# Turbulence Laboratory

Size: px
Start display at page:

Transcription

1 Objective: CE 319F Elementary Mechanics of Fluids Department of Civil, Architectural and Environmental Engineering The University of Texas at Austin Turbulence Laboratory The objective of this laboratory is to demonstrate the use of Particle Image Velocimeter (PIV) system to measure and study the velocity variations in a boundary layer. Introduction to Turbulent flow: Turbulence is an irregular motion superimposed on the main stream flow of the fluid. The fluctuating motion is quite complex and almost inaccessible to mathematical treatment. It must be noted that the mixing motion is very important for the course of flow and for the equilibrium of forces. When the Reynolds number is increased, internal flows and boundary layers formed on solid bodies undergo a remarkable transition from the laminar to turbulent regime. The effects of turbulence are as if the viscosity were increased by factors of thousands. At large Re, a continuous transfer of energy occurs from the main flow into large eddies. However, energy is dissipated preponderantly by small eddies, and the process occurs in a narrow strip inside the boundary layer, near the wall. Turbulent Boundary layer: The turbulent boundary layer can be broadly classified into three zones of velocity distribution. The zone immediately adjacent to the wall remains relatively smooth, is very thin and obeys Newton s law of viscosity. It is known as the viscous sublayer. From experimental results, the thickness of the viscous sublayer, δ is given by The nondimensional velocity distribution in the viscous sublayer: The viscous sublayer becomes larger along the wall in the direction of the flow as the shear stress decreases in the downstream direction. Beyond this layer, turbulence significantly alters the flow regime. The mixing action of turbulence causes the velocities at a given point in the flow to fluctuate with time. In laminar flow, the longitudinal pressure gradient which maintains the motion is proportional to the first power of the velocity, whereas in turbulent flow it becomes proportional to the square of the mean flow velocity. From Prandtl Mixing length it can be derived that beyond the viscous sublayer a logarithmic velocity distribution exists. 1

2 The logarithmic law is valid for values of ranging from 3 to 5. Beyond 5 no specific expression can be developed and hence this outer region is denoted by a third zone called velocity defect law. The combination of the viscous and logarithmic velocity profile for the range of from to approximately 5 is called law of the wall For a wide range of Reynolds numbers (1 5 <Re<1 7 ), the velocity profile in the turbulent boundary layer on a flat plate is approximated by the power-law equation ( ) The formula applies to about 9% of the boundary layer ( 1). For the inner 1% of the boundary, we need to resort to the equations for the law of the wall. Reynolds Stresses: The theory of stability of flows decomposes the motion into a mean flow and a disturbance superimposed on it. In the resultant motion the velocity components are given by:,, u, v, and w are the instantaneous velocities in the x, y, and z directions respectively,, and are the mean velocities (time averaged) u, v, and w are the velocity fluctuations (deviation of the instantaneous velocities from the mean) and represent turbulence The non steady disturbances or fluctuations in the velocities are a result of the mixing action of turbulence. Measurement of these fluctuating velocity components can be made with the help of PIV system. The fluctuations cause momentum exchange into and from the boundary layer. This has an effect as if shear stresses were applied to the fluid. Hence, in turbulent flow these stresses are known as apparent shear stresses or Reynolds stresses. An equation can be derived for evaluating the Reynolds stresses in the form Where, denotes the product of the fluctuating components averaged over a period of time. The total shear stress in the flow is equal to the sum of the Reynolds stress and the viscous stress: Where, total ynolds Re viscous du u v and dy viscous Re ynolds 2

3 Experiment performed with PIV: An experiment was conducted in the flume test facility at the Fluids & Hydraulics lab of the University of Texas at Austin to observe and measure the development of boundary layer at the flume bottom. A steady flow with the depth of.3 meter was running in the flume. The flow field in area near the boundary was measured by a 2D Particle Image Velocimetry (PIV) system. The PIV system consists of a light source (a Nd:YAG Laser) and a nano sense camera, which takes pictures at the time interval of.333 sec for a set of 1 images in this study. The images were processed through a sequence of analyses viz. adaptive correlation and average filter to get field velocities output. Further analysis of the measurements yields instantaneous and mean velocity profiles, turbulence, etc Fig 1. Schematic diagram of experimenalt setup The distance from the inlet of the flume to the point of measurement is 3.2m. The thickness of the boundary layer at the point of measurement can be calculated as: Mean flow Velocity =.66 m/s Characteristic dimension L= 3.2 m At 2 o C for water, ν = 1-6 m 2 /s 3

