Compressible Flow Modeling Occurring in a Depressurization Process
|
|
- Linette Bradley
- 5 years ago
- Views:
Transcription
1 Compressible Flow Modeling Occurring in a Depressurization Process Frédéric Viry 1, Vincent Bruyere 1, Thomas Paris 2, Patrick Namy 1 1 SIMTEC, 8 rue Duployé, Grenoble, 38100, France, vincent.bruyere@simtecsolution.fr 2 CEA DAM, Valduc, Is-sur-Tille, 21120, France
2 SIMTEC SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2
3 SIMTEC French company (founded in 2006) 4 Ph. D. Engineers SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2
4 SIMTEC French company (founded in 2006) 4 Ph. D. Engineers Experts in Modeling COMSOL Certified Consultants CFD Structural mechanics Electromagnetism Heat transfer Chemical engineering SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2
5 SIMTEC French company (founded in 2006) 4 Ph. D. Engineers Experts in Modeling COMSOL Certified Consultants CFD Structural mechanics Electromagnetism Heat transfer Chemical engineering Services Numerical modeling Custom-made training sessions Modeling assistance SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2
6 SIMTEC French company (founded in 2006) 4 Ph. D. Engineers Experts in Modeling COMSOL Certified Consultants CFD Structural mechanics Electromagnetism Heat transfer Chemical engineering Services Numerical modeling Custom-made training sessions Modeling assistance SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2
7 Problem Statement SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3
8 Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3
9 Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3
10 Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3
11 Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3
12 Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) Model the flow to: Study the sensitivity to the dimensions of the system; Understand the behavior of the gas flow, the time to reach the equilibrium; Coupling with others physics: e.g. chemistry, etc SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3
13 The Flow Study and its Issues SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4
14 The Flow Study and its Issues Navier-Stokes Equations (Mass and momentum balances) Energy balance Precise description of the movement! Constitutive law SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4
15 The Flow Study and its Issues Navier-Stokes Equations (Mass and momentum balances) Energy balance Precise description of the movement! Constitutive law Turbulent flow : difficult to capture numerically SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4
16 The Flow Study and its Issues Navier-Stokes Equations (Mass and momentum balances) Energy balance Precise description of the movement! Constitutive law Turbulent flow : difficult to capture numerically Shockwaves appearing at the sound speed : it breaks the continuity hypothesis! SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4
17 Overview 5
18 Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou,
19 Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou,
20 Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou, 1995 Tanks as points 5
21 Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou, 1995 Tanks as points Pipe modeled by a segment No turbulences to handle 5
22 Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou, 1995 Tanks as points Pipe modeled by a segment Location of the discontinuity given by a theoretical development No turbulences to handle Possibility to introduce the discontinuity 5
23 Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou, 1995 Tanks as points Pipe modeled by a segment Location of the discontinuity given by a theoretical development No turbulences to handle Possibility to introduce the discontinuity How to model the gas flow, the tanks and the discontinuity within COMSOL? 5
24 Gas Flow Within the Pipe 6
25 Gas Flow Within the Pipe Mass balance Mass variation 6
26 Gas Flow Within the Pipe Mass balance Mass variation Momentum balance Mass acceleration Friction forces (w/ viscosity) Pressure drop 6
27 Gas Flow Within the Pipe Mass balance Mass variation Momentum balance Mass acceleration Friction forces (w/ viscosity) Pressure drop Energy balance Internal energy variation Heat transfer by diffusion Friction forces work Pressure work 6
28 Gas Flow Within the Pipe Mass balance Mass variation Momentum balance Mass acceleration Friction forces (w/ viscosity) Pressure drop Energy balance Internal energy variation Heat transfer by diffusion Friction forces work Pressure work Constitutive law (ideal gas assumption) 6
