Chute Flow Research Articles

Fully developed self-aerated flow in steep chute with various bottom roughness

Fully developed self-aerated flow in steep chute with various bottom roughness

Identification of dominant DEM parameters for multi-component segregation during heap formation, hopper discharge and chute flow

Segregation of granular materials is a critical phenomenon in various industries, such as food processing, pharmaceuticals, and mining. The Discrete Element Method (DEM) is an effective tool for gaining insight into granular segregation by providing particle-level information and the freedom to model mixtures that are often difficult or impossible to achieve through experiments. To ensure realistic material behaviour and correct representation of segregation, it is essential to calibrate the model parameters systematically. However, in the context of multi-component segregation, it is extremely challenging and computationally expensive to consider all parameters in the calibration procedure since interaction parameters between components must also be considered. This work aims to identify the dominant DEM parameters for modelling multi-component segregation during hopper discharge, chute flow and heap formation in a mixture of pellet and sinter. Utilising a representative example of a multi-component mixture with different sizes, densities and shapes used in blast furnaces, the investigation is done for various initial configurations as well as various mass ratios of the mixture. Our findings revealed that, while only particle-geometry interaction parameters dominate the segregation after the hopper and chute flow, particle-particle parameters are also significant for segregation in the heap. We also demonstrated that the downstream segregation is significantly influenced by the segregation upstream. Moreover, we found that the effect of pellet-sinter interactions is negligible. This research provides insights into the dominant DEM parameters, facilitating more efficient and robust calibration of multi-component models in future research endeavours.

Self aeration and energy dissipation on a steep stepped chute: how does physical modelling compare to prototype observations?

For the last five decades, a number of overflow stepped chutes were built because the staircase shape is conducive to reduced construction costs and increased rate of energy dissipation. The stepped chute operations are characterised by air‐water flows that are highly turbulent flows with a large rate of energy dissipation, in comparison to smooth chutes. Herein, physical measurements were performed in a large‐size 1 V: 0.80H stepped chute model, with a steep slope typical of modern concrete gravity dams. The results are compared to visual observations of prototype spillway operation under Froude similar conditions. The detailed two‐phase flow measurements were conducted to characterise finely the self‐aeration and air diffusion process downstream of the inception region of free‐surface aeration. The bubble count rate profiles scaled with the instantaneous void fraction variance, and the relationship was biased close to the stepped invert under the influence of large‐scale vortical structures. The rate of energy dissipation was carefully estimated based upon the two‐phase flow measurements and the results are compared to earlier results on similar steep invert slopes and prototype data estimates. At the downstream end of the stepped chute, the rate of energy dissipation ranged from 43 to 46%, i.e. more than twice that on a smooth-invert chute for a similar chute length and discharge range.Graphical abstractCharacteristics of self-aerated stepped chute flows for dc/h = 1.3—(I) Prototype flow at Hinze Dam (Re = 4.0 × 107); (II) Air-water flow properties in the large-size laboratory model (1:15) stepped spillway (Re = 6.1 × 105)

Effects of vibration on granular chute flow under low-gravity conditions

The essence of most geological hazards and industrial processes is gravity-driven flows of dense particles. In this research, we use the discrete element method to simulate the particle chute flow, and discuss the effect of vibration acceleration on the granular flow under different gravity conditions. The results indicate that vibration has a greater impact on the particle flow state under low-gravity environments and low inclination angles. The granular temperature (T) and inertia number (I) increase with increasing vibration acceleration. Vibration enhances the flowability of particles by changing the stress state and reducing the volume fraction of the granular system. This work reveals the rheological state of vibration-triggered particle flow on an inclined surface under different gravity environments.

Numerical Simulation of Air Distribution in a Wide Chute

Abstract Desirable conditions of airflow should be provided for spillway chute aerators in two-phase air-water flow, especially in large-width chutes. There is no general approach to determine air entrainment, concentration distribution, and submergence along a chute introduced by an aerator shaft. The two-phase air-water modeling of Gavoshan dam in Iran as a case study of chute flow, its aerator, and the characteristics of flow into the cavity formed below the jet have been numerically investigated, and the results obtained have been validated against the laboratory experiments. The hydraulic parameters of the cavity and aerator shaft were determined to evaluate their performance and emphasize the importance of a proper aerator design. Sections with a greater distance from the bottom of the chute exhibit higher pressure magnitudes, while the mean air concentration values in the cavity are smaller in sections close to a ramp. Higher water discharge, lower pressure head in sections near the bottom of the cavity, and lower air concentration in sections near the ramp into the cavity increase the probability of cavitation occurrence.

