CHAPTER 26 FLUID

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solutionmanualforfluidmechanics7thmunson

solutionmanualforfluidmechanics7thmunson

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Hagen-Poiseuille

Hagen-Poiseuille

General T eaching Outline forPrinciples of Chemical EngineeringCourse Number:Suitable for:Majors of chemical engineering and technology, biochemical engineering, food engineering, environment engineering, applied chemistry, industry equipment and control engineering, pulp and paper, polymer and inorganic material engineering.Course character: Basic course for technologyAcademic Credits: 7Academic Hours: 114Written by Hao Shixiong Writing Date: 2006.03.06 Proofread by Proofreading Date: 2006.03.06Section ⅠBasic requirements1. The Course objectiveThe ‘principles of chemical engineering’is a requirement course for general chemical engineering speciality. It is suitable for undergraduate students in the senior years who have the usual training in mathematics, physics, chemistry, and mechanics. It includes the principles of a fluid flow, heat transfer, principles of mass transfer and separation processes, the construction and operating principle of typical equipment, the experimental and researching methods of unit operation, and the calculation and selection of typical equipment. The course aims are to train and educate students to know or understand basic unit operations of chemical engineering. The course emphasizes the combination between the theory and practices, and ability of analysis and solution to practical process.2. Previous coursesAdvanced mathematics, physics, physical chemistry, mechanics, mechani cal drawi ng3. The basic requirements and contents for each chapterChapter 1 Definitions and principlesBasic law; Material balance; Law of motion; Energy balance; Equilibrium; Units and dimensions; Physical quantities; Primary and secondary quantities; Dimensions and dimensional formulas; Conversion of units; Dimensionless equations and consistent units; Dimensi onal equati ons.Chapter 2 Fluid statics and its applicationsNature of fluids; Hydrostatic equilibrium; Applications of fluid statics; Manometers continuous gravity decanter.Chapter 3 Fluid flow phenomenaThe velocity field; Laminar flow; Shear rate, and shear stress; Newtonian and non-Newtonian fluids; Viscosity; Kinematic viscosity.Turbulence; Laminar and turbulent flow; Reynolds number and transition from laminar to turbulence flow; Nature of turbulence; Deviating velocities in turbulence flow; Eddy viscosity; Flow in boundary layers; Laminar and turbulent flow in boundary layers; Boundary-layer formation in straight tubes; Boundary-layer separation and wake formation.Chapter 4 Basic equations of fluid flowOne-dimensional flow; Mass balance; Macroscopic momentum balance; Layer flow with free surface; Momentum balance in potential flow; Discussion of Bernoulli equation; Bernoulli equation: correction for effects of solid boundaries; Kinetic-energy correction factor; Correction of Bernoulli equation for fluid friction; Pump work in Bernoulli equation.Chapter 5 Incompressible flow in pipes and channelsShear stress and skin friction in pipes; Relation between skin friction and wall shear; Relations between skin-friction factor; Laminar flow of Newtonian fluids; V elocity distribution in a pipe;A verage velocity for laminar flow in a pipe; Hagen-Poiseuille equation; Relations between maximum velocity and average velocity; Laminar flow in an annulus; Friction factor in flow through channel of noncircular cross section; Turbulent flow in pipes and channels; Effect of roughness; Hydraulically smooth; The friction factor and friction coefficient chart; Friction from changes in velocity or direction; Friction loss from sudden expansion of cross section; Friction loss from sudden contraction of cross section; Effect of fittings and valves; Form-friction losses in the Bernoulli equation.Chapter 6 Flow past immersed bodiesDrag, Drag coefficients; Drag coefficients of typical shapes; Mechanics of particle motion, Equation for one-dimensional motion of particle through fluid; Terminal velocity, drag coefficient, movement of spherical particles; The terminal velocities at the different Reynolds number; Criterion for settling regime.Chapter 7 Separation equipmentsGravity settling processes; Centrifugal settling processes; Separation of solids from gases; cyclones, filtration; Clarifying filters; Gas cleaning; Liquid clarification, discontinuous pressure filters; Filter press; Shell-and-leaf filters; Continuous pressure filters; Principles of cake filtration; Pressure drop through filter cake; Filter medium resistance; Constant-pressure filtration; Continuous filtration; Washing filter cakes.Chapter 8 T ransportation and metering of fluidsPipe and tubing; Selection of pipe sizes; Fluid-moving machinery; Developed head; Power requirement; Suction lift and cavitation; Suction lift; Positive-displacement pumps; V olumetric efficiency; Rotary pumps; Centrifugal pumps; Centrifugal pump theory; Head-flow relations for an ideal pump; The relation between head and volumetric flow; Effects of speed and impeller sizechange; Characteristic curves; Head-capacity relation; Efficiency; Centrifugal-pump characteristics; System head curve; Operating point; Operating point change; Operation in parallel and in series of centrifugal pump; Multistage centrifugal pumps; Pump priming; Fans; Blowers.Measurement of flowing fluids; Full-bore meters; V enturi meter; The basic equation for venturi meter; V enturi coefficient; Flow rate; Pressure recovery; Orifice meter; Pressure recovery; Area meters: rot meters; Theory and calibration of rotameters; Inserti on meters; Pi cot tube.Chapter 10 Heat T ransferNature of heat flow; Heat transfer by conduction; Basic law of conduction; Unsteady-state conduction; Steady-state conduction; Thermal conductivity; Steady-state conduction; Compound resistance in series; Heat flow through a cylinder.Chapter 11 Principles of heat flow in fluidsTypical heat-exchange equipment; Countercurrent and parallel-current flows; Single-pass shell-and-tube condenser; Energy balances, heat flux and heat transfer coefficient; Heat flux, A verage temperature of fluid stream; Overall heat-transfer coefficient; Mean temperature difference; Individual heat-transfer coefficients; Special cases of the overal l coeffi ci ent.Chapter 12 Heat transfer to fluids without phase changeRegimes of heat transfer in fluids; Heat transfer by forced