29 Gas Flow Within the Pipe Mass balance Mass variation Momentum balance Mass acceleration Friction forces (w/ viscosity) Pressure drop Energy balance Internal energy variation Heat transfer by diffusion Friction forces work Pressure work Constitutive law (ideal gas assumption) ODE and PDE interfaces or Pipe Flow Module interfaces 6
30 Tanks as Points 7
31 Tanks as Points Exterior Tank in 0D Junction with the pipe 7
32 Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe 7
33 Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Mass variation Mass flow at the junction 7
34 Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Energy balance Mass variation Mass flow at the junction Internal energy variation Heat transfer by convection Transfer of Heat exchanges with kinetic energy the exterior 7
35 Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Energy balance Mass variation Mass flow at the junction Internal energy variation Constitutive law (ideal gas assumption) Heat transfer by convection Transfer of Heat exchanges with kinetic energy the exterior 7
36 Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Energy balance Mass variation Mass flow at the junction Internal energy variation Constitutive law (ideal gas assumption) Heat transfer by convection Transfer of Heat exchanges with kinetic energy the exterior ODE interface 7
37 Handle the Discontinuity 8
38 Handle the Discontinuity Subsonic 8
39 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic 8
40 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic 8
41 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down 8
42 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down 8
43 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down Conditions modified because of numerical issues 8
44 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down Conditions modified because of numerical issues 8
45 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down Conditions modified because of numerical issues 8
46 Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down Conditions modified because of numerical issues Events interface 8
47 Numerical Aspects 9
48 Numerical Aspects Space Discretization 9
49 Numerical Aspects Space Discretization Study of sensivity to the mesh At least homogeneous 1000 nodes Avoid numerical loss of mass during the discharge 9
50 Numerical Aspects Space Discretization Time Discretization Study of sensivity to the mesh At least homogeneous 1000 nodes Avoid numerical loss of mass during the discharge 9
51 Numerical Aspects Space Discretization Time Discretization Study of sensivity to the mesh Speed of sound reached very quickly At least homogeneous 1000 nodes Small timestep at the beginning of the simulation (about 10-7 s) Avoid numerical loss of mass during the discharge 9
52 Numerical Aspects Space Discretization Time Discretization Study of sensivity to the mesh Speed of sound reached very quickly At least homogeneous 1000 nodes Avoid numerical loss of mass during the discharge Small timestep at the beginning of the simulation (about 10-7 s) Gas less agitated after that: COMSOL chooses well its timestep automatically 9
53 Theoretical Validation SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10
54 Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10
55 Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10
56 Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10
57 Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10
58 Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 The model respects the physics laws! SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10
59 First Comparisons with Experiments SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
60 First Comparisons with Experiments SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
61 First Comparisons with Experiments The model does not reach the real equilibrium state SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
62 First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct Some of the experimental results are not accurate enough The model does not reach the real equilibrium state A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
63 First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct Some of the experimental results are not accurate enough The model does not reach the real equilibrium state A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
64 First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct Some of the experimental results are not accurate enough The model does not reach the real equilibrium state A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
65 First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct Some of the experimental results are not accurate enough The model does not reach the real equilibrium state A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
