126 results found
Zhang H, An S, Brito-Parada PR, et al., 2024, Investigation into three-dimensional dry foam modelling using the boundary integral method, Journal of Computational Physics, Vol: 499, ISSN: 0021-9991
Understanding foam rheology relies on predictions of the foam structure and physical quantities associated with foam dynamics. In this work, we explore the modelling of dry foam dynamics using the boundary integral method, which can be used to predict the behaviour of dry foam in bulk or in confined geometries. The resultant equation for dry foam shows that the movement of foam films or lamellae is governed by the film curvature and the normal stress that the wall imposes on the fluid phase in bubbles and is characterized by three distinct motion modes: the background flow, the imposed flow due to the deformation of wall and the relaxation process of films. The singular integrals involved in the model are handled using a combined method of singularity subtraction and nonsingular contour integral. To demonstrate the validity of the method in potential applications, we consider two scenarios, for foam in bulk and in confined geometries, respectively. Dynamic foam motion is tracked using the model. The results show that the dry foam model has potentials applied in a variety of applications, such as foam flow in microfluidic devices and porous media.
Skrypnik A, Cole K, Lappan T, et al., 2024, Neutron radiography of an anisotropic drainage flow, Physical Review E, Vol: 109, ISSN: 2470-0045
Liquid drainage through foam is dominated by gravity, capillary, and viscous forces. The liquid is conducted by an isotropic network of Plateau borders; however, imposed stress changes the alignment of the foam's structural elements. Previous numerical simulations predicted that a vertical drainage flow will be deflected horizontally if the foam is sheared. We investigated this phenomenon by measuring the distribution of the liquid fraction within a foam formed in a flat rectangular cell. The foam was subjected to shear stress under a forced liquid supply from the top of the cell. Neutron radiographies of unchanged and sheared foam were analyzed to extract measurements of the liquid fraction. Deflections in the distribution of the drainage liquid were detected and found to be positively correlated with increasing foam shear.
Zhang H, Torres-Ulloa C, An S, et al., 2024, A comparative study of a viscous froth lens in two and three dimensions, Physics of Fluids, Vol: 36, ISSN: 1070-6631
The two-dimensional (2D) viscous froth model was initially designed to capture the dynamic behavior of dry foams within a Hele–Shaw cell, characterized by two parallel covering plates separated by a small gap. However, due to its inherent 2D nature, this model does not explicitly account for the dimension across the gap. To address this limitation, we have opted for a three-dimensional (3D) version of the viscous froth model. In this 3D model, the dynamic effect is introduced through the motion of the surface Plateau borders, while the configurations of films in bulk are determined via surface energy minimization subject to specified bubble volumes and surface Plateau border locations. We use this 3D model to simulate the motion of a viscous froth lens within a straight channel. The steady states of the viscous froth lens in 3D are primarily influenced by the driving velocity-to-gap size ratio, particularly at relatively small values of this ratio. By contrast, as the ratio becomes relatively large, the gap size begins to play a significant role in influencing the behavior of the viscous froth lens in 3D. Differences are observed in the steady-state configurations of the viscous froth lens in 3D when compared to those in 2D. However, the behavior of the viscous froth lens in 2D can be better aligned with the results in 3D by treating the drag coefficient required in the 2D viscous froth model as a fitting parameter. A further quantitative analysis indicates that the drag coefficient needed in the 2D viscous froth model may not serve as a uniform parameter for the entire foam structure. Instead, it may depend on the specific location along the evolving foam films over time.
Neethling SJ, Mesa D, Brito-Parada PR, 2024, An improved model for predicting froth recovery, Minerals Engineering, Vol: 205, ISSN: 0892-6875
In froth flotation, froth recovery is a key factor as it quantifies the effect that the froth has on the overall cell recovery. Froth recovery is affected by a number of variables, including froth stability, particle size and density, and the operating conditions of the flotation cell. Despite its importance, modelling froth recovery is challenging due to the large number of competing effects involved. In this paper, we present a model for froth recovery that takes into account the effects of detachment and subsequent transport of particles. The model is phenomenological and is derived from a set of coupled partial differential equations used to describe both liquid and particle motion within a froth. An analytical algebraic solution is obtained for the froth recovery by making a number of assumptions, which are discussed and justified in the paper. This model is related to a previous model produced by the authors, in which froth recovery was described in terms of a constant particle detachment fraction. Conversely, this enhanced model includes an improved description for particle detachment behaviour during coalescence events, allowing for a variable particle detachment fraction. The key parameters in the model are two dimensionless groups. The first group combines the particle settling velocity, the air addition rate and froth stability parameters such as air recovery and the change in bubble size over the froth, while the second key dimensionless group is the ratio of the surface loading on the incoming bubbles to the maximum surface loading. This model is compared to experimental results and is shown to accurately describe the evolution of the froth recovery behaviour down a bank of cells in response to the decreasing froth stability.
