Characteristic Time Scales Research Articles

Characteristic timescales for detonation-based rocket propulsion systems

Characteristic timescales for detonation-based rocket propulsion systems

Drag reduction assisted emulsification in a micro-channel

An experimental study of the turbulent dynamics of emulsification in a cross-slot microfluidic device is presented. The continuous phase contains a minute amount of an inelastic polymer (xanthan). The Reynolds numbers are sufficiently large (up to 16000) so the drag reduction phenomenon is observed during the emulsification process. The statistics of droplet sizes in the resulting emulsions are measured ex-situ by means of digital microscopy in a wide range of Reynolds numbers and polymer concentrations in the continuous phase. Integral measurements of the statistics of the pressure drops in the micro-channel allow one to systematically map the drag reduction states. Corresponding to each state, the space–time dynamics of the emulsification process are assessed by means of in-situ high speed imaging of the interface between the two fluids which further allows one to extract the characteristic time and space scales associated to the dynamics of the interface. Various dynamic regimes of the microscopic emulsification process are mapped in terms of the Reynolds number and shear thinning rheology of the continuous phase.

The NANOGrav 12.5-Year Data Set: Dispersion Measure Misestimations with Varying Bandwidths

Noise characterization for pulsar-timing applications accounts for interstellar dispersion by assuming a known frequency dependence of the delay it introduces in the times of arrival (TOAs). However, calculations of this delay suffer from misestimations due to other chromatic effects in the observations. The precision in modeling dispersion is dependent on the observed bandwidth. In this work, we calculate the offsets in infinite-frequency TOAs due to misestimations in the modeling of dispersion when using varying bandwidths at the Green Bank Telescope. We use a set of broadband observations of PSR J1643−1224, a pulsar with unusual chromatic timing behavior. We artificially restricted these observations to a narrowband frequency range, then used both the broad- and narrowband data sets to calculate residuals with a timing model that does not account for time variations in the dispersion. By fitting the resulting residuals to a dispersion model and comparing the fits, we quantify the error introduced in the timing parameters due to using a reduced frequency range. Moreover, by calculating the autocovariance function of the parameters, we obtained a characteristic timescale over which the dispersion misestimates are correlated. For PSR J1643−1224, which has one of the highest dispersion measures (DM) in the NANOGrav pulsar timing array, we find that the infinite-frequency TOAs suffer from a systematic offset of ∼22 μs due to incomplete frequency sampling, with correlations over about one month. For lower-DM pulsars, the offset is ∼7 μs. This error quantification can be used to provide more robust noise modeling in the NANOGrav data, thereby increasing the sensitivity and improving the parameter estimation in gravitational wave searches.

Simulated phase state and viscosity of secondary organic aerosols over China

Abstract. Secondary organic aerosols (SOAs) can exist in liquid, semi-solid, or amorphous solid states. Chemical transport models (CTMs), however, usually assume that SOA particles are homogeneous and well-mixed liquids, with rapid establishment of gas–particle equilibrium for simulations of SOA formation and partitioning. Missing the information of SOA phase state and viscosity in CTMs impedes accurate representation of SOA formation and evolution, affecting the predictions of aerosol effects on air quality and climate. We have previously developed a parameterization to estimate the glass transition temperature (Tg) of an organic compound based on volatility and to predict viscosity of SOA. In this study, we apply this method to predict the phase state of SOA particles over China in summer of 2018 using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem). The simulated Tg of dry SOA (Tg,org) agrees well with the value estimated from ambient volatility measurements at an urban site in Beijing. For the spatial distributions of Tg,org, simulations show that at the surface the values of Tg,org range from ∼287 to 305 K, with higher values in northwestern China, where SOA particles have larger mass fractions of low-volatility compounds. Considering water uptake by SOA particles, the SOA viscosity shows a prominent geospatial gradient in which highly viscous or solid SOA particles are mainly predicted in northwestern China. The lowest and highest SOA viscosity values both occur over the Qinghai–Tibet Plateau, where the solid phase state is predicted over dry and high-altitude areas and the liquid phase state is predicted mainly in the south of the plateau with high relative humidity during the summer monsoon season. Sensitivity simulations show that, including the formation of extremely low-volatility organic compounds, the percent time that a SOA particle is in the liquid phase state decreases by up to 12 % in southeastern China during the simulated period. With an assumption that the organic and inorganic compounds are internally mixed in one phase, we show that the water absorbed by inorganic species can significantly lower the simulated viscosity over southeastern China. This indicates that constraining the uncertainties in simulated SOA volatility distributions and the mixing state of the organic and inorganic compounds would improve prediction of viscosity in multicomponent particles in southeastern China. We also calculate the characteristic mixing timescale of organic molecules in 200 m SOA particles to evaluate kinetic limitations in SOA partitioning. Calculations show that during the simulated period the percent time of the mixing timescale longer than 1 h is >70 % at the surface and at 500 hPa in most areas of northern China, indicating that kinetic partitioning considering the bulk diffusion in viscous particles may be required for more accurate prediction of SOA mass concentrations and size distributions over these areas.