66 First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct The model does not reach the real equilibrium state Some of the experimental results are not accurate enough Measurements of temperature A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11
67 Simulation vs. (Corrected) Experimental SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12
68 Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12
69 Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12
70 Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12
71 Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium The results of the model fits to the experiments in pressure! SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12
72 Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium The results of the model fits to the experiments in pressure! Use of the model to detect experimental flaws SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12
73 Conclusions 13
74 Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it 13
75 Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it Validation of the model using theoretical and experimental results 13
76 Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it Validation of the model using theoretical and experimental results Some weaknesses on the thermal exchanges Inherent to the 0D simplification 13
77 Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it Validation of the model using theoretical and experimental results Some weaknesses on the thermal exchanges Inherent to the 0D simplification The degree of accuracy is satisfaying 13
Introduction 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 informationIntroduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald
Introduction to Fluid Mechanics Chapter 13 Compressible Flow Main Topics Basic Equations for One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas Area Variation Flow in a Constant Area Duct
More informationDESIGN & COMPUTATIONAL FLUID DYNAMICS ANALYSES OF AN AXISYMMETRIC NOZZLE AT TRANSONIC FREE STREAM CONDITIONS
DESIGN & COMPUTATIONAL FLUID DYNAMICS ANALYSES OF AN AXISYMMETRIC NOZZLE AT TRANSONIC FREE STREAM CONDITIONS S Wasim Akram 1, S. Rajesh 2 1 M.Tech Student, Department of Mechanical Engineering, Krishna
More informationCHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION
CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION 7.1 THE NAVIER-STOKES EQUATIONS Under the assumption of a Newtonian stress-rate-of-strain constitutive equation and a linear, thermally conductive medium,
More informationMass flow determination in flashing openings
Int. Jnl. of Multiphysics Volume 3 Number 4 009 40 Mass flow determination in flashing openings Geanette Polanco Universidad Simón Bolívar Arne Holdø Narvik University College George Munday Coventry University
More informationCFD in COMSOL Multiphysics
CFD in COMSOL Multiphysics Mats Nigam Copyright 2016 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective
More informationDirect Modeling for Computational Fluid Dynamics
Direct Modeling for Computational Fluid Dynamics Kun Xu February 20, 2013 Computational fluid dynamics (CFD) is new emerging scientific discipline, and targets to simulate fluid motion in different scales.
More informationIntroduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303
Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum
More informationModeling of Humidification in Comsol Multiphysics 4.4
Modeling of Humidification in Comsol Multiphysics 4.4 Indrajit Wadgaonkar *1 and Suresh Arikapudi 1 1 Tata Motors Ltd. Pimpri, Pune, India, 411018. *Corresponding author: Indrajit Wadgaonkar, Tata Motors
More informationTransport equation cavitation models in an unstructured flow solver. Kilian Claramunt, Charles Hirsch
Transport equation cavitation models in an unstructured flow solver Kilian Claramunt, Charles Hirsch SHF Conference on hydraulic machines and cavitation / air in water pipes June 5-6, 2013, Grenoble, France
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 informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationMechanical Engineering Science for Medical Engineers Level: 4 Credit value: 8 GLH: 62 TQT: 80
This unit has 6 learning outcomes. 1. Be able to solve engineering problems that involve variable and constant acceleration motion. 1.1. Apply dimensional analysis to an equation involving units of length,
More informationDetailed Outline, M E 320 Fluid Flow, Spring Semester 2015
Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous
More informationEffect of Gas Flow Rate and Gas Composition in Ar/CH 4 Inductively Coupled Plasmas
COMSOL CONFERENCE BOSTON 2011 Effect of Gas Flow Rate and Gas Composition in Ar/CH 4 Inductively Coupled Plasmas Keisoku Engineering System Co., Ltd., JAPAN Dr. Lizhu Tong October 14, 2011 1 Contents 1.
