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Short communication Effect of particle and fluid properties on the pickup velocity of fine particles Devang Dasani, Charay Cyrus, Katherine Scanlon, Rui Du, Kyle Rupp, Kimberly H. Henthorn ⁎ Missouri University of Science and Technology, Rolla, MO, United States abstract article info Article history: Received 6 April 2009 Received in revised form 21 July 2009 Accepted 7 August 2009 Available online 19 August 2009 Keywords: Pickup velocity Entrainment Electrostatic forces Pneumatic conveying Powder technology Systems involving fluid–particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids. In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems. © 2009 Elsevier B.V. All rights reserved. 1. Introduction Fluid–particle flows are readily found in a wide range of large-scale industrial applications, but they are also critical in the function of small-scale laboratory and research applications. However, it is often difficult to properly design a particulate system because of the limited availability of applicable equations. A majority of particulate systems operate inefficiently due to the lack of information needed for accurate design, scale-up, and optimization. This is especially true in systems that involve the flow of highly cohesive or non-spherical particles. One critical parameter needed to properly design conveying processes is the minimum fluid velocity required for particle entrainment, also known as pickup velocity. In two-phase conveying systems, fluid velocities below the particle pickup velocity can result in clogged pipelines or channels, and velocities much larger than what is required can lead to particle attrition, excessive pipeline abrasion, and unnecessary energy consumption. Therefore, knowledge of a material's pickup velocity is of great interest to those designing particle conveying processes. However, pickup velocity is a complex function of many variables, including particle properties, such as size, shape, density, and electrostatic behavior, and fluid properties, such as density and viscosity. Previous work has examined the effect of particle size, shape, and electrostatic behavior on the pickup velocity of particles less than 100 μm in gas-phase pneumatic conveying [1,2]. One major conclu- sion drawn from this work was that a minimum pickup velocity exists at a particle diameter located in the transition zone between inertia- dominated entrainment and entrainment dominated by particle– particle interactions. In other words, at large particle diameters (>50 μm), higher fluid velocities are required due to increased particle mass. At small particle diameters (<20 μm), particle–particle interactions, such as electrostatic and van der Waals forces, become much more significant so that pickup velocity increases with decreasing particle size. Hayden et al. also concluded that electrostatic forces dominate at intermediate particle size ranges (20–50 μm) and that irregular particle shapes result in higher pickup velocities and greater deviation in repeated experimental trials. The previous conclusions are applicable for gas–solid applications; however, many processes, including mixing and slurry flows, involve solids transport in a liquid medium. For these types of systems, the dominant forces acting on the particles are different than those in a gas–solids environment. Particle buoyancy forces become significant due to the increased liquid density relative to that of a gas. In addition, some particle–particle interactions, such as liquid bridging and electrostatic attraction, can be completely dampened in a liquid medium, while other factors, such as zeta potential, must be considered. To better understand the differences between particle entrainment in gas and liquid media, and to ultimately develop a universal expression for pickup velocity in all fluid types, a comparison Powder Technology 196 (2009) 237–240 ⁎ Corresponding author. E-mail address: [email protected] (K.H. Henthorn). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.08.007 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec

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It is a handout of mathematics compulsory discipline course operations research in bits pilani institute. This course is a part of M.Sc maths course in the college.

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Page 1: MATH_F242_1466

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PilaniPilani CampusInstruction Division

_

Please Do Not Print Unless Necessary

INSTRUCTION DIVISION

SECOND SEMESTER 2014-2015

Course Handout Part II

Date:13.01.2015

In addition to part-I (General Handout for all courses appended to the time table) this portion gives furtherspecific details regarding the course.

Course No. : MATH F242Course Title : OPERATIONS RESERACHInstructor-in-charge : CHANDRA SHEKHAR

1. Scopes and Objective of the Course:

This course begins with applications overview of Operations Research, and introduces dynamicprogramming and network models. After a review of probability distributions, inventory models andqueuing systems will be covered. Decision- making under certainty, risk, and uncertainty; along with anintroduction to game theory will be dealt. Finally simulation techniques, introduction for estimatingsolutions to problems, that are not amenable to conventional solution techniques, will be made. Studentswill also be taught the basic concepts on system reliability.

2. Text Book:

1. Hamdy A Taha, “Operations Research: An Introduction”, Pearson Education, Ninth Edition.2. Venkateswaran S and B. Singh, “Operations Research” EDD Notes.Vol.3, 1997..

3. Reference:

1. Hillier and Lieberman, “Introduction to Operations Research”, T M H, Eighth Edition, 2006.2. W.L. Winston, “Operations Research, Application and Algorithms”, 4th edition, Thomson3. Ravindran, Phillips and Solberg, “Operations Research: Principles and Practice”, Wiley

India 2/e, 2007.4. A. R. Ravindran, “Operations Research: Methodology”, CRC Press (Taylor & Francis

Group), 1e, 2011.5. D. Gross and C. M. Harris, “Fundamentals of Queuing Theory”, Wiley India, 3/e, 1998.

Page 2: MATH_F242_1466

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PilaniPilani CampusInstruction Division

_

Please Do Not Print Unless Necessary

4. Lecture Plan

LearningObjectives

Topics to be Covered LectureNos.

References

Introduction toOperationsResearch

Introduction, Historical Development,Impact of O.R., Phases of O.R.,Overview of O.R., Modeling Approach

1 Chapter 1 (T1)

Review of BasicProbability

Random variables, Binomial, Poisson,Exponential and Normal Distribution

2-4 Chapter 14 (T1)

QueueingSystems

Definition, Birth and Death process,Role of Exponential Distribution,Generalized Poisson QueueingModels,

Specialized Poisson Queues.

5-16 Chapter 7 (T2)

InventoryModels

Deterministic and ProbabilisticInventory Models

17- 22 Chapter 8 (T2)

SimulationModeling

Introduction, Generation of randomvariates from different distributions,Simulation of Single-server queueingmodel and inventory model.

23-27 Chapter 9 (T2)

Reliability Basic concepts, Hazard rate function,Reliability of the systems, failure timedistributions.

28-30 Chapter 6 (T2)

Decision analysisand Game theory

Decision analysis under uncertaintyand Game Theory

31- 34 Chapter 15 (T1)

Page 3: MATH_F242_1466

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PilaniPilani CampusInstruction Division

_

Please Do Not Print Unless Necessary

DynamicProgramming

Deterministic Dynamic Programming, 35-38 Chapter 12 (T1)

Network Models Definition, Minimal Spanning treeAlgorithm, Shortest route Problem,CPM and PERT

39-42 Chapter 6 (T1)

5. Evaluation Scheme:

Component Duration Max. Marks Date & Time Remarks

Mid Semester 90 minutes 60 12/3 2:00 -3:30 PM CB

Tutorial/Quiz/Assignment 40 CB/OB

Comprehensive 3 hours 100 11/5 FN Partially CB

6. Make-Up Policy: Only genuine cases will be entertained. For surprise quizzes, there will be no make-up.

7. Chamber Consultation Hours: To be announced in the class.

8. Notice: Notices concerning this course will be displayed on Nalanda only.

INSTRUCTOR-IN-CHARGE


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