We ve all been there, sitting in a conference room,


 Loreen Roberts
 2 years ago
 Views:
Transcription
1 As appeared in April 2013 PBE Copyright CSC Publishing Particle technology: CFD modeling made easy Ray Cocco Particulate Solid Research Inc. Using computer modeling as a tool for simulating a bulk solids processing operation can help you select new equipment or troubleshoot a problem in existing equipment. In this article, a particle technology expert explains how various computational fluid dynamics models can be used to represent what s happening in your process. We ve all been there, sitting in a conference room, when in comes the bulk solids process design geek to show computational fluid dynamics (CFD) modeling results in an array of pretty colors. As you hear lingo like twoway coupling, collisional stress tensors, and ensemble averaging, you begin to wonder whether this presenter is for real! The problem is this: While the presentation may offer insights critical to designing your unit operation, the presenter has failed to clearly describe what the modeling results show. As a result, you quickly discount the results, as do many project leaders and engineers in the same situation. Understanding the mathematical models used in particle technology isn t really that hard it just sounds hard. Most of the models are based on simple concepts, and these concepts are all you really need to understand. Just as you don t need to know how to write software to use your computer effectively, you don t need to understand the numerical calculations behind particle technology models to simulate your process and use the results to help choose new equipment or troubleshoot the operation of existing equipment. About the modeler With some training, you or another process engineer in your plant can use commercial CFD software to run particle technology calculations and generate models. Or you can contract a modeler from a particle technology consulting or engineering firm to do this. In the latter case, expect to work closely with the modeler throughout the project, supplying information about your particles and other application details to ensure that the model accurately represents your bulk solids problem. Based on experience with other bulk solids applications, the modeler will choose the most effective CFD software for modeling your problem and use the resulting model as a tool to simulate the flow behavior in your unit operation. Calculating material, energy, and momentum balances All CFD models work the same way: They reduce the complexity of the problem that is, the way particles flow in a particular unit operation so you can determine one or more of the material, energy, and momentum balances for the problem. So, what are these balances? The material balancesimply records the mass inminus the mass out plus the mass accumulated (if any) minus the mass consumed. There s a material balance for each phase solids (particles), gas, and liquid and each species (such as atoms or molecules). A good example of a material balance is a campfire: The mass in is the oxygen, the mass out is the carbon dioxide, and the mass consumed is the carbon from the wood. When no more wood is added to the fire, the carbon is consumed and the fire goes out. The energy balance is the energy coming in minus the energy coming out of the bulk solids process. The first law of thermodynamics is that energy can be neither created nor destroyed. So, going back to the campfire example, no energy is coming into the fire but a lot of energy is going out. Where does this outgoing energy come from? The fire s consumption of carbon from the wood generates carbon dioxide in an exothermic reaction that is, it releases energy in the form of heat from the mass. The momentum balance is less commonly understood. Momentum is simply mass times velocity, so in a bulk solids process, momentum is the particles mass times their velocity. While most of us understand mass and velocity, we may not understand the product of mass and velocity: This is momentum simply, moving mass.
2 There s a momentum balance for each phase, and it accounts for pressure difference, buoyancy, drag, and stress (in terms of fluid viscosity or particle collisions). More about the momentum balance. To get a better understanding of the momentum balance, consider the example of a cannonball shot from a canon. The pressure buildup in the cannon pushes the cannonball out at high velocity. Like any object, the cannonball wants to travel from high pressure to low pressure, which is why we need to correct for pressure difference when calculating the momentum balance. Particle buoyancy is due to particle density differences in the presence of gravity. Because the cannonball is more dense than the air it s traveling through, the ball wants to fall to Earth. But if the ball were less dense than the air, it would want to travel into space. The drag forces are two equal but opposite forces: the friction the air imposes on the cannonball and the friction the ball imposes on the air. This twoway coupling of the drag forces can best be demonstrated by driving with your hand out the car window: You can feel the airflow s force on your hand, but your hand is also disturbing the airflow. Particle collisions are just that: the particles colliding with each other and the walls. As an example, if you re walking at a constant rate and bump into someone, you ll bounce in one direction and the other person will bounce in another. Your momentum transfers to the other person, and vice versa. If the person weighs more than you or is moving faster, the distance you bounce will be greater. Using the balance equations in CFD modeling. For many bulk solids operations, including fluidized beds, cyclones, pneumatic conveying lines, and hoppers containing small particles, we need to model multiphase flow: the flow of particles (the particle phase or solid phase), and the flow of fluid (typically a gas) that surrounds them (the gas phase or fluid phase). Two common ways of modeling this type of multiphase flow are the EularianEularian and EularianLagrangian methods. For these CFD models, the material and momentum balance equations are treated separately for the particle and gas phases because the phases are connected only by drag forces (as in our handoutthecarwindow analogy, the drag forces are equal but opposite between the two phases). In the energy balance equation, both phases are typically treated as one mixture. EularianEularian CFD models This method s name EularianEularian indicates that it treats both the particle and gas phases using the Eularian framework developed by 18thcentury mathematician Leonhard Euler. The Eularian framework, as shown in Figure 1a, models gas flow at specific, discrete locations through which the gas flows as time passes. The framework divides a large domain into an array of smaller domains (called cells), which are represented as threedimensional cubes. If the cells are small enough, the overall gas flow can be described by vectors in X and Y coordinates. Although the overall (or macroscopic) flow may not be represented in an X and Y vector, the sum of the smaller cells X and Y vectors can reproduce the overall gas flow. Thus, for each cell in Figure 1a, the material, momentum, and energy balance equations are applied to each cell face (that is, each face of the cube) to keep track of what comes in and out of that cell. The equations we ll use in this method are NavierStokes equations. The equations with their mathematical terms are provided here just for completeness, but what s really important is what the equations stand for (explained in italics below each equation): Material balance: ( f ) ( f u) R rxn Mass accumulation + mass in and out reaction where t is time, is the particles void fraction, f is gas density, u is gas velocity, and R rxn is reaction rate. Momentum balance: ( f u) f u u P f (u v) f g Momentum change + momentum in and out = viscous losses + drag + gravity  pressure drop where P is pressure, f is viscosity effect (often described using Newton s law of gravity), is drag, and g is gravity acceleration constant. Energy balance: ( f C p ) ( f C p u) k 2 T R rxn H rxn Energy change + heat convection in and out = thermal conduction + reaction heat where C p is the particles heat capacity, k is thermal conductivity, T is temperature, and H rxn is reaction heat. For the material balance, mass accumulation is the result of the mass (particles) in and out of each cell and the reaction (such as attrition) in the cell. For the momentum balance, the momentum change results from the particle momentum in and out of each cell with respect to the viscosity losses, drag, and gravity minus the pressure drop. For the energy balance, the energy change in each cell results from the heat convection in and out, thermal conduction of the gas, and the reaction heat. The magnitude of the values we calculate for the material, momentum, and energy balances determines the direction of the particle flow, the particle momentum, and the temperature gradient in the process we re modeling.
