Flow-Measurement Sensors

Flow sensing for measurement and control is one of the most critical areas in the modern industrial process industry. Regardless of the state of the fluid, gas, or liquid, accurate flow measurements are critical. In some situations, optimum performance of a machine is dependent on the correct mix of definite proportions of liquids. The continuous manufacturing process relies on accurate monitoring and inspections involving raw materials, products, and waste throughout the process.

1 Solid Flow

While monitoring the bulk of solid materials in transit, it's necessary to weigh the quantity of material for some fixed length of the conveyor system. A flow transducer in a solid measurement is actually the assembly of a conveyor, hopper opening, and weighing platform. Small crushed particles of a solid material are carried by conveyor belt or through pipes in a slurry which is pumped through the pipes.

As can be observed from Ill. 62, the flow is measured as the necessary weight of the quantity of material on a fixed length of the conveyor system.

ILL. 62 SOLID FLOW MEASUREMENT

In this situation, the flow measurement becomes weight measurement. The material on the plat form displaces a transducer, usually a load cell, which is calibrated to provide an electrical output proportional to the weight of the solid flow. Weight is usually measured by a load cell, which is calibrated to give an indication of the solid flow.

Flow rate Q = WR/L

where Q = flow (kg/min) W = weight of material on section of length L R = conveyor speed (m/min) L = length of weighing platform (m)

2 Liquid Flow

The basic continuity equation in flow calculations is the continuity equation which states that if the overall flow rate in the system is not changing with time then the flow rate past any section is constant. The continuity equation in the simplest form can be expressed as V = Q/A

Where […]

V = flow velocity Q = volume flow rate Volume flow rate is expressed as a volume delivered per unit time. The common units are cubic meters per hour and liters per hour. Mass flow rate or mass of flow per unit time is expressed in kg/hr. Ill. 63 illustrates the fluid flow phenomenon through varying cross sectional areas.

ILL. 63 LIQUID FLOW THROUGH VARYING CROSS-SECTIONAL AREA

Incompressible fluid flow through a pipe under equilibrium conditions can be expressed by Bernoulli's theorem, which states that the sum of the pressure head, velocity head, and elevation at one point is equal to another point.

Equation 67 represents conservation of energy with no energy loss between points A and B.

The first term represents energy stored as pressure; the second term represents kinetic energy; and the third term represents energy due to position.

Where […]

V1, V2 = mean fluid velocity at points 1 and 2 (m/s) density (N/m3) P1 and P2 = pressures at two different points g = acceleration of gravity h1 and h2 = elevation above a given datum level r = fluid

The most common flow-measurement technique is to measure a pressure differential along a flow line. Sensors based on differential pressure measurement, rotameters, ultrasonic flow transducers, turbine flow transducers, electromagnetic flow transducers and laser anemometers are used for this measurement.

3 Sensors Based On Differential Pressure

Flow sensors of this type use an obstruction along the flow line, such as a nozzle, orifice plate, Venturi tube, or pitot tube. Using Bernoulli's equation with some modification, the basic relation ship between the pressure differential and flow rate is expressed as

where p = density of fluid a = area of cross section pipe at constriction A = area of cross section pipe prior to constriction […]

Δp = pressure differential between two tapping points Cd = discharge coefficient The discharge coefficient indicates the amount of disturbance to the flow stream at the area of restriction, called the throat (Ill. 64). This illustrates the flow sensing principle using an obstruction.

ILL. 64 FLOW SENSING

The conventional devices for flow sensing employ one of the following three arrangements,

1. Orifice plate

2. Nozzle

Venturi tube

As shown in Ill. 65, these all use a calibrated restriction in the flow line and thereby measure the pressure drop across the obstruction. The velocity of flow is considerably higher on the downstream side of the obstruction. According to Bernoulli's theorem, there is a pressure drop, and the magnitude of this drop is proportional to the velocity of flow through the obstruction. The relationship between the pressure drop and the flow velocity is nonlinear. In addition, the obstruction must be designed for a specific range of flows and velocities. Flows with lower velocities may not register any substantial pressure drop.

The orifice plate flow transducer is the least expensive device but has a limited measurement span.

It can be used for both liquid and gas flow with reasonable accuracy. In orifice plate meters, circular holes are cut in thin plates and bolted between flanges along the length of the pipe. The pressure tap ping for flow rate measurements can be obtained by a variety of methods. For pipes of 5 cm and larger, the pressure tappings are made at distances of D and D/2 in the upstream and downstream directions, respectively, where D is the diameter of the pipe. These instruments are inexpensive and generally have a long, maintenance-free life.

