Chapter 7 Flow Measurement by Yixin Ma 17/04/2013 2/48 Contents I.Introduction ll.Local Flow Velocity,Magnitude and Direction Ill.Gross Volume Flow Rate IV.Gross Mass Flow Rate
Chapter 7 Flow Measurement by Yixin Ma 17/04/2013 Contents I. Introduction II. Local Flow Velocity, Magnitude and Direction III. Gross Volume Flow Rate IV. Gross Mass Flow Rate 2/48
3/48 7.1 Local Flow Velocity,Magnitude and Direction 1.Flow Visualization gives an overall view of flow patterns 2.Velocity Magnitude from Pitot-Static Tube(皮托静压管) 3.Velocity Direction from Yaw Tube(偏航管)，Pivoted Vane(叶轮)and Servoed Sphere 4.Dynamic Wind-Vector(风矢量)Indicator 5.Hot-Vire and Hot-Film Anemometers(风速计) 6.Hot-Film Shock-Tube激波管)Velocity Sensors 7.Laser Doppler Anemometer 4/48 7.1.0 Flow Classifications ◆Classifications: Single-phase flow Two-phase flow Multi-phase flow ◆Flow Patterns: 2. (a)Two-phase Flow Patterns in Vertical Upflow Bubby Slug Churn Wispy-Annular Annular Bubbly Slug (b)Two-phase Flow Patterns in 0 Horizontal Flow Plug Annular 0 Stratified Annular with Mist Flow Figure 7.0 Gas/Liquid Flow Patterns Wave
7.1 Local Flow Velocity, Magnitude and Direction 1. Flow Visualization gives an overall view of flow patterns 2. Velocity Magnitude from Pitot-Static Tube (皮托静压管) 3. Velocity Direction from Yaw Tube (偏航管), Pivoted Vane(叶轮) and Servoed Sphere 4. Dynamic Wind-Vector(风矢量) Indicator 5. Hot-Wire and Hot-Film Anemometers(风速计) 6. Hot-Film Shock-Tube(激波管) Velocity Sensors 7. Laser Doppler Anemometer 3/48 7.1.0 Flow Classifications Classifications: − Single-phase flow − Two-phase flow − Multi-phase flow Flow Patterns: Figure 7.0 Gas/Liquid Flow Patterns (a) Two-phase Flow Patterns in Vertical Upflow (b) Two-phase Flow Patterns in Horizontal Flow 4/48
5/48 7.1.1 Flow Visualization -Methods Way 1:Introduction of tracer particles: ●In Liquid Flows: en Colored Dyes; n Hydrogen()bubbles formed in water by applying electric pulses. ●In Gas Flows: Smoke: Helium(氦气)-filled“soap”bubbles; n Gas molecules made luminous()by an ionizing electric spark. Way 2:Detection of flow related changes in fluid optical properties. ●Qualitative Method-Shadowgraph(阴影图)and Schilieren(纹影仪)methods: light and dark patterns related to flow conditions are produced by the bending of light rays as they pass through a region of varying density. Quantitative Technique: Interferometer:light/dark pattems are formed by interference effects resulting from phase shifts between a reference beam and the measuring beam. Particle Image Velocimetry (PIV):the liquid or gas flow must be seeded with near- neutrally-buoyant particles;the velocity of these particles is what is actually measured. Other Methods:Tomographic Techniques,Molecular Tagging Velocimetry, Holographic Techniques,etc. 6/48 7.1.1 Flow Visualization -Shadowgraph ◆Shadowgraph For compressible flow (Mach Number >0.3),density varies with velocity sufficiently to produce measurable effects; In principle,we cannot directly see a difference in temperature,a different gas, or a shock wave in the transparent air; ●However,,all these disturbances refract(折射)light rays,so they can cast(投射) shadows. Collimated light bea is used as light source. "Edgerton"shadowgram of the firing of an AK-47 assault rifle Images and artwork by Gary S.Settles,Penn State Gas Dynamics Lab
7.1.1 Flow Visualization - Methods Way 1: Introduction of tracer particles: z In Liquid Flows: Colored Dyes; Hydrogen(氢气) bubbles formed in water by applying electric pulses. z In Gas Flows: Smoke; Helium(氦气)-filled “soap” bubbles; Gas molecules made luminous(发光) by an ionizing electric spark. Way 2: Detection of flow related changes in fluid optical properties. z Qualitative Method - Shadowgraph(阴影图) and Schilieren(纹影仪) methods: light and dark patterns related to flow conditions are produced by the bending of light rays as they pass through a region of varying density. z Quantitative Technique: Interferometer: light/dark patterns are formed by interference effects resulting from phase shifts between a reference beam and the measuring beam. Particle Image Velocimetry (PIV): the liquid or gas flow must be seeded with nearneutrally-buoyant particles; the velocity