Avalos-Patiño JE, Neethling SJ, Piggott MD, 2023, A parameter-free LES model for anisotropic mesh adaptivity, Computer Methods in Applied Mechanics and Engineering, Vol: 416, Pages: 1-25, ISSN: 0045-7825
Balancing accuracy and computational cost is a challenge in the modelling of turbulent flows. A widely used method for turbulence modelling is large–eddy simulation (LES). LES allows one to describe large scale flow features at a reasonable computational cost compared to the more accurate direct numerical simulation (DNS), making it a popular choice for engineering applications. One strategy to balance accuracy and cost with LES is through the use of mesh adaptivity, which allows the degrees of freedom in a problem to be reduced by changing spatial discretisation. However, mesh adaptivity can affect accuracy when using the standard Smagorinsky LES model with an implicit filter, considering that the parameter Cs is highly dependent on the filter width, which depends on mesh resolution. This work is aimed to develop an LES model that does not require any user–defined parameters and is suitable for mesh adaptivity with implicit filter. In this study we introduce a parameter–free LES model incorporating an anisotropic eddy–viscosity formulation combined with anisotropic mesh adaptivity. In our model, the parameter Cs in the eddy–viscosity formulation of the Smagorinsky model, is replaced by a function that evaluates the relative location of turbulence fluctuations in each element with respect to the turbulence spectrum inertial range. The anisotropic formulation of the eddy–viscosity allows for the application of an appropriate filter width in different directions, improving accuracy. Additionally, the mesh adaptivity algorithm assesses the local turbulence fluctuations via local Reynolds number and vortex identification criteria. This assessment leads to the refinement of regions with higher turbulence fluctuations down to the smallest scale limit in the inertial range in the corresponding direction, and also leads to the coarsening of regions without turbulence fluctuation up to largest scale limit in the inertial range. This method
Salinas-Farran L, Neethling SJ, 2023, Modelling the curing of agglomerated ores with comparison to micro-CT, Minerals Engineering, Vol: 202, ISSN: 0892-6875
Agglomeration and the associated curing process are critical as they both improve heap permeability and provide initial intimate contact between the leaching solution and the minerals. The evaporation of water from the agglomerate surface will drive liquid motion within agglomerates, redistributing dissolved species and increasing their concentration with the resultant potential for precipitation of previously dissolved species.Models have been proposed for the particle scale leach behaviour during the active irrigation phase of heap leaching, however no models currently exist for the leach behaviour during the curing process. The aim of this paper is therefore to propose and validate such a model by including important processes such as evaporation, unsaturated liquid transport, advective and diffusive transport of dissolved species, dissolution of mineral grains, and precipitation of species once saturation is reached.A set of small-scale column leaching tests were carried out, with the system being repeated scanned using X-ray Microtomography (micro-CT) over the course of the 65 day long curing experiments. Image analysis allowed the spatial distribution of both the initial mineral grains, as well as the precipitates to be tracked as a function of time. These were then used to demonstrate that the model captured the key features of the behaviour during the leaching process, as well as providing plausible ranges for the model parameters that could not be directly measured as input parameters.Both the model and the experiments showed that reprecipitation occurs preferentially towards the surface of the agglomerates. The model was also used to carry out a sensitivity analysis, with a key finding being that leach performance during curing improves with larger agglomerates and decreased evaporation rates. This is because of decreased loss of water. The particle size effect is the opposite of what would be expected during the subsequent leaching where mass transport in
Quintanilla P, Navia D, Neethling SJ, et al., 2023, Evaluation of Changes in Feed Particle Size within an Economic Model Predictive Control Strategy for Froth Flotation, Pages: 2317-2322
This study presents the evaluation of the impact of feed particle size on an Economic Model Predictive Control (E-MPC) strategy for a flotation bank. The effect of particle size was assessed under two scenarios: (1) assuming constant floatability with no dependency on particle size, and (2) assuming variable floatability as a function of particle size. The E-MPC strategy uses a dynamic model that includes froth physics, which was previously calibrated and validated using experimental data. Two typical control variables were considered: air flowrate and pulp height setpoints. The proposed objective function depends on three flotation variables: (1) dynamic air recovery, a measurable variable used to quantify froth stability and is directly related to flotation performance, (2) metallurgical recovery at steady-state, and (3) dynamic concentrate grade. A moving horizon estimator (MHE) was implemented to estimate the model states in both scenarios. Simulation results showed that the estimation of metallurgical indicators (concentrate grade and recovery) was significantly affected by changes in the floatability parameter. A poor estimate of floatability is likely to lead to very different results for the control strategy. Future research should focus on estimating and updating the most significant parameters of the dynamic model, such as floatability, with an appropriate sampling time.
