•An anisotropic turbulence model for moderately dense gas-particle flows.•Anisotropic closure models for the Reynolds-stresses are applied.•Closure models for the individual components of the drift ...velocity are derived.•Dynamic adjustment of the correlation coefficients in coarse-grid simulations.•An a priori validation shows good agreement with highly resolved simulation data.
We present an anisotropic, dynamic multi-phase turbulence model for moderately dense gas-particle flows by spatially averaging the kinetic-theory based two-fluid model (Schneiderbauer, AIChE J., 2017; 63(8): 3544–3562). The filtered gas-particle drag force can be approximated by the resolved drag force corrected by the drift velocity (Parmentier et al., AIChE J., 2012; 58(4): 1084–1098). The drift velocity can be expressed as a correlation between the gas-phase velocity and the solid volume fraction. We propose to calculate the correlation coefficients locally and dynamically by application of a scale-similarity approach. Therefore, we show that test-filters can be employed to estimate the correlation coefficients in coarse-grid simulations. Furthermore, transport equations for the components of the highly anisotropic Reynolds-stress tensor are derived, and closure models known from single-phase LES modelling are applied to the unresolved terms with the exception of the interfacial work term, which is expressed by the correlations between the velocities of the phases. In addition, the cluster-induced turbulence production term (Capecelatro et al., J. Fluid Mech., 2015; 780: 578–635) arising in the gas-phase Reynolds-stress transport equation is closed using the drift velocity. An a priorivalidation of the developed closure models against filtered fine-grid simulation data of unbound fluidization for Geldart type A and B particles, as well as an a posteriori verification in wall-bounded fluidized beds of Geldart type A and B particles are conducted.
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•A general gas–solid turbulence model is validated for different flow regimes.•Model parameters can be determined through a dynamic adjustment procedure.•Meso-scale production of ...variances in the solids volume fraction due to clustering.•Wall boundary conditions for the turbulent kinetic energy are derived.•Dynamic adjustment procedure yields grid-size independent results.
The Spatially-Averaged Two-Fluid Model (SA-TFM) is a functional multiphase turbulence model aimed at predicting the influence of unresolved meso-scale structures on the macro-scale flow properties in coarse-grid simulations of gas-particle flows. In this study, we highlight the general applicability of the SA-TFM model due to the dynamic estimation of the model coefficients through test-filters, the anisotropic treatment of the Reynolds-stresses and the drag force correction, and additional wall-friction boundary conditions for the particle-phase velocity, Reynolds-stress and turbulent kinetic energy. The dynamic approach derives information on the unresolved meso-scale flow properties from the resolved macro-scale variables without the need for any intensive prior considerations of the specific flow structure. Thereby, the drift velocity, a measure for the drag-reduction due to the presence of meso-scale structures is estimated from the turbulent kinetic energies of the phases and the variance of the solids volume fraction. We validate the dynamic anisotropic SA-TFM against highly resolved fine-grid Two-Fluid Model simulation data and experimental measurements of Geldart type A and B particles in bubbling to turbulent flow regimes. In the course of this extensive study, we find that the predictions for the macro-scale flow properties, such as slip-velocity, bed expansion, volume fraction distribution, and mass-flux, are in good agreement with the experimental and fine-grid simulation data in a vast number of cases, ranging from unbound fluidization to pilot-scale fluidized beds, thus, implying a wide applicability of the dynamic model independent of the underlying grid-size.
•Validation of dynamic closures for heat transport in coarse-grid TFM simulations.•Drift temperature correction to the interphase heat transfer.•Correct prediction of jump-response in fluidized ...beds.•Reliable predictions of temperature difference decay between the phases.•Dynamic adjustment procedure yields grid-size independent results.
We validate a multi-scale turbulence model for the thermal energy estimation in coarse-grid simulations of moderately dense gas-particle flows. The model is based on spatially-averaging the Two-Fluid Model balance equations including the thermal energy balance equation of both phases. We found, that the drift temperature is a valid measure for the heat transfer reduction due to heterogeneous particle clusters. Furthermore, we propose the dynamic estimation of the drift temperature through the application of test-filters and the solution of transport equations for the variances of the phase temperatures and the solid volume fraction. Closure models for the Reynolds stress contributions are based on single-phase Large-Eddy Simulation models, such as gradient assumptions. In this study, we consider different test-cases including Geldart type A and type B particles in moderately dense regimes with domain averaged volume fractions ranging from 0.05 to 0.25. The operating conditions include unbounded sedimentation under gravity, as well as a turbulent-sluggish fluidization. In all cases, we discuss the influence of the meso-scale particle clusters on the macro-scale temperature distributions through the individual contributions of the unresolved terms in coarse-grid simulations. Thereby, we find that the dynamic estimation of the drift temperature leads to accurate results for the influence of local heat sinks on the global temperature difference decay between the phases and that the jump-response of a fluidized bed to an elevated gas-inflow temperature is correctly captured by the proposed multi-phase turbulence model. Furthermore, the importance of the correct estimation of the hydrodynamics for a correct prediction of the thermodynamics is highlighted.
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•A comparison between TFM, CFD-DEM, and experiments was performed.•A new modification to μ(I)-rheology to consider rolling friction in TFM was proposed.•The effect of two different ...frictional solids stresses was examined in TFM.•Four Different drag models were tested in TFM and CFD-DEM.•Using proper TFM closures improves the comparisons with CFD-DEM and experiments.