Unsteady granular chute flows at high inertial numbers

Unsteady granular chute flows at high inertial numbers

Multi-GPUs DEM algorithm and its application in the simulation of granular materials

The Discrete Element Method (DEM) is one of the most common numerical approach for modeling the physical and mechanical properties of granular materials. However, its computational efficiency can be a major bottleneck, which significantly hinders its application in engineering fields. To overcome this challenge, a multi-GPU framework with OpenMP has been developed. In this framework, the DEM particles in 3D space and their corresponding contact information are sorted in a given direction in the simulation, and each GPU device handles a subdomain of particles and relative contacts. Additionally, the contact information is densely arranged to minimize memory usage. To further enhance efficiency, sorting and packing algorithms for the contact information have been introduced. During calculating loop, the number of contacts on each device is monitored, and the spatial division of devices is adjusted to balance memory distribution. The efficacy of the multi-GPU algorithm is verified through a chute flow test. Using numerical results, the segregation process and mechanics of granular materials during sliding have been studied in detail. Furthermore, the simulations demonstrate that the developed multi-GPU algorithm greatly enhances computational efficiency and reduces memory usage per device.

How Ice Particles Increase Mobility of Rock‐Ice Avalanches: Insights From Chute Flows Simulation of Granular Rock‐Ice Mixtures by Discrete Element Method

AbstractRock‐ice avalanches occurring in cold high‐mountain regions often cause catastrophic damages due to their extremely high mobility. Rock and ice have different physical properties, such as particle size, density, friction, etc., leading to the segregation of rock and ice in the mixture and impacting its mobility. However, how ice affects the mobility of rock‐ice avalanches is still poorly understood. A series of numerical experiments were conducted by using the discrete element method to quantify the effect of rock‐ice particle size ratio and ice content on the particle segregation and mobility of their mixtures. Results show that rock‐ice particle size ratio and volumetric ice content determine the spatial distribution of ice, thereafter affecting the mobility of the rock‐ice mixture by controlling the ratio of particle collision stress and coulomb friction stress. In particular, different from conventional understanding, the ice spatial distribution can have a significantly greater influence on the mixture's mobility compared to the volumetric ice content in some scenarios. This study provides insights into the effect of granular ice on the mobility law in the early phase of rock‐ice avalanches and has important implications for their hazard assessment.

Two-phase flow modelling by an error-corrected population balance model

High-velocity aerated flow is a common phenomenon in spillways. Its accurate modelling is challenging, mainly due to the lack of realistic physics in the conventional two-phase models. To this end, this study establishes a population balance model (PBM) approach to account for the evolutionary process of air bubbles. The air-water flow in a stepped chute is examined. The model performance is evaluated by statistical metrics: correlation coefficient (CC), root mean squared error (RMSE), and mean absolute error (MAE). Compared with conventional models, the PBM generates improved air-water predictions. However, the flow parameters are still underestimated, particularly in areas with intense air-water interactions. For further development, an error-corrected PBM (EPBM) is proposed by incorporating machine learning (ML) techniques into the PBM. Compared with the PBM, the EPBM leads to a mean augmentation in velocity prediction by 19.8% for the CC, 73.0% for the RMSE, and 77.1% for the MAE. The gains in air concentration estimation are 2.0%, 67.6% and 73.5%, respectively. The EPBM generates the most accurate results, with 99.6% and 89.6% of the velocity and air concentration predictions within a 20% relative error range. The main contributions are establishing a PBM for air-water flows and developing an error-corrected PBM using ML.

