This document describes two new models for predicting the just suspended speed (Njs) for mixtures of solids in stirred tanks: the power model and the momentum model. The power model predicts the mixture Njs based on the sum of the power required to suspend each individual solid phase. The momentum model predicts the mixture Njs based on the sum of the momentum required to suspend each individual solid phase. Both models were developed because the current design heuristic, which assumes the mixture Njs is the maximum Njs of the individual phases, does not adequately capture the effects of particle interactions in mixtures. The models were tested using experimental data for mixtures of various solids up to 27% solids loading in a stirred tank.
Thermal instability of incompressible non newtonian viscoelastic fluid with...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
The present analysis is made to investigate the effects of heat source and thermal diffusion on an unsteady free convection flow along a porous vertical plate in a rotating system. The plate is subjected to constant heat and mass flux also. The problem is solved analytically and expressions for velocity. Energy and temperature profiles, skin friction and Nusselt number are obtained. The effects of different parameter entered in the problem are discussed on the primary and secondary velocities, temperature and concentration distributions, primary and secondary skin frictions and Nusselt number with the help of tables and graphs.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The role of strain rate in the dynamic response of materialsAI Publications
We start with the response of ductile materials. To understand the response of these materials to fast dynamic loadings, we introduce two approaches to dynamic viscoplasticity. These are the flowstress approach and the overstress approach, and strain rate has different roles with these two approaches. At very high loading rates the flowstress approach implies very high strength, which is hard to explain by microscale considerations, while the overstress approach does not.We then demonstrate the advantage of using the overstress approach by applying the two approaches to the elastic precursor decay problem. Next use the overstress approach to treat the following problems: 1) the 4th power law response in steady flow of ductile materials; 2) high rate stress upturn (HRSU) of ductile materials; and 3) HRSU of brittle materials. With these examples we demonstrate the advantage of using the overstress approach over the flowstress approach. It follows that HRSU means High (strain) Rate Stress Upturn and not High Rate Strength Upturn, as would follow from using the flowstress approach.
Thermal instability of incompressible non newtonian viscoelastic fluid with...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
The present analysis is made to investigate the effects of heat source and thermal diffusion on an unsteady free convection flow along a porous vertical plate in a rotating system. The plate is subjected to constant heat and mass flux also. The problem is solved analytically and expressions for velocity. Energy and temperature profiles, skin friction and Nusselt number are obtained. The effects of different parameter entered in the problem are discussed on the primary and secondary velocities, temperature and concentration distributions, primary and secondary skin frictions and Nusselt number with the help of tables and graphs.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The role of strain rate in the dynamic response of materialsAI Publications
We start with the response of ductile materials. To understand the response of these materials to fast dynamic loadings, we introduce two approaches to dynamic viscoplasticity. These are the flowstress approach and the overstress approach, and strain rate has different roles with these two approaches. At very high loading rates the flowstress approach implies very high strength, which is hard to explain by microscale considerations, while the overstress approach does not.We then demonstrate the advantage of using the overstress approach by applying the two approaches to the elastic precursor decay problem. Next use the overstress approach to treat the following problems: 1) the 4th power law response in steady flow of ductile materials; 2) high rate stress upturn (HRSU) of ductile materials; and 3) HRSU of brittle materials. With these examples we demonstrate the advantage of using the overstress approach over the flowstress approach. It follows that HRSU means High (strain) Rate Stress Upturn and not High Rate Strength Upturn, as would follow from using the flowstress approach.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Monte Carlo Implementation for Simulation of Ostwald Ripening Via Long Range ...inventionjournals
Numerical simulations based on the Monte Carlo Potts model are used to study coupling of grain growth and Ostwald ripening in two-phase polycrystalline materials. The ratio of the grain boundary energy to the interphase boundary energy is used as an input parameter. It is shown that the grain growth in two-phase polycrystalline materials is controlled by long-range diffusion and the change of the mean grain size with time obeys the growth law, <r>n = <r>0 n+kt where n is the grain growth exponent. The value of n is calculated for a broad series of volume fractions. It is found that the inverse grain growth exponent, 1/n, in agreement with the theoretical value, 1/n=1/3, noticed during computer simulations for volume fractions between 40% and 90%. However, the value of 1/n is smaller than 1/3 for volume fractions between 10% and 30%. Furthermore, the temporal development of the number of grains has been analyzed for the entire range of volume fractions. It is also seen that the quasi-stationary state is advanced at varied aging times depending on the volume fractions. Furthermore, it is shown that the simulated size distribution are symmetric and peaked at x=1 for volume fractions differ between 50% and 90%; however, the simulated size distribution become asymmetric and skew to smaller grains for lower volume fractions change between 10% and 40%.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
APPLICATION OF PARTICLE SWARM OPTIMIZATION FOR ENHANCED CYCLIC STEAM STIMULAT...Zac Darcy
Three different variations of PSO algorithms, i.e. Canonical, Gaussian Bare-bone and Lévy Bare-bone
PSO, are tested to optimize the ultimate oil recovery of a large heavy oil reservoir. The performance of
these algorithms was compared in terms of convergence behaviour and the final optimization results. It is
found that, in general, all three types of PSO methods are able to improve the objective function. The best
objective function is found by using the Canonical PSO, while the other two methods give similar results.
