Instrumentation Measurements and Experiments in Fluids

E. Rathakrishnan

Instrumentation, Measurements, and Experiments in Fluids

(^)CRC CRC Press \V*

J

Taylor &F rancis Group Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an i n f o r m a business

Contents Preface About the Book About the Author 1

2

Need and Objective of Experimental Study 1.1 Introduction 1.2 Some Fluid Mechanics Measurements 1.2.1 Wind Tunnel Studies 1.2.2 Analogue Methods 1.2.3 Flow Visualization 1.3 Measurement Systems 1.3.1 Sensing Element 1.3.2 Signal Converter 1.3.3 Display 1.3.3.1 Performance Terms 1.4 Some of the Important Quantities Associated with Fluid Flow Measurements 1.5 Summary Fundamentals of Fluid Mechanics 2.1 Introduction 2.2 Properties of Fluids 2.2.1 Pressure 2.2.2 Temperature 2.2.3 Density 2.2.4 Viscosity 2.2.5 Absolute Coefficient of Viscosity 2.2.6 Kinematic Viscosity Coefficient 2.2.7 Thermal Conductivity of Air 2.2.8 Compressibility 2.3 Thermodynamic Properties 2.3.1 Specific Heat 2.3.2 The Ratio of Specific Heats 2.4 Surface Tension 2.5 Analysis of Fluid Flow

xix xxiii xxv 1 1 1 2 2 2 3 3 3 3 4 5 6 9 9 9 10 11 11 12 12 15 15 16 16 17 17 18 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 2.6 Basic and Subsidiary Laws for Continuous Media 23 2.6.1 Systems and Control Volumes 23 2.6.2 Integral and Differential Analysis 23 2.6.3 State Equation 24 2.7 Kinematics of Fluid Flow 24 2.7.1 Boundary Layer Thickness 27 2.7.2 Displacement Thickness 27 2.7.3 Transition Point 29 2.7.4 Separation Point 29 2.7.5 Rotational and Irrotational Motion 29 2.8 Streamlines 30 2.8.1 Relationship Between Stream Function and Velocity Potential 31 2.9 Potential Flow 31 2.9.1 Two-Dimensional Source and Sink 33 2.9.2 Simple Vortex 34 2.9.3 Source-Sink Pair 35 2.10 Viscous Flows 36 2.10.1 Drag of Bodies 38 2.10.1.1 Pressure Drag 38 2.10.1.2 Skin Friction Drag 40 2.10.1.3 Comparison of Drag of Various Bodies 41 2.10.2 Turbulence 42 2.10.3 Flow Through Pipes 49 2.11 Gas Dynamics 53 2.11.1 Perfect Gas 53 2.11.2 Velocity of Sound 54 2.11.3 Mach Number 55 2.11.4 Flow with Area Change 55 2.11.4.1 Isentropic Relations 55 2.11.4.2 Area-Mach Number Relation 56 2.11.4.3 Prandtl-Meyer Function 56 2.11.5 Normal Shock Relations 57 2.11.6 Oblique Shock Relations 58 2.11.7 Flow with Friction 59 2.11.7.1 Working Formulae for Fanno-Type Flow 59 2.11.8 Flow with Simple To-Change 61 2.11.8.1 Working Formulae for Rayleigh-Type Flow . . . 61 2.12 Summary 62

3

Wind Tunnels 3.1 Introduction 3.1.1 Low-Speed Wind Tunnels 3.1.2 High-Speed Wind Tunnels 3.1.2.1 General Features 3.1.2.2 The Effuser 3.1.2.3 Test-Section 3.1.2.4 Diffuser 3.1.2.5 Driving Unit 3.1.3 Special-Purpose Tunnels 3.2 Low-Speed Wind Tunnels 3.2.1 Effuser 3.2.2 Test-Section 3.2.3 Diffuser 3.2.4 Driving Unit 3.3 Power Losses in a Wind Tunnel 3.3.1 Calculation of Percentage Energy Loss in the Various Parts of Wind Tunnel 3.3.1.1 Energy Ratio 3.3.1.2 Losses in Cylindrical Section 3.3.1.3 Losses in Convergent Cone 3.3.1.4 Losses in Diffuser 3.3.1.5 Honeycombs 3.3.1.6 Guide Vanes 3.3.1.7 Losses Due to Open-Jet Test-Section 3.3.1.8 Screens (Wire Gauze) 3.4 High-Speed Wind Tunnels 3.4.1 Blowdown-Type Wind Tunnels 3.4.1.1 Advantages 3.4.1.2 Disadvantages 3.4.2 Induction-Type Tunnels 3.4.2.1 Advantages 3.4.2.2 Disadvantages 3.4.3 Continuous Supersonic Wind Tunnels 3.4.4 Losses in Supersonic Tunnels 3.4.5 Supersonic Wind Tunnel Diffusers 3.4.5.1 Polytropic Efficiency 3.4.5.2 Isentropic Efficiency 3.4.6 Effects of Second Throat 3.4.7 Compressor Tunnel Matching 3.4.7.1 Basic Formulae for Supersonic Wind Tunnel Calculations 3.4.8 The Mass Flow 3.4.9 Blowdown Tunnel Operation 3.4.9.1 Reynolds Number Control 3.4.10 Optimum Conditions