Quintanilla P, Navia D, Neethling SJ, et al., 2023, Economic model predictive control for a rougher froth flotation cell using physics-based models, Minerals Engineering, Vol: 196, Pages: 1-16, ISSN: 0892-6875
The development of an economic model predictive control (E-MPC) strategy is presented. The strategy uses a novel dynamic flotation model that incorporates the physics of the froth phase in a flotation cell. The dynamic model was previously calibrated and validated using experimental data.Sensitivity analyses were conducted to select a suitable objective function that accounted for both process economics and control variable sensitivities. While the ultimate goal of a rougher flotation cell is to maximise the metallurgical recovery at a steady state for a specified minimum grade, it was evident that the incorporation of air recovery dynamics (which can be measured in real-time) and concentrate grade dynamics (calculated through first-principle models) led to the best results. The addition of a dynamic variable that can be easily measured online, i.e. air recovery, offers great potential to improve plant performance in existing froth flotation systems. Furthermore, a minimum concentrate grade was imposed in the E-MPC strategy. This acts as an economic constraint as it allows the metallurgical recovery to be optimised while ensuring that concentrate grade requirements are met.The dynamic optimisation problem for the E-MPC strategy was discretised using orthogonal collocations, and was implemented in Matlab using automatic differentiation via CasADi. Two typical manipulated variables were considered: air flowrate and pulp height setpoints. Based on laboratory-scale data, the implementation of the E-MPC strategy resulted in improvements ranging from +8 to +22 % in metallurgical recovery, while maintaining the specified grade. This is therefore an encouraging control strategy to explore in larger flotation systems.
Quintanilla P, Navia D, Moreno F, et al., 2023, A methodology to implement a closed-loop feedback-feedforward level control in a laboratory-scale flotation bank using peristaltic pumps, MethodsX, Vol: 10, Pages: 1-15, ISSN: 2215-0161
This paper describes the implementation of a level control strategy in a laboratory-scale flotation system. The laboratory-scale system consists of a bank of three flotation tanks connected in series, which mimics a flotation system found in mineral processing plants. Besides the classical feedback control strategy, we have also included a feedforward strategy to better account for process disturbances. Results revealed that the level control performance significantly improves when a feedforward strategy is considered. This methodology uses peristaltic pumps for level control, which has not been extensively documented even though: (1) peristaltic pumps are commonly used in laboratory-scale systems, and (2) the control implementation is not as straightforward as those control strategies that use valves. Therefore, we believe that this paper, which describes a proven methodology that has been validated in an experimental system, can be a useful reference for many researchers in the field.•Preparation of reagents to ensure that the froth stability of the froth layer is representative of an industrial flotation froth.•Calibration of instruments - convert the electrical signal from PLCs to engineering units.•Tuning PI parameters using SIMC rules by performing step-changes in each flotation cell.
Zhang H, Brito-Parada PR, Neethling SJ, et al., 2022, Yield stress of foam flow in porous media: The effect of bubble trapping, Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol: 655, Pages: 1-12, ISSN: 0927-7757
Foam behaves as a yield-stress fluid as it flows in a porous medium. Quasi-static analysis suggests that the yield stress arises from the non-smooth motion of foam films, denoted as lamellae, in pores. In order to study the effect of trapped lamellae on the motion of a moving lamella and consequently on the yield stress of foam, we conduct numerical simulations in the quasi-static limit. We propose a new method utilizing the surface energy minimization algorithm, which explicitly considers the connectivity of pores in a porous medium. We consider two different shapes of pore and vary the number of nearby trapped lamellae to investigate the effects of bubble trapping on the non-smooth and the smooth motion of a single lamella passing through a pore, respectively. We find that the trapped lamellae lead to the increased volume-averaged pressure drop and thus the increased yield stress. Notably, the motion of a lamella through a pore with rounded corners in the pore body becomes non-smooth, due to the presence of trapped lamellae. The results contribute to a better understanding of the yield stress of foam in porous media.
Mesa D, van Heerden M, Cole K, et al., 2022, Hydrodynamics in a three-phase flotation system - fluid following with a new hydrogel tracer for Positron Emission Particle Tracking (PEPT), Chemical Engineering Science, Vol: 260, Pages: 1-11, ISSN: 0009-2509
Understanding the hydrodynamics of three-phase stirred tanks, such as froth flotation cells, is paramount for the characterisation of turbulence, stability and performance. Although positron emission particle tracking (PEPT) is known for its effectiveness in measuring the hydrodynamics of particles in opaque, high solid content systems, it has not been widely used for characterising the liquid phase. This work presents a new, neutrally buoyant, alginate hydrogel tracer, designed to emulate the density of the liquid phase, which is suitable for high-speed tracking with PEPT.PEPT experiments were conducted in a bench-scale flotation cell, comparing the new tracer to ion-exchange resin tracers previously used in this system. Results showed statistically significant differences in pathlines, residence time and velocity distribution among the tracers. Moreover, the hydrodynamics of the new tracer agree with existing CFD predictions for the liquid phase. This methodology enables the comprehensive study of relative flow behaviour in complex multiphase systems.