convection in turbulent flow; Empirical equation; Effect of tube length; Estimation of wall temperature t w; Cross sections other than circular; Heat transfer in transition region between laminar and turbulent flow; Heating and cooling of fluids in forced convection outside tubes, fluids flowing normal to a single tube; Natural convection; Natural convection to air from vertical shapes and hori zontal pl ates.Chapter 13 Heat transfer to fluids with phase changeHeat transfer from condensing vapors; Dropwise and film-type condensation; Coefficients for film-type condensation; V ertical tubes, Horizontal tubes; Effect of noncondensables; Heat transfer to boiling liquids; Pool boiling of saturated liquid.Chapter 14 Radiation heat transferFundamental facts concerning radiation; Emission of radiation; Wavelength of radiation; Emissive power; Blackbody radiation; Emissivities of solids; Practical source of blackbody radiation; Laws of blackbody radiation; Absorption of radiation by opaque solids; Radiation between surfaces.Chapter 17 Principles of Diffusion and Mass T ransfer Between PhasesTheory of diffusion; Comparison of diffusion and heat transfer; Diffusion quantities; V eloc ities in diffusion; Molal flow rate, velocity, and flux; Relations between diffusivities; Interpretation of diffusion equations; Equimolal diffusion; One-component mass transfer (one-way di ffusi on).Prediction of Diffusivities; Diffusion in gases; Diffusion in liquids; Turbul ent di ffusi on.Mass transfer theories; Mass transfer coefficient; Film theory; Two-fi l m theory.Chapter18. Gas AbsorptionDefinition of absorption; Principles of absorption; Material balances; Limiting gas-liquid ratio; Rate of absorption; Calculation of tower height; Number of transfer units; Alternate forms of transfer coefficients; Effect of pressure; Temperature variations in packed towers; Stripping factor method for calculating the number of transfer units; Absorption efficiency A.Empirical correlations for mass transfer coefficients in absorption.Chapter 19 Introduction to Mass T ransfer and Separation ProcessesDefinition of separation processes; Importance and variety of separations; Economic significance of separation processes; Categorizations of separation processes; General separation process; Technological maturity of processes; Terminology and symbols.Supplementary:Phase equilibria: Phase rule; Equilibrium and equilibrium stage; Thermodynamic relationships: Equilibrium ratio ( or equilibrium constant or K value); Relative volatility----key separation factor in distillation; Ideal system and Dalton’s law, Raoult’s law; Phase equilibrium diagrams for ideal systems(t-x-y diagram; x-y diagram); Henry’s law; Azeotropes; Effect of total pressure on vapor/liquid equilibrium.Chapter 20 Equilibrium-Stage OperationsCascades. Ideal stage/equilibrium stage/theoretical stage; Equipment for stage contacts; Principles of stage processes; Terminology for stage-contact plants; Material balances; Enthalpy balances; Graphical methods for two-component system; Operating line diagram; Ideal contact stages; Determining the number of ideal stages; Absorption factor method for calculating the number of ideal stages.Supplementary:Introduction to distillation: Process description; Equilibrium/flash distillation; Principles and flow diagram of distillation.Chapter 21 DistillationContinuous distillation with Reflux. Material balances in plate columns: Overall material balances for two-component systems; Net flow rates; Operating linesNumber of ideal plates; McCabe-Thiele Method. Constant molal overflow; Reflux ratio; Condenser and top plate; Bottom plate and reboiler; Feed plate; Feed line; Construction of operating lines; Optimum feed plate location; Heating and cooling requirements; Minimum number of plates/total reflux; Minimum reflux/infinite number of plates; Invariant zone; Optimum reflux; Nearly pure products; Some special cases of distillation (Multiple feeds and side-stream drawoffs; Direct steam heating); Use of Murphree efficiency/determining the number of actual plates.Batch distillation. Simple distillation; Batch distillation with reflux. Calculation and analysisfor the operation of a distillation column.Chapter 24 Drying of SolidsIntroduction to methods for removing liquid from solid materials; Purposes and applications of drying; Classification of drying processes; Drying conditions for convecti ve dryers.Properties of moist air and humidity chart. Moist air properties: Humidity; Relative humidity; Humid volume; Humid heat; Total enthalpy of moist air; Dry-bulb temperature and wet-bulb temperature; Adiabatic saturation temperature; Dew point. Humidity chart of Air-Water system. Applications of H-I diagram.Material and energy balances; Expressions of water (moisture) content of solids; Material balances; Heat balances; Thermal efficiency of drying process; Air states when passing through the drying system.Phase equilibria and drying rates. Phase equilibria: Equilibrium water(moisture) and free water(moisture); Equilibrium-moisture curves; Bound and unbound water; Drying curves and drying rate curves under constant drying conditions; Drying mechanism of wet solids and the influencing factors: Constant-rate period (Period of controls of surface water vaporization); Drying in the falling-rate period (period of controls of water diffusing from interior to solid surface); Critical water(moisture) content and its influencing factors. Methods for increasing rate of drying.Calculation of drying time under constant drying conditions.4. T extbook and reference booksT extbook:Unit operation of chemical engineering(Sixth edition) Author: Warren L. McCabe, Julian C. Smith and Peter HarriottReference books:[1]. 姚玉英主编. 化工原理(上、下册)(新版)[M] . 天津: 天津大学出版社, 1998[2]. 赵汝溥, 管国锋. 化工原理[M] . 北京: 化学工业出版社, 1995.[3]. 大连理工大学化工原理教研室编. 化工原理(上、下册)[M]. 大连:大连理工大学出版社, 1992[4]. 陈敏恒,丛德滋,方图南,齐鸣斋编. 化工原理(上、下册)[M].(第二版).北京: 化学工业出版社, 1999[5]. 朱家骅,叶世超等编. 化工原理(上、下册)[M]. 北京:科学技术出版社, 2002[6]. 姚玉英. 化工原理例题与习题[M](第三版). 北京: 化学工业出版社, 2003[7]. 柴成敬,王军,陈常贵,郭翠梨编.化工原理课程学习指导[M]. 天津: 天津大学出版社, 2003[8]. 匡国柱. 化工原理学习指导[M]. 大连: 大连理工大学出版社, 20025. Periods for Every Unitl. Fluid flow 20 hours2. Fluid transportation 10 hours3. Separation of heterogeneous mixture 10 hours4. Heat transfer 20 hours5 Gas Absorption 24 hours6 Distillation 18 hours7 Drying of Solids 12 hours6. Evaluation Methods of the CourseThe assess method: quiz, homework and course report et al. which are determined by the teacher, and the unified final examination。