3 The cell size in the Eularian framework affects the model s accuracy, so the cells must be much smaller than the Figure 1 Modeling gas and gasparticle hydrodynamics using Eularian, EularianEularian, and EularianLagrangian frameworks a. Eularian framework for gas phase only Cell macroscopic flow we want to model. The problem is, the smaller these cells, the more equations we need to solve and the longer it takes our simulation to run. The power of Eularian framework modeling is most apparent in designing aircraft: Fifty years ago, wind tunnels were used to design planes. Today, the wind tunnels are virtually gone, and planes are designed with computers using Eularian framework CFD software. The EularianEularian framework, as shown in Figure 1b, models the particle phase using equations similar to those for the gas phase: Y coordinates Gas Material balance: ((1 ) p ) ((1 ) p v) R rxn Mass accumulation + mass in and out = reaction rate X coordinates b. EularianEularian framework for gas and particle phases Particles as fluid c. EularianLagrangian framework for gas and particle phases Momentum balance: ((1 ) p v) (1 ) p v v P s (u v) (1 ) p g Momentum change + momentum in and out = particle pressure + particle viscosity + drag + gravity where p is particle density, v is particle velocity, and s is the particles viscosity effect. With these equations, the particle phase is actually modeled as a thick fluid. However, the particle pressure and particle viscosity need closure that is, parameters (terms in the equations) that have no physical or measurable value so you need another set of equations to fill the gap. In reality, the particle pressure and particle viscosity are the particles direct impact (called the normal stress) or glancing impact (shear stress) on other particles. Because we can t really measure pressure or viscosity for particles as easily as we can for a gas, we need to calculate these values. Particle velocity a The most common of many theories on how to calculate the particle pressure and particle viscosity in bulk solids flow is the kinetic theory of granular fluids. This theory views particles similarly to atoms so we can determine the particle pressure and viscosity. In short, here s how it works: An atom s vibrational mode is related to temperature, and a particle s velocity fluctuation during flow is related to the granular temperature. So, rather than being a form of heat, the granular temperature is a form of work: It s proportional to a particle s velocity fluctuation squared. We can use the granular temperature to calculate the particle pressure and particle viscosity for our model. a Note: The arrow direction represents the particle direction; arrow length is proportional to the particle velocity. One drawback: In most CFD software, these material and momentum balance equations are based on one represen
4 tative particle size. But can we fully capture particle behavior during a process based on one particle size? If so, what should that size be? Most EularianEularian modeling uses only the Sauter mean particle size (d p50 ), simply because it s the most readily available. However, new methods are being developed to trick the EularianEularian framework to handle more particle sizes. As we ve discussed, the drag forces of the particle on the gas and of the gas on the particle are equal and opposite. This twoway coupling is how the two phases feel each other s momentum. You can use any of various equations to calculate these drag forces, but many are empirical, based on singleparticle flow or packedbed flow. Consider, however, whether the material flow in your unit operation typically fits either of these extremes: Chances are, it doesn t. For best results, work with your modeler to choose a drag equation that fits your application. In most granularfluid flow problems, this equation has the greatest impact on the model. EularianEularian modeling, also commonly called twofluid modeling, is the most common form of modeling for granularfluid flow because a computer can use it to simulate a largescale unit operation in a few weeks. However, to use this method, you re assuming that your particle phase behaves like a fluid. The small cells in your EularianEularian framework (Figure 1b) must also be small enough to accurately depict your process s important hydrodynamics. You can test whether the cells are small enough by running two simulations with different cell sizes. If the results are the same, you re good. If not, run a simulation with a smaller cell size and test it again. But remember: Each simulation takes weeks! EularianLagrangian CFD models What if we don t want to model our material flow based on assuming that our particles behave like a fluid? What if we want to model our entire particle size distribution, including the fines? Here s where we can consider a model based on the EularianLagrangian framework, developed by 19thcentury mathematician Joseph Luis Lagrange. In this framework, as shown in Figure 1c, the gas phase is modeled as in the previous frameworks (Figures 1a and b). However, the EularianLagrangian framework treats the particle phase much differently than the other frameworks. It looks at the particle phase by: 1) tracking particles and collisions independently, and 2) tracking a component of each particle s drag force on the gas that s equal to and opposite from the gas s drag force on the particle. The Newtonian equation used to calculate momentum balance for the EularianLagrangian framework is: F v P p (u v) g Particle momentum = pressure drag + gravity where F is the momentum transfer function. This equation applies to every particle in motion until the exact moment it collides with another particle, in which one particle s momentum translates into another particle s momentum. However, the problem with the EularianLagrangian framework is that each particle and each collision must be modeled. One way around this is to use a hybrid method that models only the particle trajectories, not the collisions. This requires modifying the momentum balance equation this way: F v P p (u v) g s (1 ) p Particle momentum = pressure drag + gravity collisional stresses (These collisional stresses can be calculated by an empirical equation or some form of kinetic theory of granular flow equation; work with your modeler to choose a suitable equation.) By using this hybrid equation, we no longer need to track collisions because we re simply calculating how collisions affect the particle momentum. By eliminating the need to track collisions, the hybrid equation allows us to use a much larger