The nozzle and Venturi tubes are more sophisticated and expensive transducers compared to the orifice plate flow transducer. They are more accurate, operate over a wide range of flow, and are less susceptible to flow losses. Venturi tubes offer the best accuracy compared to nozzle flow and orifice plate transducers. Their design consists of three sections: the converging section at the upstream, the throat, and the diverging conical section at the downstream. The cylindrical throat section experiences a decrease in pressure and an increase in velocity. At this point, the flow rate is steady. The Venturi tube is expensive to construct and must be calibrated.

Because of this, Venturi tubes are not suitable. for fluids that collect on the tiny wall pockets as they flow.

The nozzle flow meter is similar to the Venturi meter but occupies considerably less space. The design of the nozzle combines the simplicity of the orifice plate with the low losses of the Venturi tube. The fluid passes through the minimum flow area and expands suddenly to the pipe area. The absence of a downstream cone brings the pressure loss to the same level of the orifice meter. Nozzle flow meters can be used for both liquids and gases in situations where the volumetric flow rate has to be measured with reasonable accuracy. They are less expensive than Venturi tubes, have a longer life, and don't require recalibration.

Pitot Tube

The pitot tube is the oldest flow rate-sensing instrument. It transforms the kinetic energy of the fluid into potential energy in the form of a static head. The difference between the impact (or the dynamic pressure) and the static pressure can be related to the flow rate. The velocity head is converted into impact pressure, and the difference between the static pressure and the impact pressure becomes a measure of the flow rate.

The pitot tube is widely used for air speed measurements onboard aircraft. It consists of a cylindrical probe installed in a pipe line. As the fluid approaches the probe, the velocity decreases until it reaches zero at the point of impact on the probe. The deceleration increases the pressure. P1 and V1 are the upstream pressure and velocity, and P2 and V2 are the pressure and velocity in the neighborhood of the object. At the point of impact, V2 is zero. From Bernoulli's theorem, the velocity of fluid flow is computed, as

ILL. 65 RATE OF FLOW SENSORS (a) Orifice plate, (b) Flow nozzle, (c) Venturi tube

Solving for velocity and introducing the correction factor, C_, to account for non-uniform velocity in the pipe yields

The Pitot tube in Ill. 66 has two concentric tubes. The inner tube connects the impact hole to one side of a differential pressure gauge, and the outer tube has a series of holes bored into it to sense the static pressure. Velocity at a point is determined by the pressure differential generated by this pitot tube. Total pressure in the inner tube is equal to the sum of the static pressure and the pres sure due to impact of the fluid stream.

ILL. 66 STANDARD PITOT TUBE USED FOR FLOW MEASUREMENT

Rotameter The rotameter is another device widely used in the process-control industry for flow measurement. It consists of a tapered glass tube and a float. The float rises until the annular passage is larger enough to pass all material through pipe. The float is constructed with a diameter that completely blocks the inlet. When the flow starts in the pipeline and the fluid or gas reaches the float, the buoyant effect of fluid or gas makes the float lighter. The float passage remains closed until the pressure of the flowing material plus the fluid buoyancy effect exceeds the downward pressure due to the weight of the float. The float then rises and floats within the medium in proportion to the flow at a given pressure. The float then comes to dynamic equilibrium.

An increase in flow rate causes the float to rise, and a decrease in flow rate causes the float to drop. The forces acting on the float in the vertical column of the liquid are shown in Ill. 6

The downward forces include the effective weight of the float, Fw, as well as the forces acting on the upper surface of the float, Fd. They are shown in Equation 68. The upward forces include the forces acting upward on the lower surface of the float, F_up, and the drag force, F_drag, which tends to pull the float in the upward direction. The value of this force depends upon the float design, the flow conditions, and the absolute viscosity of the fluid.

Vf is the float volume, Af is the surface area of the float, 2 and 1 are the densities of float material and liquid, respectively, and p2 is the pressure per unit area on the upper surface of the float.

F_up = F_up + F_drag = (p1)Af + Fdrag

F_down = Fw + Fd = Vf (r2 - r1) + ( p2)Af

ILL. 67 SCHEMATIC OF ROTAMETER

Under equilibrium conditions and neglecting viscous drag forces, Equation 73 becomes

(p1) Af = Vf (r2 - r1) + ( p2)Af

Substituting and accounting for the discharge coefficient produces the desired flow equation, we have […]

If the rotameter is connected to a variable inductance transducer, an electrical output can be generated in proportion to the flow. This principle is used in the induction variable area flowmeter.

