles are calculated using a Lagrangian framework. A random walk model is used to solve the particle motion equation. The proposed model, along with turbulence modulation models from the literature, is used to simulate a particle-laden vertical pipe flow. The simulation results show that the new model provides improved predictions of the experimental data.