Effects of large particles in pipe flow at low and moderate Reynolds numbers

The presence of solid particles in a Newtonian liquid flow will affect the properties of the flow. For small particles these effects are fairly well understood. However, the behaviour of liquids laden with large particles are less well understood and even more so if the carrier liquid is a non-Newtonian fluid. In the present study we consider large particles of spherical shape. By large is here meant particles that are of the same size as the large scale length scales of the flow and larger. We are considering how particles volume fraction affects parameters such as pressure drop and velocity distribution in the pipe flow. The simulations are performed using a finite difference based in-house software and the particles are represented using an virtual boundary method. The size of the spherical particles is about 1/6 of the pipe diameter and the volume fraction is varied between 5and 20%. The fluid is either Newtonian or shear thinning modelled using a power law expression

Large eddy simulation of an aerated Rushton stirred tank

Simulations of aerated stirred reactor is performed using Large Eddy Simulation (LES). The gas phase is modelled using Lagrangian Particle Tracking (LPT). The reactor is stirred by a single impeller Rushton turbine, centred in the reactor. The air is introduced at the bottom wall through a circular sparger. The main focus is to investigate how the gas phase affects the liquid in the reactor. Effects of gas volume flow and stirrer speed are investigated. The results show that the time averaged liquid velocities in the radial and tangential directions as well as the pumping capacity decrease with increasing gas volume fraction. In the axial direction the gas redirects the radial jet upwards breaking the symmetry of the ring vortices

Numerical simulation of a gas-liquid Rushton stirred reactor - LES and LPT

Abstract in Undetermined Simulations of aerated stirred reactor is performed using a combination of large eddy simulation (LES) and Lagrangian particle tracking (LPT). A single impeller Rushton turbine is positioned at the center of the reactor and air is introduced at the bottom through a circular sparger. Effects of the gas volume flow, stirrer speed and sparger dimension are investigated. The results show that the time averaged liquid velocities in radial and tangential directions decrease with increasing gas volume fraction. In the axial direction, the gas redirects the radial jet upwards, breaking the symmetry of the ring vortices. Especially, for a narrower sparger, a more concentrated tilt upwards is observed with a larger region of negative axial velocity. Although, low aeration number is used, the periodicity from the impeller is decreasing and interfering with the creation of the trailing vortex pair. The gas dispersion increases with decreasing the sparger diameter

On the interaction between two fixed spherical particles

The variation of the drag (CD) and lift coefficients (CL) of two fixed solid spherical particles placed at different positions relative each other is studied. Simulations are carried out for particle Reynolds numbers of 50, 100 and 200 and the particle position is defined by the angle between the line connecting the centers of the particles and the free-stream direction (a) and the separation distance (do) between the particles. The flow around the particles is simulated using two different methods; the Lattice Boltzmann Method (LBM), using two different computational codes, and a conventional finite difference approach, where the Volume of Solid Method (VOS) is used to represent the particles. Comparisons with available numerical and experimental data show that both methods can be used to accurately resolve the flow field around particles and calculate the forces the particles are subjected to. Independent of the Reynolds number, the largest change in drag, as compared to the single particle case, occurs for particles placed in tandem formation. Compared to a single particle, the drag reduction for the secondary particle in tandem arrangement is as high as 60%, 70% and 80% for Re = 50, 100 and 200, respectively. The development of the recirculation zone is found to have a significant influence on the drag force. Depending on the flow Situation in-between the particles for various particle arrangements, attraction and repulsion forces are detected due to low and high pressure regions, respectively. The results show that the inter-particle forces are not negligible even under very dilute conditions. (c) 2007 Elsevier Ltd. All rights reserved

Global, regional, national, and selected subnational levels of stillbirths, neonatal, infant, and under-5 mortality, 1980-2015: a systematic analysis for the Global Burden of Disease Study 2015.