The Gaussian Bare-bone PSO may picks positions that are far away from the optimal solution. The Lévy
Bare-bone PSO has similar convergence behaviour as the Canonical PSO. For the specific optimization
problem investigated in this study, it is found that the temperature of the injection steam, CO2 composition
in the injection gas, and the gas injection rates have bigger impact on the objective function, while steam
injection rate and the liquid production rate have less impact on the objective function.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Teaching an old dog new tricks - final versionsqleahy
This presentation is designed for elementary school teachers and librarians. The powerpoint will highlight four free technology teaching tools. While the tools can be used across the curriculum, the presenter will highlight ways to use them in language arts and social studies lessons.
This presentation is designed for elementary school teachers and librarians. The presenter will highlight four free technology teaching tools that have transformed her own teaching. While the tools can be used across the curriculum, the presenter will highlight ways to use them in language arts and social studies lessons.
Although same-sex couples now are able to obtain dissolutions of their marriages in many states, there are still complicating factors facing divorcing LGBT couples. Some of these factors include different tax treatment, division of pension plans, child support, custody issues and the rights of married vs. unmarried same sex couples.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Monte Carlo Implementation for Simulation of Ostwald Ripening Via Long Range ...inventionjournals
Numerical simulations based on the Monte Carlo Potts model are used to study coupling of grain growth and Ostwald ripening in two-phase polycrystalline materials. The ratio of the grain boundary energy to the interphase boundary energy is used as an input parameter. It is shown that the grain growth in two-phase polycrystalline materials is controlled by long-range diffusion and the change of the mean grain size with time obeys the growth law, <r>n = <r>0 n+kt where n is the grain growth exponent. The value of n is calculated for a broad series of volume fractions. It is found that the inverse grain growth exponent, 1/n, in agreement with the theoretical value, 1/n=1/3, noticed during computer simulations for volume fractions between 40% and 90%. However, the value of 1/n is smaller than 1/3 for volume fractions between 10% and 30%. Furthermore, the temporal development of the number of grains has been analyzed for the entire range of volume fractions. It is also seen that the quasi-stationary state is advanced at varied aging times depending on the volume fractions. Furthermore, it is shown that the simulated size distribution are symmetric and peaked at x=1 for volume fractions differ between 50% and 90%; however, the simulated size distribution become asymmetric and skew to smaller grains for lower volume fractions change between 10% and 40%.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
APPLICATION OF PARTICLE SWARM OPTIMIZATION FOR ENHANCED CYCLIC STEAM STIMULAT...Zac Darcy
Three different variations of PSO algorithms, i.e. Canonical, Gaussian Bare-bone and Lévy Bare-bone
PSO, are tested to optimize the ultimate oil recovery of a large heavy oil reservoir. The performance of
these algorithms was compared in terms of convergence behaviour and the final optimization results. It is
found that, in general, all three types of PSO methods are able to improve the objective function. The best
objective function is found by using the Canonical PSO, while the other two methods give similar results.
The Gaussian Bare-bone PSO may picks positions that are far away from the optimal solution. The Lévy
Bare-bone PSO has similar convergence behaviour as the Canonical PSO. For the specific optimization
problem investigated in this study, it is found that the temperature of the injection steam, CO2 composition
in the injection gas, and the gas injection rates have bigger impact on the objective function, while steam
injection rate and the liquid production rate have less impact on the objective function.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Teaching an old dog new tricks - final versionsqleahy
This presentation is designed for elementary school teachers and librarians. The powerpoint will highlight four free technology teaching tools. While the tools can be used across the curriculum, the presenter will highlight ways to use them in language arts and social studies lessons.
This presentation is designed for elementary school teachers and librarians. The presenter will highlight four free technology teaching tools that have transformed her own teaching. While the tools can be used across the curriculum, the presenter will highlight ways to use them in language arts and social studies lessons.
Although same-sex couples now are able to obtain dissolutions of their marriages in many states, there are still complicating factors facing divorcing LGBT couples. Some of these factors include different tax treatment, division of pension plans, child support, custody issues and the rights of married vs. unmarried same sex couples.
Nano mechanics, geo-materials, Nano scale friction, governing equations, macro-Nano behavior of geomaterials, factors affecting Nano scale friction, behavior of soil at Nano scale, scale effect, Micro-Nano transition for frictional forces, review paper, best paper award, best paper presenter award, at PP Savani University, Kosamba, Surat.
Structure and transport coefficients of liquid Argon and neon using molecular...IOSR Journals
Molecular dynamics simulation was employed to deduce the dynamics property distribution function of Argon
and Neon liquid. With the use of a Lennnard-Jones pair potential model, an inter-atomic interaction function was observed
between pair of particles in a system of many particles, which indicates that the pair distribution function determines the
structures of liquid Argon. This distribution effect regarding the liquid structure of Lennard-Jones potential was strongly
affected such that its viscosity depends on density distribution of the model. The radial distribution function, g(r) agrees well
with the experimental data used. Our results regarding Argon and Neon show that their signatures are quite different at
each temperature, such that their corresponding viscosity is not consistent. Two sharps turning points are more
prominent in Argon, one at temperature of 83.88 Kelvin (K) with viscosity of -0.548 Pascal second (Pa-s) and the
other at temperature of 215.64 K with viscosity of -0.228 Pa-s.
