# Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows

Size: px
Start display at page:

Transcription

1 Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3.- 1

2 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical species Associated with the release of thermal energy and the increase in temperature is a local decrease in density which in turn affects the momentum balance. Therefore, all these equations are closely coupled to each other. Nevertheless, in deriving these equations we will try to point out under certain assumptions. how they can be simplified and partially uncoupled 3.-2

3 Balance Equations A time-independent control volume V for a balance quality F(t) The scalar product between the surface flux φ f and the normal vector n determines the outflow through the surface A, a source s f the rate of production of F(t) Let us consider a general quality per unit volume f(x, t). Its integral over the finite volume V, with the time-independent boundary A is given by 3.-3

4 The temporal change of F is then due to the following three effects: 1. by the flux φ f across the boundary A. This flux may be due to convection or molecular transport. By integration over the boundary A we obtain the net contribution which is negative, if the normal vector is assumed to direct outwards. 3.-4

5 2. by a local source σ f within the volume. This is an essential production of partial mass by chemical reactions. Integrating the source term over the volume leads to 3. by an external induced source s. Examples are the gravitational force or thermal radiation. Integration of s f over the volume yields 3.-5

6 We therefore have the balance equation Changing the integral over the boundary A into a volume integral using Gauss' theorem and realizing that the balance must be independent of the volume, we obtain the general balance equation in differential form 3.-6

7 Mass Balance Set the partial mass per unit volume ρ i = ρ Y i = f. The partial mass flux across the boundary is ρ i v i = φ f, where v i is called the diffusion velocity. Summation over all components yields the mass flow where v is the mass average velocity. The difference between v i defines the diffusion flux where the sum satisfies 3.-7

8 Setting the chemical source term one obtains the equation for the partial density The summation over i leads to the continuity equation 3.-8

9 Introducing the total derivative of a quantity a combination with the continuity equation yields Then using may also be written 3.-9

10 Momentum Balance Set the momentum per unit volume ρ v = f. The momentum flux is the sum of the convective momentum in flow ρ v v and the stress tensor where I is the unit tensor and τ is the viscous stress tensor. Therefore ρ v v + P = φ f. There is no local source of momentum, but the gravitational force from outside where g denotes the constant of gravity

11 The momentum equation then reads or with for we obtain 3.-11

12 Kinetic Energy Balance The scalar product of the momentum equation with v provides the balance for the kinetic energy where v 2 = v. v

13 Potential Energy Balance The gravitational force may be written as the derivative of the time-independent potential Then with the continuity equation the balance for the potential energy is 3.-13

14 Total and Internal Energy and Enthalpy Balance The first law of thermodynamics states that the total energy must be conserved, such that the local source σ f = 0. We set ρ e = f, where the total energy per unit mass is This defines the internal energy introduced in 3.-14

15 The total energy flux is which defines the total heat flux j q. The externally induced source due to radiation is Then the total energy balance may be used to derive an equation for the internal energy 3.-15

16 Using this may be written with the total derivative With the continuity equation we may substitute to find illustrating the equivalence with the first law introduced in a global thermodynamic balance

17 With the enthalpy h = u + p/ρ the energy balance equation can be formulated for the enthalpy 3.-17

18 Transport Processes In its most general form Newton's law states that the viscous stress tensor is proportional to the symmetric, trace-free part of the velocity gradient Here the suffix sym denotes that only the symmetric part is taken and the second term in the brackets subtracts the trace elements from the tensor. Newton's law thereby defines the dynamic viscosity

19 Similarly Fick's law states that the diffusion flux is proportional to the concentration gradient. Due to thermodiffusion it is also proportional to the temperature gradient. The most general form for multicomponent diffusion is written as For most combustion processes thermodiffusion can safely be neglected. For a binary mixture Fick s law reduces to where is the binary diffusion coefficient

20 For multicomponent mixtures, where one component occurs in large amounts, as for the combustion in air where nitrogen is abundant, all other species may be treated as trace species and with the binary diffusion coefficient with respect to the abundant component may be used as an approximation A generalization for an effective diffusion coefficient D i to be used for the minor species is 3.-20

21 Note that the use of does not satisfy the condition Finally, Fourier's law of thermal conductivity states that the heat flux should be proportional to the negative temperature gradient. The heat flux j q includes the effect of partial enthalpy transport by diffusion and is written which defines the thermal conductivity λ

22 In Fourier s law the Dufour heat flux has been neglected. Transport coefficients for single components can be calculated on the basis of the theory of rarefied gases