Cole K, Brito-Parada PR, Hadler K, et al., 2022, Characterisation of solid hydrodynamics in a three-phase stirred tank reactor with positron emission particle tracking (PEPT), Chemical Engineering Journal, Vol: 433, Pages: 1-13, ISSN: 1385-8947
It is challenging to measure the hydrodynamics of stirred tank reactors when they contain multiphase flows comprising liquid, gas bubbles and particles. Radioactive particle tracking techniques such as positron emission particle tracking (PEPT) are the only established techniques to determine internal flow behaviour due to the inherent opacity and density of fluid and the vessel walls. The profiles of solids flow are an important tool for robust reactor design and optimisation and offer insight into underlying transport processes and particle–fluid–bubble interactions for applications such as froth flotation. In this work, measurements with PEPT were performed with two tracer particles differing in surface hydrophobicity to characterise the solids hydrodynamics in a baffled vessel agitated with a Rushton turbine. The location data from PEPT were averaged with time to estimate the probability density function (PDF) of particle velocity in individual voxels. The peaks of these voxel distributions were used to produce profiles of solids flow in different azimuthal and horizontal slices. Bimodal vertical velocity distributions were observed in the impeller radial jet which suggest the particles experienced trajectory crossing effects due to inertia. Statistical tests were performed to compare the velocity distributions of the hydrophilic and hydrophobic tracer particles, which indicated similar average flow behaviour in the liquid or pulp phase of the vessel and differences near the air inlet, in the impeller discharge stream and pulp–froth interface. With tracers designed to represent gangue and valuable mineral species, the differences in velocity reveal interactions such as bubble–particle attachment and entrainment.
Cole K, Barker DJ, Brito-Parada PR, et al., 2022, Standard method for performing positron emission particle tracking (PEPT) measurements of froth flotation at PEPT Cape Town, MethodsX, Vol: 9, Pages: 101680-101680, ISSN: 2215-0161
Positron emission particle tracking (PEPT) is a technique for measuring the motion of tracer particles in systems of flow such as mineral froth flotation. An advantage of PEPT is that tracer particles with different physical properties can be tracked in the same experimental system, which allows detailed studies of the relative behaviour of different particle classes in flotation. This work describes the standard operating protocol developed for PEPT experiments in a flotation vessel at PEPT Cape Town in South Africa. A continuously overflowing vessel with constant air recovery enables several hours of data acquisition at steady state flow and consistent flotation conditions. Tracer particles are fabricated with different coatings to mimic mineral surface hydrophobicity and size, and a data treatment derived from a rotating disk study is utilized to produce high frequency (1 kHz) location data relative to the tracer activity. Time averaging methods are used to represent the Eulerian flow field and occupancy of the tracer behaviour based on voxel schemes in different co-ordinate systems. The average velocity of the flow in each voxel is calculated as the peak of the probability density function to represent the peak of asymmetrical or multimodal distributions.•A continuously overflowing flotation vessel was developed for extended data acquisition at steady state flow.•The data treatment enabled the direct comparison of different particle classes in the flotation vessel.•The solids flow fields was described by the probability density function of tracer particle velocity measured in different voxel schemes.