In Argon and Neon liquid, temperature and density are inversely and directly proportional to diffusion
coefficient, in that order. This characteristic suggests that the observed non linearity could result from the non
uniform thermal expansion in liquid Argon and Neon, which are between the temperature range of 21.98 K and
239.52 K.
ANALYSIS OF POSSIBILITY OF GROWTH OF SEVERAL EPITAXIAL LAYERS SIMULTANEOUSLY ...ijoejournal
We analyzed nonlinear model with varying in space and time coefficients of growth of epitaxial layers
from gas phase in a vertical reactor with account native convection. We formulate several conditions to
increase homogeneity of epitaxial layers with varying of technological process parameters.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Effect of Rotation on a Layer of Micro-Polar Ferromagnetic Dusty Fluid Heated...IJERA Editor
This paper deals with the theoretical investigation of effect of rotation on micro-polar ferromagnetic dusty fluid
layer heated from below in a porous medium. Linear stability analysis and normal mode analysis methods are
used to find an exact solution for a flat micro-polar ferromagnetic fluid layer contained between two free
boundaries . In case of stationary convection, the effect of various parameters like medium permeability
parameter, non-buoyancy magnetization parameter, micro-polar coupling parameter, spin-diffusion parameter,
micro-polar heat conduction parameter, dust particles parameter and rotation parameter has been analyzed and
results are depicted graphically. In the absence of dust particles, rotation, micro-viscous effect and micro-inertia,
the sufficient condition is obtained for non-oscillatory modes
We study the link between the indentation size effect and the density of geometrically necessary dislocations (GNDs) through the following
approach: four indents of different depth and hardness were placed in a Cu single crystal using a conical indenter with a spherical tip. The
deformation-induced lattice rotations below the indents were monitored via a three-dimensional electron backscattering diffraction method
with a step size of 50 nm. From these data we calculated the first-order gradients of strain and the GND densities below the indents. This
approach allowed us to quantify both the mechanical parameters (depth, hardness) and the lattice defects (GNDs) that are believed to be
responsible for the indentation size effect.Wefind that theGNDdensity does not increase with decreasing indentation depth but rather drops
instead.
Abstract— A scientific investigation is created to examine the nonlinear unfaltering blended convection limit
layer stream and warmth exchange of an incompressible digression hyperbolicnon-Newtonian liquid from a
non-isothermal wedge in the nearness of attractive field. The changed preservation conditions are understood
numerically subject to physically fitting limit conditions utilizing a second-arrange precise verifiable limited
distinction Keller Box method. The numerical code is accepted with past studies. The impact of various rising
non-dimensional parameters, to be specific Weissenberg number (We), power law record (n), blended
convection parameter, weight angle parameter (m), Prandtl number (Pr), Biot number, attractive parameter
(M)and dimensionless extraneous direction on speed and temperature development in the limit layer
administration are inspected in subtle element. Moreover, the impacts of these parameters on surface warmth
exchange rate and nearby skin erosion are additionally examined. Approval with prior Newtonian studies is
introduced and amazing relationship accomplished. It is found that speed is lessened with expanding We,
while, temperature is increased. Expanding n improves speed yet diminishes temperature, a comparable
pattern was seen. An expanding M is found to decline speed however temperature increments.
Keywords— Magnetic parameter, Mixed Convection parameter, Non-Newtonian digression hyperbolic liquid,
power law index, Weissenberg number, Weight inclination parameter.
Physical Characterization of a Method for Production of High Stability Suspen...Editor IJCATR
Suspensions/Dispersions are encountered in a wide range of
applications, e.g., liquid abrasive cleaners, ceramics, medicines,
inks, paints….etc. In most cases it is necessary to keep the
suspension stable for the product lifetime. A new modified
differential sedimentation measuring system is suggested and used
to identify physical parameters affecting the sedimentation in
suspensions. The technique is discussed in details. It is found that
particle sizes as well as viscosity of continuous phase are the most
important factors governing the stability of a suspension. Empirical
relations are extracted to quantitatively describe the weight effect of
each factor. The modified measuring system shows good accuracy
enough to detect fluctuations in concentration of suspended
particles due to their Brownian diffusion, as well as the particles
concentrations in the stable suspension. This study confirmed the
fact that particles diameters measured by Zetasizer are much
greater than those measured by the transmission electron
microscope. This study presents a proposal for new technique for
particle size separation based on the differential sedimentation in
viscose fluids. This new method is a differential viscosity column.
The proposed size separation technique may help to separate
engineered nano-particles with higher resolution
LATTICE BOLTZMANN SIMULATION OF NON-NEWTONIAN FLUID FLOW IN A LID DRIVEN CAVITY IAEME Publication
Lattice Boltzmann Method (LBM) is used to simulate the lid driven cavity flow to explore the mechanism of non-Newtonian fluid flow. The power law model is used to represent the class of non-Newtonian fluids (shear-thinning and shear-thickening fluids) by considering a range of 0.8 to 1.6. Investigation is carried out to study the influence of power law index and Reynolds number on the variation of velocity profiles and streamlines plots. Velocity profiles and the streamline patterns
for various values of power law index at Reynolds numbers ranging 100 to 3200 are presented. Half way bounce back boundary conditions are employed in the numerical method.