time step (interval for calculations in time) in the EularianLagrangian framework. Yet let s consider just how many equations we d need to use with the EularianLagrangian framework to model bulk solids flow behavior in a 25footdiameter, 10foottall fluidized bed containing 40 billion 100micron particles. We d need three equations to simulate the gas flow in each cell in the framework; for this fluidized bed, we d most likely need about 500,000 cells, which leads to 1.5 million equations just for the gas phase. This isn t a problem for today s desktop computers. However, we need 40 billion equations for each particle we re tracking. That s way too many calculations to get simulation results in a reasonable amount of time. Anyone even considering such an attempt will probably end up making an involuntary career move! The EularianLagrangian framework remains a useful tool, however, because it models the entire particle size distribution by assuming that particles of similar size and density in each cell can be modeled once. So if we group 10,000 particles of similar size and density in a cell (these groupings are called clouds or parcels), the number of equations we need is 1.5 million for the gas phase but only another 4 million for the particles (one equation per cloud). This gives us fewer than 2 million calculations total, so we can actually do them on a desktop computer. However, we have to carefully choose the number of cells and number of particles per cloud we use to avoid modeling errors. Using a trialanderror approach, in which we vary the number of cells and particles in a cloud each time, will help us converge on an accurate model.
5 The EularianLagrangian framework model is growing more popular because it can handle the entire particle size distribution and capture the effects of attrition, agglomeration, and fines. (Although the mathematics are more difficult to implement for this model, that s the CFD software developer s problem!) Whether you use EularianEularian or EularianLagrangian modeling, the equations in today s CFD software allow you to simulate what happens in productionscale bulk solids equipment. The process is still slow, however, with 1 minute of simulation time taking anywhere from 1 week to about 1 month. The question we need to ask is: Can a simulation lasting a couple seconds or even minutes effectively describe the steadystate behavior of particles and gas in a unit operation? In many cases, production equipment achieves steadystate operation only several minutes or, in some cases, several hours after startup. Defining physical properties, initial conditions, and boundary conditions for modeling To produce good modeling results, regardless of the model we use, we also need to define the physical properties, initial conditions, and boundary conditions of the process we re simulating: These are the inputs for the model. Physical properties. Physical properties of both the particles and gas are straightforward: For the particle phase, we need the particle size distribution (or Sauter mean particle size [d p50 ]), particle density, and particle shape (for some drag equations). For the gas phase, we need the gas density and gas viscosity. If the process we re modeling doesn t have a constant temperature, we also need the heat capacity and thermal conductivity for both the particles and gas. Initial conditions. The initial conditions are the values we use to define a Eularian framework cell s properties at time equal zero that is, before the unit operation we re modeling begins. For most bulk solids simulations, we d need to define these initial conditions: gas velocity, particle velocity, particle concentration (as volume fraction), and temperature. So, for instance, let s look at the initial conditions for producing a threedimensional EularianLagrangian model of a pilotscale (3footdiameter, 20foottall) fluidized bed, as shown in Figure 2, where the fluidizing gas is air and the particles have a 70micron median size with a 90lb/ft 3 density. (The results in Figure 2 are shown as a slice view of a threedimensional simulation after just 30 seconds and were produced using CPFDSoftware s Barracuda Virtual Reactor program.) For this simulation, the air flowrate through the sparger (airflow grid) below the bed was set to obtain a 2ft/s superficial gas velocity in the bed. The particle flowrate in and out of the vessel was set at 2.6 lb/s, and the pressure at the outlet was set at atmospheric. For this simulation, the initial conditions were set as following: The gas velocity was set at the operating superficial gas velocity (the air s volumetric flowrate divided by the crosssectional flow area), the particle velocity was set at zero, the particle concentration was set at 0.45 (the value we expect during the fluidized bed s steadystate operation), and the temperature was set at room temperature. In this case, we re using the initial conditions to predefine the particle bed at fluidization that is, when it first becomes fluidized so the simulation can run faster. Boundary conditions. The boundary conditions are the conditions at the process inlets and outlets. While it s possible to get good simulation results with poorly defined initial conditions, we can t get good results with poorly defined boundary conditions. In the pilotplant fluidized bed example in Figure 2, we had to define these inlet boundary conditions (shown at the figure s left): the fluidization air s entry through the sparger at the vessel s bottom and for the particle flow entering the inlet pipe halfway up the vessel. We also had to define the outlet boundary conditions for the particles exiting the vessel s bottom and top and the air exiting the vessel s top. For the fluidizedbed model, the vessel wall itself is another boundary condition, so we need to describe how the air and particles interact with the wall. In this case, the air velocity at the wall, flowing along the wall, was zero; particles colliding directly with the wall lost 99 percent of their momentum; and particles grazing the wall lost only 60 percent of their momentum. A close look at Figure 2 also reveals a boundary condition precaution we need to keep in mind for incoming particle flow. For this fluidized bed, we didn t want the model to simulate the vessel s inlet pipe right at the pipe s opening in the vessel wall; instead, we made the pipe s configuration, extending 1 foot out of the vessel wall, part of the model. Why? Because we don t know what the particle flow profile really looks like at the inlet pipe s opening in the vessel wall. We do know that the flow at this wall opening isn t uniform, as it would be along the vessel wall at other locations. So in Figure 2, we see that the boundary condition has been moved out 1 foot, along the inlet pipe, so that the particles in the model would have time to move to the pipe s bottom and then drop quickly into the bed, as they do in the pilotplant vessel. If the boundary condition hadn t been moved out at this point, the model would have simulated a uniform boundary condition at the wall for the inlet pipe, which would show the particles falling farther out into the bed. This wouldn t represent what was really happening in the pilotplant vessel. In fact, there are very few instances in bulk solids processing where a uniform boundary condition exists for incoming particle flow. So if you want to use a uniform boundary