23 Different forms of the energy equation We start from the enthalpy equation and neglect in the following the viscous dissipation term and the radiative heat transfer term. Then, differentiating yields where c p is the heat capacity at constant pressure of the mixture

24 We can write the heat flux as If the diffusion flux can be approximated by with an effective diffusion coefficient D i, we introduce the Lewis number and write the last term as This term vanishes if the Lewis numbers of all species can be assumed equal to unity

25 This is an interesting approximation because it leads to the following form of the enthalpy If the p= const as it is approximately the case in all applications except in reciprocating engines, the enthalpy equation would be very much simplified. The assumption Le=1 for all species is not justified in many combustion applications. In fact, deviations from that assumption lead to a number of interesting phenomena that have been studied recently in the context of flame stability and the response of flames to external disturbances. We will address these questions in some of the lectures below

26 Another important form of the energy equation is that in terms of the temperature. With and the total derivative of the enthalpy can be written as 3.-26

27 Then with the enthalpy equation without the second last term yields the temperature equation Here the last term describes the temperature change due to chemical reactions

28 It may be written as where the definition has been used for each reaction. The second term on the right hand side may be neglected, if one assumes that all specific heats c pi are equal. This assumption is very often justified since this term does not contribute as much to the change of temperature as the other terms in the equation, in particular the chemical source term

29 If one also assumes that spatial gradients of c p may be neglected for the same reason, the temperature equation takes the form For a constant pressure it is very similar to the equation for the mass fraction Y i with an equal diffusion coefficient D=λ/ρ/c p for all reactive species and a spatially constant Lewis number may be written as 3.-29

30 Lewis numbers of some reacting species occurring in methane-air flames For Le i =1 the species transport equation and the temperature equation are easily combined to obtain the enthalpy equation. Since the use of and does not require the Le=1 assumption, this formulation is often used when nonunity Lewis number effects are to be analyzed

31 For flame calculations a sufficiently accurate approximation for the transport properties is [Smooke] a constant Prandtl number and constant Lewis numbers

32 A first approximation for other hydrocarbon species can be based on the assumption that the binary diffusion coefficients of species i with respect to nitrogen is approximately proportional to Then the ratio of its Lewis number to that of methane is 3.-32

33 Balance Equations for Element Mass Fractions Summation of the balance equations for the mass fractions according to leads to the balance equations for Z j : Here the summation over the chemical source terms vanishes since the last sum vanishes for each reaction

34 The diffusion term simplifies if one assumes that the diffusion coefficients of all species are equal. If one further more assumes Le i =1 this leads to 3.-34

35 A similar equation may be derived for the mixture fraction Z. Since Z is defined according to as the mass fraction of the fuel stream, it represents the sum of element mass fractions contained in the fuel stream. The mass fraction of the fuel is the sum of the element mass fractions where 3.-35

36 With the mixture fraction may therefore be expressed as a sum of element mass fractions Then, with the assumption of Le i =1, a summation over leads to a balance equation for the mixture fraction 3.-36

37 For a one-step reaction with the reaction rate ω this equation can also be derived using and for Y F and Y O 2 with Le F = L O2 = 1 as 3.-37

38 Dividing the first of these by ν W O and subtracting yields a source-free balance 2 O2 equation for the combination which is a linear function of Z according to This leads again to 3.-38

39 For constant pressure the enthalpy equation has the same form as and a coupling relation between the enthalpy and the mixture fraction may be derived where h 1 is the enthalpy of the fuel stream and h 2 that of the oxidizer stream

40 Similarly, using and the element mass fractions may be expressed in terms of the mixture fraction where Z j,1 and Z j,2 are the element mass fractions in the fuel and oxidizer stream

41 It should be noted that the coupling relations and required a two feed system with equivalent boundary conditions for the enthalpy and the mass fractions

42 A practical example is a single jet as fuel stream with co-flowing air as oxidizer stream into an open atmosphere, such that zero gradient boundary conditions apply everywhere except at the input streams. Once the mixture fraction field has been obtained by numerical solution of the adiabatic flame temperature may be calculated using the methods of lecture 2 as a local function of Z

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### Basic Equations, Boundary Conditions and Dimensionless Parameters

Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

### Heat Transfer From A Heated Vertical Plate

Heat Transfer From A Heated Vertical Plate Mechanical and Environmental Engineering Laboratory Department of Mechanical and Aerospace Engineering University of California at San Diego La Jolla, California