TRANSIENT ANALYSIS OF PIEZOLAMINATED COMPOSITE PLATES USING HSDTP singh
Piezoelectric materials have excellent sensing and actuating capabilities have made them the most practical smart materials to integrate with laminated structures. Integrated structure system can be called a smart structure because of its ability to perform self-diagnosis and quick adaption to environment changes. An analytical procedure has been developed in the work based on higher order shear deformation theory subjected to electromechanical loading for investigating transient characteristics of smart material plates. For analysis two displacement models are to be considered i.e., model-1 accounts for strain in thickness direction is zero whereas in model-2 in-plane displacements are expanded as cubic functions of the thickness coordinate. Navier’s technique has been adopted for obtaining solutions of anti-symmetric cross–ply and angle-ply laminates of both model-1 and model-2 with simply supported boundary conditions. For obtaining transient response of a laminated composite plate attached with piezoelectric layer Newmark’s method has been used. Effect of thickness coordinate of composite laminated plates attached with piezoelectric layer subjected to electromechanical loadings is studied.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
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Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
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2. 228 chemical engineering research and design 9 1 ( 2 0 1 3 ) 227–233
Nomenclature
Roman characters
C off-bottom clearance (m)
D impeller diameter (m)
dp particle diameter (m)
g acceleration due to gravity (m/s2)
H liquid height (m)
M momentum (kg m/s2)
Mjs momentum at just suspended conditions (kg
m/s2)
Mjs,1 Mjs for particle one (kg m/s2)
Mjs,2 Mjs for particle two (kg m/s2)
Mjs,mix Mjs for mixture (kg m/s2)
Mo momentum number
N impeller rotational speed (rps or rpm)
Njs just suspended speed (rps or rpm)
Njs,1 Njs for particle 1 (rps or rpm)
Njs,2 Njs for particle 2 (rps or rpm)
Njs,max Njs maximum (rps or rpm)
Njs,mix mixture Njs (rps or rpm)
Np power number
Pjs power consumption at just suspended speed
conditions (W)
Pjs,1 Pjs for particle 1 (W)
Pjs,2 Pjs for particle 2 (W)
Pjs,mix Pjs for mixture (W)
r radius (m)
S Zwietering’s Njs constant
T tank diameter (m)
Vz velocity in the axial direction
Wb baffle width (m)
xS mass fraction of the solids in the slurry
xL mass fraction of the liquid in the slurry
X Zwietering’s mass ratio percent (mass of
solid/mass of liquid × 100)
Greek characters
kinematic viscosity (m2/s)
L liquid density (kg/m3)
S solid density (kg/m3)
sl slurry density (kg/m3)
sl,1 unimodal slurry density for particle 1 (kg/m3)
sl,2 unimodal slurry density for particle 2 (kg/m3)
sl,mix mixture slurry density (kg/m3)
Some of the parameters that affect Njs are included in this
correlation but the accuracy of the exponents has been ques-
tioned by many authors. Kasat and Pandit (2005) compiled the
different exponents on the common parameters suggested
by various authors. Their comparison showed that the Zwi-
etering correlation is still the one that predicts the data most
closely. The Zwietering correlation, however, does not provide
an answer for mixed slurry Njs.
The literature on mixed slurry suspension is only beginning
to be developed, and initial studies focused on dilute slurries.
Baldi et al. (1978) studied a mixture of glass beads with two
particle sizes and found that Njs can be predicted using an
average particle size, at low solids loadings. Montante and
Magelli (2007) did a computational study on the distribution
of solids for dilute slurries with two solid phases which have
different densities but same particle sizes. They showed that
the two solids phases are not affected by each other. Recently
Ayranci and Kresta (2011) reported results for a wide vari-
ety of binary mixtures at high solids loadings (up to 56 wt%).
Their study showed that the presence of a second solid phase
may significantly affect the mixture Njs. This effect is ampli-
fied for mixtures above 20 wt% solids, because at that point
the particle–particle interactions start to dominate. The par-
ticle sizes and the densities of the two solid phases play an
important role in the mixture Njs.
The current design heuristic for mixed slurries is to assume
that the mixture is composed of only the particle fraction that
is hardest to suspend. The Njs for that fraction is predicted
using the Zwietering correlation, and treated as the mixture
Njs. This design heuristic has many flaws, some of which were
shown by Ayranci and Kresta (2011). Of the five mixtures they
tested, only one mixture followed the design heuristic up to
high solids loadings, and a second mixture followed it up to
13 wt%, but then failed. The other mixtures did not follow the
design heuristic. The ratio of the particle size, the particle den-
sity, and the solids loadings of the two solid phases all had an
effect on mixture Njs. A more robust and physically realistic
model for predicting mixture Njs is needed.
In this study we propose and test two models that are based
on the total power and the total momentum required to sus-
pend solids in a stirred tank.
2. Model development
2.1. Current design heuristic
The current design heuristic is based on the maximum uni-
modal Njs in a mixture:
Njs,mix = max(Njs,1, Njs,2) (2)
For example, if a mixture Njs needed to be determined for
a mixture of 1.5 wt% SG with 1.5 wt% B, the Njs of the uni-
modal slurries of the two particles should be calculated and
the maximum value should be used as the mixture Njs. The
unimodal slurry Njs is predicted from the Zwietering correla-
tion (Eq. (1)). In the example the unimodal slurry Njs is 318 rpm
for 1.5 wt% SG and 1142 rpm for 1.5 wt% B. The mixture Njs is
the maximum of the two values, which is 1142 rpm.
2.2. Power model
The power model is proposed based on a hypothesis that the
power required to suspend a mixture is the sum of the power
required to suspend each of the solid phases in the mixture.