6 condition for incoming particles in a simulation, you should model the condition farther upstream from where the particles flow into your process. This allows the bias introduced into your model by the uniform boundary condition to work itself out, so the model will provide results that are more representative of what s happening in the vessel. And in some cases, you may need to model your entire process including all the equipment upstream and downstream from the unit operation you re interested in to capture all the physics involved in the process. A word of advice if you want useful modeling results: Do it right, or don t do it all. How to ensure that your model provides useful results We ve looked at some pretty complex equations in this article. But take heart: In the end, what you need to understand is that CFD modeling a bulk solids unit operation is nothing more than adding all your material, momentum, and energy flows. Making a model that s useful and can solve your problem in a reasonable amount of time typically involves dividing the model s large domain into arrays of smaller domains. However, all models are based on assumptions and numerical tricks, and they don t capture all the physics in a process. As statistician George Box Figure 2 Simulating a pilotplant fluidized bed: boundary conditions and results after 30 seconds Boundary conditions Particle and air exit Slice Slice view showing results after 30 seconds a said, All models are wrong; some models are useful. You can determine whether the model you ve produced is useful by working with your modeler to answer the following questions: 1. Are the physical properties of the particles and gas used in producing the model correct? And are all the physical properties known? 2. Are the operating conditions used to produce the model correct? How do we know? 3. Is the model threedimensional? 4. Have we validated the model against experimental data for the same equipment (for instance, validating a cyclone model against data from cyclone experiments)? 5. Have we used realistic (rather than uniform) boundary conditions for the model? (For instance, if we used a uniform boundary condition for the incoming particle flow, is the boundary condition modeled far enough upstream to prevent biased results?) 6. Did the simulation run long enough to capture the particles steadystate behavior in the process? 7. What are the model s important controlling parameters, and what effect do they have on the results? 8. How accurate are these controlling parameters in the model? 9. Have we precisely described the boundary conditions at the wall to reflect how the particles interact with the wall? 10. Does the model look right, or as we expected to look? If not, why? One caveat: In particle technology, the real benefit of modeling is to get a better idea of the physics in your unit operation. Using modeling as your only scaleup tool is unwise. Tests using lab or pilotscale equipment will provide more accurate scaleup results. PBE Particle entry Air entry at sparger For further reading Find more information on this topic in articles listed under Particle analysis and System or equipment design, fabrication in Powder and Bulk Engineering s article index (in the December 2012 issue and at PBE s website, and in books available on the website at the PBE Bookstore. You can also purchase copies of past PBE articles at Particle exit a Note: Red represents regions of high particle concentrations, and blue represents regions of low particle concentrations. Ray Cocco is president of Particulate Solid Research Inc., 4201 West 36th Street, Ste. 200, Chicago, IL 60632; chicago.com). He holds a PhD in chemical engineering from Auburn University in Auburn, Ala., and writes PBE s Particle Professor column.
150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces
Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationEnergy Transformations IDS 101
Energy Transformations IDS 101 It is difficult to design experiments that reveal what something is. As a result, scientists often define things in terms of what something does, what something did, or what
More informationPrediction of Minimum Fluidisation Velocity Using a CFDPBM Coupled Model in an Industrial Gas Phase Polymerisation Reactor
Journal of Engineering Science, Vol. 10, 95 105, 2014 Prediction of Minimum Fluidisation Velocity Using a CFDPBM Coupled Model in an Industrial Gas Phase Polymerisation Reactor Vahid Akbari and Mohd.
More informationDispersed Multiphase Flow Modeling using Lagrange Particle Tracking Methods Dr. Markus Braun Ansys Germany GmbH
Dispersed Multiphase Flow Modeling using Lagrange Particle Tracking Methods Dr. Markus Braun Ansys Germany GmbH 2011 ANSYS, Inc., Markus Braun 1 Overview The Euler/Lagrange concept Breaking the barrier
More informationCOURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics
COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid
More informationModeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics!
http://www.nd.edu/~gtryggva/cfdcourse/! Modeling Complex Flows! Grétar Tryggvason! Spring 2011! Direct Numerical Simulations! In direct numerical simulations the full unsteady NavierStokes equations
More informationAtomic Motion and Interactions
Atomic Motion and Interactions 1. Handout: Unit Notes 2. Have You Seen an Atom Lately? 1. Lab: Oil Spreading on Water 2. Demo: Computer animation of spreading oil 3. Lab: Mixing Alcohol and Water 4. Demo:
More informationReview of Fluid Mechanics
Chapter 3 Review of Fluid Mechanics 3.1 Units and Basic Definitions Newton s Second law forms the basis of all units of measurement. For a particle of mass m subjected to a resultant force F the law may
More informationPhysic 602 Conservation of Momentum. (Read objectives on screen.)
