Flow : the motion of a fluid (1) Blood flowmeters : - ultrasonic (doppler, transit time) -electromagnetic (2) Gas flowmeters : - pneumotachometer

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Sydney Poole
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1 Flow Sensors

2 Flow : the motion of a fluid (1) Blood flowmeters : - ultrasonic (doppler, transit time) -electromagnetic (2) Gas flowmeters : - pneumotachometer -spirometer - Wright's respirometer - rotameter - ball float meter Flow rate : (1) mass flow rate : mass transferred per unit of time (ex:[kg/sec]) (2) volumetric flow rate : volume of material transferred per unit of time(ex:[cc/sec]) (3) Total flow or flow volume : integration of flowrate

Reynolds Numbers The performance of flowmeters is also influenced by Reynolds Number : - a dimensionless unit - defined as the ratio of the liquid's inertial forces to

3 Reynolds Numbers The performance of flowmeters is also influenced by Reynolds Number : - a dimensionless unit - defined as the ratio of the liquid's inertial forces to its drag forces. Re ζvd = µ where Re is the Reynolds number ζ is the fluid density V is the mean fluid velocity - Re > 4000 : turbulent flow - Re < 2000 : laminar flow

- The secondary element measures the differential pressure and provides the signal or read-out that is converted

4 Differential Pressure Meters - Having a primary and secondary element - The primary element causes a change in kinetic energy, which creates the differential pressure in the pipe. - The secondary element measures the differential pressure and provides the signal or read-out that is converted to the actual flow value. Common differential pressure flowmeters include (a) the orifice, (b) ventruri tube, (c) flow nozzle, (d) pitot tube, and (e) elbow-tap meter.

5 - Variable-area meters, often called rotameters - consist essentially of a tapered tube and a float - Constant differential pressure devices - no secondary flowreading devices are necessary

6 Positive Displacement Meters - consists of separating liquids into accurately measured increments and moving them on - each segment is counted by a connecting register - every increment represents a discrete volume -(a) Reciprocating piston meters -(b) Oval-gear meters -(c) Nutating-disk meters -(d) Rotary-vane meters, Helix flowmeter

8 Velocity Meters - operate linearly with respect to the volume flow rate. - no square-root relationship (as with differential pressure devices) so greater rangeability - minimum sensitivity to viscosity changes when used at Reynolds numbers above 10,000. -(a) Turbine meters -(b) Vortex meters -(c) Electromagnetic meters -(d) Ultrasonic flowmeters -(e) Mass Flowmeters -(f) Coriolis meters -(g) Thermal-type mass flowmeters -(h) Open Channel Meters -(i) Weirs -(j) Flumes

15 Medical Applications

Electromagnetic Blood Flowmeter :Faraday's principle of electromagnetic induction can be applied to any electrical conductor (including blood) which moves through a magnetic field.

16 Electromagnetic Blood Flowmeter :Faraday's principle of electromagnetic induction can be applied to any electrical conductor (including blood) which moves through a magnetic field. This probe applies an alternating magnetic field (typically at 400 Hz) across the vessel and detects the voltage induced by the flow via small electrodes (microvolt region) in contact with the vessel. 1 e u B dl 0 L = where B = magnetic flux density, T L = length between electrodes, m u = instantaneous velocity of blood, m/s

Ultrasonic Blood Flowmeter : (1) transit time methods in which the blood velocity is calculated from the time taken to cross the vessel oblique to the direction of flow.

17 Ultrasonic Blood Flowmeter : (1) transit time methods in which the blood velocity is calculated from the time taken to cross the vessel oblique to the direction of flow. (2) The most practical form of ultrasonic blood flowmeter is the continuous wave doppler system with the doppler-shifted components being fed to a zero-crossing detector. Forward and reverse flow is represented by the doppler- shifted components above and below the ultrasonic frequency.

18 Transit Time V D θ t t d u V D D =, tu = v + V cosθ v V cosθ s td = v s V cos 2 s u d v ( t t ) 2D cosθ 2DV cosθ θ s

19 f f f f 1 ' = f Vs (1 ) v 1 ' = f Vs (1 + ) v Vo ' = (1 + ) f v Vo ' = (1 ) f v Doppler Effect Observer : stationary Source : approaching Observer : stationary Source : going away Observer : approaching Source : stationary Observer : going away Source : stationary f ' = v λ ' wavelength is modified f ' = v ' λ velocity is modified 1 Vo f '' = (1 + ) f Vo (1 ) v v 2Vo 2Vo 2Vo f '' f = f f f v V v v o cosθ Target : approaching Source/Observer : stationary

20 Pneumotachometer : This measures the flow rate of gases during breathing. The breath is passed through a short tube (Fleisch tube) in which there is a fine mesh which presents a small resistance to the flow. The resulting pressure drop across the mesh is in proportion to the flow rate. The pressure drop is very small (e.g. 2 mmhg) and so the measuring circuit must be of high quality and produce very little drift with time. Fleisch tube : It consists of a wide bore tube in which there is a mesh or screen which slightly restricts the airflow through it. The resistance to flow presented by the screen produces a differential pressure which is proportional to the airflow through the device. Spirometer : These measure the volumes of gases breathed in or out. They are usually displacement (bell) devices, a bellows, or a small turbine device with gears to drive a pointer.