Pjs,mix = Pjs,1 + Pjs,2 (3)
where Pjs,mix is the power required to suspend the mixture,
and Pjs,1 and Pjs,2 are the power required to suspend the first
and the second solid phases, respectively. The power required
to suspend each solid phase is calculated at the just suspended
condition based on the unimodal slurry density:
Pjs = slNjs
3
D5
Np (4)
sl =
1
(xs/ s) + (xL/ L)
(5)
3. chemical engineering research and design 9 1 ( 2 0 1 3 ) 227–233 229
In combining Eqs. (3) and (4) to find Njs,mix, the impeller
diameter term, D, cancels out. Current practice is to use the
slurry density to correct for the presence of the solids and
assume that the power number is constant, which also allows
us to eliminate Np. This assumption has some uncertainty
due to the presence of a low concentration layer at the top
of the vessel which will increase the solids concentration in
the bottom of the vessel, and the possibility of a lower solids
concentration in the vicinity of the impeller due to centrifugal
forces. Micheletti et al. (2003) and Jafari et al. (2012) inves-
tigated whether there is an effect of solids concentration,
particle size, and particle type on the power number. Jafari
et al. (2012) found that in general the power number decreases
at high solids loadings by of the order of 20%, while Micheletti
et al. (2003) found that it either stays the same, or increases by
about 20%. Our measurements of Np at varying Re for single
phase and 25 wt% small glass beads showed that the power
number for the single phase and the slurry are almost the
same. The assumption that the power number remains the
same for each slurry (Pjs,mix, Pjs,1, and Pjs,2) was applied, with
the understanding that this may introduce some error into the
model.
When D and Np are cancelled out the mixture Njs becomes
a function of the densities of the mixed and the unimodal
slurries and the Njs’s of the unimodal slurries.
Njs,mix =
sl,1N3
js,1
+ sl,2N3
js,2
sl,mix
1/3
(6)
In Eq. (6), Njs,1 and Njs,2 can be calculated using Eq. (1), or
replaced with the experimental values.
It should be noted that the power model does not include
any terms to take the particle–particle interactions into
account; therefore, it is very likely that the mixture Njs will not
be accurately predicted when particle–particle interactions are
strong.
2.3. Momentum model
A second hypothesis is that the momentum required to sus-
pend a mixture is equivalent to the sum of the momentum
required to suspend each of the solid phases in the mixture.
Mjs,mix = Mjs,1 + Mjs,2 (7)
where Mjs,mix is the momentum required to suspend the
mixture, and Mjs,1 and Mjs,2 are the momentum required to
suspend each individual unimodal slurry. The momentum,
M, can be calculated through the dimensionless momentum
number (Mo) (Machado et al., 2011):
Mo =
D/2
0 LV2
z 2 rdr
LN2D4
=
M
LN2D4
(8)
The momentum required to suspend each solid phase is
calculated at just suspended conditions:
Mjs = Mo slN2
jsD4
(9)
In combining Eqs. (7) and (9) to find Njs,mix, the momen-
tum number and impeller diameter are constant, so the terms
cancel out. Like the power model, the mixture Njs is thus a
Fig. 1 – The experimental setup with a PBT impeller. Njs is
determined by visual observation below the tank bottom.
function of the mixed and unimodal slurry densities and the
Njs of the unimodal slurries, this time to the power of two:
Njs,mix =
sl,1N2
js,1
+ sl,2N2
js,2
sl,mix
1/2
(10)
3. Experimental procedure
Fig. 1 shows the experimental setup. A fully baffled (Wb = T/10)
cylindrical plexiglass tank with an inner diameter of 24 cm
was used for the measurements. The cylindrical tank was
placed inside a square tank to prevent optical distortion. In
order to maintain stability at high impeller speeds, both tanks
were bolted to a steel frame. The just suspended speed was
observed visually from the bottom of the tank.
A Lightnin A310 impeller and a four bladed 45◦ down
pumping PBT both with a diameter of D = T/3 were used. The
impellers were attached to a shaft with a diameter of 1.27 mm
(T/20). The off-bottom clearance was defined as the distance
between the bottom of the impeller hub and the bottom of
the tank. The blades were flush with the bottom of the hub
for both impellers. The dimensionless off-bottom clearance,
C/T, was varied from 0.15 to 0.33. Water was used as the liquid
phase for all the experiments.
Seven different particles with various physical properties
were tested: nickel (Ni), small glass (SG), urea formalde-
hyde (UF), bronze (B), sand (S), large glass (LG), and ion
4. 230 chemical engineering research and design 9 1 ( 2 0 1 3 ) 227–233
Table 1 – Particle properties.
Type Size (m) Density
(kg/m3)
Vt (m/s)
Nickel (Ni) 61–104 8900 0.139
Small glass beads (SG) 74–125 2500 0.066
Urea formaldehyde (UF) 150–250 1323 0.044
Bronze (B) 150–297 8855 0.225
Sand (S) 350–500 2656 0.144
Large glass beads (LG) 595–841 2500 0.177
Ion exchange resin (R) 677 1370 0.086
exchange resin (R). The particle properties are given in Table 1.
The particles were chosen to give a wide range of densi-
ties (1.3 < SG < 8.9) and particle sizes (61 m < dp < 841 m). The
mixtures tested are given in Table 2 along with the ranges of
solids loadings. For each data set the mass of the more dense
particles was kept constant while the mass of the less dense
particles increased. A set of experiments where the mass of
the dense particle is higher than the mass of the less dense
particle was also conducted to validate the models tested for
all cases. This set of experiments was for the mixture of R with
LG at C/T = 0.25.
At the beginning of every experiment, the tank was filled
with water and particles were weighed and poured into it.
The liquid height was then adjusted to give H = T. The shaft
was attached to the motor, and the off-bottom clearance
was adjusted. Once the desired clearance was achieved, the
impeller was started. The impeller speed was increased in
steps and the system was left for 2 min to reach steady state.