On the breakup frequency of bubbles and droplets in turbulence: A compilation and evaluation of experimental data

The dispersed phase in liquid–liquid emulsions and air–liquid mixtures can often be fragmented into smaller sizes by the surrounding turbulent carrier phase. The critical parameter that controls this process is the breakup frequency, which is defined from the breakup kernel in the population balance equation. The breakup frequency controls how long it takes for the dispersed phase to reach the terminal size distribution for given turbulence. In this article, we try to summarize the key experimental results and compile the existing datasets under a consistent framework to find out what is the characteristic timescale of the problem and how to account for the inner density and viscosity of the dispersed phase. Furthermore, by pointing out the inconsistency of existing experimental data, the key important unsolved questions and related problems on the breakup frequency of bubbles and droplets are discussed.

Investigating Fire–Atmosphere Interaction in a Forest Canopy Using Wavelets

Wildland fire–atmosphere interaction generates complex turbulence patterns, organized across multiple scales, which inform fire-spread behaviour, firebrand transport, and smoke dispersion. Here, we utilize wavelet-based techniques to explore the characteristic temporal scales associated with coherent patterns in the measured temperature and the turbulent fluxes during a prescribed wind-driven (heading) surface fire beneath a forest canopy. We use temperature and velocity measurements from tower-mounted sonic anemometers at multiple heights. Patterns in the wavelet-based energy density of the measured temperature plotted on a time–frequency plane indicate the presence of fire-modulated ramp–cliff structures in the low-to-mid-frequency band (0.01–0.33 Hz), with mean ramp durations approximately 20% shorter and ramp slopes that are an order of magnitude higher compared to no-fire conditions. We then investigate heat- and momentum-flux events near the canopy top through a cross-wavelet coherence analysis. Briefly before the fire-front arrives at the tower base, momentum-flux events are relatively suppressed and turbulent fluxes are chiefly thermally-driven near the canopy top, owing to the tilting of the flame in the direction of the wind. Fire-induced heat-flux events comprising warm updrafts and cool downdrafts are coherent down to periods of a second, whereas ambient heat-flux events operate mainly at higher periods (above 17 s). Later, when the strongest temperature fluctuations are recorded near the surface, fire-induced heat-flux events occur intermittently at shorter scales and cool sweeps start being seen for periods ranging from 8 to 35 s near the canopy top, suggesting a diminishing influence of the flame and increasing background atmospheric variability thereat. The improved understanding of the characteristic time scales associated with fire-induced turbulence features, as the fire-front evolves, will help develop more reliable fire behaviour and scalar transport models.

How Does the Inner Retinal Network Shape the Ganglion Cells Receptive Field? A Computational Study.