Respirometer :It is useful to measure the volume or flow rate of gases entering or leaving the lungs during anaesthesia, particularly if assisted ventilation is being used.

22 Respirometer :It is useful to measure the volume or flow rate of gases entering or leaving the lungs during anaesthesia, particularly if assisted ventilation is being used. The best known device for this is the Wright's respirometer which can be fitted into the breathing circuit and works by directing the gases on to a rotating vane which drives a gear train attached to a pointer moving over a dial. Wright s respirometer : A gas volume meter for use in the breathing circuit of an anaesthetic machine or ventilator which works by directing the breathing gases through oblique slots in a small cylinder enclosing a small vane which is made to rotate.

23 Some Sensors in detail

24 Overview Pitot-static Tube A Pitot-static Tube is a flow velocity meter which is capable of measuring fluid velocities as a localized point (as opposed to an averaged velocity across a larger section). A schematic of a Pitot tube is shown below. Typical Pitot Static Tube The Pitot tube yields a pressure measurement which is typically measured with a differential manometer. The fluid velocity can obtained from the pressure value in accordance with incompressible (or compressble) fluid theory.

25 Pros and Cons Pros: - Simple construction. - Relatively inexpensive. - Almost no calibration required. - Induces minimal pressure drops in the flow. - Requires only a few access holes into the flow conduit; no wide open cut needed. Cons: - Accuracy and spatial resolution may not be high enough for some applications. - Tube must be aligned with the flow velocity to obtain good results. Any misalignment in yaw should not exceed ±5.

26 Introduction The Pitot tube (named after Henri Pitot in 1732) measures a fluid velocity by converting the kinetic energy of the flow into potential energy. The conversion takes place at the stagnation point, located at the Pitot tube entrance (see the schematic below). A pressure higher than the free-stream (i.e. dynamic) pressure results from the kinematic to potential conversion. This "static" pressure is measured by comparing it to the flow's dynamic pressure with a differential manometer. Converting the resulting differential pressure measurement into a fluid velocity depends on the particular fluid flow regime the Pitot tube is measuring. Specifically, one must determine whether the fluid regime is incompressible, subsonic compressible, or supersonic. Cross-section of a Typical Pitot Static Tube

27 Incompressible Flow A flow can be considered incompressible if its velocity is less than 30% of its sonic velocity. For such a fluid, the Bernoulli equation describes the relationship between the velocity and pressure along a streamline, Evaluated at two different points along a streamline, the Bernoulli equation yields, If z 1 = z 2 and point 2 is a stagnation point, i.e., v 2 = 0, the above equation reduces to, The velocity of the flow can hence be obtained, or more specifically,

28 Subsonic Compressible Flow For flow velocities greater than 30% of the sonic velocity, the fluid must be treated as compressible. In compressible flow theory, one must work with the Mach number M, defined as the ratio of the flow velocity v to the sonic velocity c, When a Pitot tube is exposed to a subsonic compressible flow (0.3 < M < 1), fluid traveling along the streamline that ends on the Pitot tube's stagnation point is continuously compressed. If we assume that the flow decelerated and compressed from the free-stream state isentropically, the velocitypressure relationship for the Pitot tube is, where γ is the ratio of specific heat at constant pressure to the specific heat at constant volume,

29 If the free-stream density ρ static is not available, then one can solve for the Mach number of the flow instead, where is the speed of sound (i.e. sonic velocity), R is the gas constant, and T is the free-stream static temperature.

30 Supersonic Compressible Flow For supersonic flow (M > 1), the streamline terminating at the Pitot tube's stagnation point crosses the bow shock in front of the Pitot tube. Fluid traveling along this streamline is first decelerated nonisentropically to a subsonic speed and then decelerated isentropically to zero velocity at the stagnation point. The flow velocity is an implicit function of the Pitot tube pressures, Note that this formula is valid only for Reynolds numbers R > 400 (using the probe diameter as the characteristic length). Below that limit, the isentropic assumption breaks down.