Physic 602 Conservation of Momentum (Read objectives on screen.) Good. You re back. We re just about ready to start this lab on conservation of momentum during collisions and explosions. In the lab, we
More informationDifferential relations for fluid flow
Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow
More informationSUPERCHARGED SCIENCE. Unit 2: Motion.
SUPERCHARGED SCIENCE Unit 2: Motion www.sciencelearningspace.com Appropriate for Grades: Lesson 1 (K12), Lesson 2 (K12) Duration: 612 hours, depending on how many activities you do! We re going to study
More informationPairwise Interaction Extended PointParticle (PIEP) Model for dropletladen flows: Towards application to the midfield of a spray
Pairwise Interaction Extended PointParticle (PIEP) Model for dropletladen flows: Towards application to the midfield of a spray Georges Akiki, Kai Liu and S. Balachandar * Department of Mechanical &
More informationUnit 5: Energy (Part 2)
SUPERCHARGED SCIENCE Unit 5: Energy (Part 2) www.sciencelearningspace.com Appropriate for Grades: Lesson 1 (K12), Lesson 2 (K12) Duration: 615 hours, depending on how many activities you do! We covered
More informationIntroduction to Heat and Mass Transfer. Week 10
Introduction to Heat and Mass Transfer Week 10 Concentration Boundary Layer No concentration jump condition requires species adjacent to surface to have same concentration as at the surface Owing to concentration
More informationConservation of Momentum
Learning Goals Conservation of Momentum After you finish this lab, you will be able to: 1. Use Logger Pro to analyze video and calculate position, velocity, and acceleration. 2. Use the equations for 2dimensional
More informationWallace Hall Academy
Wallace Hall Academy CfE Higher Physics Unit 1  Dynamics Notes Name 1 Equations of Motion Vectors and Scalars (Revision of National 5) It is possible to split up quantities in physics into two distinct
More informationThe SI unit for Energy is the joule, usually abbreviated J. One joule is equal to one kilogram meter squared per second squared:
Chapter 2 Energy Energy is an extremely loaded term. It is used in everyday parlance to mean a number of different things, many of which bear at most a passing resemblance to the term as used in physical
More informationDo Now: What does momentum mean to you?
Do Now: What does momentum mean to you? Momentum All moving objects have what Newton called a quantity of motion. What is this quantity of motion? Today we call it momentum. Momentum is a characteristic
More informationCOVENANT UNIVERSITY NIGERIA TUTORIAL KIT OMEGA SEMESTER PROGRAMME: MECHANICAL ENGINEERING
COVENANT UNIVERSITY NIGERIA TUTORIAL KIT OMEGA SEMESTER PROGRAMME: MECHANICAL ENGINEERING COURSE: GEC 223 DISCLAIMER The contents of this document are intended for practice and leaning purposes at the
More informationChapter: States of Matter
Table of Contents Chapter: States of Matter Section 1: Matter Section 2: Changes of State Section 3: Behavior of Fluids 1 What is matter? Matter is anything that takes up space and has mass. Matter Matter
More information6. Find the centripetal acceleration of the car in m/s 2 a b c d e. 32.0
PHYSICS 5 TEST 2 REVIEW 1. A car slows down as it travels from point A to B as it approaches an S curve shown to the right. It then travels at constant speed through the turn from point B to C. Select
More informationDIRECT NUMERICAL SIMULATION OF LIQUID SOLID FLOW
DIRECT NUMERICAL SIMULATION OF LIQUID SOLID FLOW http://www.aem.umn.edu/solidliquid_flows Sponsored by NSFGrand Challenge Grant Fluid Mechanics & CFD Computer Scientists D.D. Joseph Y. Saad R. Glowinski
More informationInterparticle force and stress models for wet and dry particulate flow at the intermediate flow regime
Interparticle force and stress models for wet and dry particulate flow at the intermediate flow regime Xi Yu 1, Raffaella Ocone 3, Sotos Generalis 2, Yassir Makkawi 1 1 Chemical Engineering & Applied
More informationUnit 6: Linear Momentum
Unit 6: Linear Momentum The concept of linear momentum is closely tied to the concept of force in fact, Newton first defined his Second Law not in terms of mass and acceleration, but in terms of momentum.
More informationHydraulics Prof. Dr. Arup Kumar Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati
Hydraulics Prof. Dr. Arup Kumar Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati Module No. # 08 Pipe Flow Lecture No. # 05 Water Hammer and Surge Tank Energy cannot be consumed
More informationsome are moving faster and some slower at any moment
Lecture 9: Kinetic Theory of Gases, Part 4, and Heat Engines We now know that the temperature of a gas is proportional to the average energy of each molecule But we also know that all the molecules don
More informationChapter 4 Newton s Laws
Chapter 4 Newton s Laws Isaac Newton 16421727 Some inventions and discoveries: 3 laws of motion Universal law of gravity Calculus Ideas on: Sound Light Thermodynamics Reflecting telescope In this chapter,
More informationMechanical Energy Thermal Energy Chemical Energy Electrical Energy Electromagnetic Energy
Physical Science PHYSICS UNIT 4 Study Guide. Chapter 15  Energy Key Terms Energy Kinetic Energy Potential Gravitational Potential Elastic Potential Mechanical Energy Thermal Energy Chemical Energy Electrical
More informationFor example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then:
Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing
More informationPhysics Nov BoseEinstein Gases
Physics 3 3Nov24 8 BoseEinstein Gases An amazing thing happens if we consider a gas of noninteracting bosons. For sufficiently low temperatures, essentially all the particles are in the same state
More informationInelastic Collisions
Experiment 5 Inelastic Collisions 5.1 Objectives Measure the momentum and kinetic energy of two objects before and after a perfectly inelastic onedimensional collision. Observe that the concept of conservation
More informationNotes: Matter & Change (text Ch. 1 &10)
Name Per. Notes: Matter & Change (text Ch. 1 &10) NOTE: This set of class notes is not complete. We will be filling in information in class. If you are absent, it is your responsibility to get missing
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture  17 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture  17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In
More informationParticle Systems. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2017
Particle Systems CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2017 Particle Systems Particle systems have been used extensively in computer animation and special effects since their
More informationFinal Review. If a car has 3,000kgm/s of momentum, and a mass of 1,000kg. How fast is it moving? A ball that has momentum must also have energy.