chapter 1 Fluid Properties

chapter 1 Fluid Properties

which may be either solid surfaces or interfaces with
other fluids.
Subsequent: 随后的,后来的,并发的
3
1.1 Definition of a Fluid
What is a fluid?
from a scientific or engineering point of view.
问题2: 试问自由落体和加速度a向x方向运动状态下的液体所受的单 位质量力大小(fX. fY. fZ)分别为多少?
自由落体:X=Y=0,Z=0,加速运动:X=-a, Y=0,Z=-g。
1.3 Fluid Properties
1.3.1.2 Suface Force pressu of a Fluid
8
1.1 Definition of a Fluid
Some materials, such as slurries(泥浆), tar(柏油), putty(油 灰, 灰泥), toothpaste, and so on, are not easily classified since they will behave as a solid if the applied shearing stress is small, but if the stress exceeds some critical
2



Wx X m Wy Y m Wz Z m
18
1.3 Fluid Properties
Figure 1.2
Wx X a m
Wy Y 0 m
Wz Z g m
19
问题1: 比较重力场(质量力只有重力)中,水和水银所受的单位质 量力f水和f水银的大小? A. f水<f水银; B. f水=f水银; C. f水>f水银; D、不一定。

生物学导论中英对照版

生物学导论中英对照版

Chapter 41. The fluid mosaic model states that AA) The cell membrane is a phospholipid bilayer withembedded proteins and that it is in constantmotion.B) Water is repelled from both surfaces of the cell membrane.C) There is a liquid portion between the parts of thecell membrane that facilitates the passage ofmolecules through the membrane.D) All of the above.2. The endoplasmic reticulum is responsible for DA) Increasing the surface area where chemical reactions can occur.B) Transporting substances throughout the cell.C) Metabolizing fat and degrading toxic substances.D) All of the above.3. Long cellular organelles of movement are: CA) cilia.B) microfilaments inside cell.C) flagella.D) endoplasmic reticulum.4. White blood cells (leukocytes) engulf invading bacteria and viruses by DA) pinocytosis.B) budding.C) active transport.D) phagocytosis5. The site of protein synthesis is the AA) ribosome.B) golgi apparatus.C) nucleus.D) mitochondria.Chapter 71. The "Central Dogma" of protein synthesis can be summed up as follows: AA) DNA --> transcription --> RNA --> translation.B) DNA --> translation --> RNA --> transcription.C) DNA --> RNA --> transcription --> translation.D) DNA --> RNA --> translation --> transcription.2. Which is the correct genetic sequence? AA) Promotor, initiation code, gene, terminator code, terminator region.第四章1. 流动镶嵌模型指的是?A 细胞膜磷脂双分子层内含嵌入式的蛋白质,它是在不断地运动的B 细胞膜两面都有亲水性C 细胞膜上有一个液体部分用来促使分子通过细胞膜D 以上都是2. 内质网负责:A 增加化学反应发生地的表面积B 把物质运输出细胞C 代谢脂肪和降解有毒物质D 以上都是3. 长细胞的运动细胞器是?A 纤毛B 细胞微丝C 鞭毛D 内质网4. 白细胞通过什么吞噬细菌和病毒?A 胞吞作用B 发芽C 主动运输D 吞噬作用5. 蛋白质的合成地点是?A 核糖体B 高尔基体C 细胞核D 线粒体第七章1.“中心法则”在蛋白质合成过程中可概括如下?A DNA ->转录-> RNA->翻译B DNA-> 翻译->RNA->转录C DNA ->RNA->转录->翻译D DNA-> RNA->翻译->转录2.那个是正确的基因序列?A 起始子,起始密码,基因,终止密码,终止区域B) Promotor, initiation code, gene, terminator region, terminator code.C) Initiation code, promotor, gene, terminator code, terminator region.D) Initiation code, promotor, gene, terminator region, terminator code.3. One way to introduce new DNA into an organism is AA) gene splicing.B) replication.C) removing introns.D) transcription.4. A DNA gene strand with the base sequence CCA - TAT - TCG will be transcribed into RNA with the base sequence: BA) CCA - TAT - TCG.B) GGU - AUA - AGCC) CCA - UAU - UCG.D) GGT - ATA - AGC.5. In eukaryotic cells, mature RNA is formed by the AA) removal of introns.B) removal of exons.C) addition of introns.D) addition of exons.Chapter 81. Which statement is true? AA) Technically, mitosis is a nuclear event and doesnot involve cytokinesis, which is a cytoplasmicevent.B) Cytokinesis is a part of mitosisC) The terms cytokinesis and mitosis can be used synonymously.D) None of the above.2.During which phase of mitosis do the C chromosomes begin their migration to their respective poles?A) ProphaseB) MetaphaseC) AnaphaseD) Telophase3. A benign tumor BA) Tends to spread beyond its original area ofgrowth, but spreads more slowly that amalignant tumor.B) Can cause damage by interfering with normal B 起始子,起始密码,基因,终止区域,终止密码C 起始密码,起始子,基因,终止密码,终止区域D 起始密码,起始子,基因,终止区域,终止密码3.将新的DNA导入一个有机体的方法是?A 基因剪接B 复制C 删除插入D 转录4.碱基顺序为CCA-TAT-TCG的DNA基因链转录为RNA时的碱基顺序是?A CCA - TAT - TCG.B GGU - AUA - AGC.C CCA - UAU - UCG.D GGT - ATA - AGC.5. 真核细胞中,成熟RNA是由什么构成的?A 内含子的去除B 外显子的去除C 内含子的添加D 外显子的添加第八章1.哪个陈述是真实的?A 从技术上讲,有丝分裂是一个核事件,不涉及属于胞质事件的胞质分裂。