31 Hot-Wire Anemometer Overview The Hot-Wire Anemometer is the most well known thermal anemometer, and measures a fluid velocity by noting the heat convected away by the fluid. The core of the anemometer is an exposed hot wire either heated up by a constant current or maintained at a constant temperature (refer to the schematic below). In either case, the heat lost to fluid convection is a function of the fluid velocity. By measuring the change in wire temperature under constant current or the current required to maintain a constant wire temperature, the heat lost can be obtained. The heat lost can then be converted into a fluid velocity in accordance with convective theory. Typical Hot-Wire Anemometer

32 Further Information Typically, the anemometer wire is made of platinum or tungsten and is 4 ~ 10 µm (158 ~ 393 µin) in diameter and 1 mm (0.04 in) in length. Typical commercially available hot-wire anemometers have a flat frequency response (< 3 db) up to 17 khz at the average velocity of 9.1 m/s (30 ft/s), 30 khz at 30.5 m/s (100 ft/s), or 50 khz at 91 m/s (300 ft/s). Due to the tiny size of the wire, it is fragile and thus suitable only for clean gas flows. In liquid flow or rugged gas flow, a platinum hot-film coated on a 25 ~ 150 mm (1 ~ 6 in) diameter quartz fiber or hollow glass tube can be used instead, as shown in the schematic below. Another alternative is a pyrex glass wedge coated with a thin platinum hot-film at the edge tip, as shown schematically below.

33 Pros and Cons Pros: - Excellent spatial resolution. - High frequency response, > 10 khz (up to 400 khz). Cons: - Fragile, can be used only in clean gas flows. - Needs to be recalibrated frequently due to dust accumulation (unless the flow is very clean). - High cost.

34 Introduction Consider a wire that's immersed in a fluid flow. Assume that the wire, heated by an electrical current input, is in thermal equilibrium with its environment. The electrical power input is equal to the power lost to convective heat transfer, where I is the input current, R w is the resistance of the wire, T w and T f are the temperatures of the wire and fluid respectively, A w is the projected wire surface area, and h is the heat transfer coefficient of the wire. The wire resistance R w is also a function of temperature according to, where α is the thermal coefficient of resistance and R Ref is the resistance at the reference temperature T Ref. The heat transfer coefficient h is a function of fluid velocity v f according to King's law, where a, b, and c are coefficients obtained from calibration (c ~ 0.5).

35 Combining the above three equations allows us to eliminate the heat transfer coefficient h, Continuing, we can solve for the fluid velocity, Two types of thermal (hot-wire) anemometers are commonly used: constanttemperature and constant-current. The constant-temperature anemometers are more widely used than constantcurrent anemometers due to their reduced sensitivity to flow variations. Noting that the wire must be heated up high enough (above the fluid temperature) to be effective, if the flow were to suddenly slow down, the wire might burn out in a constant-current anemometer. Conversely, if the flow were to suddenly speed up, the wire may be cooled completely resulting in a constant-current unit being unable to register quality data.

36 Constant-Temperature Hot-Wire Anemometers For a hot-wire anemometer powered by an adjustable current to maintain a constant temperature, T w and R w are constants. The fluid velocity is a function of input current and flow temperature, Furthermore, the temperature of the flow T f can be measured. The fluid velocity is then reduced to a function of input current only. Constant-Current Hot-Wire Anemometers For a hot-wire anemometer powered by a constant current I, the velocity of flow is a function of the temperatures of the wire and the fluid, If the flow temperature is measured independently, the fluid velocity can be reduced to a function of wire temperature T w alone. In turn, the wire temperature is related to the measured wire resistance R w. Therefore, the fluid velocity can be related to the wire resistance.

37 Overview Laser Doppler velocimeter The laser Doppler velocimeter sends a monochromatic laser beam toward the target and collects the reflected radiation. According to the Doppler effect, the change in wavelength of the reflected radiation is a function of the targeted object's relative velocity. Thus, the velocity of the object can be obtained by measuring the change in wavelength of the reflected laser light, which is done by forming an interference fringe pattern (i.e. superimpose the original and reflected signals). Typical Laser Doppler Velocimeter

38 Further Information A laser power source is the essential part of a laser Doppler velocimeter (LDV). Typically, a Helium-Neon (HeNe) or Argon ion laser with a power of 10 mw to 20 W is used. Lasers have many advantages over other radiation/wave sources, including excellent frequency stability, small beam diameter (high coherence), and highly-focused energy. Laser Dopplers can be configured to act as flow meters or anemometers, by detecting the velocity of reflective particles entrained within a transparent flow field. They can also be used as a vibrometers by monitoring the cyclic Doppler shift reflected from a vibrating surface. To improve signal-to-noise ratios, a highly reflective material (e.g. tape with small reflective beads) can be attached to the vibrating target.