The rotameter acts as the primary sensor of the flow. An inductive transducer is the secondary transducer which provides a signal as an armature connected to it changes position as the float position changes. Two coils are connected to the arms of an AC bridge circuit. When the armature is sym metrically located with respect to the two coils, their impedances are equal, and the bridge is balanced, producing no output. If there is fluid flow, the float changes position resulting in the movement of the soft iron armature. This causes a change in the impedance of the coils. The bridge becomes unbalanced. Since the output voltage is a function of the flow rate, the output voltage is amplified and used to operate a servo motor.

4 Ultrasonic Flow Transducers for Flow Measurement

Ultrasonic flow meters measure fluid velocity by passing high-frequency sound waves through the fluid. Sometimes called transit time flowmeters, they operate by measuring the transmission time difference of an ultrasonic beam passed through a homogeneous fluid contained in a pipe at both upstream and downstream locations. Ill. 68 illustrates the principles of ultrasonic flow sensing.

ILL. 68 ULTRASONIC FLOW SENSING

The transducer consists of transmitter and receiver pairs. One pair, A and B, act as transmitters, and the other pair, C and D, act as receivers. If a sound pulse is transmitted from transmitter B to receiver C, the transit time is calculated as

tBC = d / sin a(C - V cos a)

If the pulse is transmitted from transmitter A to receiver D, the transit time is tAD = d / sin a(C + V cos a)

where d = diameter of the tube (m) V = velocity of fluid flow (m/s)

_ = the angle between the path of sound and the pipe wall C = sound velocity in the fluid (m/s)-assume V __ C

The transit time difference, _t, is the difference between Equation 76 and Equation 7

It is proportional to flow velocity and fluid flow and can be used as an input to the computer. By measuring the transit times at both upstream and downstream locations, the fluid velocity can be expressed independently of the sound velocity in the fluid. Since the measurement is independent of the velocity of sound through the fluid, the effects of pressure and temperature are avoided.

Ill. 69 presents a photograph of an ultrasonic level sensor with a digital read out.

Ultrasonic Doppler Flow Meter The Doppler effect is a useful technique used to measure the velocity of a fluid and hence its flow. In Doppler flow meters, continuous ultrasonic waves are beamed into the fluid. The transducer is normally bonded to the wall of the pipe so as to transmit a beam into the flow. The particles in the fluid scatter the beam and cause a frequency shift which is proportional to the particle velocity. If fr and ft are the respective receiving and transmitting frequencies, then the Doppler shift, fd, can be represented as fd = fr - ft Ultrasonic flow meters are used to measure liquid velocities with minimal pressure loss. The flow measurement is insensitive to pressure, temperature, and viscosity variations. The method has advantages, including bi-directional sensing, high accuracy, wide ranges, and a rapid response.

Although it's an expensive technique, it can be employed for measurement in tubes and pipes of varying sizes.

5 Drag-Force Flow Meter

In this type of flow meter, a suitable obstruction is inserted into the flow path. As a result, the fluid applies a drag force on the object which is sensed and used as a measure of the flow. The drag force, Fd, acting on the object immersed in the fluid is represented by Equation 79:

where Cd is the coefficient of the drag A is the area of cross section […]

rho = is the fluid density V is the velocity (m/s) The drag force of the body can be measured by attaching the drag body to a suitable force monitoring device.

Ill. 70 shows a cantilever beam arrangement with bonded strain gauges. The drag force is transmitted as a strain in the cantilever beam. The strain is suitably calibrated and measured. The main advantage of this type of flow meter is its high dynamic response. The accuracy of the instrument is and repeatability. Drag force flow meters are useful for highly viscous flows, such as hot asphalt, tar, or slurries at high pressures.

ILL. 70 DRAG FORCE TYPE FLOW SENSOR: Strain gauge mounted on cantilever; Target plate (area A)

6 Turbine Flow Meter

The turbine flow meter is a popular method for flow measurement. As shown in Ill. 71, a permanent magnet is enclosed in a rotary body. Each time the rotating magnet passes the pole of the pick up coil, the change in the permeability of the magnetic circuit produces a voltage signal at the output terminal. The output signal is a frequency that is proportional to the flow rate. The voltage pulse is counted by means of a digital counter to give the total flow.