of these particles is what is actually measured. Other Methods: Tomographic Techniques, Molecular Tagging Velocimetry, Holographic Techniques, etc. 5/48 7.1.1 Flow Visualization - Shadowgraph "focused" shadowgram of a common firecracker explosion Sunlight shadowgram of a martini glass A prehistoric shadowgraphy "Edgerton" shadowgram of the firing of an AK-47 assault rifle Images and artwork by Gary S. Settles, Penn State Gas Dynamics Lab Shadowgraph z For compressible flow (Mach Number >0.3), density varies with velocity sufficiently to produce measurable effects; z In principle, we cannot directly see a difference in temperature, a different gas, or a shock wave in the transparent air; z However, all these disturbances refract(折射) light rays, so they can cast (投射) shadows. z Collimated light beam is used as light source. 6/48
7/48 7.1.1 Flow Visualization -Schlieren ◆Schlieren Similar physics bases as shadowgraphy; The collimated light is focused with a lens,and a knife-edge is placed at the focal point,positioned to block about half the light. It Measures the first derivative of density in the direction of the knife-edge; Schlieren imaging of a focusing ultrasonic transducer http://en.wikipedia.org/wiki/Schlieren_photograph 8/48 7.1.1 Flow Visualization -PIV Principle Laser light sheet △y Flow plane At time between two pulses Velocity at A Ax particle displacement in x direction Ux=Ax/ras△f+0 Ay particle displacement in y direction Uy=△y/△t as At+0 Fig.7.1(a)Particle Image Velocimetry. Using multiple-exposure method,the location of particles at two times separated by a known time interval are used to compute the magnitude and direction of the particle's velocity
7.1.1 Flow Visualization - Schlieren Color schlieren image of the thermal plume from a burning candle, disturbed by a breeze from the right. Photographed by Gary S. Settles, Penn State University http://en.wikipedia.org/wiki/Schlieren_photograph Schlieren z Similar physics bases as shadowgraphy; z The collimated light is focused with a lens, and a knife-edge is placed at the focal point, positioned to block about half the light. z It Measures the first derivative of density in the direction of the knife-edge; Shock waves produced by a T-38 Talon during flight Schlieren imaging system setup: linear lens-based configuration Schlieren imaging of a focusing ultrasonic transducer 7/48 7.1.1 Flow Visualization – PIV Principle Fig. 7.1(a) Particle Image Velocimetry. Using multiple-exposure method, the location of particles at two times separated by a known time interval are used to compute the magnitude and direction of the particle’s velocity. 8/48
9/48 7.1.1 Flow Visualization -PIV Principle Universal mount and shutter Laser light Fiber manipulator sheet optics Laser Fiber optic cable Shutter drive unit CCD camera Computer with two monitors Timing box Fig.7.1(b)Particle Image Velocimetry.Using CCD camera to record images A complete system consists of a laser light source with optics,an image recording medium,a programmable time delay and sequence generator,camera interface,computer,and image acquisition/analysis software. 10/48 7.1.1 Flow Visualization -PIV Principle Fig.7.2 PIV Image of Transient Vortex(Structure in a Circular Jet Under good conditions and with proper equipment and technique,the accuracy of PIV technique is adequate for many applications Demonstration webpage:http://www.piv.de/piv/index.php
7.1.1 Flow Visualization – PIV Principle Fig. 7.1(b) Particle Image Velocimetry. Using CCD camera to record images A complete system consists of a laser light source with optics, an image recording medium, a programmable time delay and sequence generator, camera interface, computer, and image acquisition/analysis software. 9/48 7.1.1 Flow Visualization – PIV Principle Fig. 7.2 PIV Image of Transient Vortex (漩涡) Structure in a Circular Jet Under good conditions and with proper equipment and technique, the accuracy of PIV technique is adequate for many applications Demonstration webpage: http://www.piv.de/piv/index.php 10/48