More informationCFD ANALYSIS OF CD NOZZLE AND EFFECT OF NOZZLE PRESSURE RATIO ON PRESSURE AND VELOCITY FOR SUDDENLY EXPANDED FLOWS. Kuala Lumpur, Malaysia
International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN(P): 2249-6890; ISSN(E): 2249-8001 Vol. 8, Issue 3, Jun 2018, 1147-1158 TJPRC Pvt. Ltd. CFD ANALYSIS
More informationReversibility, Irreversibility and Carnot cycle. Irreversible Processes. Reversible Processes. Carnot Cycle
Reversibility, Irreversibility and Carnot cycle The second law of thermodynamics distinguishes between reversible and irreversible processes. If a process can proceed in either direction without violating
More informationAA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS
AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS Hierarchy of Mathematical Models 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 2 / 29
More informationMulti-source Aeroacoustic Noise Prediction Method
Multi-source Aeroacoustic Noise Prediction Method Jonathan SCOTT CFD Engineer 03/12/2013 1 Introduction Trend to reduce engine displacement while increasing break power by turbo charging engines Traditionally
More informationOn the Effect of Variable Opening Geometries, and Operating Conditions on High Pressure Hydrogen Releases: Ignition Risks
On the Effect of Variable Opening Geometries, and Operating Conditions on High Pressure Hydrogen Releases: Ignition Risks Wissam Nakhle A Thesis in the Department of Mechanical and Industrial Engineering
More informationHelium two-phase flow in a thermosiphon open loop
Presented at the COMSOL Conference 2009 Milan COMSOL Conference 2009 Milan October 14-16 2009 Helium two-phase flow in a thermosiphon open loop Florian Visentin, Bertrand Baudouy CEA Saclay Accelerator,
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 Navier-Stokes equations (N-S), which simpler, inviscid, form is the Euler equations. For
More informationBiological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems
Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Arthur T. Johnson, PhD, PE Biological Resources Engineering Department
More informationExercise 7 - Fluiddynamic Systems
Exercise 7 - Fluiddynamic Systems 7.1 Valves The flow of fluids between reservoirs is determined by valves, whose inputs are the pressure up- and downstream, denoted by p in and p out respectively. Here,
More informationFLOWS IN LIQUID FOAMS
FLOWS IN LIQUID FOAMS A finite element approach A. SAUGEY, E. JANIAUD, W. DRENCKHAN, S. HUTZLER, D. WEAIRE Physics Department,, TRINITY COLLEGE DUBLIN Facing a problem of fluid flow in a physical system,
More informationProblem C3.5 Direct Numerical Simulation of the Taylor-Green Vortex at Re = 1600
Problem C3.5 Direct Numerical Simulation of the Taylor-Green Vortex at Re = 6 Overview This problem is aimed at testing the accuracy and the performance of high-order methods on the direct numerical simulation
More information1. INTRODUCTION TO CFD SPRING 2019
1. INTRODUCTION TO CFD SPRING 2019 1.1 What is computational fluid dynamics? 1.2 Basic principles of CFD 1.3 Stages in a CFD simulation 1.4 Fluid-flow equations 1.5 The main discretisation methods Appendices
More informationChapter 1: Basic Concepts
What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms
More informationdynamics of f luids in porous media
dynamics of f luids in porous media Jacob Bear Department of Civil Engineering Technion Israel Institute of Technology, Haifa DOVER PUBLICATIONS, INC. New York Contents Preface xvii CHAPTER 1 Introduction
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 informationAER1310: TURBULENCE MODELLING 1. Introduction to Turbulent Flows C. P. T. Groth c Oxford Dictionary: disturbance, commotion, varying irregularly
1. Introduction to Turbulent Flows Coverage of this section: Definition of Turbulence Features of Turbulent Flows Numerical Modelling Challenges History of Turbulence Modelling 1 1.1 Definition of Turbulence
More informationA Phase Field Approach to Model Laser Power Control in Spot Laser Welding
A Phase Field Approach to Model Laser Power Control in Spot Laser Welding V.Bruyere 1, C. Touvrey 2*, P.Namy 1 1 SIMTEC, 8 rue Duployé, Grenoble, 38100 France 2 CEA DAM, Valduc, 21120 Is sur Tille *Corresponding
More informationFluid Mechanics - Course 123 COMPRESSIBLE FLOW
Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Flow of compressible fluids in a p~pe involves not only change of pressure in the downstream direction but also a change of both density of the fluid and
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 informationThree-dimensional simulation of cavitating flows in piping systems R. Klasinc, R. Reitbauer, H. Knoblauch
Computer Methods in Water Resources XII 559 Three-dimensional simulation of cavitating flows in piping systems R. Klasinc, R. Reitbauer, H. Knoblauch Management E-mail: klasinc@kwb. tu-graz. ac. at Abstract
More informationWilliam В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.