Salinas-Farran L, Batchelor A, Neethling SJ, 2022, Multimodal assessment of the curing of agglomerated ores in the presence of chloride ions, Hydrometallurgy, Vol: 207, ISSN: 0304-386X
Agglomeration and subsequent curing are widely used as pre-treatment for ore prior to heap leaching as it both improve the permeability of the heap and brings leaching solution into close contact with the ore, initializing the leaching reactions. Despite its widespread use there have been limited studies into the processes occurring within the agglomerates over the curing process. In this study both destructive and non-destructive imaging techniques are used to assess both the physical and chemical changes occurring within the agglomerates as they cure.The SEM/EDX is one of the most popular imaging techniques for mineral samples. It can only be carried out once for a given sample due to its destructive preparation method but provides detailed mineralogical information. A complementary tool is X-ray Microtomography (XMT), which is non-destructive and can be used to image the same object multiple times over the course of the experiment. Its main limitation, though, is that the acquired images are of X-ray attenuation values and need to be independently assigned to different mineral classifications based on, for instance, the corresponding SEM images. Combining the ability of SEM/EDX measurements to identify different mineral phases with the 3D time resolved XMT measurements can thus produce superior results to those achievable using either of the modalities on their own.In this study, we propose a methodology for quantifying the formation and depletion of mineral components of agglomerates. These methodologies will be demonstrated in ores agglomerated using a combination of sulphuric acid and ferric sulphate as well as in samples in which sodium chloride is added to the agglomeration recipe. The curing process was tracked beyond the typical time scales used industrially, highlighting that the presence of chloride ions makes a substantial difference to the chemical and structural evolution of the sample. Over this curing process most of the observed leaching occurs dur
Ilankoon IMSK, Dushyantha NP, Mancheri N, et al., 2022, Constraints to rare earth elements supply diversification: evidence from an industry survey, Journal of Cleaner Production, Vol: 331, ISSN: 0959-6526
Rare earth elements (REEs) are crucial to accomplishing renewable energy targets throughout the world, including electrical vehicles and wind energy. Despite the extensive requirements of REEs, current supply chains are mainly fulfilled by the Chinese rare earth (RE) industry. This has resulted in price volatility, supply chain uncertainties, and RE trade disputes. The authors identified 13 factors as constraints to develop RE supply chains outside China and these constraints were rated by the major RE companies outside China, including RE industry experts. The survey results obtained from RE industry experts have been statistically analysed to ascertain the key factors that affect the development of independent rare earth (RE) supply chains outside China. 4 key factors were identified as statistically important, among them, business uncertainties within the RE industry and the Chinese RE influences on global supply chains being the dominant factors.
Zhang H, Brito-Parada P, Neethling S, et al., 2022, VISCOUS FROTH LENS: STEADY-STATE ANALYSIS, Pages: 2164-2168
We extend the quasi-static foam simulation method into the steady-state viscous foam modelling. The simulation of steady-state viscous foam flow is transferred into a surface energy minimization problem with varying equivalent “surface tension” along foam films. We simulate the motion of a viscous froth lens propagating in a straight channel. We find the 120° rule used in dynamic simulations stimulates the deformation of the lens structure if the same resolution of the film discretization is used. The proposed method cannot replace a dynamic simulation when the unsteady flow process is of interest. However, the results by the proposed method suggest that the 120° rule for the interior threefold point could be inefficient for high driven velocities. This is because films are highly curved near the interior-three fold point for high driven velocities, which results in dynamic contact angles deviating from the 120° rule. We suggest that a more advanced “vertex dynamics” rule should be implemented to incorporate the effect of the dynamic contact angles at the interior three-fold point.
Quintanilla P, Neethling SJ, Mesa D, et al., 2021, A dynamic flotation model for predictive control incorporating froth physics. Part II: Model calibration and validation, Minerals Engineering, Vol: 173, Pages: 1-15, ISSN: 0892-6875
Modelling for flotation control purposes is the key stage of the implementation of model-based predicted controllers. In Part I of this paper, we introduced a dynamic model of the flotation process, suitable for control purposes, along with sensitivity analysis of the fitting parameters and simulations of important control variables. Our proposed model is the first of its kind as it includes key froth physics aspects. The importance of including froth physics is that it improves the estimation of the amount of material (valuables and entrained gangue) in the concentrate, which can be used in control strategies as a proxy to estimate grade and recovery.In Part II of this series, experimental data were used to estimate the fitting parameters and validate the model. The model calibration was performed to estimate a set of model parameters that provide a good description of the process behaviour. The model calibration was conducted by comparing model predictions with actual measurements of variables of interest. Model validation was then performed to ensure that the calibrated model properly evaluates all the variables and conditions that can affect model results. The validation also allowed further assessing the model’s predictive capabilities.For model calibration and validation purposes, experiments were carried out in an 87-litre laboratory scale flotation tank. The experiments were designed as a randomised full factorial design, manipulating the superficial gas velocity and tailings valve position. All experiments were conducted in a 3-phase system (solid-liquid–gas) to ensure that the results obtained, as well as the behaviour of the flotation operation, are as similar as possible to those found in industrial flotation cells.In total, six fitting parameters from the model were calibrated: two terms from the equation for overflowing bubble size; three parameters from the bursting rate equation; and the number of pulp bubble size classes. After the mode