73 73 73 74 75 75 75 75 75 76 76 76 76 77 77 77 77 78 79 80 81 83 84 85 86 90 91 91 92 92 92 93 93 95 96 97 97 98 101 104 105 109 111 113

3.5 3.6

3.7

3.8

3.9

3.4.11 Running Time of Blowdown Wind Tunnels Hypersonic Tunnels 3.5.1 Hypersonic Nozzle Instrumentation and Calibration of Wind Tunnels 3.6.1 Low-Speed Wind Tunnels 3.6.2 Speed Setting 3.6.3 Flow Direction 3.6.3.1 Yaw Sphere 3.6.3.2 Claw Yaw Meter 3.6.4 Turbulence 3.6.4.1 Turbulence Sphere 3.6.4.2 Pressure Sphere 3.6.4.3 Limitations of Turbulence Sphere 3.6.5 Hot-Wire Anemometer 3.6.6 Rakes 3.6.7 Surging Wind Tunnel Balance 3.7.1 Wire Balances 3.7.2 Strut-Type Balances 3.7.3 Platform-Type Balance 3.7.4 Yoke-Type Balance 3.7.5 Pyramid-Type Balance 3.7.6 Strain-Gauge Balance 3.7.6.1 Strain-Gauge Operation Theory 3.7.6.2 Basic Equations of Strain-Gauge Transducer 3.7.6.3 Strain-Gauge Signal-Measuring Devices 3.7.6.4 Balancing Bridge 3.7.7 Balance Calibration 3.7.8 Wind Tunnel Boundary Correction Calibration of Supersonic Wind Tunnels 3.8.1 Calibration 3.8.2 Mach Number Determination 3.8.3 Pitot Pressure Measurement 3.8.4 Static Pressure Measurement 3.8.5 Determination of Flow Angularity 3.8.6 Determination of Turbulence Level 3.8.7 Determination of Test-Section Noise 3.8.8 The Use of Calibration Results 3.8.9 Starting of Supersonic Tunnels 3.8.10 Starting Loads 3.8.11 Reynolds Number Effects 3.8.12 Model Mounting-Sting Effects Calibration and Use of Hypersonic Tunnels 3.9.1 Calibration of Hypersonic Tunnels 3.9.2 Mach Number Determination

114 116 119 119 120 120 121 122 123 124 124 126 128 128 129 129 130 131 132 133 134 135 135 136 139 139 140 140 141 142 144 144 145 145 146 146 147 147 148 148 149 149 149 150 150

3.9.3 3.9.4

Determination of Flow Angularity Determination of Turbulence Level 3.9.4.1 Blockage Tests 3.9.4.2 Starting Loads 3.9.5 Reynolds Number Effects 3.9.6 Force Measurements 3.10 Flow Visualization 3.11 Hypervelocity Facilities 3.11.1 Hotshot Tunnels 3.11.2 Plasma Are Tunnels 3.11.3 Shock Tubes 3.11.4 Shock Tunnels 3.11.5 Gun Tunnels 3.12 Ludwieg Tube 3.12.1 Operating Principle of Ludwieg Tube (Koppenwallner, 2000) 3.12.2 Some Specific Advantages and Disadvantages of Ludwieg Tube 3.12.2.1 Advantages of Ludwieg Tube Tunnel Compared to Standard Blowdown Tunnels 3.12.2.2 Disadvantages of Ludwieg Tube Tunnel 3.12.3 Hypersonic Simulation Requirements 3.12.3.1 Mach-Reynolds Simulation for Compressibility and Viscous Effects 3.12.3.2 Simulation of Real Gas Effects 3.12.3.3 Industrial Tunnels 3.12.3.4 Research Tunnels 3.12.4 Pressure Measuring System 3.13 Summary