流体力学C-名词解释

流体力学C-名词解释

Chapter 1 Fluid statics 流体静力学1. 连续介质假定(Continuum assumption):The real fluid is considered as no -gap continuousmedia, called the basic assumption of continuity of fluid, or the continuum hypothesis of fluid. 流体是由连续分布的流体质点(fluid particle)所组成,彼此间无间隙。

它是流体力学中最基本的假定,1755年由欧拉提出。

在连续性假设之下,表征流体状态的宏观物理量在空间和时间上都是连续分布的,都可以作为空间和时间的函数。

2. 流体质点(Fluid particle ): A fluid element that is small enough with enough moles to makesure that the macroscopic mean density has definite value is defined as a Fluid Particle. 宏观上足够小,微观上足够大。

3. 流体的粘性(Viscosity ): is an internal property of a fluid that offers resistance to sheardeformation. It describes a fluid's internal resistance to flow and may be thought as a measure of fluid friction. 流体在运动状态下抵抗剪切变形的性质,称为黏性或粘滞性。

它表示流体的部流动阻力,也可当做一个流体摩擦力量。

The viscosity of a gas increases with temperature, the viscosity of a liquid decreases with temperature. 4. 牛顿摩擦定律(Newton’s law of viscosity ):5. The dynamic viscosity (动力黏度)is also called absolute viscosity (绝对黏度). The kinematicviscosity (运动黏度)is the ratio of dynamic viscosity to density.6. Compressibility (压缩性):As the temperature is constant, the magnitude ofcompressibility is expressed by coefficient of volume compressibility (体积压缩系数) к , a relative variation rate (相对变化率) of volume per unit pressure.The bulk modulus of elasticity (体积弹性模量) E is the reciprocal of coefficient of volumecompressibility к.7. 流体的膨胀性(expansibility; dilatability):The coefficient of cubical expansion (体积热膨胀系数) αt is the relative variation rate of volume per unit temperature change.8. 表面力Surface tension : A property resulting from the attractive forces between molecules.σ-----单位长度所受拉力9. 表面力 Surface force ——is the force exerted on the contact surface by the contacted fluidor other body. Its value is proportional to contact area. 作用在所研究流体外表面上与表du dzτμ=μνρ=面积大小成正比的力。

高中生物必修三知识点总结填空版

高中生物必修三知识点总结填空版

高中生物必修三知识点总结填空版Chapter 1 The Internal Environment and Homeostasis of the Human Body1.Body fluids XXX: intracellular fluid (which accounts for about 2/3 of body fluids) and extracellular fluid (which accounts for about 1/3 of body fluids)。

including blood plasma。

tissue fluid。

lymph。

and cerebrospinal fluid.2.The internal environment of blood cells。

lymph cells。

capillary wall cells。

XXX different.3.The nship een blood plasma。

tissue fluid。

lymph。

and intracellular fluid is XXX.4.The main components of blood plasma are proteins。

XXX is similar to that of blood plasma。

but with less protein.5.The physical and chemical properties of the internal environment include: (1) Osmotic pressure。

XXX。

the osmotic pressure of plasma is XXX sodium ions。

while over 90% of the osmotic pressure of extracellular fluid is determined by sodium ions。