7.l.2 Velocity Magnitude from Pitot-Static Tube(皮托静压管) 11/48 Assuming steady one-dimensional flow of an incompressible frictionless fluid: V= Pstag-Pstat (7.1) P Pstag:stagnation(淤塞；停滞；驻点)or total pressure,free stream Pstat:static pressure,free stream V:flow velocity Static tops(several,equally p fluid mass density Free streom spaced around circumference) If p is accurately known,the Pstat,m Measured deviation from the idea Pstag.m values theoretical result of Eq.(7.1) can be traced to inaccurate p.V Pstot Psto Stagnaticn measurement of P_stag True values point and Pstat. Tube support-一 The static pressure is usually the more difficult to measure accurately. Inclined Figure 7.3 Pitot-Static Tube differential manometer 12/48 7.1.2 Velocity Magnitude from Pitot-Static Tube The difference between true (Pstat) and measured(Pstat,m)values of static pressure may be due to the following: 1 Misalignment of the tube axis Flow Pstot,mPstot Influence of and velocity vector. pVy2 hole-tip spacing 2 Nonzero tube diameter. 0 1012 3 Influence of stagnation point on -0.0 the tube-support leading edge. -0.02 Incompressible turbulent flow While errors in the stagnation pressure are likely to be smaller than Support those in the static pressure,several possible sources of error are present: Pstat,m Pstat Flow Influence of ①Misalignment. PVY hole-support spacing 0.05 2 Two-and three-dimensional 0.04 velocity fields.The stagnation 0.03 0.02 Incompress ble turbulent flow pressure measured correspond to 0.01 ■一=一。》 some sort of average velocity. 0 0 6 8 0 12名8 ③Effect of viscosity.. Figure 7.4 Static Pressure Errors
Assuming steady one-dimensional flow of an incompressible frictionless fluid: ܸ ൌ ଶ ೞೌିೞೌ ఘ (7.1) ܲ௦௧ : stagnation(淤塞;停滞;驻点) or total pressure, free stream ܲ௦௧௧ : static pressure, free stream V : flow velocity ρ : fluid mass density Figure 7.3 Pitot-Static Tube If ρ is accurately known, the deviation from the idea theoretical result of Eq.(7.1) can be traced to inaccurate measurement of ܲ_ݐݏ݃ܽ .ݐܽݐݏ_ܲ and The static pressure is usually the more difficult to measure accurately. 7.1.2 Velocity Magnitude from Pitot-Static Tube(皮托静压管) Figure 7.3 Pitot-Static Tube 11/48 The difference between true (ܲ௦௧௧) and measured (ܲ௦௧௧, m) values of static pressure may be due to the following: ① Misalignment of the tube axis and velocity vector. ② Nonzero tube diameter. ③ Influence of stagnation point on the tube-support leading edge. While errors in the stagnation pressure are likely to be smaller than those in the static pressure, several possible sources of error are present: ① Misalignment. ② Two- and three-dimensional velocity fields. The stagnation pressure measured correspond to some sort of average velocity. ③ Effect of viscosity. 7.1.2 Velocity Magnitude from Pitot-Static Tube Figure 7.4 Static Pressure Errors 12/48
13/48 7.1.2 Velocity Magnitude from Pitot-Static Tube An important application of the Pitot-static tube is found in aircraft and missiles( 弹，导弹).The stagnation-and static-pressure readings of a tube fastened to a vehicle are used to determine the airspeed and Mach number while the static reading alone is utilized to measure altitude. When a pitot for subs-static tube is employed in a compressible fluid,Eq.(7.1)no longer applies.There are special equations for subsonic(亚音速的)flow(Mach numberNM1) calculation respectively. The measurement of stagnation and static pressures may be combined in a single probe, or two separate probes,one for stagnation and the other for static,may be employed. Two independent static taps Wedge static-pressure probe Used to measure velocity direction as well. 0.05in. Flow To align with flow, rotate to balance two static-tap readings Figure 7.8 Several Examples of Commonly Used Forms of Pitot-Static Probe 14/48 7.1.2 Velocity Magnitude from Pitot-Static Tube Simple total-pressure Venturi shield total tube tube Flow (b) Flow (d) Total Pressure Tube also used for sub-and supersonic flow View 4-4 Boundary-loyer 222ZZ2Z222 total tube 0.001in.L0.003in. Flow d Figure 7.8 Several Examples of Commonly Used Forms of Pitot-Static Probe