153 153 153 153 153 154 155 155 156 157 158 159 160 161

Flow Visualization 4.1 Introduction 4.2 Visualization Techniques 4.2.1 Smoke Tunnel 4.2.1.1 Smoke Production Methods 4.2.1.2 Wood Smoke 4.2.1.3 Kerosene Smoke Generator 4.2.2 Design of Smoke Tunnel 4.2.2.1 Application of Smoke Visualization 4.3 Compressible Flows 4.3.1 Interferometer 4.3.1.1 Formation of Interference Patterns 4.3.1.2 Quantitative Evaluation 4.3.2 Fringe-Displacement Method 4.3.3 Schlieren System

175 175 175 176 177 177 178 180 182 184 185 185 187 189 189

162 164

164 165 165 166 166 167 167 167 167

4.3.4 4.3.5

4.4 5

6

Range and Sensitivity of the Schlieren System Optical Components' Quality Requirements 4.3.5.1 Schlieren Mirrors 4.3.5.2 Light Source 4.3.5.3 Condenser Lens 4.3.5.4 Focusing Lens 4.3.5.5 Knife-Edge 4.3.5.6 Color Schlieren 4.3.5.7 Short Duration Light Source 4.3.6 Sensitivity of the Schlieren Method for Shock and Expansion Studies 4.3.7 Shadowgraph 4.3.8 Comparison of Schlieren and Shadowgraph Methods Summary

193 193 193 194 194 194 194 194 195 197 199 201 201

Hot-Wire Anemometry 5.1 Introduction 5.2 Operating Principle 5.3 Hot-Wire Filaments 5.4 Constant Current Hot-Wire Anemometer CCA 5.4.1 Mean Velocity Measurements 5.4.2 Fluctuating Velocity Measurements 5.4.3 Thermal Inertia of Hot-Wire 5.4.4 RMS Measurements of the Fluctuating Velocities 5.4.5 Measurement of Velocity Components 5.4.6 Measurement of Temperature by Constant Current Method 5.4.7 Measurement of Steady-State Temperature 5.4.8 Measurement of Temperature Fluctuations 5.5 Constant Temperature Hot-Wire Anemometers 5.5.1 Relation Between Flow Velocity and Output Voltage 5.6 Hot-Wire Probes 5.7 Hot-Wire Bridge for Classroom Demonstration 5.7.1 Hot-Wire Bridge Operating Procedure 5.7.2 A Note of Caution 5.8 Effect of Compressibility 5.9 Limitations of Hot-Wire Anemometer 5.10 Summary

203 203 203 204 209 209 210 212 213 214

Analogue Methods 6.1 Introduction 6.2 Hele-Shaw Apparatus 6.2.1 Basic Equations of Hele-Shaw Analogy 6.3 Electrolytic Tank

229 229 229 233 235

215 215 215 216 217 218 220 221 221 222 223 224

6.4

7

Hydraulic Analogy 6.4.1 Theory of the Analogy 6.4.1.1 Shallow Water Flow 6.4.1.2 Gas Flow 6.5 Hydraulic Jumps (Shocks) 6.5.1 General Equations for Attached Oblique Shocks 6.5.2 General Equations for Slant (Oblique) Attached Hydraulic Jumps 6.5.3 Limitation of the Analogy 6.5.3.1 Two-Dimensionality 6.5.3.2 Specific Heats Ratio 6.5.3.3 Velocity of Wave Propagation 6.5.3.4 Vertical Accelerations 6.5.3.5 Viscosity and Heat Conductivity 6.5.3.6 Surface Tension 6.5.3.7 Appropriate Technique for Different Types of Problems 6.5.4 Depth Measurement 6.6 Velocity Measurement 6.7 Experimental Study 6.7.1 Towing Tank 6.7.1.1 Flow Past Shockless Lifting and Nonlifting Airfoils 6.7.2 Streamline Similarity and Transonic Similarity Rule . . . 6.8 Application of the Hydraulic Analogy to Supersonic Airfoils 6.8.1 Aerodynamic Forces on Airfoils 6.8.2 Hydrodynamic Forces on Airfoils 6.8.3 Measurements with a Semi-Wedge Airfoil 6.9 Experimental Study 6.10 Summary

238 239 239 240 243 245

Pressure-Measurement Techniques 7.1 Introduction 7.1.1 Pressure-Measuring Devices 7.1.2 Principle of Manometer 7.2 Barometers 7.2.1 Syphon Barometer 7.2.2 Fortin Barometer 7.2.3 Aneroid Barometer 7.3 Manometers 7.3.1 Inclined Manometer 7.3.2 Micro Manometer 7.3.3 Betz Manometer 7.4 Dial-Type Pressure Gauge