### CBE 6333, R. Levicky 1 Differential Balance Equations

CBE 6333, R. Levicky 1 Differential Balance Equations We have previously derived integral balances for mass, momentum, and energy for a control volume. The control volume was assumed to be some large object,

### CONSERVATION LAWS. See Figures 2 and 1.

CONSERVATION LAWS 1. Multivariable calculus 1.1. Divergence theorem (of Gauss). This states that the volume integral in of the divergence of the vector-valued function F is equal to the total flux of F

### Differential Balance Equations (DBE)

Differential Balance Equations (DBE) Differential Balance Equations Differential balances, although more complex to solve, can yield a tremendous wealth of information about ChE processes. General balance

### Express Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology

Express Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology Dimitrios Sofialidis Technical Manager, SimTec Ltd. Mechanical Engineer, PhD PRACE Autumn School 2013 - Industry

### 4. Introduction to Heat & Mass Transfer

4. Introduction to Heat & Mass Transfer This section will cover the following concepts: A rudimentary introduction to mass transfer. Mass transfer from a molecular point of view. Fundamental similarity

### High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

### 1 The basic equations of fluid dynamics

1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which

### ME6130 An introduction to CFD 1-1

ME6130 An introduction to CFD 1-1 What is CFD? Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically

### State of Stress at Point

State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,

### Lecture 24 - Surface tension, viscous flow, thermodynamics

Lecture 24 - Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms

### Contents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1

Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors

### Energy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)

Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact

### ACETYLENE AIR DIFFUSION FLAME COMPUTATIONS; COMPARISON OF STATE RELATIONS VERSUS FINITE RATE KINETICS

ACETYLENE AIR DIFFUSION FLAME COMPUTATIONS; COMPARISON OF STATE RELATIONS VERSUS FINITE RATE KINETICS by Z Zhang and OA Ezekoye Department of Mechanical Engineering The University of Texas at Austin Austin,

### - momentum conservation equation ρ = ρf. These are equivalent to four scalar equations with four unknowns: - pressure p - velocity components

J. Szantyr Lecture No. 14 The closed system of equations of the fluid mechanics The above presented equations form the closed system of the fluid mechanics equations, which may be employed for description

### Scalars, Vectors and Tensors

Scalars, Vectors and Tensors A scalar is a physical quantity that it represented by a dimensional number at a particular point in space and time. Examples are hydrostatic pressure and temperature. A vector

### 6 J - vector electric current density (A/m2 )

Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J - vector electric current density (A/m2 ) M - vector magnetic current density (V/m 2 ) Some problems

### Dynamic Process Modeling. Process Dynamics and Control

Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits

### When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

### Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary

### Heat Transfer and Energy

What is Heat? Heat Transfer and Energy Heat is Energy in Transit. Recall the First law from Thermodynamics. U = Q - W What did we mean by all the terms? What is U? What is Q? What is W? What is Heat Transfer?

### 240EQ014 - Transportation Science

Coordinating unit: 240 - ETSEIB - Barcelona School of Industrial Engineering Teaching unit: 713 - EQ - Department of Chemical Engineering Academic year: Degree: 2015 MASTER'S DEGREE IN CHEMICAL ENGINEERING

### 1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

### CE 204 FLUID MECHANICS

CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Fax: +90-216-677-1486 E-mail:

### FLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions

FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or

### The derivation of the balance equations

Chapter 3 The derivation of the balance equations In this chapter we present the derivation of the balance equations for an arbitrary physical quantity which starts from the Liouville equation. We follow,

### SILICON PROCESS- NEW HOOD DESIGN FOR TAPPING GAS COLLECTION

SILICON PROCESS- NEW HOOD DESIGN FOR TAPPING GAS COLLECTION M. Kadkhodabeigi 1, H. Tveit and K. H. Berget 3 1 Department of Materials Science and Engineering, Norwegian University of Science and Technology

### Electromagnetism - Lecture 2. Electric Fields

Electromagnetism - Lecture 2 Electric Fields Review of Vector Calculus Differential form of Gauss s Law Poisson s and Laplace s Equations Solutions of Poisson s Equation Methods of Calculating Electric

### Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

### Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics

Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.

### Physics of the Atmosphere I

Physics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uni-heidelberg.de heidelberg.de Last week The conservation of mass implies the continuity equation:

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

### Electrostatic Fields: Coulomb s Law & the Electric Field Intensity

Electrostatic Fields: Coulomb s Law & the Electric Field Intensity EE 141 Lecture Notes Topic 1 Professor K. E. Oughstun School of Engineering College of Engineering & Mathematical Sciences University

### Customer Training Material. Lecture 2. Introduction to. Methodology ANSYS FLUENT. ANSYS, Inc. Proprietary 2010 ANSYS, Inc. All rights reserved.