William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory
More informationOutlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer
Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer
More informationScience. Circular Motion. Atomic Structure and Nuclear Chemistry. Kinematics; Motion in One and Two Dimensions
Inquiry -P-1.1 -P-1.2 -P-1.3 -P-1.4 -P-1.5 -P-1.6 -P-1.7 -P-1.8 -P-1.9 -P-2.1 -P-1.1 -P-2.1 -P-2.2 -P-2.3 Circular Motion Use appropriate safety procedures when conducting investigations. Use appropriate
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 informationApplication of COMSOL Multiphysics in Transport Phenomena Educational Processes
Application of COMSOL Multiphysics in Transport Phenomena Educational Processes M. Vasilev, P. Sharma and P. L. Mills * Department of Chemical and Natural Gas Engineering, Texas A&M University-Kingsville,
More informationV/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0
UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational
More informationGroup #4 (Firko, Johnson)
roceedings of MIT Mechanical Engineering.67 Section 3: Thursday M Fall 007, appalardo Laboratory, Building 3 Group 4 (Firko, Johnson) FLUID SLUG CORNER IMACT DUE TO THE SUDDEN INTRODUCTION OF HIGH RESSURE
More informationHervé Guillard, INRIA Projet Smash, B.P. 93, Sophia-Antipolis Cedex, France,
TRAVELING WAVE ANALYSIS OF TWO-PHASE DISSIPATIVE MODELS Hervé Guillard, INRIA Projet Smash, B.P. 93, 06902 Sophia-Antipolis Cedex, France, Herve.Guillard@sophia.inria.fr Joint work with : Mathieu Labois,
More informationEFFECT OF LIQUID PHASE COMPRESSIBILITY ON MODELING OF GAS-LIQUID TWO-PHASE FLOWS USING TWO-FLUID MODEL
EFFECT OF LIQUID PHASE COMPRESSIBILITY ON MODELING OF GAS-LIQUID TWO-PHASE FLOWS USING TWO-FLUID MODEL Vahid SHOKRI 1*,Kazem ESMAEILI 2 1,2 Department of Mechanical Engineering, Sari Branch, Islamic Azad
More informationAPPLIED FLUID DYNAMICS HANDBOOK
APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.-nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /
More informationPhysics Overview. High School Core Science Standards Physics
Overview The standards establish the scientific inquiry skills and core content for all courses in DoDEA schools. The learning framework of this course focuses on the basic concepts of physics in relation
More informationContents. Preface... xvii
Contents Preface... xvii CHAPTER 1 Idealized Flow Machines...1 1.1 Conservation Equations... 1 1.1.1 Conservation of mass... 2 1.1.2 Conservation of momentum... 3 1.1.3 Conservation of energy... 3 1.2
More informationComputational Analysis of an Imploding Gas:
1/ 31 Direct Numerical Simulation of Navier-Stokes Equations Stephen Voelkel University of Notre Dame October 19, 2011 2/ 31 Acknowledges Christopher M. Romick, Ph.D. Student, U. Notre Dame Dr. Joseph
More informationInfluence of high temperature gradient on turbulence spectra
NIA CFD Conference, Hampton, August 6-8, 2012 Future Directions in CFD Research, A Modeling and Simulation Conference Influence of high temperature gradient on turbulence spectra Sylvain Serra Françoise
More informationFluid Mechanics Theory I
Fluid Mechanics Theory I Last Class: 1. Introduction 2. MicroTAS or Lab on a Chip 3. Microfluidics Length Scale 4. Fundamentals 5. Different Aspects of Microfluidcs Today s Contents: 1. Introduction to
More informationFurther Applications of Newton s Laws - Friction Static and Kinetic Friction
urther pplications of Newton s Laws - riction Static and Kinetic riction The normal force is related to friction. When two surfaces slid over one another, they experience a force do to microscopic contact
More informationMicro-scale modelling of internally
Micro-scale modelling of internally unstable soils Dr Tom Shire School of Engineering, University of Glasgow 1 st September 2017 Outline Internal instability Micro-scale modelling Hydromechanical criteria
More informationUnderstanding Transport Phenomena Concepts in Chemical Engineering with COMSOL Multiphysics