We consider a model of basic inner retinal connectivity where bipolar and amacrine cells interconnect and both cell types project onto ganglion cells, modulating their response output to the brain visual areas. We derive an analytical formula for the spatiotemporal response of retinal ganglion cells to stimuli, taking into account the effects of amacrine cells inhibition. This analysis reveals two important functional parameters of the network: (1) the intensity of the interactions between bipolar and amacrine cells and (2) the characteristic timescale of these responses. Both parameters have a profound combined impact on the spatiotemporal features of retinal ganglion cells' responses to light. The validity of the model is confirmed by faithfully reproducing pharmacogenetic experimental results obtained by stimulating excitatory DREADDs (Designer Receptors Exclusively Activated by Designer Drugs) expressed on ganglion cells and amacrine cells' subclasses, thereby modifying the inner retinal network activity to visual stimuli in a complex, entangled manner. Our mathematical model allows us to explore and decipher these complex effects in a manner that would not be feasible experimentally and provides novel insights in retinal dynamics.

Radiopharmaceutical transport in solid tumors via a 3-dimensional image-based spatiotemporal model

Lutetium-177 prostate-specific membrane antigen (177Lu-PSMA)-targeted radiopharmaceutical therapy is a clinically approved treatment for patients with metastatic castration-resistant prostate cancer (mCRPC). Even though common practice reluctantly follows “one size fits all” approach, medical community believes there is significant room for deeper understanding and personalization of radiopharmaceutical therapies. To pursue this aim, we present a 3-dimensional spatiotemporal radiopharmaceutical delivery model based on clinical imaging data to simulate pharmacokinetic of 177Lu-PSMA within the prostate tumors. The model includes interstitial flow, radiopharmaceutical transport in tissues, receptor cycles, association/dissociation with ligands, synthesis of PSMA receptors, receptor recycling, internalization of radiopharmaceuticals, and degradation of receptors and drugs. The model was studied for a range of values for injection amount (100–1000 nmol), receptor density (10–500 nmol•l–1), and recycling rate of receptors (10–4 to 10–1 min–1). Furthermore, injection type, different convection-diffusion-reaction mechanisms, characteristic time scales, and length scales are discussed. The study found that increasing receptor density, ligand amount, and labeled ligands improved radiopharmaceutical uptake in the tumor. A high receptor recycling rate (0.1 min–1) increased radiopharmaceutical concentration by promoting repeated binding to tumor cell receptors. Continuous infusion results in higher radiopharmaceutical concentrations within tumors compared to bolus administration. These insights are crucial for advancing targeted therapy for prostate cancer by understanding the mechanism of radiopharmaceutical distribution in tumors. Furthermore, measures of characteristic length and advection time scale were computed. The presented spatiotemporal tumor transport model can analyze different physiological parameters affecting 177Lu-PSMA delivery.

The dynamics of fibres dispersed in viscoelastic turbulent flows

This study explores the dynamics of finite-size fibres suspended freely in a viscoelastic turbulent flow. For a fibre suspended in Newtonian flows, two different flapping regimes were identified by Rosti et al. (Phys. Rev. Lett., vol. 121, issue 4, 2018, 044501): one dominated by time scales from the flow, and another dominated by time scales associated with its natural frequency. We explore in this work how the fibre dynamics is modified by the elasticity of the carrier fluid. For this, we perform direct numerical simulations of a two-way coupled fibre–fluid system in a parametric space spanning different Deborah numbers, fibre bending stiffness (flexible to rigid) and linear density difference between the fibre and the flow (neutrally buoyant to denser-than-fluid fibres). We examine how these parameters influence various fibre characteristics such as the frequency of flapping, curvature, and alignment with the fluid strain and polymer stretching directions. Results reveal that the neutrally buoyant fibres, depending on their flexibility, oscillate with large and small time scales transpiring from the flow, but the smaller time scales are suppressed as the polymer elasticity increases. Polymer stretching is uncommunicative to denser-than-fluid fibres, which flap with large time scales from the flow when flexible, and with their natural frequency when rigid. Thus the characteristic elastic time scale has a subdominant effect when the fibres are neutrally buoyant, while its effect is absent when the fibres become more inertial. In addition, we also explore the fibre's bending curvature and its preferential alignment with the flow to identify the other roles of viscoelasticity in modifying the coupled fluid–structure dynamics. Inertial fibres have larger curvatures and are less responsive to the polymer presence, whereas the neutrally buoyant fibres show quantitative changes. The perceptible passivity of the denser fibres is again reflected in the way they align preferentially with the polymeric stretching directions: the neutrally buoyant fibres show a higher alignment with the polymer stretching directions compared to the denser ones. In a nutshell, the polymers exert a larger influence on neutrally buoyant fibres, which are more reflective of the polymeric influence in the flow. The study addresses comprehensively the interplay between polymer elasticity and the fibre structural properties in determining its response behaviour in an elasto-inertial turbulent flow.