Physics Name: Date: Period: Final Review Write the appropriate formulas with all units below. Impulse Momentum Conservation of Momentum Rank these in order from least to most momentum:.01kg mass moving
More informationMSc. Thesis Project. Simulation of a Rotary Kiln. MSc. Cand.: Miguel A. Romero Advisor: Dr. Domenico Lahaye. Challenge the future
MSc. Thesis Project Simulation of a Rotary Kiln MSc. Cand.: Miguel A. Romero Advisor: Dr. Domenico Lahaye 1 Problem Description What is a Rotary Kiln? A Rotary Kiln is a pyroprocessing device used to raise
More informationCENG 501 Examination Problem: Estimation of Viscosity with a Falling  Cylinder Viscometer
CENG 501 Examination Problem: Estimation of Viscosity with a Falling  Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic
More informationShell Balances in Fluid Mechanics
Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell
More informationJet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering
Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Indian Institute of Technology, IIT Bombay Module No. # 01 Lecture No. # 08 Cycle Components and Component
More informationConceptual Physics Fundamentals
Conceptual Physics Fundamentals Chapter 3: EQUILIBRIUM AND LINEAR MOTION This lecture will help you understand: Aristotle on Motion Galileo s Concept of Inertia Mass A Measure of Inertia Net Force The
More information(Refer Slide Time: 00:10)
Chemical Reaction Engineering 1 (Homogeneous Reactors) Professor R. Krishnaiah Department of Chemical Engineering Indian Institute of Technology Madras Lecture No 10 Design of Batch Reactors Part 1 (Refer
More informationKinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature Bởi: OpenStaxCollege We have developed macroscopic definitions of pressure and temperature. Pressure is the force divided by
More informationGALILEAN RELATIVITY. Projectile motion. The Principle of Relativity
GALILEAN RELATIVITY Projectile motion The Principle of Relativity When we think of the term relativity, the person who comes immediately to mind is of course Einstein. Galileo actually understood what
More informationUnderstanding segregation mechanisms Segregation can occur by several different mechanisms, depending on the particles physical characteristics and th
Predicting, diagnosing, and solving mixture segregation problems Herman Purutyan and John W. Carson Jenike & Johanson, Inc. Keeping a dry bulk material mixture together from the blender to the final package
More informationAgenda. Chapter 10, Problem 26. All matter is made of atoms. Atomic Structure 4/8/14. What is the structure of matter? Atomic Terminology
Agenda Today: HW Quiz, Thermal physics (i.e., heat) Thursday: Finish thermal physics, atomic structure (lots of review from chemistry!) Chapter 10, Problem 26 A boy reaches out of a window and tosses a
More informationEnergy and Energy Resources
chapter 32 Energy and Energy Resources section 1 What is energy? PS 4.1d: Different forms of energy include heat, light, electrical, mechanical, sound, nuclear, and chemical. Energy is transformed in many
More informationME224 Lab 6 Viscosity Measurement
1. Introduction ME224 Lab 6 Viscosity Measurement (This lab is adapted from IBMPC in the laboratory by B G Thomson & A F Kuckes, Chapter 7) A solid body moving through a fluid has a force pushing on it
More informationChapter 1: Useful definitions
Chapter 1: Useful definitions 1.1. Crosssections (review) The Nuclear and Radiochemistry class listed as a prerequisite is a good place to start. The understanding of a crosssection being fundamentai
More informationInelastic Collisions
Experiment 4 Inelastic Collisions 4.1 Objectives Measure the momentum and kinetic energy of two objects before and after a perfectly inelastic onedimensional collision. Observe that the concept of conservation
More informationCP Snr and Hon Freshmen Study Guide
CP Snr and Hon Freshmen Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Displacement is which of the following types of quantities? a. vector
More informationNotes 4: Differential Form of the Conservation Equations
Low Speed Aerodynamics Notes 4: Differential Form of the Conservation Equations Deriving Conservation Equations From the Laws of Physics Physical Laws Fluids, being matter, must obey the laws of Physics.
