Instrumentation, Measurements, and Experiments in Fluids

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$E. Rathakrishnan Instrumentation, Measurements, and Experiments in Fluids (^)CRC \V* CRC Press J Taylor &F$

1 E. Rathakrishnan Instrumentation, Measurements, and Experiments in Fluids (^)CRC \V* CRC Press J Taylor &F rancis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

Contents Preface About the Book About the Author xix xxiii xxv 1 Need and Objective of Experimental Study 1 1.1 Introduction 1 1.2 Some Fluid Mechanics Measurements 1 1.2.1 Wind Tunnel Studies 2 1.2.2 Analogue Methods 2 1.

2 Contents Preface About the Book About the Author xix xxiii xxv 1 Need and Objective of Experimental Study Introduction Some Fluid Mechanics Measurements Wind Tunnel Studies Analogue Methods Flow Visualization Measurement Systems Sensing Element Signal Converter Display Performance Terms Some of the Important Quantities Associated with Fluid Flow Measurements Summary 6 2 Fundamentals of Fluid Mechanics Introduction Properties of Fluids Pressure Temperature Density Viscosity Absolute Coefficient of Viscosity Kinematic Viscosity Coefficient Thermal Conductivity of Air Compressibility Thermodynamic Properties Specific Heat The Ratio of Specific Heats Surface Tension Analysis of Fluid Flow 19

2.5.1 Relation Between Local and Material Rates of Change 20 2.5.2 Graphical Description of Fluid Motion 21 2.5.2.1 Pathline 22 2.5.2.2 Streakline 22 2.5.2.3 Streamlines 22 2.5.2.4 Timelines 22 2.

3 2.5.1 Relation Between Local and Material Rates of Change Graphical Description of Fluid Motion Pathline Streakline Streamlines Timelines Basic and Subsidiary Laws for Continuous Media Systems and Control Volumes Integral and Differential Analysis State Equation Kinematics of Fluid Flow Boundary Layer Thickness Displacement Thickness Transition Point Separation Point Rotational and Irrotational Motion Streamlines Relationship Between Stream Function and Velocity Potential Potential Flow Two-Dimensional Source and Sink Simple Vortex Source-Sink Pair Viscous Flows Drag of Bodies Pressure Drag Skin Friction Drag Comparison of Drag of Various Bodies Turbulence Flow Through Pipes Gas Dynamics Perfect Gas Velocity of Sound Mach Number Flow with Area Change Isentropic Relations Area-Mach Number Relation Prandtl-Meyer Function Normal Shock Relations Oblique Shock Relations Flow with Friction Working Formulae for Fanno-Type Flow Flow with Simple To-Change Working Formulae for Rayleigh-Type Flow Summary 62

3 Wind Tunnels 73 3.1 Introduction 73 3.1.1 Low-Speed Wind Tunnels 73 3.1.2 High-Speed Wind Tunnels 74 3.1.2.1 General Features 75 3.1.2.2 The Effuser 75 3.1.2.3 Test-Section 75 3.1.2.4 Diffuser 75 3.

4 3 Wind Tunnels Introduction Low-Speed Wind Tunnels High-Speed Wind Tunnels General Features The Effuser Test-Section Diffuser Driving Unit Special-Purpose Tunnels Low-Speed Wind Tunnels Effuser Test-Section Diffuser Driving Unit Power Losses in a Wind Tunnel Calculation of Percentage Energy Loss in the Various Parts of Wind Tunnel Energy Ratio Losses in Cylindrical Section Losses in Convergent Cone Losses in Diffuser Honeycombs Guide Vanes Losses Due to Open-Jet Test-Section Screens (Wire Gauze) High-Speed Wind Tunnels Blowdown-Type Wind Tunnels Advantages Disadvantages Induction-Type Tunnels Advantages Disadvantages Continuous Supersonic Wind Tunnels Losses in Supersonic Tunnels Supersonic Wind Tunnel Diffusers Polytropic Efficiency Isentropic Efficiency Effects of Second Throat Compressor Tunnel Matching Basic Formulae for Supersonic Wind Tunnel Calculations The Mass Flow Blowdown Tunnel Operation Reynolds Number Control Optimum Conditions 113

3.4.11 Running Time of Blowdown Wind Tunnels 114 3.5 Hypersonic Tunnels 116 3.5.1 Hypersonic Nozzle 119 3.6 Instrumentation and Calibration of Wind Tunnels 119 3.6.1 Low-Speed Wind Tunnels 120 3.6.2 Speed Setting 120 3.