Mean-field analysis of the glassy dynamics of an elastoplastic model of super-cooled liquids

Abstract We present a mean-field theory of a coarse-grained model of a super-cooled liquid in which relaxation occurs via local plastic rearrangements. Local relaxation can be induced by thermal fluctuations or by the long-range elastic consequences of other rearrangements. We extract the temperature dependence of both the relaxation time and the lengthscale of dynamical correlations. We find two dynamical regimes. First, a regime in which the characteristic time and length scales diverge as a power law at a critical temperature $T_c$. This regime is found by an approximation that neglects activated relaxation channels, which can be interpreted as akin to the one found by the mode-coupling transition of glasses. In reality, only a cross-over takes place at $T_c$. The residual plastic activity leads to a second regime characterised by an Arrhenius law below $T_c$. In this case, we show that the lengthscale governing dynamical correlations diverges as a power law as $T\to 0$, and is logarithmically related to the relaxation time.

Frequency-Dependent Microelectrophoresis Study of Colloids with Tunable Surface Charge.

Nonaqueous poly(methyl methacrylate) (PMMA) colloidal suspensions in a solvent that is simultaneously matched in both density and refractive index have been important for real-space studies of colloidal self-assembly, but their complex electrostatic character remains largely unexplored. Electrophoresis is a powerful tool for determining the surface potential and charge of the colloidal suspension; however, because of refractive index matching, standard electrophoresis measurements are not feasible. We carry out microscope-based microelectrophoresis measurements on PMMA colloids in cyclohexyl bromide and cis-trans decalin to measure particle charge as a function of salt concentration in both DC and frequency-variable AC fields. The colloid charge depends on salt concentration and reverses sign near 0.35 μM, providing evidence that solution ions are actively modifying the colloid surface. The frequency dependence of the electrophoretic mobility yields the characteristic time scale for electric double-layer polarization and provides intriguing evidence for Manning condensation and polyion formation.

Modelling dynamics of photosynthetic units and microalgae growth based on high throughput pulsed light screens

Light-dark cycles on the s timescale are typical of cell cycling through photobioreactors and high-rate ponds and can significantly impact microalgae cultivation efficiency. Here, a novel formulation of the Camacho-Rubio microalgae growth model was developed to simulate dynamic growth under pulsed light (s timescale). It captures the dynamics of the photosynthetic units (PSUs: open, closed and photoinhibited) and their impact on biomass productivity. Theoretical knowledge of PSU mediated processes operating on characteristic timescales was used to identify intra- and inter-light cycle variable dynamics and guide the model formulation. For model calibration, dynamic profiles of microalgae growth under pulsed light in a High-Throughput Screening platform were employed, after Principal Component Analysis (PCA), to remove biological noise. Model parameters were estimated for Chlorella sp., and the model validated against additional data under both pulsed and continuous light. The average prediction error for OD750 (measure of biomass) was 8% under pulsed light and 15% under continuous light. For OD680/OD750 (measure of Chlorophyll cell−1) it was 8% under pulsed and continuous light, demonstrating the model’s ability to represent highly variable conditions with good accuracy.