263 263 263 264 264 266 266 268 268 271 273 273 274

245 246 246 246 246 247 248 248 248 249 250 250 251 251 253 255 255 255 255 256 259

7.5

7.6

7.7 7.8

7.9 7.10 7.11 7.12 7.13 7.14

7.15

7.16 7.17

7.18 7.19 8

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 Pitot, Static, and Pitot-Static Tubes 280 7.6.1 Dynamic Head Measurement 281 7.6.1.1 Incompressible Flow 282 Pitot-Static Tube Characteristics 287 7.7.1 Pitot-Static Tube Limitations 291 Factors Influencing Pitot-Static Tube Performance 291 7.8.1 Turbulence Effect 292 7.8.2 Velocity Gradient Effect 292 7.8.3 Viscosity Effects 293 7.8.4 Vibration Effect on Pitot-Static Probe Measurements... 293 7.8.5 Misalignment Effect 295 Pitot Probes 295 Static Probes 296 Pitot-Static Probes 296 Yaw Effect in Compressible Flow 297 Static Pressure Measurement in Compressible Flows 297 Determination of Flow Direction 299 7.14.1 Yaw Sphere 301 7.14.2 Claw Yaw Probe 302 7.14.3 Three-Hole and Five-Hole Yaw Probes 302 7.14.4 Cobra Probe 303 Low-Pressure Measurement 304 7.15.1 The McLeod Gauge 304 7.15.2 Pirani Gauge 306 7.15.3 Knudsen Gauge 308 7.15.4 Ionization Gauge 309 Preston and Stanton Tubes 309 Sound Measurements 310 7.17.1 Introduction 310 7.17.2 Sound and Noise 310 7.17.3 Pure Tone 312 7.17.4 Broadband and White Noise 312 7.17.5 Sound Units 312 7.17.6 Human Hearing Limits 313 7.17.7 Impulse Sound 314 Dynamic Pressure Gauges 315 Summary 317

Velocity Measurements 8.1 Introduction 8.2 Velocity and Mach Number from Pressure Measurements 8.3 Laser Doppler Anemometer

323 323 323 325

8.4 8.5 8.6 8.7

9

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 Measurement of Velocity by Hot-Wire Anemometer 329 Measurement of Velocity Using Vortex-Shedding Technique... 329 Fluid-Tet Anemometer 331 Summary 332

Temperature Measurement 9.1 Introduction 9.2 Temperature Scales 9.2.1 The International Practical Temperature Scale 9.3 Temperature Measurement 9.3.1 Fluid Thermometers 9.3.1.1 Mercury-in-Glass Thermometer 9.3.2 Beckmann Thermometer 9.3.3 Gas Thermometer 9.3.4 Temperature Gauges Using Fluids 9.4 Temperature Measurement by Thermal Expansion 9.4.1 Bimetallic Thermometers 9.5 Temperature Measurements by Electrical Effects 9.5.1 Thermocouples 9.5.2 Measurement of Thermocouple Voltage 9.5.2.1 External Reference Junction 9.5.2.2 Software Compensation 9.5.2.3 Hardware Compensation 9.5.2.4 Voltage-to-Temperature Conversion 9.5.2.5 Noise Rejection 9.5.2.6 Tree Switching 9.5.2.7 Analogue Filter 9.5.2.8 Integration 9.5.2.9 Guarding 9.6 Practical Thermocouple Measurements 9.6.1 Poor Junction Connections 9.6.2 Decalibration 9.6.3 Shunt Impedance 9.6.4 Galvanic Action 9.6.5 Thermal Shunting 9.6.6 Wire Calibration 9.6.7 Documentation 9.6.8 Diagnostics 9.6.8.1 Event Record 9.6.8.2 Zone Box Test 9.6.9 Thermocouple Resistance

335 335 335 337 338 338 338 339 340 342 343 343 345 346 346 350 352 352 353 358 359 359 359 359 359 360 360 360 361 361 362 362 362 362 363 364

9.7

The Resistance Temperature Detector 9.7.1 Metal Film RTDs 9.7.1.1 Resistance Measurements 9.7.1.2 Four-Wire Ohms 9.7.2 Measurement Errors with Three-Wire Bridge 9.7.3 Resistance to Temperature Conversion 9.7.3.1 Protection 9.7.3.2 Self-Heating 9.7.3.3 Thermal Shunting 9.7.3.4 Thermal EMF 9.7.4 Thermistors 9.7.4.1 Measurement with Thermistor 9.8 Temperature Measurement with Pyrometers 9.8.1 Optical Pyrometer 9.8.2 Radiation Pyrometer 9.8.3 Infrared Thermography 9.8.4 Fusion Pyrometers 9.8.5 Thermal Paints 9.9 Temperature Measurement in Fluid Flows 9.9.1 Static Temperature Determination 9.9.2 Total Temperature Measurement 9.10 Temperature-Measuring Problems in Fluid Flows 9.10.1 Conduction Error 9.10.2 Radiation Error 9.11 Dynamic Response of Temperature Sensors 9.12 Summary