5 Running Time of Blowdown Wind Tunnels Hypersonic Tunnels Hypersonic Nozzle Instrumentation and Calibration of Wind Tunnels Low-Speed Wind Tunnels Speed Setting Flow Direction Yaw Sphere Claw Yaw Meter Turbulence Turbulence Sphere Pressure Sphere Limitations of Turbulence Sphere Hot-Wire Anemometer Rakes Surging Wind Tunnel Balance Wire Balances Strut-Type Balances Platform-Type Balance Yoke-Type Balance Pyramid-Type Balance Strain-Gauge Balance Strain-Gauge Operation Theory Basic Equations of Strain-Gauge Transducer Strain-Gauge Signal-Measuring Devices Balancing Bridge Balance Calibration Wind Tunnel Boundary Correction Calibration of Supersonic Wind Tunnels Calibration Mach Number Determination Pitot Pressure Measurement Static Pressure Measurement Determination of Flow Angularity Determination of Turbulence Level Determination of Test-Section Noise The Use of Calibration Results Starting of Supersonic Tunnels Starting Loads Reynolds Number Effects Model Mounting-Sting Effects Calibration and Use of Hypersonic Tunnels Calibration of Hypersonic Tunnels Mach Number Determination 150

3.9.3 Determination of Flow Angularity 153 3.9.4 Determination of Turbulence Level 153 3.9.4.1 Blockage Tests 153 3.9.4.2 Starting Loads 153 3.9.5 Reynolds Number Effects 153 3.9.6 Force Measurements 154 3.

6 3.9.3 Determination of Flow Angularity Determination of Turbulence Level Blockage Tests Starting Loads Reynolds Number Effects Force Measurements Flow Visualization Hypervelocity Facilities Hotshot Tunnels Plasma Are Tunnels Shock Tubes Shock Tunnels Gun Tunnels Ludwieg Tube Operating Principle of Ludwieg Tube (Koppenwallner, 2000) Some Specific Advantages and Disadvantages of Ludwieg Tube Advantages of Ludwieg Tube Tunnel Compared to Standard Blowdown Tunnels Disadvantages of Ludwieg Tube Tunnel Hypersonic Simulation Requirements Mach-Reynolds Simulation for Compressibility and Viscous Effects Simulation of Real Gas Effects Industrial Tunnels Research Tunnels Pressure Measuring System Summary 167 Flow Visualization Introduction Visualization Techniques Smoke Tunnel Smoke Production Methods Wood Smoke Kerosene Smoke Generator Design of Smoke Tunnel Application of Smoke Visualization Compressible Flows Interferometer Formation of Interference Patterns Quantitative Evaluation Fringe-Displacement Method Schlieren System 189

4.3.4 Range and Sensitivity of the Schlieren System 193 4.3.5 Optical Components' Quality Requirements 193 4.3.5.1 Schlieren Mirrors 193 4.3.5.2 Light Source 194 4.3.5.3 Condenser Lens 194 4.3.5.4 Focusing Lens 194 4.

7 4.3.4 Range and Sensitivity of the Schlieren System Optical Components' Quality Requirements Schlieren Mirrors Light Source Condenser Lens Focusing Lens Knife-Edge Color Schlieren Short Duration Light Source Sensitivity of the Schlieren Method for Shock and Expansion Studies Shadowgraph Comparison of Schlieren and Shadowgraph Methods Summary Hot-Wire Anemometry Introduction Operating Principle Hot-Wire Filaments Constant Current Hot-Wire Anemometer CCA Mean Velocity Measurements Fluctuating Velocity Measurements Thermal Inertia of Hot-Wire RMS Measurements of the Fluctuating Velocities Measurement of Velocity Components Measurement of Temperature by Constant Current Method Measurement of Steady-State Temperature Measurement of Temperature Fluctuations Constant Temperature Hot-Wire Anemometers Relation Between Flow Velocity and Output Voltage Hot-Wire Probes Hot-Wire Bridge for Classroom Demonstration Hot-Wire Bridge Operating Procedure A Note of Caution Effect of Compressibility Limitations of Hot-Wire Anemometer Summary Analogue Methods Introduction Hele-Shaw Apparatus Basic Equations of Hele-Shaw Analogy Electrolytic Tank 235