Lecture 2 Introduction to CFD Methodology Introduction to ANSYS FLUENT L2-1 What is CFD? Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions,

### CFD Application on Food Industry; Energy Saving on the Bread Oven

Middle-East Journal of Scientific Research 13 (8): 1095-1100, 2013 ISSN 1990-9233 IDOSI Publications, 2013 DOI: 10.5829/idosi.mejsr.2013.13.8.548 CFD Application on Food Industry; Energy Saving on the

### Introduction to CFD Analysis

Introduction to CFD Analysis 2-1 What is CFD? Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically

### Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

### Elasticity Theory Basics

G22.3033-002: Topics in Computer Graphics: Lecture #7 Geometric Modeling New York University Elasticity Theory Basics Lecture #7: 20 October 2003 Lecturer: Denis Zorin Scribe: Adrian Secord, Yotam Gingold

### = 800 kg/m 3 (note that old units cancel out) 4.184 J 1000 g = 4184 J/kg o C

Units and Dimensions Basic properties such as length, mass, time and temperature that can be measured are called dimensions. Any quantity that can be measured has a value and a unit associated with it.

### This paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00

Imperial College London BSc/MSci EXAMINATION June 2008 This paper is also taken for the relevant Examination for the Associateship SUN, STARS, PLANETS For Second Year Physics Students Wednesday, 4th June

### CHEMICAL ENGINEERING AND CHEMICAL PROCESS TECHNOLOGY - Vol. I - Interphase Mass Transfer - A. Burghardt

INTERPHASE MASS TRANSFER A. Burghardt Institute of Chemical Engineering, Polish Academy of Sciences, Poland Keywords: Turbulent flow, turbulent mass flux, eddy viscosity, eddy diffusivity, Prandtl mixing

### A subgrid-scale model for the scalar dissipation rate in nonpremixed combustion

Center for Turbulence Research Proceedings of the Summer Program 1998 11 A subgrid-scale model for the scalar dissipation rate in nonpremixed combustion By A. W. Cook 1 AND W. K. Bushe A subgrid-scale

### Viscous flow in pipe

Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum - Navier-Stokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................

### Chapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations

Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.

### Governing Equations of Fluid Dynamics

Chapter 2 Governing Equations of Fluid Dynamics J.D. Anderson, Jr. 2.1 Introduction The cornerstone of computational fluid dynamics is the fundamental governing equations of fluid dynamics the continuity,

### Computational Fluid Dynamics (CFD) and Multiphase Flow Modelling. Associate Professor Britt M. Halvorsen (Dr. Ing) Amaranath S.

Computational Fluid Dynamics (CFD) and Multiphase Flow Modelling Associate Professor Britt M. Halvorsen (Dr. Ing) Amaranath S. Kumara (PhD Student), PO. Box 203, N-3901, N Porsgrunn, Norway What is CFD?

### FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

### HEAT TRANSFER IM0245 3 LECTURE HOURS PER WEEK THERMODYNAMICS - IM0237 2014_1

COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE HEAT TRANSFER IM05 LECTURE HOURS PER WEEK 8 HOURS CLASSROOM ON 6 WEEKS, HOURS LABORATORY, HOURS OF INDEPENDENT WORK THERMODYNAMICS

### Gauss Formulation of the gravitational forces

Chapter 1 Gauss Formulation of the gravitational forces 1.1 ome theoretical background We have seen in class the Newton s formulation of the gravitational law. Often it is interesting to describe a conservative

### Sound. References: L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol. 2, Gas Dynamics, Chapter 8

References: Sound L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol., Gas Dynamics, Chapter 8 1 Speed of sound The phenomenon of sound waves is one that

### Compressible Fluids. Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004

94 c 2004 Faith A. Morrison, all rights reserved. Compressible Fluids Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004 Chemical engineering

### Heterogeneous Catalysis and Catalytic Processes Prof. K. K. Pant Department of Chemical Engineering Indian Institute of Technology, Delhi

Heterogeneous Catalysis and Catalytic Processes Prof. K. K. Pant Department of Chemical Engineering Indian Institute of Technology, Delhi Module - 03 Lecture 10 Good morning. In my last lecture, I was

### Swissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to:

I. OBJECTIVE OF THE EXPERIMENT. Swissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to: 1) Viscosity of gas (cf. "Viscosity of gas" experiment)