Quintanilla P, Neethling SJ, Navia D, et al., 2021, A dynamic flotation model for predictive control incorporating froth physics. Part I: Model development, Minerals Engineering, Vol: 173, Pages: 1-23, ISSN: 0892-6875
It is widely accepted that the implementation of model-based predictive controllers (MPC) ensures optimal operation if an accurate model of the process is available. In the case of froth flotation, modelling for control purposes is a challenging task due to inherent process instabilities. Most models for control have only focused on the pulp phase rather than the froth phase, which is usually oversimplified or even neglected. Despite the fact that froth stability can significantly affect the overall performance of flotation cells, there is still a gap in literature regarding flotation models for control purposes that properly include froth physics.In this paper we describe the development of a dynamic flotation model suitable for model predictive control, incorporating equations that describe the physics of flotation froths. Unlike other flotation models for control in the literature, the model proposed here includes important variables related to froth stability, such as bursting rate and air recovery, as well as simplified equations to calculate froth recovery and entrainment. These model equations allow estimating the amount of valuable material reporting to the concentrate, which can be used as a proxy to estimate grade and recovery. Additionally, pulp-froth interface physics was also included in our model, which enables a more accurate prediction of relevant flotation variables.A sensitivity analysis of the parameters showed that two out of seven parameters were highly sensitive. The highly sensitive parameters are the exponential factor n of the equation for the overflowing bubble size, and the constant value a of the equation for the bursting rate. Although the other parameters showed a reasonably lower sensitivity than n and a, the results also revealed that there is a significant difference in the prediction accuracy if the parameters are poorly estimated. Further simulations of important variables for control exhibited a good adaptability to changes in typ
Salinas Farran L, Neethling S, 2021, Measuring and Modelling Agglomerate Performance using X-ray Micro Tomography, Hydroprocess
Avalos Patino J, Dargaville S, Neethling S, et al., 2021, Impact of inhomogeneous unsteady participating media in a coupled convection-radiation system using finite element based methods, International Journal of Heat and Mass Transfer, Vol: 176, Pages: 1-16, ISSN: 0017-9310
Combined convection–radiation is a common phenomenon in many engineering problems. A differentially–heated rectangular enclosure is a widely–used benchmark for testing numerical techniques developed for solving the coupled momentum and energy equations related to combined convection–radiation. Previous studies have tended to describe the phenomenon in cases using simplified characteristics for the participating media including the assumptions of: (i) uniform distribution, (ii) homogeneous cross section, (iii) grey gas radiation and (iv) under steady state conditions. The effects of an inhomogeneous unsteady participating media, e.g. composed of a mixture of gases, are arguably understudied. In this work the effect of an inhomogeneous unsteady participating media on combined convection–radiation inside a rectangular enclosure is considered, under both grey and non-grey gas modelling approaches involving a mixture of gases. A key novelty in this work is the inclusion of the ability to handle inhomogeneous participating media which change in space, time and absorption cross section values as a result of the convection–radiation coupling, allowing us to assess different gas modelling approaches. A global gas radiation model is used and a new non–uniform discretisation method for the absorption distribution function is introduced; this method allows a better handling of those energy groups in which the Planck absorption coefficient is low, improving the performance of the spherical harmonics method and mitigating ray–effects on finite elements in angle discretisation. The momentum and energy equations are solved numerically using finite element based discretisation methods. The radiative transfer equation is solved numerically using both spherical harmonics and finite elements for the angular discretisation, with their relative performance compared. The results highlight the importance that the characteristics of the partic
Quintanilla P, Neethling SJ, Brito-Parada PR, 2021, Modelling for froth flotation control: A review, Minerals Engineering, Vol: 162, ISSN: 0892-6875
Flotation is a conceptually simple operation; however, as a multiphase process with inherent instability, it exhibits complex dynamics. One of the most efficient ways to increase flotation performance is by implementing advanced controllers, such as Model Predictive Control (MPC). This type of controller is very dependent on the model that represents the dynamics of the process. Although model development is one of the most crucial parts in MPC, flotation models have been mainly developed for simulation purposes (i.e. analysis and design) rather than control purposes. This paper presents a critical literature review on modelling for froth flotation control. Models reviewed have been sub-classified as empirical, phenomenological and hybrid according to their characteristics. In particular, it is highlighted that models have so far primarily focused on the pulp phase, with the froth phase often neglected; when the froth phase is included, kinetics models such as those used for the pulp phase, are commonly used to represent it. Froth physics are, however, dominated by processes such as coalescence, liquid motion and solids motion, which have been previously modelled through complex, steady-state models used for simulation purposes, rather than control purposes. There remains a need to develop appropriate models for the froth phase and more complex models for the pulp phase that can be used as part of MPC strategies. The challenges associated with the development of such models are discussed, with the aim of providing a pathway towards better controlled froth flotation circuits.