ILL. 71 FLOW SENSING BY TURBINE FLOW METER Ferrous material; Frequency to voltage converter; Rotor bearing; Turbine rotor with magnetic pick up

The main advantage of the turbine flow meter is the linear relationship between the volume flow rate and the angular velocity of the rotor which is […]

where

Q is the volume flow rate k is a constant depending on the fluid property n is the rotor angular velocity (rad/s) Q = kn

Turbine flow meters are not suited for fluids that contain abrasive particles. Any damage to the turbine blades must be followed by an immediate recalibration of the meter. The paddle wheel flow meter is a variation of the turbine flow meter. In such flow meters, the fluid drives a small paddle wheel that is located on the side of the pipe.

7 Rotor Torque Mass Flow Meter

In some applications, it's necessary to measure the mass flow rate rather than the volume flow rate. Such applications exist in process-control industries as well as aerospace industries where mass flow rate information is needed. The measurement concept is based on Newton's second law of motion, wherein the force required to alter the velocity of the fluid stream is used as a measurement.

Ill. 72 describes the basic rotor torque mass flow meter. The fluid is given a constant rotational velocity in a direction normal to the direction of flow. The fluid is first passed through straightening vanes to remove any angular swirls and then allowed to flow through an assembly which consists of a set of vanes rotating at constant speed about the axis of the flow meter.

ILL. 72 ROTOR TORQUE MASS FLOW METER

Straightening vanes; Pick up;

The torque needed to drive the rotating vanes is proportional to the magnitude of the angular momentum applied to the fluid, which in turn is proportional to the mass of the fluid through the assembly.

The torque, T, transmitted to the impeller is expressed by […]

where[…]

T = torque transmitted I = mass moment of inertia

__ angular velocity k = radius of gyration

8 Fluid Measurement Using Laser Doppler Effect

Laser Doppler anemometers utilize a non-invasive procedure to measure the instantaneous flow velocities of liquids or gases flowing in a transparent channel. The technique can be employed only in situations where […]

• Adequate transmission of laser light through the fluid is possible.

• The fluid contains sufficient particles of contamination so that the laser beam can use the effect of scattering.

As shown in Ill. 73, the principle is based on the Doppler shift phenomenon in which the frequency of the scattered light from the moving object differs from that of the incident beam by an amount proportional to the fluid velocity.

ILL. 73 LASER DOPPLER ANEMOMETER: Laser scattering on interaction with fluid flow.

A laser beam is focused at a point in the fluid where the velocity is to be measured. The laser beam is scattered by the small particles flowing in the liquid. Due to viscous effects, the small particles move at the same velocity as the fluid, so the measurement of the particle velocity is the same as the fluid velocity. Signal processing of the photodetector output produces the magnitude of the Doppler frequency shift, which is directly proportional to the instantaneous velocity of flow.

Frequency shift: delta f = 2V cos / c f0

Here, V is the particle velocity, f0 is the frequency of the laser beam, is the angle between the laser beam and the particle in the fluid, and c is the speed of light. The output voltage of the instrument is directly proportional to the instantaneous velocities of the fluids.

Related developments in the area of laser anemometry include the dual-beam laser velocimeter, which looks at the interference pattern of two laser beams interacting on the fluid at a plane.

The interaction results in a fringe pattern, and the fringe separation is a measure of the fluid velocity. The laser Doppler velocimeter is used for a wide range of velocities of fluid and gas flows. High accuracy's in the range of are possible. These instruments have been used in the aerospace industry to measure vortex flow near the wing tips of aircraft, flow between the gas turbine compressor blades, investigation of boundary layers, combustion phenomenon in jet propulsion systems, and in biological areas for in vivo blood-flow measurement.

9 Hot Wire Anemometers

Hot wire anemometry is an important method of fluid velocity measurement and is primarily used for mean and fluctuating velocity measurements. The method is used in aerodynamic applications to measure liquids and gases at high speeds and to measure non-conductive liquids at low speeds.

Its operation is based on the principle that the convective heat transfer from a small 5 _m diameter platinum-tungsten wire is a function of the fluid velocity. The wire is heated by the passage of current through it (Ill. 74). When it's exposed to the fluid flow, heat is dissipated from the wire by convection, and there is a decrease in the wire resistance. The rate of heat loss depends on the shape and characteristics of the wire, properties of the fluid, and the fluid velocity. By maintaining the first two factors at constant values, the instrument response becomes a function of the fluid velocity only.