The universal power spectrum of quasars in optical wavelengths

Context. The optical variability of quasars is one of the few windows through which we can explore the behaviour of accretion discs around supermassive black holes. Aims. We aim to establish the dependence of variability properties, such as characteristic timescales and the variability amplitude, on basic quasar parameters such as black hole mass and the accretion rate, controlling for the rest-frame wavelength of emission. Methods. Using large catalogues of quasars, we selected the g-band light curves for 4770 objects from the Zwicky Transient Facility archive. All the selected objects fall into a narrow redshift bin, 0.6 < z < 0.7, but cover a wide range of accretion rates in Eddington units (REdd) and black hole masses (M). We grouped these objects into 26 independent bins according to these parameters, calculated low-resolution g-band variability power spectra for each of these bins, and approximated the power spectra with a simple analytic model that features a break at a timescale, tb. Results. We find a clear dependence of the break timescale, tb, on REdd, on top of the known dependence of tb on the black hole mass, M. In our fits, tb ∝ M0.65 − 0.55REdd0.35−0.3, where the ranges in the exponents correspond to the best-fitting parameters of different power spectrum models. This mass dependence is slightly steeper than that found in other studies. Scaling tb to the orbital timescale of the innermost stable circular orbit (ISCO), tISCO, results approximately in tb/tISCO ∝ (REdd/M)0.35. In the standard thin disc model, (REdd/M) ∝ Tmax4, where Tmax is the maximum disc temperature, so that tb/tISCO appears to scale approximately with the maximum temperature of the disc to a small power. The observed values of tb are ∼10 longer than the orbital timescale at the light-weighted average radius of the disc region emitting in the (observer frame) g-band. The different scaling of the break frequency with M and REdd shows that the shape of the variability power spectrum cannot be solely a function of the quasar luminosity, even for a single rest-frame wavelength. Finally, the best-fitting models have slopes above the break in the range between −2.5 and −3. A slope of −2, as in the damped random walk models, fits the data significantly worse.

Anomalous Pressure Diffusion and Deformation in Two‐ and Three‐Dimensional Heterogeneous Fractured Media

AbstractIn fractured and stress‐sensitive reservoirs and aquifers, hydromechanical coupling is important, in connection with their heat and solute transport properties, and because the fluid production or extraction leads to land subsidence and potentially to induced seismicity. Classical dual‐porosity poroelasticity (DPP) models cannot upscale pressure diffusion and deformation in fractured porous media, which are characterized by anomalous behaviors that manifest in strong tailing in the temporal evolution of flow rate and subsidence. We study these behaviors using detailed numerical simulations of fluid production in naturally fractured formations characterized by multi‐Gaussian distributions of the matrix permeability. We find that the tailing behaviors depend on the permeability contrast between fracture and matrix, on the permeability distribution in the matrix, and on the correlation length. We use a non–equilibrium, multi‐porosity model to quantify the coupled behaviors of anomalous pressure diffusion, fluid flow and deformation. The model is parameterized by medium and fluid properties, which set the characteristic pressure diffusion time scales. It allows to identify the emerging scaling regimes and scaling behaviors of flow rate and subsidence. We propose a model implementation that captures the full anomalous evolution of flow rates and displacements observed in the detailed numerical simulations in terms of the permeability distribution and matrix length scales. The presented results shed new light on the controls of medium heterogeneity and geometry on pressure diffusion, fluid production and subsidence in highly heterogeneous fractured media.