Salinas Farran L, Neethling S, 2020, Micro-CT-based assessment of the performance of agglomerated sulphide ores: The impact of long curing times and the addition of chloride ions, International Mineral Processing Congress
Snelling B, Neethling S, Horsburgh K, et al., 2020, Uncertainty quantification of landslide generated waves using Gaussian process emulation and variance-based sensitivity analysis, Water, Vol: 12, ISSN: 2073-4441
Simulations of landslide generated waves (LGWs) are prone to high levels of uncertainty. Here we present a probabilistic sensitivity analysis of an LGW model. The LGW model was realised through a smooth particle hydrodynamics (SPH) simulator, which is capable of modelling fluids with complex rheologies and includes flexible boundary conditions. This LGW model has parameters defining the landslide, including its rheology, that contribute to uncertainty in the simulated wave characteristics. Given the computational expense of this simulator, we made use of the extensive uncertainty quantification functionality of the Dakota toolkit to train a Gaussian process emulator (GPE) using a dataset derived from SPH simulations. Using the emulator we conducted a variance-based decomposition to quantify how much each input parameter to the SPH simulation contributed to the uncertainty in the simulated wave characteristics. Our results indicate that the landslide’s volume and initial submergence depth contribute the most to uncertainty in the wave characteristics, while the landslide rheological parameters have a much smaller influence. When estimated run-up is used as the indicator for LGW hazard, the slope angle of the shore being inundated is shown to be an additional influential parameter. This study facilitates probabilistic hazard analysis of LGWs, because it reveals which source characteristics contribute most to uncertainty in terms of how hazardous a wave will be, thereby allowing computational resources to be focused on better understanding that uncertainty.
Snelling BE, Collins GS, Piggott MD, et al., 2020, Improvements to a smooth particle hydrodynamics simulator for investigating submarine landslide generated waves, International Journal for Numerical Methods in Fluids, Vol: 92, Pages: 744-764, ISSN: 0271-2091
Submarine landslides can exhibit complex rheologies, including a finite yield stress and shear thinning, yet are often simulated numerically using a Newtonian fluid rheology and simplistic boundary conditions. Here we present improvements made to a Smoothed Particle Hydrodynamics simulator to allow the accurate simulation of submarine landslide generated waves. The improvements include the addition of Bingham and Herschel‐Bulkley rheologies, which better simulate the behavior of submarine mudflows. The interaction between the base of the slide and the slope is represented more accurately through the use of a viscous stress boundary condition. This condition treats the interface between the seafloor and the slide as a fluid boundary layer with a user‐defined viscosity and length scale. Modifications to the pressure and density calculations are described that improve their stability for landslide generated wave scenarios. An option for pressure decomposition is introduced to prevent particle locking under high pressure. This facilitates the application of this simulator to landslide scenarios beneath significant water depths. Additional modifications to the reaveraging and renormalization routines improve the stability of the free surface and fluid density. We present the mathematical formulations of these improvements alongside commentary on their performance and applicability to landslide generated wave modeling. The modifications are verified against analytical fluid flow solutions and a wave generation experiment.
Salinas Farran L, Neethling S, 2019, Quantifying the effects of mass transport and mineralogy in the curing and leaching of agglomerated ores, Procemin-Geomet
Lombardo AG, Simon BA, Taiwo O, et al., 2019, A pore network model of porous electrodes in electrochemical devices, JOURNAL OF ENERGY STORAGE, Vol: 24, ISSN: 2352-152X
Wang P, Cilliers JJ, Neethling SJ, et al., 2019, The behavior of rising bubbles covered by particles, Chemical Engineering Journal, Vol: 365, Pages: 111-120, ISSN: 1385-8947
A systematic investigation of the influence of particle coverage on the dynamics of rising bubbles was carried out using high-speed photography and image analysis techniques to study bubble behavior in terms of changes in velocity and aspect ratio. The buoyancy force and drag force exerted on the bubbles and the effect of particles were calculated to further understand their behavior. Results show that particles attached on the bubbles strongly dampen the oscillations observed in bubble aspect ratio and decrease its velocity and acceleration. The particles also render the bubbles more spherical and slow their velocity. It was found that the overall velocity of a bubble is directly correlated to its aspect ratio and inversely correlated to its particle coverage, while the acceleration and the aspect ratio and its change are inversely correlated. Interestingly, the trend observed in the oscillation and the oscillation period of particle-laden bubbles is similar for different levels of particle coating. A drag modification factor ηp, which quantifies the drag influence of particles on bubble velocity, was identified from force analysis. A modified drag coefficient for uncoated and particle-laden bubbles was introduced, which allows, for the first time, to predict the behavior of rising bubbles in gas-liquid-particle systems.