We employ a two-fluid model (TFM) as well as a computational fluid dynamics coupled to discrete element method (CFD-DEM) approach to study the time averaged hydrodynamics of single- and multiple-spout fluidized beds. Simulations are validated against the experimental data of (van Buijtenen et al., Numerical and experimental study on multiple-spout fluidized beds, Chemical Engineering Science 66 (2011) 2368–2376) with four different interphase drag correlations. The kinetic theory of granular flow used for solving the motion of the solid phase in TFM, includes realistic particle–wall boundary conditions for momentum transfer and the flux of pseudo-thermal energy. Frictional stresses in TFM are modelled based on a μ(I)-rheology. We propose a new ad hoc modification of the μ(I)-rheology to account for the effect of rolling friction in TFM. In contrast, in CFD-DEM rolling friction is accounted by an additional torque. Our results show that there is a good agreement between both approaches with respect to time averaged volume fraction, solids velocities, solids fluxes and granular temperature.
Gas-particle flows are commonly simulated through a two-fluid model at the industrial scale. However, these simulations need a very fine grid to have accurate flow predictions, which is prohibitively ...demanding in terms of computational resources. To circumvent this problem, the filtered two-fluid model has been developed, where the large-scale flow field is numerically resolved and small-scale fluctuations are accounted for through subgrid-scale modeling. In this study, we have performed fine-grid two-fluid simulations of dilute gas-particle flows in periodic domains and applied explicit filtering to generate data sets. Then, these data sets have been used to develop artificial neural network (ANN) models for closures such as the filtered drag force and solid phase stress for the filtered two-fluid model. The set of input variables for the subgrid drag force ANN model that has been found previously to work well for dense flow regimes is found to work as well for the dilute regime. In addition, we present a Galilean invariant tensor basis neural network (TBNN) model for the filtered solid phase stress, which can nicely capture the anisotropic nature of the solid phase stress arising from subgrid-scale velocity fluctuations. Finally, the predictions provided by this new TBNN model are compared to those obtained from a simple eddy-viscosity ANN model.
Gas-particle flows are commonly simulated through two-fluid model at industrial-scale. However, these simulations need very fine grid to have accurate flow predictions, which is prohibitively ...demanding in terms of computational resources. To circumvent this problem, the filtered two-fluid model has been developed, where large-scale flow field is numerically resolved and small-scale fluctuations are accounted for through subgrid-scale modeling. In this study, we have performed fine-grid two-fluid simulations of dilute gas-particle flows in periodic domains and applied explicit filtering to generate datasets. Then, these datasets have been used to develop artificial neural network (ANN) models for closures such as the filtered drag force and solid phase stress for the filtered two-fluid model. The set of input variables for the subgrid drag force ANN model that has been found previously to work well for dense flow regimes is found to work as well for the dilute regime. In addition, we present a Galilean invariant tensor basis neural network (TBNN) model for the filtered solid phase stress which can capture nicely the anisotropic nature of the solid phase stress arising from subgrid-scale velocity fluctuations. Finally, the predictions provided by this new TBNN model are compared with those obtained from a simple eddy-viscosity ANN model.
In recent years, intrathecal baclofen (ITB) has attained an important role in the treatment of severe spasticity and dystonia in children. There are principal differences between the use of ITB in ...children and its use in neurology and oncology in adults. Here, we present a consensus report on best practice for the treatment of severe spastic and dystonic movement disorders with ITB. Using a problem-orientated approach to integrate theories and methods, the consensus was developed by an interdisciplinary group of experienced ITB users and experts in the field of movement disorders involving 14 German centers. On the basis of the data pooled from more than 400 patients, the authors have summarized their experience and supporting evidence in tabular form to provide a concise, but still a comprehensive information base that represents our current understanding regarding ITB treatment options in children and adolescents.
Purpose: Markers for epileptic seizures are rare and their use has not been established in the evaluation of seizures and febrile convulsions (FC). Brain‐type natriuretic peptide (BNP) is a ...natriuretic, diuretic, and vasodilator compound first discovered in the hypothalamus but mainly synthesized in the myocardium. The aim of this study was to assess whether epileptic seizures or FC are related to increased secretion of the N‐terminal fragment of BNP (NT‐proBNP).
Methods: Sixty‐five postictal children (43 boys, 22 girls) and 31 children with epilepsy (20 boys, 11 girls) after a seizure‐free period for at least 2 months serving as controls were enrolled. Postictal NT‐proBNP levels were analyzed and controlled 24–48 h thereafter.
Results: Plasma concentration of NT‐proBNP was significantly higher 4 h postictal compared to 24–48 h postictal (p < 0.001). Subgroup analysis revealed increased NT‐proBNP levels in children with tonic–clonic seizures and FC compared to children with partial motor seizures (p < 0.001), syncope (SYN; p < 0.01), or control population (p < 0.001).
Conclusions: Our results suggest that elevated plasma NT‐proBNP levels are not specific for cardiac dysfunction. Postictal measurement of plasma NT‐proBNP seems to be useful in discriminating different types of epilepsy, FC, and SYN in childhood.
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