After steady state was reached, the particle behavior at the
bottom of the tank was observed for 15–45 s to determine
whether Njs was reached. The particles behind the baffles
were consistently the last particles to be suspended. The just
suspended speed was reached when no particles remained
stationary at the bottom of the tank for more than 1 or 2 s
(Zwietering, 1958). After that the motor was switched off and
the off-bottom clearance was adjusted for the new measure-
ment. More details about the experimental setup and the
procedure are given in Ayranci and Kresta (2011).
4. Results and discussion
First the current design heuristic results are presented to pro-
vide a baseline for comparison. Next the performance of the
power and momentum models is tested for all six mixtures of
solids, two impellers, and varying off-bottom clearances, and
the performance of the two models is compared. The power
and the momentum models require the use of unimodal slurry
Njs’s. Initially the unimodal slurry Njs’s are calculated from the
Zwietering correlation, and then the experimental values are
used. The performance of the power model is compared for
the two cases.
0
200
400
600
800
1000
1200
1400
1600
1800
2000a
b
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,max(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.33
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.33
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.33
LG+B C/T=0.15
LG+B C/T=0.25
LG+B C/T=0.33
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.33
Standard deviation: 10%
PBT - Current design heuristic
=
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,max(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.325
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.325
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.325
LG+B C/T=0.15
LG+B C/T=0.25
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.325
UF+S C/T=0.25
Standard deviation: 12.6%
A310 - Current design heuristic
=
Fig. 2 – The parity plot between the current design heuristic
and the experimental data. The current design heuristic
uses the maximum Njs in the mixture, calculated using the
Zwietering correlation. (a) PBT and (b) A310.
4.1. Test of current design heuristic
Fig. 2a and b compares the prediction of Njs,max using the
Zwietering correlation to the experimental mixture Njs. In the
Zwietering correlation, S is a function of impeller and tank
geometry and particle properties. Fig. 2a and b represents the
best possible predictions using the current form of the Zwi-
etering correlation since the S values were obtained for the
specific particles and the geometries used here (Ayranci and
Kresta, 2011). For each mixture the wt% of the more diffi-
cult to suspend solids remains constant as the wt% of the
easier to suspend solids increases. The prediction of mix-
ture Njs is constant because the Njs of the easier to suspend
solids does not change enough with increasing concentration
to overtake Njs,max. In Fig. 2a the mixture Njs for R with LG at
Table 2 – Particle mixtures and solids loadings.
Less dense particles (wt%) Denser particles (wt%) Total solids loading Density ratio Particle size ratio
wt% vol%
SG (1.5–26) B (1.5–1.3) 3–27.3 0.8–12 ∼1:3.5 ∼1:2
LG (1.5–26) B (1.5–1.3) 3–27.3 0.8–12 ∼1:3.5 ∼3:1
R (1.5–26) B (1.5) 3–27.5 1.3–21.8 ∼1:6.5 ∼3:1
R (1.5–25) LG (1.5–1.4) 3–26.4 1.7–20 ∼1:1.8 ∼1:1
SG (1.5–26) Ni (1.5–1.3) 3–27.3 0.77–14.9 ∼1:3.6 ∼1:1
UF (1–10) S (1–5) 2–15 1.1–9.1 ∼1:2 ∼1:2
5. chemical engineering research and design 9 1 ( 2 0 1 3 ) 227–233 231
Table 3 – The list of S values used in the calculations for
unimodal slurry Njs.
Impeller D C Sa
A310 T/3
0.15 6.84
0.25 7.54
0.325 7.97
PBT T/3
0.15 5.4
0.25 6.18
0.33 7.15
a
The S values were taken from Ayranci and Kresta (2011).
C/T = 0.15 remains constant even though the concentration of
R changes at each experimental point and the experimental
Njs does in fact increase. The predicted mixture Njs is similar
to the experimental data at the lowest solids concentration,
but is consistently lower than the experimental Njs when the
concentration increases. The current design heuristic fails
to capture the physics behind mixed solids suspension. The
effect of the presence of both solid phases must be included
in the model. The standard deviation between the measured
and the predicted values for all of the mixtures at varying off-
bottom clearances is 10% for the PBT and 12.6% for the A310.
The fact that the trend does not follow the experimental data
is of greater concern.
0
200
400
600
800
1000
1200
1400
1600
1800
2000a
b
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.33
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.33
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.33
LG+B C/T=0.15
LG+B C/T=0.25
LG+B C/T=0.33
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.33
Standard deviation: 8.3%
PBT - Power Model
(using Zwietering for unimodal Njs)
= +
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.325
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.325
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.325
LG+B C/T=0.15
LG+B C/T=0.25
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.325
UF+S C/T=0.25
Standard deviation: 9.7%
A310 - Power Model
(using Zwietering for unimodal Njs)
Fig. 3 – The prediction of mixture Njs without any
experimental data using the power model and the
Zwietering correlation with the (a) PBT and (b) A310.
4.2. Power model and momentum model using
Zwietering unimodal Njs
To find the mixture Njs through the power or momentum mod-
els, the slurry densities are first calculated from Eq. (5). The
unimodal slurry Njs’s are calculated from the Zwietering cor-
relation (Eq. (1)). The S values used in the calculations are given
in Table 3. The mixture Njs is then calculated from Eq. (6) for
the power model, and from Eq. (10) for the momentum model.