39 Pros and Cons Pros: - Non-contacting measurement. - Very high frequency response. Cons: - Sufficient transparency is required between the laser source, the target surface, and the photodetector (receiver). - Accuracy is highly dependent on alignment of emitted and reflected beams. - Expensive; fortunately, prices have dropped as commercial lasers have matured.

40 Doppler Effect The Doppler effect, named after Austrian physicist J. C. Doppler who first described it for sound in 1842, states that waves emitted from a source moving toward an observer are squeezed; i.e. the wave's wavelength is decreased and frequency is increased, as shown in the schematic below. Conversely, waves emitted from a source moving away from an observer are stretched; i.e. the wave's wavelength is increased and frequency is decreased. The waves can be acoustic waves or electro-magnetic radiation. Doppler Effect

41 Doppler Formula Consider a monochromatic (single frequency) light source, such as a laser, with frequency f and wavelength λ. The speed of light c is related to the frequency and wavelength by, c = λ f Assume that the light source is a distance d from the observer. If the light source and the observer are both stationary, the light wave takes n cycles to propagate from the source to the observer, n = d / λ Suppose now the light source moves toward the observer at a velocity v. The distance required to propagate to the observer shrinks from d to, (1 - v / c) d while the number n remains the same. Thus, the wavelength is compressed by a ratio of v /cand the observed wavelength λ r is, λ r = (1 - v/c) λ Since the speed of light is constant, c = λ f = λ r f r the observed frequency is found to be, If this observed frequency f r can be measured and/or compared to the at rest frequency f, the velocity of the light source can be obtained.

42 Irradiance of Two Light Beams Consider a monochromatic light source, such as a laser, that has frequency f and wavelength λ, that sends a light beam to illuminate a moving target. Further assume that the target moves toward the observer at the velocity v. According to the Doppler effect, the wavelength of the reflected light is compressed to λ r and the frequency increases to f r. A light detector can collect both incident and reflected light. Mathematically, the sum of these two light beams is, where A is the amplitude of the incident light and A r is the amplitude of the reflected light. The irradiance is found to be,

43 Simplifying the third term in the last equation above (via a trigonometric product rule), we have, Suppose the relative velocity v is much less than the speed of light (v «c). The observed frequency f r does not change very much from the original frequency f. As a result, the final term in the equation above is the only low frequency component. All of the other terms in the equation are at a frequency of f, f r, or higher. By adding a low pass filter to the measurement, the frequency difference between the incident and reflected light beams can be obtained, allowing one to find the velocity of the target based on the Doppler effect. Such a low-pass filter is usually employed by Ultrasonic Doppler velocimeters. In Laser Doppler anemometry, optical methods such as the interference of two laser beams are more preferable.

44 Interference of Two Plane Waves Typical laser Doppler anemometers use two equal-intensity laser beams (split from a single beam) that intersect across the target area at a known angle θ, as shown in the schematic below. Given that the laser light has a wavelength λ, we would like to find the spacing δ of the interference fringes where the combined laser light intensity is zero.

45 Consider an isosceles triangle bounded by a fringe and two wave fronts, as illustrated by the blue triangle in the schematic above. Recalling basic geometric properties of triangles, we find that the following three triangles (and subtriangles) are geometrically similar, Furthermore, letting the angle amongst three of the triangle's angles,, we have the following relationships Simplifying the above equations gives, which yields the solution for a,

46 In order to link δ to λ and θ, the base of the triangle ABC is used in the following equations, The fringe spacing δ can now be expressed in terms of the laser properties,

47 Laser Doppler Anemometer A typical laser Doppler anemometer issues two split laser beams to form a fringe pattern across the targeted area, as described above. When the targeted area is within a flowfield, as shown in the schematic below, entrained particles passing through the fringes produce a burst of reflected light whose flicker frequency depends on the fringe spacing and the particle velocity normal to the fringes. Laser Doppler Optical System

48 The frequency of the Doppler burst f D is the velocity of the particle normal to the fringes v n divided by the fringe spacing δ, f D = v n / δ Since the fringe spacing σ is a function of the laser wavelength λ and crossing angle θ, the Doppler frequency becomes, The normal velocity of the particle is found to be, Note that there are no negative terms in the above formula. In other words, the direction of the particle motion can not be determined by this formula. Furthermore, the measured velocity of the particle is the velocity component normal to the fringe pattern, not the actual velocity.

FLOW MEASUREMENT. INC 102 Fundamental of Instrumentation and Process Control 2/2560

FLOW MEASUREMENT. INC 102 Fundamental of Instrumentation and Process Control 2/2560 FLOW MEASUREMENT INC 102 Fundamental of Instrumentation and Process Control 2/2560 TABLE OF CONTENTS A. INTRODUCTION B. LOCAL FLOW MEASUREMENT B.1 Particle Image Velocimetry (PIV) B.2 Laser doppler anemometry