Experimental method to determine the mode-I in-situ bond strength-toughness development during automated placement of uncured thermoset carbon/epoxy tows

In-situ bond strength toughness (IBST), commonly referred to as tow tackiness, is a first order property affecting the adherence quality and defect formation (e.g., wrinkles, folds) during automated tow placement (ATP) processing of uncured thermoset polymer matrix composite (PMC) tows. Tow-tow IBST develops over characteristic millisecond timescales (tc≤50ms) due to the rapid tow placement velocity of ∼1 m/s. In this paper, an experimental method is presented to determine millisecond timescale tow-tow mode-I IBST in terms of fracture mechanics-based traction-separation relationship. The test specimen consists of two tows bonded to rigid platens with a pre-crack between them to induce crack initiation. Experiments are performed using IM7-G/8552 carbon/epoxy prepregs for both long and short timescales at a constant debonding rate of 5 mm/s, contact pressure of 0.23 MPa, and bonding temperature of 40 °C. In addition, high-speed two-dimensional digital image correlation (2D-DIC) is used to image and measure the tow-tow interfacial deformation during debonding. The peak traction and apparent energy release rate are found to significantly decrease (about 60 %) at the short millisecond timescale contact hold times compared to longer (i.e., second) timescale.

Efficient numerical algorithm for multi-level ionization of high-atomic-number gases

An efficient numerical algorithm for laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the system of differential equations describing ionization evolution. Using analytical solutions resolves the multiscale issue of ionization due to different characteristic time scales of ionization processes and the main code time step. Algorithm efficiency and memory requirements are significantly improved by using a locally reduced system of differential equations. The algorithm also assigns proper orbital quantum numbers and their projections to ionization states. The algorithm is verified and validated using experimental data.

A physics-based model for fluvial valley width

Abstract. The width of fluvial valley floors is a key parameter to quantifying the morphology of mountain regions. Valley floor width is relevant to diverse fields including sedimentology, fluvial geomorphology, and archaeology. The width of valleys has been argued to depend on climatic and tectonic conditions, on the hydraulics and hydrology of the river channel that forms the valley, and on sediment supply from valley walls. Here, we derive a physically based model that can be used to predict valley width and test it against three different datasets. The model applies to valleys that are carved by a river migrating laterally across the valley floor. We conceptualize river migration as a Poisson process, in which the river changes its direction stochastically at a mean rate determined by hydraulic boundary conditions. This approach yields a characteristic timescale for the river to cross the valley floor from one wall to the other. The valley width can then be determined by integrating the speed of migration over this timescale. For a laterally unconfined river that is not uplifting, the model predicts that the channel-belt width scales with river flow depth. Channel-belt width corresponds to the maximum width of a fluvial valley. We expand the model to include the effects of uplift and lateral sediment supply from valley walls. Both of these effects lead to a decrease in valley width in comparison to the maximum width. We identify a dimensionless number, termed the mobility–uplift number, which is the ratio between the lateral mobility of the river channel and uplift rate. The model predicts two limits: at high values of the mobility–uplift number, the valley evolves to the channel-belt width, whereas it corresponds to the channel width at low values. Between these limits, valley width is linked to the mobility–uplift number by a logarithmic function. As a consequence of the model, valley width increases with increasing drainage area, with a scaling exponent that typically has a value between 0.4 and 0.5, but can also be lower or higher. We compare the model to three independent datasets of valleys in experimental and natural uplifting landscapes and show that it closely predicts the first-order relationship between valley width and the mobility–uplift number.