Fig. 3a and b shows the power model parity plots for the PBT
and the A310. While some data points are on the parity line, a
similar trend to the current design heuristic (Fig. 2a and b) is
seen: the data flattens out as the solids loading is increased.
A comparison of the power model (Fig. 3a and b) with the cur-
rent design heuristic (Fig. 2a and b) shows that there is no
significant improvement from the current design heuristic to
the power model prediction. The standard deviation is 8.3%
for the PBT and 9.7% for the A310. The low standard devia-
tion does not give information about the trend, and the trend
shows that the physics is not captured.
Fig. 4a and b shows the momentum model parity plots
for the PBT and the A310 impellers. The trend in these fig-
ures is very similar to the power model, and also the current
design heuristic. This may indicate that there is no signifi-
cant difference between the two models and the heuristic. It
should, however, be noted that these predictions use the Zwi-
etering correlation for unimodal slurry Njs’s. The Zwietering
0
200
400
600
800
1000
1200
1400
1600
1800
200a
b
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.33
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.33
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.33
LG+B C/T=0.15
LG+B C/T=0.25
LG+B C/T=0.33
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.33
Standard deviation: 8.8%
PBT - Momentum model
(using Zwietering for unimoldal Njs)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.325
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.325
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.325
LG+B C/T=0.15
LG+B C/T=0.25
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.325
UF+S C/T=0.25
Standard deviation: 8.8%
A310 - Momentum model
(using Zwietering for unimodal Njs)
Fig. 4 – The prediction of mixture Njs without any
experimental data using the momentum model and the
Zwietering correlation with the (a) PBT and (b) A310.
6. 232 chemical engineering research and design 9 1 ( 2 0 1 3 ) 227–233
correlation is known to have limited accuracy above 10 wt%
solids, so above this concentration the predictions are not very
reliable. In order to test the true strength of the power and
momentum models, the experimental unimodal slurry Njs’s
are used in a second test.
4.3. Power model and momentum model using
experimental data
Fig. 5a and b shows the mixture Njs predicted from power
model where the unimodal slurry Njs is obtained from experi-
ments. These plots show a completely different trend than the
predictions using Zwietering unimodal slurry Njs’s. The pre-
dicted Njs’s follow the parity line closely. Most of the data is
within ±20% of the parity line. This indicates that the physics
of the solids suspension is captured up to 20 wt% solids for
all mixtures. Beyond 20 wt% solids, particle–particle interac-
tions can become quite strong. For the LG + B, R + B, and R + LG
mixtures Njs increases with increasing solids and the model
captures Njs up to the highest loading tested, 27 wt% solids.
The data for UF + S goes up to only 10 wt% solids. For the SG + B
mixture there is an unexpected drop in Njs above 20 wt% SG
(Ayranci and Kresta, 2011) and for SG + Ni Njs is constant. The
power model cannot predict these effects because there are no
terms for particle–particle interactions. Based on this informa-
tion the data points above 20 wt% SG for both SG + B and SG + Ni
mixtures were eliminated from the data set shown in Fig. 5a
and b and from subsequent analysis. The resulting standard
0
200
400
600
800
1000
1200
1400
1600
1800
2000a
b
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.33
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.33
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.33
LG+B C/T=0.15
LG+B C/T=0.25
LG+B C/T=0.33
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.33
Standard deviation: 9.6%
PBT - Power model
= +
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.325
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.325
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.325
LG+B C/T=0.15
LG+B C/T=0.25
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.325
UF+S C/T=0.25
Standard deviation: 9%
A310 - Power model
= +
Fig. 5 – The parity plot for the power model at varying
clearances for all mixtures with the (a) PBT and (b) A310.
0
200
400
600
800
1000
1200
1400
1600
1800
2000a
b
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.33
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.33
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.33
LG+B C/T=0.15
LG+B C/T=0.25
LG+B C/T=0.33
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.33
Standard deviation: 17.3%
PBT - Momentum model
= +
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs,predicted(rpm)
Njs, measured (rpm)
SG+B C/T=0.15
SG+B C/T=0.25
SG+B C/T=0.325
SG+Ni C/T=0.15
SG+Ni C/T=0.25
SG+Ni C/T=0.325
R+B C/T=0.15
R+B C/T=0.25
R+B C/T=0.325
LG+B C/T=0.15
LG+B C/T=0.25
R+LG C/T=0.15
R+LG C/T=0.25
R+LG C/T=0.325
UF+S C/T=0.25
Standard deviation: 15.7%
A310 - Momentum model
= +
Fig. 6 – The parity plot for the momentum model at varying
clearances for all mixtures with the (a) PBT and (b) A310.
error is 9.6% for the PBT and 9% for the A310. The mixture Njs
can be predicted accurately with the power model up to 27 wt%
solids for a range of off-bottom clearances, with two separate
impellers, in the absence of particle–particle interactions.
Fig. 6a and b shows the momentum model results for exper-
imental Njs. The momentum model captures the physics, but
over-predicts the mixture Njs, leaving more data points outside
the ±20% range. The standard error of the momentum model
prediction is 17.3% for the PBT and 15.7% with the A310. In
Fig. 7 comparison of the power and momentum models with
both the PBT and the A310 shows that the momentum model
consistently over-predicts mixture Njs. The standard devia-
tion between the two models is 6.4% when the data for both
impellers is combined. We conclude that the power model
provides a better prediction of mixture Njs.
The performance of the power model has been analyzed in
terms of parity plots up to this point. This allows the compari-
son of model accuracy for different data sets, but prevents the
visibility of some details, such as the effect of solids loading. A
closer look at the raw data is required to observe these details.