An important application of the Pitot-static tube is found in aircraft and missiles (飞 弹,导弹). The stagnation- and static- pressure readings of a tube fastened to a vehicle are used to determine the airspeed and Mach number while the static reading alone is utilized to measure altitude. When a pitot for subs-static tube is employed in a compressible fluid, Eq. (7.1) no longer applies. There are special equations for subsonic(亚音速的) flow (Mach number NM 1) calculation respectively. The measurement of stagnation and static pressures may be combined in a single probe, or two separate probes, one for stagnation and the other for static, may be employed. 7.1.2 Velocity Magnitude from Pitot-Static Tube Figure 7.8 Several Examples of Commonly Used Forms of Pitot-Static Probe Used to measure velocity direction as well. 13/48 Figure 7.8 Several Examples of Commonly Used Forms of Pitot-Static Probe 7.1.2 Velocity Magnitude from Pitot-Static Tube Total Pressure Tube also used for sub- and supersonic flow 14/48
7.1.3 Velocity Direction from Yaw Tube(偏航管)，Pivote/4s Vane(回转叶片)，and Servoed Sphere(伺服球) Flow-velocity direction information is of interest in flight vehicles where angle-of-attack measurements are utilized in attitude measurement and control,stability augmentation( 大，增加)，and gust(一阵强风)alleviation(缓解)systems. Yaw tubes are employed to determine the direction of local flow velocity. Angle of Attack:the angle between the object's reference line and the oncoming flow. The simplest form of yaw tube is useful for finding the angular inclination in one plane only. Subsonic Taps 1 3 are connected to a differential- pressure instrument that reads zero when the 7 tube is aligned with the flow; A center tap 2 is often included to read the m stagnation pressure after alignment is attained 之=Angle of attack (valid only if the angle of attack is zero). 中=Angle of yaw Tops 1 and 3 each 40 from 2 Figure 7.10 Yaw Tubes 16/48 7.1.3 Velocity Direction from Yaw Tube,Pivoted Vane,and Servoed Sphere (b):Operates on similar principle with(a).It may be utilized in regions where the flow direction changes greatly,since its sensing holes may be located very close together. (c)&(d):The two-axis probes could be designed to allow rotation about each axis;however,the complexity and size of such a design are generally prohibitive (价格或费用高昂得令人难以承受). ld) Subsonic or Subsonic or supersonic supersonic Subsonic or supersonic 20 (5o 4 Claw probe Double-claw probe 04 with total top no total tap Figure 7.10 Yaw Tubes
Flow-velocity direction information is of interest in flight vehicles where angle-of-attack measurements are utilized in attitude measurement and control, stability augmentation(扩 大,增加), and gust(一阵强风) alleviation (缓解) systems. 7.1.3 Velocity Direction from Yaw Tube(偏航管), Pivoted Vane(回转叶片), and Servoed Sphere(伺服球) Figure 7.10 Yaw Tubes Yaw tubes are employed to determine the direction of local flow velocity. Angle of Attack: the angle between the object's reference line and the oncoming flow. The simplest form of yaw tube is useful for finding the angular inclination in one plane only. ¾ Taps 1 & 3 are connected to a differentialpressure instrument that reads zero when the tube is aligned with the flow; ¾ A center tap 2 is often included to read the stagnation pressure after alignment is attained (valid only if the angle of attack is zero). 15/48 Figure 7.10 Yaw Tubes (b): Operates on similar principle with (a). It may be utilized in regions where the flow direction changes greatly, since its sensing holes may be located very close together. (c) & (d): The two-axis probes could be designed to allow rotation about each axis; however, the complexity and size of such a design are generally prohibitive (价格或费用高昂得令人难以承受). 7.1.3 Velocity Direction from Yaw Tube, Pivoted Vane, and Servoed Sphere 16/48