Laser-induced indirect ignition of non-premixed turbulent shear layers

This study uses direct numerical simulations to investigate the forced ignition of temporally-evolving turbulent subsonic shear layers separating a gaseous stream of methane (CH4) and a stagnant gas environment of molecular oxygen (O2). Ignition is forced by a thermal-energy source that heats up a small volume of gas during periods of time much shorter than the characteristic acoustic time scale. The kernel, including its initial rounded conical shape, resembles experimental observations after optical breakdown is achieved in a gas irradiated by a focused laser. Particular emphasis is placed on ignition phenomena observed when the laser is focused on the O2 environment outside the turbulent shear layer, where the local composition is far beyond the lean flammability limit. This represents an indirect mode of non-premixed ignition that develops after a relatively long period of time has passed since laser-energy deposition, when the eddies near the oxidizer edge of the turbulent shear layer are intercepted by a baroclinically-generated subsonic vortex of hot dissociated O2 ejected from the laser-energy deposition zone. The success of indirect ignition depends on the orientation of the laser beam, the thickness of the shear layer, and the kernel standoff distance from the oxidizer edge of the shear layer. An ignition Damköhler number is defined that accounts for these averaged effects in six different simulation cases. For near-unity ignition Damköhler numbers, the solution is also sensitive to the local instantaneous flow field prevailing near the oxidizer edge of the shear layer, in that a modification of the instantaneous pre-deposition flow field, while preserving its turbulence statistics, can produce different ignition outcomes.Novelty and significance statement This work investigates forced ignition in a canonical flow configuration – a non-premixed turbulent CH4/O2 shear layer – and analyzes mechanisms by which ignition can be unexpectedly achieved in adverse conditions. In particular, an ensuing laser-generated advection of hot dissociated gas is observed to ignite the shear layer even when the mixture at the laser focal point is not flammable, an observation first made in early experiments. This flow phenomenon, whose consequences on ignition of non-premixed turbulent flows have not previously been analyzed by direct numerical simulation, can significantly separate the laser-energy deposition zone from the ignition location and is linked to baroclinically generated vorticity due to the rounded conical shape of the energy kernel. The phenomenology analyzed here may impact the design of laser-based ignition systems for chemical propulsion.

Segregation–rheology feedback in bidisperse granular flows: a coupled Stokes’ problem

The feedback between particle-size segregation and rheology in bidisperse granular flows is studied using the Stokes’ problem configuration. A method of lines scheme is implemented to solve the coupled momentum and segregation equations for a normally graded particle size distributed bulk at constant solids volume fraction. The velocity profiles develop quickly into a transient state, decoupled from segregation yet determined by the particle size. From this transient state, the velocity profile changes due to the particles’ relative movement, which redistributes the frictional response, hence its rheology. Additionally, the particles’ relative friction is modified via a frictional coefficient ratio, by analogy with the particles’ size ratio. While positive values of this coefficient exacerbate the nonlinearity of the velocity profiles induced by size differences, negative values dampen this behaviour. The numerical solutions reproduce well the analytical solutions for the velocity profile, which can be obtained from the steady-state conditions of the momentum and segregation equations for the transient and steady states, respectively. Segregation–momentum balances and four characteristic time scales can be established to propose two non-dimensional quantities, including specific Schmidt and Péclet numbers that describe broadly the segregation–rheology feedback. The proposed scheme, theoretical solutions and non-dimensional numbers offer a combined approach to understand segregation and flow dynamics within a granular bulk, extensible across many flow configurations.

Mechanical Analysis of the Forces Involved in a Pilot-Scale Blast Furnace Raceway Formation by Means of CFD/DEM Simulations

The CFD/DEM approach was used for investigating the forces playing a role in a furnace raceway formation and stability. The configuration is an actual pilot-scale hot blast furnace filled only with coke particles. In such a system, the raceway was unstable, with successively a growing phase and a collapse. The CFD/DEM numerical simulations were coupled with a core-shrinking model to mimic coke particle combustion. However, the kinetic reactions and heat transfers were not numerically predicted. Instead, the characteristic combustion timescale of one coke particle was imposed, and the combustion zone was adjusted to match the global combustion measured in the pilot-scale experiment. The results showed that the standard contact model was not enough to resist the pressure exerted by the granular weight on the raceway. However, the addition of a cohesive force, through the Johnson-Kendall-Roberts (JKR) model, allowed the qualitative reproduction of the gas pressure fluctuations and the collapse cycles in accordance with the experiment. A sensitivity analysis of the flow rate showed that CFD/DEM is able to reproduce quantitatively the time between two collapses, as observed in the experiment. Predicted raceway size and shapes are also in agreement with the experimental observations in the range of investigated parameters.