Fig. 8 compares the power model predictions to experimental
data and the current design heuristic for two representative
cases at C/T = 0.25. As the solids loadings increase the mixture
Njs increases. At low solids loadings the power model predic-
tions fall on top of the experimental data for both mixtures.
As the solids loadings are increased the mixture Njs increases
both with the power model predictions and the experimen-
tal data, and the power model starts to give moderately
7. chemical engineering research and design 9 1 ( 2 0 1 3 ) 227–233 233
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Njs-MomentumModel(rpm)
Njs - Power Model (rpm)
PBT
A310
Standard deviation: 6.4%
PBT and A310
Momentum vs Power model
Fig. 7 – Comparison of the momentum model and the
power model at varying clearances for all particles with the
PBT and A310.
400
600
800
1000
1200
1400
1600
0 5 10 15 20 25 30
Njs,mix(rpm)
Xw
LG+B Experimental
LG+B Power Model
LG+B Heuristic
R+LG Experimental
R+LG Power Model
R+LG Heuristic
PBT - Power Model and Heuristic
Fig. 8 – Comparison of mixture Njs obtained from
experiments, power model, and current design heuristic for
LG + B and R + LG mixtures with PBT at C/T = 0.25.
over-predicted Njs,mix. This figure shows that the power model
tends to over-predict mixture Njs, but provides a significant
improvement over the current design heuristic, shown as the
dashed lines. If the heuristic was used for design, a signifi-
cant number of particles would not be suspended. The power
model, in all cases, provides conservative design but never
beyond 20% error.
Reviewing the data, the current design heuristic is rejected
because the trends are not captured. The momentum model
clearly over-predicts Njs,mix, based on Fig. 7. The power model
is recommended with use of experimental unimodal data
where possible.
5. Conclusions
The objective of this study was to propose and test two mod-
els to accurately predict mixed slurry Njs. Analysis of the
experimental data for several mixtures at varying off-bottom
clearances and solids loadings for two impeller geometries led
to the following conclusions:
• The current design heuristic is inadequate for the prediction
of mixture Njs since it ignores the addition of a second solid
phase, and cannot predict the basic trend.
• The momentum model consistently over-predicts Njs and is
rejected.
• When the Zwietering correlation is used for unimodal slurry
Njs the power and momentum models lose strength and
show similar behavior to the current design heuristic. The
authors recommend use of experimental unimodal slurry
Njs if possible.
• The power model, as given below, predicts mixture Njs accu-
rately for both the PBT and the A310 impellers up to 27 wt%
solids over a range of off-bottom clearances when unimodal
slurry Njs’s are obtained from experiments.
Njs,mix =
sl,1N3
js,1
+ sl,2N3
js,2
sl,mix
1/3
Acknowledgments
The authors would like to thank Lightnin and NSERC for fund-
ing, Sherritt Metals Inc. for providing nickel particles, and
Maria Garcia from Rowan University for sharing data for sand
and urea formaldehyde.
References
Armenante, P.M., Nagamine, E.U., 1998. Effect of low off-bottom
impeller clearance on the minimum agitation speed for
complete suspension of solids in stirred tanks. Chem. Eng.
Sci. 53, 1757–1775.
Ayranci, I., Kresta, S.M., 2011. Design rules for suspending
concentrated mixtures of solids in stirred tanks. Chem. Eng.
Res. Des. 89 (10), 1961–1971.
Baldi, G., Conti, R., Alaria, E., 1978. Complete suspension of
particles in mechanically agitated vessels. Chem. Eng. Sci. 33,
21–25.
Ibrahim, S., Nienow, A.W., 1996. Particle suspension in the
turbulent regime: the effect of impeller type and
impeller/vessel configuration. Trans. IChemE 74 (Part A),
679–688.
Jafari, R., Tanguy, P.A., Chaouki, J., 2012. Experimental
investigation on solid dispersion, power consumption and
scale-up in moderate to dense solid–liquid suspensions.
Chem. Eng. Res. Des. 90, 201–212.
Kasat, G.R., Pandit, A.B., 2005. Review on mixing characteristics in
solid–liquid and solid–liquid–gas reactor vessels. Can. J.
Chem. Eng. 83, 618–643.
Machado, M.B., Nunhez, J.R., Nobes, D., Kresta, S.M., 2011.
Impeller characterization and selection: balancing efficient
hydrodynamics with process mixing requirements. AIChE J.
58 (8), 2573–2588.
Micheletti, M., Nikiforaki, L., Lee, K.C., Yianneskis, M., 2003.
Particle concentration and mixing characteristics of
moderate-to-dense solid–liquid suspensions. Ind. Eng. Chem.
Res. 42, 6236–6249.
Montante, G., Magelli, F., 2007. Mixed solid distribution in stirred
vessels: experiments and computational fluid dynamics
simulations. Ind. Eng. Chem. Res. 46, 2885–2891.
Myers, K.J., Fasano, J.B., 1992. The influence of baffle off-bottom
clearance on the solids suspension of pitched-blade and
high-efficiency impellers. Can. J. Chem. Eng. 70, 596–599.
Nienow, A.W., 1968. Suspension of solid particles in turbine
agitated baffled vessels. Chem. Eng. Sci. 23, 1453–1459.
Zwietering, Th.N., 1958. Suspending of solid particles in liquid by
agitators. Chem. Eng. Sci. 8, 244–253.