17/48 7.1.3 Velocity Direction from Yaw Tube,Pivoted Vane,and Servoed Sphere Determination of angles of attack and yaw aboard flight vehicles is often accomplished with vane-type probes. These devices are essentially one-or two-axis weather vanes with suitable damping to reduce oscillation and with motion pickups to provide electrical angle signals. Limitation of this type of device for certain high-speed,high-altitude applications have led to the development of the servoed-sphere type of sensor. Rotary motion transducer 0n6 Pivot point Boom-mounted Flush-mounted transducer Angle-of-attack,angle-of-yow probe transducers Single-oxis probe Flow Figure 7.11 Vane-Type Probes 18/48 7.1.3 Velocity Direction from Yaw Tube,Pivoted Vane,and Servoed Sphere A servo-driven sphere is continuously and automatically aligned with the velocity vector by means of two independent servosystems using the differential-pressure signals P,-P2 and P3-P as error signals. A fifth tap measures the stagnation pressure. Angle of sideslip-Taps 1.2 |会lf db 0 Angle of attack -Taps 3,4 1.0 10 Stognation pressureTop 5 100 Frequency,cps /告ul Taps 1,2,3.4-0.188 in.dia each42°from stagnation point System frequency Tap 5-0.5 in.dia Nose of vehicl response 6.5-in.-dia sphere -90+ Flow Flow angle P3-P Amplifier Servo Rotary m Motion angle volve hydroulic actuator pickup signal Sphere Differential taps pressure tronsducer Sphere rotation ongle Angle-of-attack servo system Angle-of-sideslip system functionally identical Figure 7.12 Servoed-sphere Probes
7.1.3 Velocity Direction from Yaw Tube, Pivoted Vane, and Servoed Sphere Figure 7.11 Vane-Type Probes Determination of angles of attack and yaw aboard flight vehicles is often accomplished with vane-type probes. These devices are essentially one- or two-axis weather vanes with suitable damping to reduce oscillation and with motion pickups to provide electrical angle signals. Limitation of this type of device for certain high-speed, high-altitude applications have led to the development of the servoed-sphere type of sensor. 17/48 7.1.3 Velocity Direction from Yaw Tube, Pivoted Vane, and Servoed Sphere Figure 7.12 Servoed-sphere Probes A servo-driven sphere is continuously and automatically aligned with the velocity vector by means of two independent servosystems using the differential-pressure signals P1-P2 and P3-P4 as error signals. A fifth tap measures the stagnation pressure. 18/48
19/48 7.1.4 Dynamic Wind-Vector Indicator Measure the magnitude and direction of flow velocity in terms of the drag force exerted on a hollow sphere.The drag force on a body is given by PaCa tovs (7.11) Ca:drag coefficient of body,0.567 for these transducers; A:projected(投影)area of body. Hollow sphere Flexure rods (Force-component isolotors) Wind Wire Flexure plates vector roughening (Spring restraint] rings Differential tronsformer (a) (Full-scale motion =0.030 in.) Figure 7.14 Wind Vector Indicator (b 7.1.5Hot-Wire and Hot-Film Anemometers(热线与热膜风速仪 20/48 Two types of hot-wire anemometers: 1Constant-current type:A fine resistant wire carying a fixed current is exposed to the flow velocity.The wire attains(达到某状况)an equilibrium temperature when the i2 R heat generated in it is just balanced by the convective(对流的，heat loss from its surface. 2 Constant-temperature form:the current through the wire is adjusted to keep the wire temperature (as measured by its resistance)constant.The current becomes a measure of flow velocity.It has more advantages than the constant current type lungsten wire 0.0003 in.dia,0.04 in.long Resistance 1 ohm ←V,perpendicular to wire R》R.R2,尺，Rw 16→ Wire support 24 R R2 Bolonce-detecting galvanometer Hot wire- R Measure Figure 7.15 Hot-Wire Anemometer 所
7.1.4 Dynamic Wind-Vector Indicator Measure the magnitude and direction of flow velocity in terms of the drag force exerted on a hollow sphere. The drag force on a body is given by ܨௗ ൌ ܥௗ ఘమ ଶ (7.11) Cd: drag coefficient of body, 0.567 for these transducers; A: projected (投影) area of body. Figure 7.14 Wind Vector Indicator 19/48 7.1.5 Hot-Wireand Hot-Film Anemometers (热线与热膜风速仪) Figure 7.15 Hot-Wire Anemometer Two types of hot-wire anemometers: ① Constant-current type: A fine resistant wire carrying a fixed current is exposed to the flow velocity. The wire attains (达到某状况) an equilibrium temperature when the ݅ ଶܴ heat generated in it is just balanced by the convective (对流的) heat loss from its surface. ② Constant-temperature form: the current through the wire is adjusted to keep the wire temperature (as measured by its resistance) constant. The current becomes a measure of flow velocity. It has more advantages than the constant current type. 20/48