More informationThis Week. 9/5/2018 Physics 214 Fall
This Week Momentum Is momentum in basketball physics? Rockets and guns How do spaceships work? Collisions of objects They get impulses! Practical Propulsion 9/5/2018 Physics 214 Fall 2018 1 Momentum What
More informationInaugural University of Michigan Science Olympiad Invitational Tournament. Hovercraft
Inaugural University of Michigan Science Olympiad Invitational Tournament Test length: 50 Minutes Hovercraft Team number: Team name: Student names: Instructions: Do not open this test until told to do
More informationSEMESTER REVIEW FOR FINAL EXAM
SEMESTER REVIEW FOR FINAL EXAM ACCELERATION When is an object s acceleration not equal to zero? What is the equation for acceleration? ANGULAR SPEED AND MOMENTUM Does an object on the outside of a spinning
More informationPrimary Objectives. Content Standards (CCSS) Mathematical Practices (CCMP) Materials. Before Beginning
THE FALL OF JAVERT Could Inspector Javert have survived the fall? Mathalicious 2013 lesson guide At the end of the popular musical Les Misérables, a dejected Inspector Javert throws himself off a bridge
More information3. FORMS OF GOVERNING EQUATIONS IN CFD
3. FORMS OF GOVERNING EQUATIONS IN CFD 3.1. Governing and model equations in CFD Fluid flows are governed by the NavierStokes equations (NS), which simpler, inviscid, form is the Euler equations. For
More informationEnvironment Air Pollution Prof. Mukesh Sharma Department of Civil Engineering Indian Institute of Technology, Kanpur
Environment Air Pollution Prof. Mukesh Sharma Department of Civil Engineering Indian Institute of Technology, Kanpur Lecture No. 35 Air Pollution Control Devices 1 What had we done last time? [Conversation
More informationMinimum fluidization velocity, bubble behaviour and pressure drop in fluidized beds with a range of particle sizes
Computational Methods in Multiphase Flow V 227 Minimum fluidization velocity, bubble behaviour and pressure drop in fluidized beds with a range of particle sizes B. M. Halvorsen 1,2 & B. Arvoh 1 1 Institute
More informationReview Chapters 19. Did you read the article on helmets before coming to class? A. Yes B. No
Review Chapters 19 Did you read the article on helmets before coming to class? A. Yes B. No Review Sessions Th 46 in W112 BNSN Th 68 in 377 CB F 35 in 445 MARB Forces on an object Block inside monument
More informationAerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)
Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation
More informationfluid mechanics as a prominent discipline of application for numerical
1. fluid mechanics as a prominent discipline of application for numerical simulations: experimental fluid mechanics: wind tunnel studies, laser Doppler anemometry, hot wire techniques,... theoretical fluid
More informationCollisions. Objective. Introduction
Collisions Objective To study conservation of momentum and kinetic energy during a collision between two bodies. Introduction In this experiment a moving air puck makes a glancing collision with a puck
More informationConservation of Momentum. Last modified: 08/05/2018
Conservation of Momentum Last modified: 08/05/2018 Links Momentum & Impulse Momentum Impulse Conservation of Momentum Example 1: 2 Blocks Initial Momentum is Not Enough Example 2: Blocks Sticking Together
More informationPE = mgh. Potential energy. What is g here? Let s pick up where we left off last time..the topic was gravitational potential energy
Let s pick up where we left off last time..the topic was gravitational potential energy Now, let s talk about a second form of energy Potential energy Imagine you are standing on top of half dome in Yosemite
More informationPage 2. Example Example Example Jerk in a String Example Questions B... 39
Page 1 Dynamics Newton's Laws...3 Newton s First Law... 3 Example 1... 3 Newton s Second Law...4 Example 2... 5 Questions A... 6 Vertical Motion...7 Example 3... 7 Example 4... 9 Example 5...10 Example
More informationLecture 19: Introduction to Kinetics First a CH 302 Kinetics Study Guide (Memorize these first three pages, they are all the background you need)
Lecture 19: Introduction to Kinetics First a CH 302 Kinetics Study Guide (Memorize these first three pages, they are all the background you need) Reaction Rate: The most important issue in kinetics is
More informationENGR 292 Fluids and Thermodynamics
ENGR 292 Fluids and Thermodynamics Scott Li, Ph.D., P.Eng. Mechanical Engineering Technology Camosun College Jan.13, 2017 Review of Last Class Course Outline Class Information Contact Information, Website
More informationTurbulence  Theory and Modelling GROUPSTUDIES:
Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 0460480 Johan Revstedt, tel 04643 0 Turbulence  Theory and Modelling GROUPSTUDIES: Turbulence
More informationGood Vibes: Introduction to Oscillations
Chapter 14 Solutions Good Vibes: Introduction to Oscillations Description: Several conceptual and qualitative questions related to main characteristics of simple harmonic motion: amplitude, displacement,
More information(a) (i) One of the assumptions of the kinetic theory of gases is that molecules make elastic collisions. State what is meant by an elastic collision.
1 (a) (i) One of the assumptions of the kinetic theory of gases is that molecules make elastic collisions. State what is meant by an elastic collision. State two more assumptions that are made in the kinetic
More informationContents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
More informationForce, Friction & Gravity Notes
Force, Friction & Gravity Notes Key Terms to Know Speed: The distance traveled by an object within a certain amount of time. Speed = distance/time Velocity: Speed in a given direction Acceleration: The
More informationHigh Speed Aerodynamics. Copyright 2009 Narayanan Komerath
Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil
More informationPhysics 9 Monday, February 13, 2012
Physics 9 Monday, February 13, 2012 learningcatalytics.com class session ID: 927092 This week and next week: heat, thermal physics, etc. It s an important topic for you, so we re reading two authors presentations
More information7 The NavierStokes Equations
18.354/12.27 Spring 214 7 The NavierStokes Equations In the previous section, we have seen how one can deduce the general structure of hydrodynamic equations from purely macroscopic considerations and
More informationFiltered TwoFluid Model for GasParticle Suspensions. S. Sundaresan and Yesim Igci Princeton University
Filtered TwoFluid Model for GasParticle Suspensions S. Sundaresan and Yesim Igci Princeton University Festschrift for Professor Dimitri Gidaspow's 75th Birthday II Wednesday, November 11, 2009: 3:15
More informationUnit 1 : Mechanics and Heat. Homework 1  Average and Instantaneous Speed.