6.4 Hydraulic Analogy 238 6.4.1 Theory of the Analogy 239 6.4.1.1 Shallow Water Flow 239 6.4.1.2 Gas Flow 240 6.5 Hydraulic Jumps (Shocks) 243 6.5.1 General Equations for Attached Oblique Shocks 245 6.

8 6.4 Hydraulic Analogy Theory of the Analogy Shallow Water Flow Gas Flow Hydraulic Jumps (Shocks) General Equations for Attached Oblique Shocks General Equations for Slant (Oblique) Attached Hydraulic Jumps Limitation of the Analogy Two-Dimensionality Specific Heats Ratio Velocity of Wave Propagation Vertical Accelerations Viscosity and Heat Conductivity Surface Tension Appropriate Technique for Different Types of Problems Depth Measurement Velocity Measurement Experimental Study Towing Tank Flow Past Shockless Lifting and Nonlifting Airfoils Streamline Similarity and Transonic Similarity Rule Application of the Hydraulic Analogy to Supersonic Airfoils Aerodynamic Forces on Airfoils Hydrodynamic Forces on Airfoils Measurements with a Semi-Wedge Airfoil Experimental Study Summary Pressure-Measurement Techniques Introduction Pressure-Measuring Devices Principle of Manometer Barometers Syphon Barometer Fortin Barometer Aneroid Barometer Manometers Inclined Manometer Micro Manometer Betz Manometer Dial-Type Pressure Gauge 274

7.5 Pressure Transducers 276 7.5.1 Linear Variable Differential Transformer LVDT 278 7.5.2 Capacitance Pickup 279 7.5.3 Optical-Type Pressure Transducer 279 7.

9 7.5 Pressure Transducers Linear Variable Differential Transformer LVDT Capacitance Pickup Optical-Type Pressure Transducer Pitot, Static, and Pitot-Static Tubes Dynamic Head Measurement Incompressible Flow Pitot-Static Tube Characteristics Pitot-Static Tube Limitations Factors Influencing Pitot-Static Tube Performance Turbulence Effect Velocity Gradient Effect Viscosity Effects Vibration Effect on Pitot-Static Probe Measurements Misalignment Effect Pitot Probes Static Probes Pitot-Static Probes Yaw Effect in Compressible Flow Static Pressure Measurement in Compressible Flows Determination of Flow Direction Yaw Sphere Claw Yaw Probe Three-Hole and Five-Hole Yaw Probes Cobra Probe Low-Pressure Measurement The McLeod Gauge Pirani Gauge Knudsen Gauge Ionization Gauge Preston and Stanton Tubes Sound Measurements Introduction Sound and Noise Pure Tone Broadband and White Noise Sound Units Human Hearing Limits Impulse Sound Dynamic Pressure Gauges Summary Velocity Measurements Introduction Velocity and Mach Number from Pressure Measurements Laser Doppler Anemometer 325

8.3.1 LDA Principle 325 8.3.2 Doppler Shirt Equation 326 8.3.3 Reference Beam System 328 8.3.4 Fringe System 328 8.4 Measurement of Velocity by Hot-Wire Anemometer 329 8.

10 8.3.1 LDA Principle Doppler Shirt Equation Reference Beam System Fringe System Measurement of Velocity by Hot-Wire Anemometer Measurement of Velocity Using Vortex-Shedding Technique Fluid-Tet Anemometer Summary Temperature Measurement Introduction Temperature Scales The International Practical Temperature Scale Temperature Measurement Fluid Thermometers Mercury-in-Glass Thermometer Beckmann Thermometer Gas Thermometer Temperature Gauges Using Fluids Temperature Measurement by Thermal Expansion Bimetallic Thermometers Temperature Measurements by Electrical Effects Thermocouples Measurement of Thermocouple Voltage External Reference Junction Software Compensation Hardware Compensation Voltage-to-Temperature Conversion Noise Rejection Tree Switching Analogue Filter Integration Guarding Practical Thermocouple Measurements Poor Junction Connections Decalibration Shunt Impedance Galvanic Action Thermal Shunting Wire Calibration Documentation Diagnostics Event Record Zone Box Test Thermocouple Resistance 364