364 366 366 368 368 369 370 370 370 370 370 372 372 372 373 374 374 375 375 377 377 378 378 380 381 383

Measurement of Wall Shear Stress 10.1 Introduction 10.2 Measurement Methods 10.2.1 Floating Element Method 10.2.2 Momentum Integral Method 10.2.3 Preston Tube 10.2.4 Fence Technique 10.2.5 Heat Transfer Gauge 10.2.6 Law of the Wall 10.3 Summary

389 389 390 390 391 391 393 394 395 396

Mass and Volume Flow Measurements 11.1 Introduction 11.2 Direct Methods 11.2.1 Tanks 11.2.2 Displacement Meters 11.3 Indirect Methods 11.3.1 Variable-Head Meters

399 399 400 400 400 402 402

11.3.2 Some Practical Details of Obstruction Meters 11.3.3 Sonic Nozzle 11.3.4 Pitot Tubes 11.3.5 Rotameters 11.3.6 Drag-Body Meters 11.3.7 Ultrasonic Flow Meters 11.3.8 Vortex-Shedding Flow Meters 11.3.9 Measurement of Gross Mass Flow Rate 11.4 Volume Flow Meter 11.4.1 Direct Mass Flow Meters 11.5 Summary

407 412 413 414 415 416 418 419 420 422 423

Special Flows 12.1 Introduction 12.2 Geophysical Flows 12.2.1 Rotating Tank 12.3 Experiment on Taylor-Proudman Theorem 12.4 Experiment on Ekman Layer 12.5 Experiment on Spin-Up and Spin-Down 12.6 Transition and Reverse Transition 12.6.1 Transition in a Channel Flow — A Visualization 12.6.1.1 Experimental Procedure 12.6.2 Reverse Transition or Relaminarization 12.6.2.1 Experimental Procedure 12.7 Measurement in Boundary Layers 12.7.1 Laminar Boundary Layer on a Fiat Plate 12.7.2 Turbulent Boundary Layer on a Fiat Plate 12.8 Summary

429 429 429 430 430 432 432 433 435 436 436 437 438 438 440 441

Data Acquisition and Processing 13.1 Introduction 13.2 Data Acquisition Principle 13.2.1 Generation of Signal 13.2.2 Signal Conditioning 13.2.3 Multiplexing 13.2.3.1 Multichannel Analogue Multiplexed System 13.2.3.2 Simultaneously Sampled Multiplexer System 13.2.3.3 Multichannel Digital Multiplexer System... 13.2.3.4 Low-Level Multiplexing System 13.3 Data Conversion 13.3.1 Data Storage and Display 13.3.1.1 Data Processing 13.3.2 Digital Interfacing

445 445 445 446 446 447 448 448 448 449 450 451 452 452

14

13.4 Personal Computer Hardware 13.4.1 Central Processing Unit (CPU) 13.4.1.1 Instruction Register and Decoder 13.4.1.2 Arithmetic Logic Unit (ALU) 13.4.2 Input/Output Units 13.4.2.1 Input/Output Addressing 13.4.2.2 System Buses 13.4.3 Input/Output Servicing 13.5 Data Acquisition Using Personal Computers 13.5.1 The GPIB Interface 13.5.1.1 DT 2805 ADC/DAC Interface 13.6 Digitization Errors Due to A / D Conversion 13.7 Summary

452 453 453 453 454 455 456 458 459 459 464 465 466

Uncertainty Analysis 14.1 Introduction 14.2 Estimation of Measurement Errors 14.3 External Estimate of the Error 14.3.1 Dependence and Independence of Errors 14.3.2 Estimation of External Error 14.4 Internal Estimate of the Error 14.5 Uncertainty Analysis 14.5.1 Uses of Uncertainty Analysis 14.6 Uncertainty Estimation 14.7 General Procedure 14.7.1 Uncertainty in Flow Mach Number 14.8 Uncertainty Calculation 14.9 Summary

471 471 471 472 474 476 476 477 477 478 478 479 481 482

References

485

Index

487