Fluent用户手册

Fluent用户手册

The FLUENT User's Guide tells you what you need to know to use FLUENT. At the end of the User's Guide, you will find a Reference Guide, a nomenclature list, a bibliography, and an index.!! Under U.S. and international copyright law, Fluent is unable to distribute copies of the papers listed in the bibliography, other than those published internally by Fluent. Please use your library or a document delivery service to obtain copies of copyrighted papers.A brief description of what's in each chapter follows:∙Chapter 1, Getting Started, describes the capabilities of FLUENT and the way in which it interacts with other Fluent Inc. and third-party programs. It also advises you on how to choose the appropriate solverformulation for your application, gives an overview of the problem setup steps, and presents a samplesession that you can work through at your own pace. Finally, this chapter provides information aboutaccessing the FLUENT manuals on CD-ROM or in the installation area.∙Chapter 2, User Interface, describes the mechanics of using the graphical user interface, the text interface, and the on-line help. It also provides instructions for remote and batch execution. (See the separate Text Command List for information about specific text interface commands.)∙Chapter 3, Reading and Writing Files, contains information about the files that FLUENT can read and write, including hardcopy files.∙Chapter 4, Unit Systems, describes how to use the standard and custom unit systems available in FLUENT.∙Chapter 5, Reading and Manipulating Grids, describes the various sources of computational grids and explains how to obtain diagnostic information about the grid and how to modify it by scaling, translating, and other methods. This chapter also contains information about the use of non-conformal grids.∙Chapter 6, Boundary Conditions, explains the different types of boundary conditions available in FLUENT, when to use them, how to define them, and how to define boundary profiles and volumetric sources and fix the value of a variable in a particular region. It also contains information about porousmedia and lumped parameter models.∙Chapter 7, Physical Properties, explains how to define the physical properties of materials and the equations that FLUENT uses to compute the properties from the information that you input.∙Chapter 8, Modeling Basic Fluid Flow, describes the governing equations and physical models used by FLUENT to compute fluid flow (including periodic flow, swirling and rotating flows, compressibleflows, and inviscid flows), as well as the inputs you need to provide to use these models.∙Chapter 9, Modeling Flows in Moving Zones, describes the use of single rotating reference frames, multiple moving reference frames, mixing planes, and sliding meshes in FLUENT.∙Chapter 10, Modeling Turbulence, describes FLUENT's models for turbulent flow and when and how to use them.∙Chapter 11, Modeling Heat Transfer, describes the physical models used by FLUENT to compute heat transfer (including convective and conductive heat transfer, natural convection, radiative heat transfer,and periodic heat transfer), as well as the inputs you need to provide to use these models.∙Chapter 12, Introduction to Modeling Species Transport and Reacting Flows, provides an overview of the models available in FLUENT for species transport and reactions, as well as guidelines for selectingan appropriate model for your application.∙Chapter 13, Modeling Species Transport and Finite-Rate Chemistry, describes the finite-rate chemistry models in FLUENT and how to use them. This chapter also provides information about modeling species transport in non-reacting flows.∙Chapter 14, Modeling Non-Premixed Combustion, describes the non-premixed combustion model and how to use it. This chapter includes details about using prePDF.∙Chapter 15, Modeling Premixed Combustion, describes the premixed combustion model and how to use it.∙Chapter 16, Modeling Partially Premixed Combustion, describes the partially premixed combustion model and how to use it.∙Chapter 17, Modeling Pollutant Formation, describes the models for the formation of NOx and soot and how to use them.∙Chapter 18, Introduction to Modeling Multiphase Flows, provides an overview of the models for multiphase flow (including the discrete phase, VOF, mixture, and Eulerian models), as well as guidelines for selecting an appropriate model for your application.∙Chapter 19, Discrete Phase Models, describes the discrete phase models available in FLUENT and how to use them.∙Chapter 20, General Multiphase Models, describes the general multiphase models available in FLUENT (VOF, mixture, and Eulerian) and how to use them.∙Chapter 21, Modeling Solidification and Melting, describes FLUENT's model for solidification and melting and how to use it.∙Chapter 22, Using the Solver, describes the FLUENT solvers and how to use them.∙Chapter 23, Grid Adaption, explains the solution-adaptive mesh refinement feature in FLUENT and how to use it.∙Chapter 24, Creating Surfaces for Displaying and Reporting Data, explains how to create surfaces in the domain on which you can examine FLUENT solution data.∙Chapter 25, Graphics and Visualization, describes the graphics tools that you can use to examine your FLUENT solution.∙Chapter 26, Alphanumeric Reporting, describes how to obtain reports of fluxes, forces, surface integrals, and other solution data.∙Chapter 27, Field Function Definitions, defines the flow variables that appear in the variable selection drop-down lists in FLUENT panels, and tells you how to create your own custom field functions.∙Chapter 28, Parallel Processing, explains the parallel processing features in FLUENT and how to use them. This chapter also provides information about partitioning your grid for parallel processing.18. Introduction to Modeling Multiphase FlowsA large number of flows encountered in nature and technology are a mixture of phases. Physical phases of matter are gas, liquid, and solid, but the concept of phase in a multiphase flow system is applied in a broader sense. In multiphase flow, a phase can be defined as an identifiable class of material that has a particular inertial response to and interaction with the flow and the potential field in which it is immersed. For example, different-sized solid particles of the same material can be treated as different phases because each collection of particles with the same size will have a similar dynamical response to the flow field.This chapter provides an overview of multiphase modeling in FLUENT, and Chapters 19 and 20 provide details about the multiphase models mentioned here. Chapter 21 provides information about melting and solidification.18.1 