Wang P, Cilliers JJ, Neethling SJ, et al., 2019, Effect of particle size on the rising behavior of particle-laden bubbles, Langmuir, Vol: 35, Pages: 3680-3687, ISSN: 0743-7463
The rising behavior of bubbles, initially half and fully coated with glass beads of various sizes, was investigated. The bubble velocity, aspect ratio, and oscillation periods were determined using high-speed photography and image analysis. In addition, the acting forces, drag modification factor, and modified drag coefficient were calculated and interpreted. Results show that the aspect ratio oscillation of the rising bubbles is similar, irrespective of the attached particle size. As the particle size is increased, the rising bubbles have a lower velocity and aspect ratio amplitude, with the time from release to each aspect ratio peak increasing. Higher particle coverage is shown to decrease the bubble velocity and dampen the oscillations, reducing the number of aspect ratio peaks observed. The highest rise velocities correspond to the lowest aspect ratios and vice versa, whereas a constant aspect ratio yields a constant rise velocity, independent of the particle size. Force analysis shows that the particle drag modification factor increases with the increased particle size and is greatest for fully laden bubbles. The modified drag coefficient of particle-laden bubbles increases with the increased particle size, although it decreases with the increased Reynolds number independent of the particle size. The drag force exerted by the particles plays a more dominant role in decreasing bubble velocities as the particle size increases. The results and interpretation produced a quantitative description of the behavior of rising particle-laden bubbles and the development of correlations will enhance the modeling of industrial applications.
Neethling SJ, Brito Parada P, Hadler K, et al., 2019, The transition from first to zero order flotation kinetics and its implications for the efficiency of large flotation cells, Minerals Engineering, Vol: 132, Pages: 149-161, ISSN: 0892-6875
Flotation cells have traditionally been modelled using first order kinetics, often distributed over multiple floatable species. This description is valid as long as the kinetics are not restricted by the available bubble surface area. If this carrying capacity limit is approached, the behaviour will transition toward zero order kinetics with respect to the concentration of floatable species in the pulp, with this transition being associated with a significant degradation in performance. In this paper we develop a model which describes the transition from first to zero order kinetics. A dimensionless group is introduced, which is the ratio of the flotation rate under first order kinetics to the rate at maximum bubble carrying capacity. At values of this dimensionless group much less than 1 the kinetic equation reduces to the familiar k-Sb relationship, but with a progressive deviation away from first order kinetics as the value increases through 1, with zero order kinetics obtained for values of the dimensionless group much greater than one. This dimensionless group is a function of the cell size, being proportional to the ratio of the cell volume to its cross-sectional area.Since mechanical flotation cells continue to get larger, mainly due to the capital and operating cost benefits that they provide for a given residence time, the potential for deleterious zero order effects is likely to increase. This is also why zero order behaviour is virtually never encountered at the laboratory scale. The propensity for zero order kinetics also increases with both the floatability and concentration of floatable material in the pulp, as well as with the fineness of the grind. This means that cleaner cells are likely to be very susceptible to exhibiting zero order kinetics, while scavenger cells are likely to continue to exhibit first order kinetics for any foreseeable flotation cell size. The cell size at which zero order kinetics effects will degrade the performance of rougher
Reyes F, Cilliers JJ, Neethling SJ, 2019, Quantifying mineral liberation by grade and surface exposure using X-ray micro-tomography for flotation processes, Pages: 1570-1579
Liberation is a key driver in all mineral separation processes as it limits the maximum possible grade for a given recovery. In flotation, this is further complicated by the fact that it is surface exposure of the floatable minerals that determines the ultimate performance. Liberation, grade and surface exposure are commonly quantified using Scanning Electron Microscopy coupled to Energy Dispersive X-ray spectroscopy (SEM/EDX) analysis of polished sections. The intrinsically 2D nature of this technique can result in significant sampling errors and stereological effects that can affect the quantification of the ore's textural characteristics. X-ray micro-Tomography (XMT) is an imaging method that can non-invasively and non-destructively delineate ore fragments in 3D, thus providing an alternative method that eliminates the need for stereological corrections and readily provides surface exposure. A methodology and automated algorithm were designed for extracting this information from images of closely packed particles, thus allowing samples containing a large number of particles to be assessed. The main drawback of XMT is that, unlike SEM/EDX, it cannot directly measure the mineralogy of the sample, instead producing a 3D X-ray attenuation map. We therefore also present an algorithm for calibrating the thresholding of the XMT images based on SEM/EDX images of sections through the same sample, thus allowing the liberation analysis to be carried out on a 3D mineral map in which the uncertainty in the mineral assignment is small and statistically quantified. The methodology was tested on low grade porphyry copper ore as this is both an industrially relevant and traditionally difficult system to quantify using XMT due to the similarity in the X-ray attenuation of the sulphide species, especially the pyrite and chalcopyrite. As each 3D volume imaged contain 100-1000s of grains, large data sets can be readily produced. By dividing these particles into classes based on both
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