Particle force-based density segregation theory for multi-component granular mixtures in a periodic chute flow

Density segregation of multi-component granular mixtures in a dense, gravity-driven flow over a rough and bumpy periodic chute surface is studied using theory and simulations. An existing theoretical model for predicting the steady-state concentration field of each species in a binary mixture using the forces acting on the particles is generalised for multi-component mixtures in this work. In addition, the rheological model for binary mixtures is also extended to multi-component mixtures. In contrast to the percolation velocity-based empirical segregation models that do not account for the rheology and need prior knowledge of the velocity field, the present approach accounts for the inter-coupling of rheology with segregation. The momentum balance equations are solved, along with the mixture rheological model as well as the multi-component density segregation model, to obtain concentration fields using an iterative numerical method. The theoretical predictions are compared with discrete element method (DEM) simulations for ternary, quaternary and quinary granular mixtures differing in density. The steady-state profiles for the concentration of different species as well as other flow properties predicted from the theory are in excellent agreement with the DEM simulation results for a variety of compositions over a range of inclination angles for different density ratios. Through this work, we take the first essential step towards proposing a generalised particle force-based segregation theory for multi-component mixtures differing in size and/or density.

A second-order non-local model for granular flows

We determine a constitutive equation for developed three-dimensional granular flows based on a series of discrete element method simulations. In order to capture non-local phenomena, normal stress differences, and secondary flows, we extend a previously proposed granular temperature-sensitive rheological model by considering Rivlin-Ericksen tensors up to second order. Three model parameters are calibrated with the inertial number and a dimensionless granular temperature. We validate our model by running finite difference method simulations of inclined chute flows. The model successfully predicts the velocity and stress fields in this geometry, including secondary vortical flows that previous first-order models could not predict and slow creeping zones that local models miss. It simultaneously captures the non-trivial variation among diagonal components of the stress tensor throughout the domain.

Effect of Vibration On Characteristics of Granular Inclined Chute Flow Under Low-gravity

Effect of Vibration On Characteristics of Granular Inclined Chute Flow Under Low-gravity

The CTCN-LightGBM Joint Model for Industrial Balanced Loading Prediction

Balanced industrial loading mainly relies on accurate multi-adjustment values, including the truck speed and chute flow. However, the existing models are weak in real-time loading prediction because the single-objective regression may ignore the correlation of multi-adjustment parameters. To solve the problem, we propose a joint model that fuses the composited-residual-block temporal convolutional network and the light gradient boosting machine (i.e., called CTCN-LightGBM). First, the instance selection deviations and abnormal supplement methods are used for data preprocessing and normalization. Second, we propose a side-road dimensionality reduction convolutional branch in the composited-residual-block temporal convolutional network to extract collaborative features effectively. Third, the feature re-enlargement method reconstructs extracted features with the original features to improve extraction accuracy. Fourth, the reconstructed feature matrix is utilized as the input of the light gradient boosting machine to predict multi-adjustment values parallelly. Finally, we compare the CTCN-LightGBM with other related models, and the experimental results show that our model can obtain superior effects for multi-adjustment value prediction.

Chute flows of dry granular media: Numerical simulations by a well-posed multilayer model and comparisons with experiments

Debris flows and avalanches are dangerous natural phenomena, characterized by the gravity-driven motion of granular media immersed in a fluid. For an appropriate hazard assessment or disaster mitigation by scenario investigation, it is crucial to capture the underlying dynamics of the granular solid phase. For this purpose, a multilayer depth-averaged approach represents a promising and computationally efficient tool over fully three-dimensional models. Here we use a mathematically well-posed multilayer model, which implements the µ(I)-rheology and a dilatancy law depending on the inertial number, I, and compare the numerical results of the model with laboratory experiments of steady uniform chute flows over an erodible bed. The well-posedness of the model for any value of I, which is essential to get convergent numerical solutions, is achieved by considering an approximation of the in-plane stress gradients, directly emerging from the µ(I)-rheology. The predicted velocity profiles show a very good agreement with the experimental ones, measured by particle image velocimetry (PIV). The volume fraction profiles by the multilayer model are also in good qualitative agreement with those measured by using the stochastic-optical method (SOM), while they tend to overestimate the volume fraction measurements in the more dilute upper region, closer to the free surface.