BACKGROUND: Established in 2000, Millennium Development Goal 4 (MDG4) catalysed extraordinary political, financial, and social commitments to reduce under-5 mortality by two-thirds between 1990 and 2015. At the country level, the pace of progress in improving child survival has varied markedly, highlighting a crucial need to further examine potential drivers of accelerated or slowed decreases in child mortality. The Global Burden of Disease 2015 Study (GBD 2015) provides an analytical framework to comprehensively assess these trends for under-5 mortality, age-specific and cause-specific mortality among children under 5 years, and stillbirths by geography over time. METHODS: Drawing from analytical approaches developed and refined in previous iterations of the GBD study, we generated updated estimates of child mortality by age group (neonatal, post-neonatal, ages 1-4 years, and under 5) for 195 countries and territories and selected subnational geographies, from 1980-2015. We also estimated numbers and rates of stillbirths for these geographies and years. Gaussian process regression with data source adjustments for sampling and non-sampling bias was applied to synthesise input data for under-5 mortality for each geography. Age-specific mortality estimates were generated through a two-stage age-sex splitting process, and stillbirth estimates were produced with a mixed-effects model, which accounted for variable stillbirth definitions and data source-specific biases. For GBD 2015, we did a series of novel analyses to systematically quantify the drivers of trends in child mortality across geographies. First, we assessed observed and expected levels and annualised rates of decrease for under-5 mortality and stillbirths as they related to the Soci-demographic Index (SDI). Second, we examined the ratio of recorded and expected levels of child mortality, on the basis of SDI, across geographies, as well as differences in recorded and expected annualised rates of change for under-5 mortality. Third, we analysed levels and cause compositions of under-5 mortality, across time and geographies, as they related to rising SDI. Finally, we decomposed the changes in under-5 mortality to changes in SDI at the global level, as well as changes in leading causes of under-5 deaths for countries and territories. We documented each step of the GBD 2015 child mortality estimation process, as well as data sources, in accordance with the Guidelines for Accurate and Transparent Health Estimates Reporting (GATHER). FINDINGS: Globally, 5·8 million (95% uncertainty interval [UI] 5·7-6·0) children younger than 5 years died in 2015, representing a 52·0% (95% UI 50·7-53·3) decrease in the number of under-5 deaths since 1990. Neonatal deaths and stillbirths fell at a slower pace since 1990, decreasing by 42·4% (41·3-43·6) to 2·6 million (2·6-2·7) neonatal deaths and 47·0% (35·1-57·0) to 2·1 million (1·8-2·5) stillbirths in 2015. Between 1990 and 2015, global under-5 mortality decreased at an annualised rate of decrease of 3·0% (2·6-3·3), falling short of the 4·4% annualised rate of decrease required to achieve MDG4. During this time, 58 countries met or exceeded the pace of progress required to meet MDG4. Between 2000, the year MDG4 was formally enacted, and 2015, 28 additional countries that did not achieve the 4·4% rate of decrease from 1990 met the MDG4 pace of decrease. However, absolute levels of under-5 mortality remained high in many countries, with 11 countries still recording rates exceeding 100 per 1000 livebirths in 2015. Marked decreases in under-5 deaths due to a number of communicable diseases, including lower respiratory infections, diarrhoeal diseases, measles, and malaria, accounted for much of the progress in lowering overall under-5 mortality in low-income countries. Compared with gains achieved for infectious diseases and nutritional deficiencies, the persisting toll of neonatal conditions and congenital anomalies on child survival became evident, especially in low-income and low-middle-income countries. We found sizeable heterogeneities in comparing observed and expected rates of under-5 mortality, as well as differences in observed and expected rates of change for under-5 mortality. At the global level, we recorded a divergence in observed and expected levels of under-5 mortality starting in 2000, with the observed trend falling much faster than what was expected based on SDI through 2015. Between 2000 and 2015, the world recorded 10·3 million fewer under-5 deaths than expected on the basis of improving SDI alone. INTERPRETATION: Gains in child survival have been large, widespread, and in many places in the world, faster than what was anticipated based on improving levels of development. Yet some countries, particularly in sub-Saharan Africa, still had high rates of under-5 mortality in 2015. Unless these countries are able to accelerate reductions in child deaths at an extraordinary pace, their achievement of proposed SDG targets is unlikely. Improving the evidence base on drivers that might hasten the pace of progress for child survival, ranging from cost-effective intervention packages to innovative financing mechanisms, is vital to charting the pathways for ultimately ending preventable child deaths by 2030. FUNDING: Bill & Melinda Gates Foundation