4 Z Distance (mm) Z Distance (mm) A comparison of the mean velocity with the instantaneous velocity is shown in Figures 2 and Time Averaged Profile Instantaneous Profile Velocity Profile on Boundary Velocity (m/s) Fig 2. Mean and Instantaneous Velocity (longitudinal) 35 3 Time Averaged Profile Instantaneous Profile Velocity Profile on Boundary Velocity (m/s) Fig 3. Mean and Instantaneous Velocity (transverse) 4

5 Velocity (m/s) It can be clearly seen that both u and v are zero at the flume bottom. The horizontal velocity u increases sharply from zero from the wall and then grows steadily at lower rate with greater distance above the wall. The vertical velocity component seems to be almost negligible. From the PIV measurements, we obtain the velocity gradient at the wall The shear stress at the wall is: Power-law equation Law of the wall PIV Measurements Distance from wall (mm) Fig 4. Velocity profiles by measurements and theoretical prediction The PIV measurement of the longitudinal velocity profile is compared with the theoretical prediction by the power-law and the law of the wall over different distance above wall. The experimental results are in good agreement with the predicted ones. Mean motion and fluctuations: Upon close investigation it appears that the most striking feature of turbulent motion consists in the fact that the velocity and pressure at a fixed point in space do not remain constant with time but perform very irregular fluctuations of high frequency. The fluctuations so observed with the help of PIV have been depicted in Fig 5. 5

6 Velocity (m/s) mm above wall 6.65 mm above wall mm above wall Instantaneous Velocity (U) Oscillation Time (s) Fig 5. Velocity fluctuations at different heights above the wall It can be clearly seen from the figure that the fluctuations are less near the wall (at.12 mm). However, the fluctuations are the most significant for the measurements made at 6.65 mm. Thus, the measurements suggest the presence of a very thin viscous sublayer near the plate and higher fluctuations indicate the presence of turbulence. Turbulence Intensity The degree of disturbance in the flow can be quantitatively evaluated in terms of turbulent intensity of the flow. The turbulence intensity of a stream can be defined in terms of the time averages of the three fluctuating velocity components or each individual ones. But, generally the Turbulence Intensity is expressed in terms of the root-mean-square of fluctuations normalized with mean flow velocity. 6

7 u 2 u Distance from wall (mm) Fig 6. Turbulence Intensity A comparison of the turbulence intensity of the longitudinal components is made between the PIV measurement and the DNS numerical results of Spalart (1 st Ed,Fig 7.33, Pope, S., Turbulent) with the same normalization. A remarkable agreement can be observed between them. It is noted that the maximum value occurs very near to the wall, it is zero at the wall since the fluctuations die out (a) Numerical Result (b) PIV measurements Fig 7. Comparison of Turbulence Intensity between PIV measurements and DNS Data of Spalart

8 Picture of the PIV system being used for measurement of boundary layer at flume bottom. 8

9 Vector Map representing the velocity distribution in the boundary layer. 9

### Principles of Convection

Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

### Fluid Mechanics. Chapter 9 Surface Resistance. Dr. Amer Khalil Ababneh

Fluid Mechanics Chapter 9 Surface Resistance Dr. Amer Khalil Ababneh Wind tunnel used for testing flow over models. Introduction Resistances exerted by surfaces are a result of viscous stresses which create

### DAY 19: Boundary Layer

DAY 19: Boundary Layer flat plate : let us neglect the shape of the leading edge for now flat plate boundary layer: in blue we highlight the region of the flow where velocity is influenced by the presence