Understanding Transport Phenomena Concepts in Chemical Engineering with COMSOL Multiphysics Erick S. Vasquez, Ph.D. Department of Chemical and Materials Engineering, University of Dayton, Dayton, OH, USA
More informationComparison of Fluid Flow and Heat Transfer for 1D and 2D Models of an In-Line Pulse Tube Refrigerator
205 1 Comparison of Fluid Flow and Heat Transfer for 1D and 2D Models of an In-Line Pulse Tube Refrigerator K.W. Martin 1,2, C. Dodson 1, A. Razani 3 1 Spacecraft Component Thermal Research Group Kirtland
More informationModeling and Analysis of Dynamic Systems
Modeling and Analysis of Dynamic Systems Dr. Guillaume Ducard Fall 2017 Institute for Dynamic Systems and Control ETH Zurich, Switzerland G. Ducard c 1 / 34 Outline 1 Lecture 7: Recall on Thermodynamics
More informationA Discussion of Low Reynolds Number Flow for the Two-Dimensional Benchmark Test Case
A Discussion of Low Reynolds Number Flow for the Two-Dimensional Benchmark Test Case M. Weng, P. V. Nielsen and L. Liu Aalborg University Introduction. The use of CFD in ventilation research has arrived
More information.u= 0 ρ( u t +(u. )u)= ρ g p+.[µ( u+ t u)]
THETIS is a numerical simulation tool developed by University of Bordeaux. It is a versatile code to solve different problems: fluid flows, heat transfers, scalar transports or porous mediums. The potential
More informationCalculating equation coefficients
Fluid flow Calculating equation coefficients Construction Conservation Equation Surface Conservation Equation Fluid Conservation Equation needs flow estimation needs radiation and convection estimation
More informationKINETIC BOOKS PHYSICS CORRELATED TO SOUTH CAROLINA PHYSICS STANDARDS CORRELATION
Virtual Standard P-1: The student will demonstrate an understanding of how scientific inquiry and technological design, including mathematical analysis, can be used appropriately to pose questions, seek
More informationThermal Analysis of Fairchild Dornier 728Jet Wing/Fuselage Interface using MSC.Patran Thermal. Paper number D. Konopka, J. Hyer, A.
2001-32 Thermal Analysis of Fairchild Dornier 728Jet Wing/Fuselage Interface using MSC.Patran Thermal Paper number 2001-32 D. Konopka, J. Hyer, A. Schönrock Fairchild Dornier GmbH PO Box 1103 82230 Wessling
More informationBoundary-Layer Theory
Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22
More informationModel Studies on Slag-Metal Entrainment in Gas Stirred Ladles
Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Anand Senguttuvan Supervisor Gordon A Irons 1 Approach to Simulate Slag Metal Entrainment using Computational Fluid Dynamics Introduction &
More information1. INTRODUCTION TO CFD SPRING 2018
1. INTRODUCTION TO CFD SPRING 018 1.1 What is computational fluid dynamics? 1. Basic principles of CFD 1.3 Stages in a CFD simulation 1.4 Fluid-flow equations 1.5 The main discretisation methods Appendices
More informationA drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension
A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension forces. 2 Objectives 3 i i 2 1 INTRODUCTION Property:
More informationENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids
CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific
More informationAssessment of Implicit Implementation of the AUSM + Method and the SST Model for Viscous High Speed Flow
Assessment of Implicit Implementation of the AUSM + Method and the SST Model for Viscous High Speed Flow Simone Colonia, René Steijl and George N. Barakos CFD Laboratory - School of Engineering - University
More informationA Plasma Torch Model
A Plasma Torch Model B. Chinè School of Materials Science and Engineering Costa Rica Institute of Technology, Cartago, Costa Rica bchine@itcr.ac.cr October 18 20, 2017 Presentation overview DC plasma torch
More informationAnalysis of Head Loss in Pipe System Components: Quasi-one-Dimensional Nozzle Flow
Analysis of Head Loss in Pipe System Components: Quasi-one-Dimensional Nozzle Flow Charles Ndambuki Muli School of Education, The Presbyterian University of East Africa, P.O. Box 387-00902, Kikuyu, Kenya.