Multiphase Flow RegimesMultiphase flow can be classified by the following regimes, grouped into four categories:gas-liquid or liquid-liquid flowsbubbly flow: discrete gaseous or fluid bubbles in a continuous fluiddroplet flow: discrete fluid droplets in a continuous gasslug flow: large bubbles in a continuous fluidstratified/free-surface flow: immiscible fluids separated by a clearly-defined interfacegas-solid flowsparticle-laden flow: discrete solid particles in a continuous gaspneumatic transport: flow pattern depends on factors such as solid loading, Reynolds numbers, and particle properties. Typical patterns are dune flow, slug flow, packed beds, and homogeneous flow.fluidized beds: consist of a vertical cylinder containing particles where gas is introduced through a distributor. The gas rising through the bed suspends the particles. Depending on the gas flow rate, bubbles appear and rise through the bed, intensifying the mixing within the bed.liquid-solid flowsslurry flow: transport of particles in liquids. The fundamental behavior of liquid-solid flows varies with the properties of the solid particles relative to those of the liquid. In slurry flows, the Stokes number (seeEquation 18.4-4) is normally less than 1. When the Stokes number is larger than 1, the characteristic of the flow is liquid-solid fluidization.hydrotransport: densely-distributed solid particles in a continuous liquidsedimentation: a tall column initially containing a uniform dispersed mixture of particles. At the bottom, the particles will slow down and form a sludge layer. At the top, a clear interface will appear, and in the middle a constant settling zone will exist.three-phase flows (combinations of the others listed above)Each of these flow regimes is illustrated in Figure 18.1.1.Figure 18.1.1: Multiphase Flow Regimes18.2 Examples of Multiphase SystemsSpecific examples of each regime described in Section 18.1 are listed below:Bubbly flow examples: absorbers, aeration, air lift pumps, cavitation, evaporators, flotation, scrubbersDroplet flow examples: absorbers, atomizers, combustors, cryogenic pumping, dryers, evaporation, gas cooling, scrubbersSlug flow examples: large bubble motion in pipes or tanksStratified/free-surface flow examples: sloshing in offshore separator devices, boiling and condensation in nuclear reactorsParticle-laden flow examples: cyclone separators, air classifiers, dust collectors, and dust-laden environmental flowsPneumatic transport examples: transport of cement, grains, and metal powdersFluidized bed examples: fluidized bed reactors, circulating fluidized bedsSlurry flow examples: slurry transport, mineral processingHydrotransport examples: mineral processing, biomedical and physiochemical fluid systemsSedimentation examples: mineral processing18.3 Approaches to Multiphase ModelingAdvances in computational fluid mechanics have provided the basis for further insight into the dynamics of multiphase flows. Currently there are two approaches for the numerical calculation of multiphase flows: the Euler-Lagrange approach and the Euler-Euler approach.18.3.1 The Euler-Lagrange ApproachThe Lagrangian discrete phase model in FLUENT (described in Chapter 19) follows the Euler-Lagrange approach. The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes equations, while the dispersed phase is solved by tracking a large number of particles, bubbles, or droplets through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.A fundamental assumption made in this model is that the dispersed second phase occupies a low volume fraction, even though high mass loading ( ) is acceptable. The particle or droplet trajectories are computed individually at specified intervals during the fluid phase calculation. This makes the model appropriate for the modeling of spray dryers, coal and liquid fuel combustion, and some particle-laden flows, but inappropriate for the modeling of liquid-liquid mixtures, fluidized beds, or any application where the volume fraction of the second phase is not negligible.18.3.2 The Euler-Euler ApproachIn the Euler-Euler approach, the different phases are treated mathematically as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phasic volume fraction is introduced. These volume fractions are assumed to be continuous functions of space and time and their sum is equal to one. Conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases. These equations are closed by providing constitutive relations that are obtained from empirical information, or, in the case of granular flows , by application of kinetic theory.In FLUENT, three different Euler-Euler multiphase models are available: the volume of fluid (VOF) model, the mixture model, and the Eulerian model.The VOF ModelThe VOF model (described in Section 20.2) is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. Applications of the VOF model include stratified flows , free-surface flows, filling, sloshing , the motion of large bubbles in a liquid, the motion of liquid after a dam break, the prediction of jet breakup (surface tension), and the steady or transient tracking of any liquid-gas interface.The Mixture ModelThe mixture model (described in Section 20.3) is designed for two or more phases (fluid or particulate). As in the Eulerian model, the phases are treated as interpenetrating continua. The mixture model solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases. Applications of the mixture model include particle-laden flows with low loading, bubbly flows, sedimentation , and cyclone separators. The mixture model can also be used without relative velocities for the dispersed phases to model homogeneous multiphase flow.The Eulerian ModelThe Eulerian model (described in Section 20.4) is the most complex of the multiphase models in FLUENT. It solves a set of n momentum and continuity equations for each phase. Coupling is achieved through the pressure and interphase exchange coefficients. The manner in which this coupling is handled depends upon the type of phases involved; granular (fluid-solid) flows are handled differently than non-granular (fluid-fluid) flows. For granular flows , the properties are obtained from application of kinetic theory. Momentum exchange between the phases is also dependent upon the type of mixture being modeled. FLUENT's user-defined functions allow you tocustomize the calculation of the momentum exchange. Applications of the Eulerian multiphase model include bubble columns , risers , particle suspension, and fluidized beds .18.4 Choosing a Multiphase ModelThe first step in solving any multiphase problem is to determine which of the regimes described inSection 18.1 best represents your flow. Section 18.4.1 provides some broad