### Experiments on the perturbation of a channel flow by a triangular ripple

Experiments on the perturbation of a channel flow by a triangular ripple F. Cúñez *, E. Franklin Faculty of Mechanical Engineering, University of Campinas, Brazil * Correspondent author: fernandodcb@fem.unicamp.br

### Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In

### Problem 4.3. Problem 4.4

Problem 4.3 Problem 4.4 Problem 4.5 Problem 4.6 Problem 4.7 This is forced convection flow over a streamlined body. Viscous (velocity) boundary layer approximations can be made if the Reynolds number Re

### Basic Fluid Mechanics

Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible

### 2.3 The Turbulent Flat Plate Boundary Layer

Canonical Turbulent Flows 19 2.3 The Turbulent Flat Plate Boundary Layer The turbulent flat plate boundary layer (BL) is a particular case of the general class of flows known as boundary layer flows. The

### UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

### 7.6 Example von Kármán s Laminar Boundary Layer Problem

CEE 3310 External Flows (Boundary Layers & Drag, Nov. 11, 2016 157 7.5 Review Non-Circular Pipes Laminar: f = 64/Re DH ± 40% Turbulent: f(re DH, ɛ/d H ) Moody chart for f ± 15% Bernoulli-Based Flow Metering

### Watershed Sciences 6900 FLUVIAL HYDRAULICS & ECOHYDRAULICS

Watershed Sciences 6900 FLUVIAL HYDRAULICS & ECOHYDRAULICS WEEK Four Lecture 6 VELOCITY DISTRIBUTION Joe Wheaton FOR TODAY, YOU SHOULD HAVE READ 1 LET S GET ON WITH IT TODAY S PLAN VELOCITY DISTRIBUTIONS

### Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing.

Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Thus, it is very important to form both a conceptual understanding and a quantitative

### 4.2 Concepts of the Boundary Layer Theory

Advanced Heat by Amir Faghri, Yuwen Zhang, and John R. Howell 4.2 Concepts of the Boundary Layer Theory It is difficult to solve the complete viscous flow fluid around a body unless the geometry is very

### Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity

Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity Tobias Knopp D 23. November 28 Reynolds averaged Navier-Stokes equations Consider the RANS equations with

### MOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow

TRANSPORT PHENOMENA MOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow Introduction to Turbulent Flow 1. Comparisons of laminar and turbulent flows 2. Time-smoothed equations of change for incompressible

### 7. Basics of Turbulent Flow Figure 1.

1 7. Basics of Turbulent Flow Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds

### Turbulence - Theory and Modelling GROUP-STUDIES:

Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 046-0480 Johan Revstedt, tel 046-43 0 Turbulence - Theory and Modelling GROUP-STUDIES: Turbulence

### Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

### Turbulent boundary layer

Turbulent boundary layer 0. Are they so different from laminar flows? 1. Three main effects of a solid wall 2. Statistical description: equations & results 3. Mean velocity field: classical asymptotic

### Transport processes. 7. Semester Chemical Engineering Civil Engineering

Transport processes 7. Semester Chemical Engineering Civil Engineering 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite Control Volume Analysis 4. Differential Analysis of Fluid Flow 5. Viscous

### 6.2 Governing Equations for Natural Convection

6. Governing Equations for Natural Convection 6..1 Generalized Governing Equations The governing equations for natural convection are special cases of the generalized governing equations that were discussed

### Turbulent eddies in the RANS/LES transition region

Turbulent eddies in the RANS/LES transition region Ugo Piomelli Senthil Radhakrishnan Giuseppe De Prisco University of Maryland College Park, MD, USA Research sponsored by the ONR and AFOSR Outline Motivation

Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

### Numerical Methods in Aerodynamics. Turbulence Modeling. Lecture 5: Turbulence modeling

Turbulence Modeling Niels N. Sørensen Professor MSO, Ph.D. Department of Civil Engineering, Alborg University & Wind Energy Department, Risø National Laboratory Technical University of Denmark 1 Outline

### REE Internal Fluid Flow Sheet 2 - Solution Fundamentals of Fluid Mechanics

REE 307 - Internal Fluid Flow Sheet 2 - Solution Fundamentals of Fluid Mechanics 1. Is the following flows physically possible, that is, satisfy the continuity equation? Substitute the expressions for