Analytical solutions for vortex flow at the tangential inlet of a vertical dropshaft

Vertical dropshafts with tangential intake structures are often used in urban drainage systems to route surface flow into underground systems. Vortex flow driven by a tangential inlet is the typical flow pattern in the vertical dropshaft. However, analytical solutions of the key hydraulic transition from chute flow to vortex flow have not been investigated, and theoretical guidelines of the vortex dropshaft are not available. In the present study, a series of theoretical analytical solutions are proposed to determine the circumferential flow generated at the vertical dropshaft inlet. The contraction ratio of the tapering chute, dropshaft size, and flow depth at the joint section determines the vortex flow performance in the vertical dropshaft. Based on the free surface drop height, theoretical criteria are proposed to describe the spiral movement intensity in the vertical dropshaft. Systemic experiments for different vortex dropshaft models are tested, and the experimental observations agree with the theoretical analysis. The present investigation provides a general reference for a tangential dropshaft inlet design that can smoothly route rotational flow down a vertical dropshaft.

Effect of base roughness on flow behaviour and size segregation in dry granular flows

Three bases with increasing roughness were designed by adjusting the geometric relationships of particles bonded to the base, to study the roughness effect on flow behaviour and size segregation in bidisperse granular chute flows. In light of limited research on accurate tracking of different particles in bidisperse granular flows, particle tracking velocimetry, which allows tracking of large and small particles down to the pixel level, was used to measure the velocity and displacement of large and small particles separately. Experimental results show that when the critical inclination θc increases from 31·9° to 36·1°, the mixing point of the large and small particles decreases from 67 to 39 cm. Moreover, the overall flow is suppressed in the stream-wise direction and promoted in the depth-wise direction as the base roughness increases.

Air entrainment mechanism of chute bottom aerators in high-speed chute flows

In high-head dam projects, chute aerators are commonly applied as artificial aeration devices to prevent cavitation erosion damage in high-speed spillway and tunnel flows. These specific chute air–water flows are generated by jet lower-surface aeration above the bottom cavity and jet impact aeration on the bottom floor. These air entrainment processes determine the total air flux transport downstream of the chute flow. However, the differential air fluxes caused by the two different aeration mechanisms remain unclear. Based on physical model investigations, the two air entrained processes are observed by a high-speed camera, and detailed air flux data are measured in the aerator cavity and impact areas. The effects of the jet lower-surface disintegrating and then instantaneously reattaching to the chute floor are discussed. The measured air flux data indicate that the inertial jet impact entrainment dominates with increasing the Froude number, while the air flux proportion of the jet lower-surface aeration increases with the aerator height. A general prediction model for aerator cavity entrainment is proposed, considering the effects of the Froude number and jet lower-surface aeration. The scale effects of the coupling mechanism on chute aerator air entrainment highlight that aerator cavity air entrainment primarily depends on the inertial jet impact, and the main effects of aerator design on entrainment performance are manifested in the air cavity properties.

On the shape and size of granular roll waves

This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number $Fr$ of the incoming flow exceeds a critical value, $Fr>Fr_{cr}$ . We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of $Fr$ , the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number $Fr$ .

Extended kinetic theory for granular flow in a vertical chute

We consider steady, fully-developed flows of deformable, inelastic grains driven by gravity between identical bumpy walls. Using constitutive relations from extended kinetic theory (EKT) for the erodible bed near the centreline and the collisional flow between the surfaces of the bed and the walls, we calculate the fields of mean velocity, fluctuation velocity and solid volume fraction across the chute. We consider both situations in which the solid volume fraction at and near the centreline is high enough to form a bed and when it is not. We compare results predicted by EKT with recent discrete element simulations results, and obtain very good agreement.

Flow aeration and surface fluctuations in moderate-slope stepped chute: from aeration inception to fully developed aerated flow

ABSTRACT Although stepped chute flows have been studied for a variety of chute geometries and flow conditions, reports on air–water flow development in the fully developed aerated region are not as comprehensive as those in the nonaerated and developing aerated regions. In this paper, skimming air–water flows in a large stepped chute (1V:2.5H) were studied comparatively for two step heights, showing different stages for velocity and aeration development downstream the inception point. The mean air concentration reached a constant level while the bubble frequency kept increasing slowly in the fully developed region. The developed mean air concentration was related to the sloping angle, step height and flow discharge. The results provided possible prediction of maximum bubble frequency and its longitudinal evolution, and a glance at the scale effect on it. The free-surface fluctuations and splash height were presented, with particular attention to the effects of step height on the turbulence and aeration modification.