More informationAn Overview of Impellers, Velocity Profile and Reactor Design
An Overview of s, Velocity Profile and Reactor Design Praveen Patel 1, Pranay Vaidya 1, Gurmeet Singh 2 1 Indian Institute of Technology Bombay, India 1 Indian Oil Corporation Limited, R&D Centre Faridabad
More informationFluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
More informationModule 2 : Convection. Lecture 12 : Derivation of conservation of energy
Module 2 : Convection Lecture 12 : Derivation of conservation of energy Objectives In this class: Start the derivation of conservation of energy. Utilize earlier derived mass and momentum equations for
More informationSimulation of a Thermo-Acoustic Refrigerator
Simulation of a Thermo-Acoustic Refrigerator Sohaib Ahmed 1, Abdul Rehman 1, Ammad Fareed 1, Syed Muhammad Sabih ul Haque 1, Ali Muhammad Hadi 1 1 National University of Sciences and Technology (NUST),
More informationTAU Extensions for High Enthalpy Flows. Sebastian Karl AS-RF
TAU Extensions for High Enthalpy Flows Sebastian Karl AS-RF Contents Motivation Extensions available in the current release: Numerical schemes for super- and hypersonic flow fields Models for gas mixtures,
More informationTheoretical Gas Flow through Gaps in Screw-type Machines
Theoretical Gas Flow through Gaps in Screw-type Machines Prof. Dr.-Ing. K. Kauder, Dipl.-Ing. D. Stratmann University of Dortmund, Fachgebiet Fluidenergiemaschinen (The experimental part of these studies
More informationCHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE
CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE In this chapter, the governing equations for the proposed numerical model with discretisation methods are presented. Spiral
More informationTable of Contents. Preface... xiii
Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...
More informationvector H. If O is the point about which moments are desired, the angular moment about O is given:
The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment
More informationStructure Formation and Particle Mixing in a Shear Flow Boundary Layer
Structure Formation and Particle Mixing in a Shear Flow Boundary Layer Matthew Palotti palotti@astro.wisc.edu University of Wisconsin Center for Magnetic Self Organization Ellen Zweibel University of Wisconsin
More informationComputational Engineering
Coordinating unit: 205 - ESEIAAT - Terrassa School of Industrial, Aerospace and Audiovisual Engineering Teaching unit: 220 - ETSEIAT - Terrassa School of Industrial and Aeronautical Engineering Academic
More informationPlasma Modeling with COMSOL Multiphysics
Plasma Modeling with COMSOL Multiphysics Copyright 2014 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their
More informationAn Introduction to COMSOL Multiphysics v4.3b & Subsurface Flow Simulation. Ahsan Munir, PhD Tom Spirka, PhD
An Introduction to COMSOL Multiphysics v4.3b & Subsurface Flow Simulation Ahsan Munir, PhD Tom Spirka, PhD Agenda Provide an overview of COMSOL 4.3b Our products, solutions and applications Subsurface
More informationPTT 277/3 APPLIED THERMODYNAMICS SEM 1 (2013/2014)
PTT 77/3 APPLIED THERMODYNAMICS SEM 1 (013/014) 1 Energy can exist in numerous forms: Thermal Mechanical Kinetic Potential Electric Magnetic Chemical Nuclear The total energy of a system on a unit mass:
More informationSPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow
SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow 1. Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95.