### BOUNDARY LAYER ANALYSIS WITH NAVIER-STOKES EQUATION IN 2D CHANNEL FLOW

Proceedings of,, BOUNDARY LAYER ANALYSIS WITH NAVIER-STOKES EQUATION IN 2D CHANNEL FLOW Yunho Jang Department of Mechanical and Industrial Engineering University of Massachusetts Amherst, MA 01002 Email:

### External Flow and Boundary Layer Concepts

1 2 Lecture (8) on Fayoum University External Flow and Boundary Layer Concepts By Dr. Emad M. Saad Mechanical Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Mechanical

### Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,

Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =

### Introduction to Turbulence AEEM Why study turbulent flows?

Introduction to Turbulence AEEM 7063-003 Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Peter.disimile@uc.edu Intro to Turbulence: C1A Why 1 Most flows encountered in engineering and

### Chapter 6 An introduction of turbulent boundary layer

Chapter 6 An introduction of turbulent boundary layer T-S Leu May. 23, 2018 Chapter 6: An introduction of turbulent boundary layer Reading assignments: 1. White, F. M., Viscous fluid flow. McGraw-Hill,

### Chapter 8: Flow in Pipes

Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks

### Turbulent Boundary Layers & Turbulence Models. Lecture 09

Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects

### NPTEL Quiz Hydraulics

Introduction NPTEL Quiz Hydraulics 1. An ideal fluid is a. One which obeys Newton s law of viscosity b. Frictionless and incompressible c. Very viscous d. Frictionless and compressible 2. The unit of kinematic

### Chapter 3 NATURAL CONVECTION

Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,

### Unit operations of chemical engineering

1 Unit operations of chemical engineering Fourth year Chemical Engineering Department College of Engineering AL-Qadesyia University Lecturer: 2 3 Syllabus 1) Boundary layer theory 2) Transfer of heat,

### Abstract Particle image velocimetry (PIV)

Computation of Pressure Distribution Using PIV Velocity Data R. Gurka'l), A. Liberzon''), D. Hefet~'~), D. Rubinstein"), U. Shavit(')* 'I) Agricultural Engineering, Technion, Haifa 32000, Israel (anuri@tr.technian.ac.il)

### There are no simple turbulent flows

Turbulence 1 There are no simple turbulent flows Turbulent boundary layer: Instantaneous velocity field (snapshot) Ref: Prof. M. Gad-el-Hak, University of Notre Dame Prediction of turbulent flows standard

### PROPERTIES OF THE FLOW AROUND TWO ROTATING CIRCULAR CYLINDERS IN SIDE-BY-SIDE ARRANGEMENT WITH DIFFERENT ROTATION TYPES

THERMAL SCIENCE, Year, Vol. 8, No. 5, pp. 87-9 87 PROPERTIES OF THE FLOW AROUND TWO ROTATING CIRCULAR CYLINDERS IN SIDE-BY-SIDE ARRANGEMENT WITH DIFFERENT ROTATION TYPES by Cheng-Xu TU, a,b Fu-Bin BAO

### Boundary-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

### Wall turbulence with arbitrary mean velocity profiles

Center for Turbulence Research Annual Research Briefs 7 Wall turbulence with arbitrary mean velocity profiles By J. Jiménez. Motivation The original motivation for this work was an attempt to shorten the

### Introduction to Heat and Mass Transfer. Week 12

Introduction to Heat and Mass Transfer Week 12 Next Topic Convective Heat Transfer» Heat and Mass Transfer Analogy» Evaporative Cooling» Types of Flows Heat and Mass Transfer Analogy Equations governing

### 5. Secondary Current and Spiral Flow

5. Secondary Current and Spiral Flow The curve of constant velocity for rectangular and triangular cross-section obtained by Nikuradse are shown in Figures and 2. In all cases the velocities at the corners

### Turbulence Modeling I!

Outline! Turbulence Modeling I! Grétar Tryggvason! Spring 2010! Why turbulence modeling! Reynolds Averaged Numerical Simulations! Zero and One equation models! Two equations models! Model predictions!