ILL. 74 SCHEMATIC OF HOT WIRE OPERATION Hot wire probe; For measurement

Basic heat-transfer equations can be explained using King's law for convective heat transfer from the heated wire: by […]

where h = convective coefficient of heat transfer K = thermal conductivity of hot wire

= density of fluid v = velocity of fluid stream D = diameter of hot wire

_ = coefficient of viscosity of the fluid

The output of the bridge circuit with a calibrated computer interface provides a measure of the fluid flow velocity. Hot wire anemometers are suited for measurement in clean fluids. One important application is the measurement of fluid turbulence achieved by using proper compensation circuitry and calibration.

10 Electromagnetic Flow Meter

The operating principle of the electromagnetic flow meter is based on the voltage which is generated in an electrically conducting fluid as it moves through a magnetic field. This method is useful for measuring flows of conducting liquids that may have abrasive materials and are not suited for other measurement methods. It can't be used for electrically non-conducting fluids (like gases) and produces satisfactory results for low conductivity fluids (like water).

Ill. 75 illustrates the operating principle of the electromagnetic flowmeter. In electro magnetic flow sensing, a pair of electrodes are inserted on the opposite sides of a non-conducting and nonmagnetic pipe which carries the liquid. The pipe is surrounded by an electromagnet, which produces the magnetic field. The voltage is induced across the electrodes. The magnitude of the emf is proportional to the rate at which the field lines are cut. Assuming a constant magnetic field, the magnitude of the voltage appearing across the electrodes will be proportional to the velocity.

ILL. 75 ELECTROMAGNETIC FLOW METER According to Faraday's law, the induced voltage, e, is given by

e = Blv * 10^-8 V

where B = magnetic flux density l = length of the conductor (pipe diameter) V = velocity of the conductor (cm/s)

Electromagnetic flow sensing can be used in pipes of any size. The use of electro-magnetic sensors will not cause any obstruction in the fluid flow and will not cause any specific pressure drop.

The output voltage has a large linear range and a good transient response. The output is not affected by variations in viscosity, pressure, or temperature. In summary, electromagnetic flow meters are useful for monitoring corrosive fluids, solid contaminated liquids, paper pulp, detergents, cement slurries, and greasy liquids.

SUMMARY Flow Sensors

Flow Sensors for Flow Measurement:

Ultrasonic flow meters measure fluid velocity by passing high frequency sound waves through the fluid.

They operate by measuring the transmission time difference of an ultrasonic beam passed through a homogeneous fluid contained in a pipe at both an upstream and downstream location.

ILL. 76 ULTRASONIC FLOW SENSING Receivers; Control circuits; Transmitters

Measurement Using Laser Doppler Effect:

This principle is based on the Doppler shift phenomenon in which the frequency of the scattered light from the moving object differs from that of the incident beam by an amount proportional to the fluid velocity. The beam is focused at a point in the fluid where the velocity is to be measured. Signal processing of the photodetector output produces the magnitude of the Doppler frequency shift which is directly proportional to the instantaneous velocity of flow.

where V is the particle velocity, f0 is the frequency of the beam, is the angle between the laser beam, and the particle c is the speed of light. The output voltage of is proportional to the instantaneous velocities of the fluids.

Applications These techniques have been used in the aerospace industry to measure vortex flow near the wing tips of air craft, flow between the gas turbine compressor blades, investigation of boundary layers, combustion phenomenon in jet propulsion systems, and in biological areas for in vivo blood-flow measurement.

Features High accuracy in the range of is possible.

Electromagnetic Flow Meter Theory Principle:

The electromagnetic flow meter is based on the voltage which is generated in an electrically conducting fluid as it moves through a magnetic field. A pair of electrodes are inserted on the opposite sides of a nonconducting and nonmagnetic pipe which carries the liquid. The pipe is surrounded by an electromagnet, which produces the magnetic field. The voltage is induced across the electrodes. The magnitude of the emf is proportional to the rate at which the field lines are cut. Assuming a constant magnetic field, the magnitude of the voltage appearing across the electrodes will be proportional to the velocity.

Applications Electromagnetic flow meters are useful for monitoring corrosive fluids, solid contaminated liquids, paper pulp, detergents, and cement slurries.

Features

• Can be used in pipes of any size.

• Use of electro-magnetic sensors will not cause any obstruction in the fluid flow

• The output has a large linear range and a good transient response. The output is not affected by variations in viscosity, pressure and temperature.

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