More informationSimplified Model of WWER-440 Fuel Assembly for ThermoHydraulic Analysis
1 Portál pre odborné publikovanie ISSN 1338-0087 Simplified Model of WWER-440 Fuel Assembly for ThermoHydraulic Analysis Jakubec Jakub Elektrotechnika 13.02.2013 This work deals with thermo-hydraulic processes
More informationDESIGN AND CFD ANALYSIS OF A CENTRIFUGAL PUMP
DESIGN AND CFD ANALYSIS OF A CENTRIFUGAL PUMP 1 CH.YADAGIRI, 2 P.VIJAYANAND 1 Pg Scholar, Department of MECH, Holymary Institute of Technology, Ranga Reddy, Telangana, India. 2 Assistant Professor, Department
More informationFlow Focusing Droplet Generation Using Linear Vibration
Flow Focusing Droplet Generation Using Linear Vibration A. Salari, C. Dalton Department of Electrical & Computer Engineering, University of Calgary, Calgary, AB, Canada Abstract: Flow focusing microchannels
More information2. Conservation Equations for Turbulent Flows
2. Conservation Equations for Turbulent Flows Coverage of this section: Review of Tensor Notation Review of Navier-Stokes Equations for Incompressible and Compressible Flows Reynolds & Favre Averaging
More informationSeveral forms of the equations of motion
Chapter 6 Several forms of the equations of motion 6.1 The Navier-Stokes equations Under the assumption of a Newtonian stress-rate-of-strain constitutive equation and a linear, thermally conductive medium,
More informationComputational Astrophysics
Computational Astrophysics Lecture 1: Introduction to numerical methods Lecture 2:The SPH formulation Lecture 3: Construction of SPH smoothing functions Lecture 4: SPH for general dynamic flow Lecture
More informationS.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100
Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]-113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum
More informationCHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES
Thermodynamics: An Engineering Approach 8th Edition in SI Units Yunus A. Çengel, Michael A. Boles McGraw-Hill, 2015 CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Lecture slides by Dr. Fawzi Elfghi
More information2. FLUID-FLOW EQUATIONS SPRING 2019
2. FLUID-FLOW EQUATIONS SPRING 2019 2.1 Introduction 2.2 Conservative differential equations 2.3 Non-conservative differential equations 2.4 Non-dimensionalisation Summary Examples 2.1 Introduction Fluid
More informationAn Overview of Fluid Animation. Christopher Batty March 11, 2014
An Overview of Fluid Animation Christopher Batty March 11, 2014 What distinguishes fluids? What distinguishes fluids? No preferred shape. Always flows when force is applied. Deforms to fit its container.
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 informationPrediction of CO Burnout using a CHEMKIN based Network Tool
Prediction of CO Burnout using a CHEMKIN based Network Tool Engler-Bunte-Institut / Bereich Verbrennungstechnik Universität Karlsruhe Contents Complex reaction schemes vs. complex transport models. Complex
More informationSoft Bodies. Good approximation for hard ones. approximation breaks when objects break, or deform. Generalization: soft (deformable) bodies
Soft-Body Physics Soft Bodies Realistic objects are not purely rigid. Good approximation for hard ones. approximation breaks when objects break, or deform. Generalization: soft (deformable) bodies Deformed
More information1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature
CHAPTER 11 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature 2.In Equation 11.7 the subscript p on the partial derivative refers to differentiation at
More informationLecture23. Flowmeter Design.
Lecture23 Flowmeter Design. Contents of lecture Design of flowmeter Principles of flow measurement; i) Venturi and ii) Orifice meter and nozzle Relationship between flow rate and pressure drop Relation
More informationFundamentals of Fluid Mechanics
Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department
More informationInvestigation of an implicit solver for the simulation of bubble oscillations using Basilisk
Investigation of an implicit solver for the simulation of bubble oscillations using Basilisk D. Fuster, and S. Popinet Sorbonne Universités, UPMC Univ Paris 6, CNRS, UMR 79 Institut Jean Le Rond d Alembert,
More information