### Chapter 7: Natural Convection

7-1 Introduction 7- The Grashof Number 7-3 Natural Convection over Surfaces 7-4 Natural Convection Inside Enclosures 7-5 Similarity Solution 7-6 Integral Method 7-7 Combined Natural and Forced Convection

### Numerical Heat and Mass Transfer

Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 19 Turbulent Flows Fausto Arpino f.arpino@unicas.it Introduction All the flows encountered in the engineering practice become unstable

### Computation of turbulent natural convection at vertical walls using new wall functions

Computation of turbulent natural convection at vertical alls using ne all functions M. Hölling, H. Herig Institute of Thermo-Fluid Dynamics Hamburg University of Technology Denickestraße 17, 2173 Hamburg,

### ME 144: Heat Transfer Introduction to Convection. J. M. Meyers

ME 144: Heat Transfer Introduction to Convection Introductory Remarks Convection heat transfer differs from diffusion heat transfer in that a bulk fluid motion is present which augments the overall heat

### Chapter 8 Flow in Conduits

57:00 Mechanics of Fluids and Transport Processes Chapter 8 Professor Fred Stern Fall 013 1 Chapter 8 Flow in Conduits Entrance and developed flows Le = f(d, V,, ) i theorem Le/D = f(re) Laminar flow:

### Fundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.

Fundamental Concepts of Convection : Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 6.1 Boundary Layers: Physical Features Velocity Boundary Layer

### y * x * Shumpei HARA

th International Symposium on Turbulence and Shear Flow Phenomena (TSFP), Chicago, USA, July, 7 ANALYSIS OF THE TURBULENT KINETIC ENERGY BUDGET FOR MEANDERING MOTION APPEARING IN A BACKWARD-FACING STEP

### ROLE OF LARGE SCALE MOTIONS IN TURBULENT POISEUILLE AND COUETTE FLOWS

10 th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 ROLE OF LARGE SCALE MOTIONS IN TURBULENT POISEUILLE AND COUETTE FLOWS Myoungkyu Lee Robert D. Moser

### UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow

UNIT II Real fluids The flow of real fluids exhibits viscous effect that is they tend to "stick" to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons

### Transactions on Engineering Sciences vol 9, 1996 WIT Press, ISSN

A study of turbulence characteristics in open channel transitions as a function of Froude and Reynolds numbers using Laser technique M.I.A. El-shewey, S.G. Joshi Department of Civil Engineering, Indian

### 15. Physics of Sediment Transport William Wilcock

15. Physics of Sediment Transport William Wilcock (based in part on lectures by Jeff Parsons) OCEAN/ESS 410 Lecture/Lab Learning Goals Know how sediments are characteried (sie and shape) Know the definitions

### Heat and Mass Transfer Unit-1 Conduction

1. State Fourier s Law of conduction. Heat and Mass Transfer Unit-1 Conduction Part-A The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature

### Convection in Three-Dimensional Separated and Attached Flow

Convection in Three-Dimensional Separated and Attached Flow B. F. Armaly Convection Heat Transfer Laboratory Department of Mechanical and Aerospace Engineering, and Engineering Mechanics University of

### Fluid Mechanics. du dy

FLUID MECHANICS Technical English - I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's

### SECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES

SECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES Yosuke Hasegawa Institute of Industrial Science The University of Tokyo Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan ysk@iis.u-tokyo.ac.jp

### Turbulence Instability

Turbulence Instability 1) All flows become unstable above a certain Reynolds number. 2) At low Reynolds numbers flows are laminar. 3) For high Reynolds numbers flows are turbulent. 4) The transition occurs

### Fluid Mechanics II Viscosity and shear stresses

Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small

### On the influence of bed permeability on flow in the leeside of coarse-grained bedforms

On the influence of bed permeability on flow in the leeside of coarse-grained bedforms G. Blois (1), J. L. Best (1), G. H. Sambrook Smith (2), R. J. Hardy (3) 1 University of Illinois, Urbana-Champaign,

### HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1

HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the

### Manhar Dhanak Florida Atlantic University Graduate Student: Zaqie Reza

REPRESENTING PRESENCE OF SUBSURFACE CURRENT TURBINES IN OCEAN MODELS Manhar Dhanak Florida Atlantic University Graduate Student: Zaqie Reza 1 Momentum Equations 2 Effect of inclusion of Coriolis force

### CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW

CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW 4.1 Introduction Boundary layer concept (Prandtl 1904): Eliminate selected terms in the governing equations Two key questions (1) What are the

### OpenFOAM selected solver

OpenFOAM selected solver Roberto Pieri - SCS Italy 16-18 June 2014 Introduction to Navier-Stokes equations and RANS Turbulence modelling Numeric discretization Navier-Stokes equations Convective term {}}{

### PIV STUDY OF LONGITUDINAL VORTICES IN A TURBULENT BOUNDARY LAYER FLOW

ICAS CONGRESS PIV STUDY OF LONGITUDINAL VORTICES IN A TURBULENT BOUNDARY LAYER FLOW G. M. Di Cicca Department of Aerospace Engineering, Politecnico di Torino C.so Duca degli Abruzzi, 4 - I 19 Torino, ITALY

### Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions

Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,

### Chapter 10 Flow in Conduits

Chapter 10 Flow in Conduits 10.1 Classifying Flow Laminar Flow and Turbulent Flow Laminar flow Unpredictable Turbulent flow Near entrance: undeveloped developing flow In developing flow, the wall shear

### This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.

This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. Title Modified logarithmic law for velocity distribution subjected to upward seepage. Author(s) Cheng, Nian-Sheng;

### 1. Introduction Some Basic Concepts

1. Introduction Some Basic Concepts 1.What is a fluid? A substance that will go on deforming in the presence of a deforming force, however small 2. What Properties Do Fluids Have? Density ( ) Pressure

### centrifugal acceleration, whose magnitude is r cos, is zero at the poles and maximum at the equator. This distribution of the centrifugal acceleration

Lecture 10. Equations of Motion Centripetal Acceleration, Gravitation and Gravity The centripetal acceleration of a body located on the Earth's surface at a distance from the center is the force (per unit

### Chapter 6. Losses due to Fluid Friction

Chapter 6 Losses due to Fluid Friction 1 Objectives To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. To correlate this in terms of the

### The JHU Turbulence Databases (JHTDB)

The JHU Turbulence Databases (JHTDB) TURBULENT CHANNEL FLOW AT Re τ = 5200 DATA SET Data provenance: M. Lee 1 & R. D. Moser 1 Database ingest and Web Services: Z. Wu 2, G. Lemson 2, R. Burns 2, A. Szalay

### Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers

Entropy 6, 8[], 5-3 5 Entropy ISSN 99-43 www.mdpi.org/entropy/ Unsteady Volumetric Entropy Generation Rate in Laminar Boundary Layers E. J. Walsh & D. Hernon Stokes Research Institute, Dept. of Mechanical

### Lecture 3: Fundamentals of Fluid Flow: fluid properties and types; Boundary layer structure; unidirectional flows

GEOL 440 Sedimentology and stratigraphy: processes, environments and deposits Lecture 3: Fundamentals of Fluid Flow: fluid properties and types; Boundary layer structure; unidirectional flows Why study

### A combined application of the integral wall model and the rough wall rescaling-recycling method

AIAA 25-299 A combined application of the integral wall model and the rough wall rescaling-recycling method X.I.A. Yang J. Sadique R. Mittal C. Meneveau Johns Hopkins University, Baltimore, MD, 228, USA

### An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction

1 An-Najah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies

### Chapter 8: Flow in Pipes

8-1 Introduction 8-2 Laminar and Turbulent Flows 8-3 The Entrance Region 8-4 Laminar Flow in Pipes 8-5 Turbulent Flow in Pipes 8-6 Fully Developed Pipe Flow 8-7 Minor Losses 8-8 Piping Networks and Pump