guidelines for determining appropriate models for each regime, and Section 18.4.2 provides details about how to determine the degree of interphase coupling for flows involving bubbles, droplets, or particles, and the appropriate model for different amounts of coupling.18.4.1 General GuidelinesIn general, once you have determined the flow regime that best represents your multiphase system, you can select the appropriate model based on the following guidelines. Additional details and guidelines for selecting the appropriate model for flows involving bubbles, droplets, or particles can be found in Section 18.4.2.For bubbly, droplet, and particle-laden flows in which the dispersed-phase volume fractions are less than or equal to 10%, use the discrete phase model. See Chapter 19 for more information about the discrete phase model.For bubbly, droplet, and particle-laden flows in which the phases mix and/or dispersed-phase volume fractions exceed 10%, use either the mixture model (described in Section 20.3) or the Eulerian model (described in Section 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case.For slug flows, use the VOF model. See Section 20.2 for more information about the VOF model.For stratified/free-surface flows, use the VOF model. See Section 20.2 for more information about the VOF model.For pneumatic transport, use the mixture model for homogeneous flow (described in Section 20.3) or the Eulerian model for granular flow (described in Section 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case.For fluidized beds, use the Eulerian model for granular flow. See Section 20.4 for more information about the Eulerian model.For slurry flows and hydrotransport , use the mixture or Eulerian model (described, respectively, inSections 20.3 and 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case.For sedimentation, use the Eulerian model. See Section 20.4 for more information about the Eulerian model.For general, complex multiphase flows that involve multiple flow regimes, select the aspect of the flow that is of most interest, and choose the model that is most appropriate for that aspect of the flow. Note that the accuracy of results will not be as good as for flows that involve just one flow regime, since the model you use will be valid for only part of the flow you are modeling.18.4.2 Detailed GuidelinesFor stratified and slug flows, the choice of the VOF model, as indicated in Section 18.4.1, is straightforward. Choosing a model for the other types of flows is less straightforward. As a general guide, there are some parameters that help to identify the appropriate multiphase model for these other flows: the particulate loading, , and the Stokes number, St. (Note that the word ``particle'' is used in this discussion to refer to a particle, droplet, or bubble.)The Effect of Particulate LoadingParticulate loading has a major impact on phase interactions. The particulate loading is defined as the mass density ratio of the dispersed phase ( d) to that of the carrier phase ( c):The material density ratiois greater than 1000 for gas-solid flows, about 1 for liquid-solid flows, and less than 0.001 for gas-liquid flows. Using these parameters it is possible to estimate the average distance between the individual particles of the particulate phase. An estimate of this distance has been given by Crowe et al. [ 42]:where . Information about these parameters is important for determining how the dispersed phase shouldbe treated. For example, for a gas-particle flow with aparticulate loading of 1, the interparticle space is about 8; the particle can therefore be treated as isolated (i.e., very low particulate loading).Depending on the particulate loading, the degree of interaction between the phases can be divided into three categories:For very low loading, the coupling between the phases is one-way; i.e., the fluid carrier influences the particles via drag and turbulence, but the particles have no influence on the fluid carrier. The discrete phase, mixture, and Eulerian models can all handle this type of problem correctly. Since the Eulerian model is the most expensive, the discrete phase or mixture model is recommended.For intermediate loading, the coupling is two-way; i.e., the fluid carrier influences the particulate phase via drag and turbulence, but the particles in turn influence the carrier fluid via reduction in mean momentum and turbulence. The discrete phase, mixture, and Eulerian models are all applicable in this case, but you need to take into account other factors in order to decide which model is more appropriate. See below for information about using the Stokes number as a guide.For high loading, there is two-way coupling plus particle pressure and viscous stresses due to particles (four-way coupling). Only the Eulerian model will handle this type of problem correctly.The Significance of the Stokes NumberFor systems with intermediate particulate loading, estimating the value of the Stokes number can help you select the most appropriate model. The Stokes number can be defined as the relation between the particle response time and the system response time:where and t s is based on the characteristic length ( L s) and the characteristic velocity ( V s) of thesystem under investigation: .For , the particle will follow the flow closely and any of the three models (discrete phase, mixture, or Eulerian) is applicable; you can therefore choose the least expensive (the mixture model, in most cases), or themost appropriate considering other factors. For , the particles will move independently of the flowand either the discrete phase model or the Eulerian model is applicable. For , again any of the three models is applicable; you can choose the least expensive or the most appropriate considering other factors. ExamplesFor a coal classifier with a characteristic length of 1 m and a characteristic velocity of 10 m/s, the Stokes number is 0.04 for particles with a diameter of 30 microns, but 4.0 for particles with a diameter of 300 microns. Clearly the mixture model will not be applicable to the latter case.For the case of mineral processing, in a system with a characteristic length of 0.2 m and a characteristic velocity of 2 m/s, the Stokes number is 0.005 for particles with a diameter of 300 microns. In this case, you can choose between the mixture and Eulerian models. (The volume fractions are too high for the discrete phase model, as noted below.)Other ConsiderationsKeep in mind that the use of the discrete phase model is limited to low volume fractions. Also, the discrete phase model is the only multiphase model that allows you to specify the particle distribution or include combustion modeling in your simulation.。