Homework 1  Average and Instantaneous Speed. 1 Two pupils wish to measure the average speeds of cars as they travel between Craighall Crescent and Craighall Avenue. State what apparatus they would use,
More information( ) Notes. Fluid mechanics. Inviscid Euler model. Lagrangian viewpoint. " = " x,t,#, #
Notes Assignment 4 due today (when I check email tomorrow morning) Don t be afraid to make assumptions, approximate quantities, In particular, method for computing time step bound (look at max eigenvalue
More informationThe SI units of mass are kilograms (kg) and of velocity are meters / second (m/s). Therefore, the units of momentum are kg m/s.
Momentum Introduction As was pointed out in the previous chapter, some of the most powerful tools in physics are based on conservation principles. The idea behind a conservation principle is that there
More informationN H 2 2 NH 3 and 2 NH 3 N H 2
Chemical Equilibrium Notes (Chapter 18) So far, we ve talked about all chemical reactions as if they go only in one direction. However, as with many things in life, chemical reactions can go both in the
More informationHonors Physics Semester 2 Final Exam Review Answers
Honors Physics Semester 2 Final Exam Review Answers 1600 kg 800 kg 9 m/s A truck with mass 1600 kg collides with a car with mass 800 kg at rest. They stick together and continue to move to the right. 1.
More informationA First Course on Kinetics and Reaction Engineering Unit D and 3D Tubular Reactor Models
Unit 34. 2D and 3D Tubular Reactor Models Overview Unit 34 describes two and threedimensional models for tubular reactors. One limitation of the ideal PFR model is that the temperature and composition
More informationShell/Integral Balances (SIB)
Shell/Integral Balances (SIB) Shell/Integral Balances Shell or integral (macroscopic) balances are often relatively simple to solve, both conceptually and mechanically, as only limited data is necessary.
More informationKey Concept Heat in Earth s atmosphere is transferred by radiation, conduction, and convection.
Section 2 Atmospheric Heating Key Concept Heat in Earth s atmosphere is transferred by radiation, conduction, and convection. What You Will Learn Solar energy travels through space as radiation and passes
More informationCollision Theory. and I 2
Collision Theory To explain why chemical reactions occur, chemists have proposed a model, known as collision theory, which states that molecules must collide in order to react. These collisions can involve
More informationConcepTest PowerPoints
ConcepTest PowerPoints Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for
More informationMOMENTUM! Momentum Impulse Conservation of Momentum in 1 Dimension
MOMENTUM! Momentum Impulse Conservation of Momentum in 1 Dimension Momentum Defined p = m v p = momentum vector m = mass v = velocity vector Momentum Facts p = m v Momentum is a vector quantity! Velocity
More informationPart I Electrostatics. 1: Charge and Coulomb s Law July 6, 2008
Part I Electrostatics 1: Charge and Coulomb s Law July 6, 2008 1.1 What is Electric Charge? 1.1.1 History Before 1600CE, very little was known about electric properties of materials, or anything to do
More information2010 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Some of the topics we will explore: How do we describe motion? (Speed,
More informationPhysics 9 Wednesday, March 2, 2016
Physics 9 Wednesday, March 2, 2016 You can turn in HW6 any time between now and 3/16, though I recommend that you turn it in before you leave for spring break. HW7 not due until 3/21! This Friday, we ll
More information1. The Properties of Fluids
1. The Properties of Fluids [This material relates predominantly to modules ELP034, ELP035] 1.1 Fluids 1.1 Fluids 1.2 Newton s Law of Viscosity 1.3 Fluids Vs Solids 1.4 Liquids Vs Gases 1.5 Causes of viscosity
More informationQ2. A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book.
AP Physics 1 Dynamics Practice Problems FACT: Inertia is the tendency of an object to resist a change in state of motion. A change in state of motion means a change in an object s velocity, therefore
More informationJune 9, Phosphate Conference Clearwater Convention June Abstract:
PUMP CONSULTING & TRAINING LLC Joseph R. Askew 1811 Stonecrest Ct. Lakeland, Fl. 33813 8636443118Office Phone 8638999896Cell Phone Email: pmpcnslt@tampabay.rr.com Objectivity in pump selection,
More informationAn Introduction to Electricity and Circuits
An Introduction to Electricity and Circuits Materials prepared by Daniel Duke 4 th Sept 2013. This document may be copied and edited freely with attribution. This course has been designed to introduce
More informationPHY131H1F  Class 9. Today, finishing Chapter 5: Kinetic Friction Static Friction Rolling without slipping (intro) Drag
PHY131H1F  Class 9 Today, finishing Chapter 5: Kinetic Friction Static Friction Rolling without slipping (intro) Drag Microscopic bumps and holes crash into each other, causing a frictional force. Kinetic
More informationChemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017
Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering
More informationPreparing for Six Flags Physics Concepts
Preparing for Six Flags Physics Concepts uniform means constant, unchanging At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given
More informationAdvanced Chemical Reaction Engineering Prof. H. S. Shankar Department of Chemical Engineering IIT Bombay. Lecture  03 Design Equations1
(Refer Slide Time: 00:19) Advanced Chemical Reaction Engineering Prof. H. S. Shankar Department of Chemical Engineering IIT Bombay Lecture  03 Design Equations1 We are looking at advanced reaction engineering;
More informationReal Science4Kids. Level I. Dr. R. W. Keller
Real Science4Kids Level I Dr. R. W. Keller Cover design: David Keller Opening page: David Keller Illustrations: Janet Moneymaker, Rebecca Keller Copyright 2004, 2005 Gravitas Publications, Inc. All rights
More information