### Open channel flow Basic principle

Open channel flow Basic principle INTRODUCTION Flow in rivers, irrigation canals, drainage ditches and aqueducts are some examples for open channel flow. These flows occur with a free surface and the pressure

### Boiler efficiency measurement. Department of Energy Engineering

Boiler efficiency measurement Department of Energy Engineering Contents Heat balance on boilers Efficiency determination Loss categories Fluegas condensation principals Seasonal efficiency Emission evaluation

### Science Standard Articulated by Grade Level Strand 5: Physical Science

Concept 1: Properties of Objects and Materials Classify objects and materials by their observable properties. Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 PO 1. Identify the following observable properties

### k 2f, k 2r C 2 H 5 + H C 2 H 6

hemical Engineering HE 33 F pplied Reaction Kinetics Fall 04 Problem Set 4 Solution Problem. The following elementary steps are proposed for a gas phase reaction: Elementary Steps Rate constants H H f,

### Interactive simulation of an ash cloud of the volcano Grímsvötn

Interactive simulation of an ash cloud of the volcano Grímsvötn 1 MATHEMATICAL BACKGROUND Simulating flows in the atmosphere, being part of CFD, is on of the research areas considered in the working group

### The Navier Stokes Equations

1 The Navier Stokes Equations Remark 1.1. Basic principles and variables. The basic equations of fluid dynamics are called Navier Stokes equations. In the case of an isothermal flow, a flow at constant

### STOICHIOMETRY OF COMBUSTION

STOICHIOMETRY OF COMBUSTION FUNDAMENTALS: moles and kilomoles Atomic unit mass: 1/12 126 C ~ 1.66 10-27 kg Atoms and molecules mass is defined in atomic unit mass: which is defined in relation to the 1/12

### LES SIMULATION OF A DEVOLATILIZATION EXPERIMENT ON THE IPFR FACILITY

LES SIMULATION OF A DEVOLATILIZATION EXPERIMENT ON THE IPFR FACILITY F. Donato*, G. Rossi**, B. Favini**, E. Giacomazzi*, D. Cecere* F.R. Picchia*, N.M.S. Arcidiacono filippo.donato@enea.it * ENEA-UTTEI/COMSO

### Mechanics 1: Conservation of Energy and Momentum

Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation

### NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

### The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM

1 The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM tools. The approach to this simulation is different

### Chapter 28 Fluid Dynamics

Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example

### Graduate Certificate Program in Energy Conversion & Transport Offered by the Department of Mechanical and Aerospace Engineering

Graduate Certificate Program in Energy Conversion & Transport Offered by the Department of Mechanical and Aerospace Engineering Intended Audience: Main Campus Students Distance (online students) Both Purpose:

### Distinguished Professor George Washington University. Graw Hill

Mechanics of Fluids Fourth Edition Irving H. Shames Distinguished Professor George Washington University Graw Hill Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok

### Chapter 8 Maxwell relations and measurable properties

Chapter 8 Maxwell relations and measurable properties 8.1 Maxwell relations Other thermodynamic potentials emerging from Legendre transforms allow us to switch independent variables and give rise to alternate

### CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

### Heating & Cooling in Molecular Clouds

Lecture 8: Cloud Stability Heating & Cooling in Molecular Clouds Balance of heating and cooling processes helps to set the temperature in the gas. This then sets the minimum internal pressure in a core

### TFAWS AUGUST 2003 VULCAN CFD CODE OVERVIEW / DEMO. Jeffery A. White. Hypersonic Airbreathing Propulsion Branch

TFAWS AUGUST 2003 VULCAN CFD CODE OVERVIEW / DEMO Jeffery A. White Hypersonic Airbreathing Propulsion Branch VULCAN DEVELOPMENT HISTORY Evolved from the LARCK code development project (1993-1996). LARCK

### The content is based on the National Science Teachers Association (NSTA) standards and is aligned with state standards.