9.7 The Resistance Temperature Detector 364 9.7.1 Metal Film RTDs 366 9.7.1.1 Resistance Measurements 366 9.7.1.2 Four-Wire Ohms 368 9.7.2 Measurement Errors with Three-Wire Bridge 368 9.7.3 Resistance to Temperature Conversion 369 9.

11 9.7 The Resistance Temperature Detector Metal Film RTDs Resistance Measurements Four-Wire Ohms Measurement Errors with Three-Wire Bridge Resistance to Temperature Conversion Protection Self-Heating Thermal Shunting Thermal EMF Thermistors Measurement with Thermistor Temperature Measurement with Pyrometers Optical Pyrometer Radiation Pyrometer Infrared Thermography Fusion Pyrometers Thermal Paints Temperature Measurement in Fluid Flows Static Temperature Determination Total Temperature Measurement Temperature-Measuring Problems in Fluid Flows Conduction Error Radiation Error Dynamic Response of Temperature Sensors Summary 383 Measurement of Wall Shear Stress Introduction Measurement Methods Floating Element Method Momentum Integral Method Preston Tube Fence Technique Heat Transfer Gauge Law of the Wall Summary 396 Mass and Volume Flow Measurements Introduction Direct Methods Tanks Displacement Meters Indirect Methods Variable-Head Meters 402

11.3.2 Some Practical Details of Obstruction Meters 407 11.3.3 Sonic Nozzle 412 11.3.4 Pitot Tubes 413 11.3.5 Rotameters 414 11.3.6 Drag-Body Meters 415 11.3.7 Ultrasonic Flow Meters 416 11.3.8 Vortex-Shedding Flow Meters 418 11.

12 Some Practical Details of Obstruction Meters Sonic Nozzle Pitot Tubes Rotameters Drag-Body Meters Ultrasonic Flow Meters Vortex-Shedding Flow Meters Measurement of Gross Mass Flow Rate Volume Flow Meter Direct Mass Flow Meters Summary 423 Special Flows Introduction Geophysical Flows Rotating Tank Experiment on Taylor-Proudman Theorem Experiment on Ekman Layer Experiment on Spin-Up and Spin-Down Transition and Reverse Transition Transition in a Channel Flow A Visualization Experimental Procedure Reverse Transition or Relaminarization Experimental Procedure Measurement in Boundary Layers Laminar Boundary Layer on a Fiat Plate Turbulent Boundary Layer on a Fiat Plate Summary 441 Data Acquisition and Processing Introduction Data Acquisition Principle Generation of Signal Signal Conditioning Multiplexing Multichannel Analogue Multiplexed System Simultaneously Sampled Multiplexer System Multichannel Digital Multiplexer System Low-Level Multiplexing System Data Conversion Data Storage and Display Data Processing Digital Interfacing 452

13.4 Personal Computer Hardware 452 13.4.1 Central Processing Unit (CPU) 453 13.4.1.1 Instruction Register and Decoder 453 13.4.1.2 Arithmetic Logic Unit (ALU) 453 13.4.2 Input/Output Units 454 13.4.2.1 Input/Output Addressing 455 13.

13 13.4 Personal Computer Hardware Central Processing Unit (CPU) Instruction Register and Decoder Arithmetic Logic Unit (ALU) Input/Output Units Input/Output Addressing System Buses Input/Output Servicing Data Acquisition Using Personal Computers The GPIB Interface DT 2805 ADC/DAC Interface Digitization Errors Due to A/D Conversion Summary Uncertainty Analysis Introduction Estimation of Measurement Errors External Estimate of the Error Dependence and Independence of Errors Estimation of External Error Internal Estimate of the Error Uncertainty Analysis Uses of Uncertainty Analysis Uncertainty Estimation General Procedure Uncertainty in Flow Mach Number Uncertainty Calculation Summary 482 Ref erences 485 Index 487

Detailed 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