### Laminar Flow. Chapter ZERO PRESSURE GRADIENT

Chapter 2 Laminar Flow 2.1 ZERO PRESSRE GRADIENT Problem 2.1.1 Consider a uniform flow of velocity over a flat plate of length L of a fluid of kinematic viscosity ν. Assume that the fluid is incompressible

UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes

### 6. Laminar and turbulent boundary layers

6. Laminar and turbulent boundary layers John Richard Thome 8 avril 2008 John Richard Thome (LTCM - SGM - EPFL) Heat transfer - Convection 8 avril 2008 1 / 34 6.1 Some introductory ideas Figure 6.1 A boundary

### OE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004

OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie

### AER1310: 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

### Turbulence: Basic Physics and Engineering Modeling

DEPARTMENT OF ENERGETICS Turbulence: Basic Physics and Engineering Modeling Numerical Heat Transfer Pietro Asinari, PhD Spring 2007, TOP UIC Program: The Master of Science Degree of the University of Illinois

### Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers)

Chapter 5 Phenomena of laminar-turbulent boundary layer transition (including free shear layers) T-S Leu May. 3, 2018 Chapter 5: Phenomena of laminar-turbulent boundary layer transition (including free

### Physical Properties of Fluids

Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel

### Transport by convection. Coupling convection-diffusion

Transport by convection. Coupling convection-diffusion 24 mars 2017 1 When can we neglect diffusion? When the Peclet number is not very small we cannot ignore the convection term in the transport equation.

### MECHANISM BEHIND FREE /NATURAL CONVECTION

CONVECTIVE HEAT TRANSFER By: Prof K. M. Joshi, Assi. Professor, MED, SSAS Institute of Technology, Surat. MECHANISM BEHIND FREE /NATURAL CONVECTION The stagnate layer of fluid in immediate vicinity of

### APPLICATION OF THE DEFECT FORMULATION TO THE INCOMPRESSIBLE TURBULENT BOUNDARY LAYER

APPLICATION OF THE DEFECT FORMULATION TO THE INCOMPRESSIBLE TURBULENT BOUNDARY LAYER O. ROUZAUD ONERA OAt1 29 avenue de la Division Leclerc - B.P. 72 92322 CHATILLON Cedex - France AND B. AUPOIX AND J.-PH.

### R09. d water surface. Prove that the depth of pressure is equal to p +.

Code No:A109210105 R09 SET-1 B.Tech II Year - I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal

### Lecture 2 Flow classifications and continuity

Lecture 2 Flow classifications and continuity Dr Tim Gough: t.gough@bradford.ac.uk General information 1 No tutorial week 3 3 rd October 2013 this Thursday. Attempt tutorial based on examples from today

### CFD STUDIES IN THE PREDICTION OF THERMAL STRIPING IN AN LMFBR

CFD STUDIES IN THE PREDICTION OF THERMAL STRIPING IN AN LMFBR K. Velusamy, K. Natesan, P. Selvaraj, P. Chellapandi, S. C. Chetal, T. Sundararajan* and S. Suyambazhahan* Nuclear Engineering Group Indira

### FLOW-NORDITA Spring School on Turbulent Boundary Layers1

Jonathan F. Morrison, Ati Sharma Department of Aeronautics Imperial College, London & Beverley J. McKeon Graduate Aeronautical Laboratories, California Institute Technology FLOW-NORDITA Spring School on

### BOUNDARY LAYER FLOWS HINCHEY

BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER PHENOMENA When a body moves through a viscous fluid, the fluid at its surface moves with it. It does not slip over the surface. When a body moves at high speed,

### Visualization of flow pattern over or around immersed objects in open channel flow.

EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:

### DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT

10 th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017 DNS STUDY OF TURBULENT HEAT TRANSFER IN A SPANWISE ROTATING SQUARE DUCT Bing-Chen Wang Department

### Turbulence Solutions

School of Mechanical, Aerospace & Civil Engineering 3rd Year/MSc Fluids Turbulence Solutions Question 1. Decomposing into mean and fluctuating parts, we write M = M + m and Ũ i = U i + u i a. The transport