Literacy Advantage Physical Science Physical Science Literacy Advantage offers a tightly focused curriculum designed to address fundamental concepts such as the nature and structure of matter, the characteristics

### Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

### The soot and scale problems

Dr. Albrecht Kaupp Page 1 The soot and scale problems Issue Soot and scale do not only increase energy consumption but are as well a major cause of tube failure. Learning Objectives Understanding the implications

### 11 Navier-Stokes equations and turbulence

11 Navier-Stokes equations and turbulence So far, we have considered ideal gas dynamics governed by the Euler equations, where internal friction in the gas is assumed to be absent. Real fluids have internal

### Vacuum Technology. Kinetic Theory of Gas. Dr. Philip D. Rack

Kinetic Theory of Gas Assistant Professor Department of Materials Science and Engineering University of Tennessee 603 Dougherty Engineering Building Knoxville, TN 3793-00 Phone: (865) 974-5344 Fax (865)

### PERFORMANCE EVALUATION OF A MICRO GAS TURBINE BASED ON AUTOMOTIVE TURBOCHARGER FUELLED WITH LPG

PERFORMANCE EVALUATION OF A MICRO GAS TURBINE BASED ON AUTOMOTIVE TURBOCHARGER FUELLED WITH LPG Guenther Carlos Krieger Filho, guenther@usp.br José Rigoni Junior Rafael Cavalcanti de Souza, rafael.cavalcanti.souza@gmail.com

### Lecture 8 - Turbulence. Applied Computational Fluid Dynamics

Lecture 8 - Turbulence Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Turbulence What is turbulence? Effect of turbulence

### Part IV. Conclusions

Part IV Conclusions 189 Chapter 9 Conclusions and Future Work CFD studies of premixed laminar and turbulent combustion dynamics have been conducted. These studies were aimed at explaining physical phenomena

### Exergy: the quality of energy N. Woudstra

Exergy: the quality of energy N. Woudstra Introduction Characteristic for our society is a massive consumption of goods and energy. Continuation of this way of life in the long term is only possible if

### Basic Principles in Microfluidics

Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces

### DIFFUSION IN SOLIDS. Materials often heat treated to improve properties. Atomic diffusion occurs during heat treatment

DIFFUSION IN SOLIDS WHY STUDY DIFFUSION? Materials often heat treated to improve properties Atomic diffusion occurs during heat treatment Depending on situation higher or lower diffusion rates desired

### Ravi Kumar Singh*, K. B. Sahu**, Thakur Debasis Mishra***

Ravi Kumar Singh, K. B. Sahu, Thakur Debasis Mishra / International Journal of Engineering Research and Applications (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue 3, May-Jun 3, pp.766-77 Analysis of

### C H A P T E R 3 FUELS AND COMBUSTION

85 C H A P T E R 3 FUELS AND COMBUSTION 3.1 Introduction to Combustion Combustion Basics The last chapter set forth the basics of the Rankine cycle and the principles of operation of steam cycles of modern

### Natural Convection. Buoyancy force

Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

### Heat and Mass Transfer in. Anisotropic Porous Media

Adv. Theor. Appl. Mech., Vol. 5, 2012, no. 1, 11-22 Heat and Mass Transfer in Anisotropic Porous Media Safia Safi Climatic Engineering Department. Faculty of engineering University Mentouri Constantine

### Distance Learning Program

Distance Learning Program Leading To Master of Engineering or Master of Science In Mechanical Engineering Typical Course Presentation Format Program Description Clarkson University currently offers a Distance

### Perfect Fluidity in Cold Atomic Gases?

Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables τ

### HEAT AND MASS TRANSFER

MEL242 HEAT AND MASS TRANSFER Prabal Talukdar Associate Professor Department of Mechanical Engineering g IIT Delhi prabal@mech.iitd.ac.in MECH/IITD Course Coordinator: Dr. Prabal Talukdar Room No: III,

### Probability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur

Probability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #15 Special Distributions-VI Today, I am going to introduce

### Model of a flow in intersecting microchannels. Denis Semyonov

Model of a flow in intersecting microchannels Denis Semyonov LUT 2012 Content Objectives Motivation Model implementation Simulation Results Conclusion Objectives A flow and a reaction model is required

### Transport Phenomena. The Art of Balancing. Harry Van den Akker Robert F. Mudde. Delft Academic Press

Transport Phenomena The Art of Balancing Harry Van den Akker Robert F. Mudde Delft Academic Press Delft Academic Press First edition 2014 Published by Delft Academic Press /VSSD Leeghwaterstraat, 2628

### An Introduction to Partial Differential Equations

An Introduction to Partial Differential Equations Andrew J. Bernoff LECTURE 2 Cooling of a Hot Bar: The Diffusion Equation 2.1. Outline of Lecture An Introduction to Heat Flow Derivation of the Diffusion

### Indiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.

.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations

### 4 Microscopic dynamics

4 Microscopic dynamics In this section we will look at the first model that people came up with when they started to model polymers from the microscopic level. It s called the Oldroyd B model. We will