欧洲最新流体力学课件第四章

欧洲最新流体力学课件第四章

In vector form, the acceleration can be written as
dV V a x, y , z , t V . V dt t


First term is on and is nonzero only for unsteady flows. Second term is called the advective (or convective) acceleration and accounts for the effect of the fluid particle moving to a new location in the flow, where the velocity is different (it can thus be nonzero even for steady flows).
Meccanica dei Fluidi I
11
Chapter 4: Fluid Kinematics
Streamlines and streamtubes
A streamtube consists of a bundle of individual streamlines. Since fluid cannot cross a streamline (by definition), fluid within a streamtube must remain there. Streamtubes are, obviously, instantaneous quantities and they may change significantly with time. In the converging portion of an incompressible flow field, the diameter of the streamtube must decrease as the velocity increases, so as to conserve mass.
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CHAPTER 26: FLUID & ELECTROLYTE OUTLINE G. LEWIS Be sure to read the chapter carefully. Read the objectives listed below, chapter summary, and do the questions at the end of the chapter. You may wish to use this outline, the website, and the CD IP tutorial to prepare for lecture and tests. Check and review your notes daily. The outline may not follow the lecture/text exactly.Objectives:1.List the factors that determine body water content and describe the effect of each.2.Indicate the relative fluid volume and solute composition of the fluid compartments of thebody.3.Contrast the overall osmotic effects of electrolytes and non-electrolytes.4.Identify some factors that determine fluid shifts in the body.5.Explain how water enters and leaves the body.6.Describe the feedback mechanisms that regulate water intake and hormonal controls of wateroutput in urine.7.Explain the importance of obligatory water loss.8.Describe possible causes and consequence of dehydration, hypotonic hydration, and edema.9.Describe how electrolytes are lost from the body.10.Explain the importance of sodium electrolyte balance and note its relationship tocardiovascular function.11.Describe the mechanisms involved in regulating sodium and water balance.12.Describe how potassium, calcium, and other electrolyte balance of plasma is regulated.13.List important sources of acids in the body. the 3 major chemical buffer systems of the body and describe how they operate toresist pH changes.15.Explain the influence of the respiratory system on acid-base balance.16.Explain how the kidneys regulate hydrogen and bicarbonate ion concentrations in the blood.17.Distinguish between acidosis and alkalosis resulting from respiratory and metabolic factors.18.Describe the importance of respiratory and renal compensations to acid-base balance.19.Discuss reasons for infants and elderly being at risk for fluid and electrolyte imbalances.FLUID, ELECTROLYTE, AND ACID-BASE BALANCEI.Body FluidsA.Body Water Content1.Total body water is a function of –a.Due to their low body fat –b.The body water content of men is about –2.Body water declines throughout life –B.Fluid Compartments –1.Intracellular Fluid -2.Extracellular Fluids -a.Plasma -b.Interstitial fluid -position of Fluids1.Solutesa.Electrolytes -b.Non-electrolytes -c.Electrolytes have greater osmotic –parison of extracellular and intracellular fluids (cations/anions)- see chartD.Movement of fluids between compartments1.Anything that changes solute –2.Hydrostatic pressure forces –3.Movement of water between the interstitial fluid and –4.Ion fluxes between the interstitial and –II.Water BalanceA.For the body to remain properly hydrated -1.Most water enters the body –2. Water output is due to -B.Regulation of water Intake1.The thirst mechanism is –2.Thirst is quenched as the –C.Regulation of Water Output1.Drinking is –2.Beyond obligatory –D.Influence of ADH1.The amount of water reabsorbed –a.When ADH levels are low –b. When ADH levels are high -3.Role of the hypothalamus –E.Disorders of Water Balance1.Dehydration -2.Hypotonic Hydration -3.Edema -III.Electrolyte BalanceA.Central Role of Sodium in Fluid and Electrolyte Balance1.Sodium is the most –2.Since all body fluids are in –B.Regulation of Sodium Balance1.Influence of Aldosterone -2.Renin-Angiotensin mechanism –3.Cardiovascular System Baroreceptors -4.Estrogens -5.Influence and Regulation of Atrial Natriuretic Factor6.Influence of other hormones (glucocorticoids)C.Regulation of Potassium Balance1.Potassium is critical to the maintenance of –2.Regulatory site – cortical collecting duct -3.Influence of plasma potassium -4.Aldosterone levels -D.Regulation of Calcium and Phosphate Balance1.Parathyroid Hormonea.Bones -b.Small intestine -c.Kidneys -2.Influence of Calcitonin –E.Regulation of other anions -IV.Acid-Base BalanceA.Abundance of hydrogen ions -1.Alkalosis -2.Acidosis -B.Chemical Buffer Systems1. A buffer system is –2.Bicarbonate Buffer System –a.When a strong acid is added –b.When a strong base is added –c.Bicarbonate concentration of –3.Phosphate Buffer System -4.Protein Buffer System -C.Respiratory System Regulation of Hydrogen Ion Concentration1.Carbon dioxide from –2.When Hypercapnia –3. When blood pH rises -D.Renal Mechanisms of Acid-Base Balance1.Only the kidneys can rid the body –a.Bicarbonate ions can be conserved from filtrate – (reabsorption)b. Type A intercalated cells, excrete H+, generate new bicarbonate Ionsc. Ammonium ions are weak acids –d.Bicarbonate ion secretion when the body is in alkalosis –E.Abnormalities of Acid-Base Balance1.Respiratory Acidosis -2.Respiratory Alkalosis -3.Metabolic Acidosis -4.Metabolic Alkalosis -5.Effects of Acidosis or Alkalosis -6.Respiratory and Renal Compensation -V.Developmental and Aging Aspects of Fluid, Electrolyte, & Acid-Base BalanceA.Early DevelopmentB. Childhood -C. Aging。

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