UNIVERSIT DEGLI STUDI DI SALERNO Bachelor Degree in
UNIVERSITÀ DEGLI STUDI DI SALERNO Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control (Strumentazione e Controllo dei Processi Chimici) Measuring devices of the main process variables Flow rate measurements Rev. 3. 2 – March 28, 2019
FLOW RATE UNIT OF MEASUREMENT FLOW RATE § 2. 2. 1 pag. 9 Magnani, Ferretti and Rocco (2007) MASS (m) (kg/s) 09. 06. 12 VOLUMETRIC (V) (L/s) Process Instrumentation and Control - Prof M. Miccio MOLAR (N) (kmol/s) 2
FLOW RATE METERS CLASSIFICATIONS First classification (by contrast) 09. 06. 12 Volumetric Mass Trasducer Non-Trasducer Intrusive Non-Intrusive Static Rotary Process Instrumentation and Control - Prof M. Miccio 3
FLOW RATE METERS CLASSIFICATIONS Second Classification based on measuring principle Differential pressure 09. 06. 12 Variable Area Velocity Direct Mass Measurement Process Instrumentation and Control - Prof M. Miccio Rotary 4
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 5
CONTRACTION-BASED FLOW METERS 1 2 d 1 A 1 d 2 A 2 HYPOTHESES: 1. horizontal position 2. ρ = constant 3. v # f (r ) 4. Δploc= 0 5. circular pipe From Bernoulli’s principle (§ 2. 2. 4 page 15 - Magnani, Ferretti and Rocco, 2007): IDEAL CASE γ ideal flow coefficient of a contraction REAL CASE Velocity is not uniform in cross sectional area (ξ<1, real case) where β is the contraction ratio 09. 06. 12 Local pressure drop (vortices formation) Process Instrumentation and Control - Prof M. Miccio 6
CONTRACTION-BASED FLOW METERS Hypotheses: • • • compressible fluid (Gas or Vapor); small (P 1 - P 2); K = calibration factor [m 2] “PI ON TI” CORRECTION 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 7
CONTRACTION-BASED FLOW METERS (orifice plates, flow nozzles, Venturi meter) from Magnani, Ferretti and Rocco (2007) 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 8
ORIFICE PLATE or ORIFICE METER d 1 • • 09. 06. 12 d 2 for VOLUMETRIC FLOWRATE MEASUREMENT of GAS or LIQUIDS sharp restriction of the cross sectional area of the fluid flow; thin diaphragm thickness; design and installation meeting to STANDARD REGULATIONS (e. g. : UNI) orifice can be off-axis; orifice plate can be shaped as a semicircle; orifice plate can have a groove interacting with the fluid. Process Instrumentation and Control - Prof M. Miccio 9
DIAPHRAGMS Examples vent (optional) Φ=2, 5 mm C. F. R. Internal to the pipe purge (optional) Φ=2, 5 mm 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 10
ORIFICE PLATE INSTALLATION • Re > 500 • HORIZONTAL POSITION Exploded view drawing • UNDISTURBED AND STRAIGHT PIPELINE 20 D UPSTREAM AND 5 D DOWNSTREAM 09. 06. 12 d = orifice diameter D = pipe diameter β = d/D<1 Process Instrumentation and Control - Prof M. Miccio 11
PRESSURE PROFILE OF A LIQUID IN A CONTRACTION [(P/ρg)+(v 2/2 g)] Friction loss P Pressure drop due to the orifice Kinetic energy Pressure and potential energy upstream 09. 06. 12 vena contracta downstream Process Instrumentation and Control - Prof M. Miccio orifice_meter. swf 12
ORIFICE PLATE POSITIONING OF PRESSURE SENSORS 1. at vena contracta 2. on the carrier ring 3. on the pipeline VENA CONTRACTA TAPS M =1* PIPE DIA N VARIES WITH b RATIO 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 13
ORIFICE PLATE POSITIONING OF PRESSURE SENSORS 1. at vena contracta 2. on the carrier ring 3. on the pipeline LINE TAPS on the pipeline CORNER TAPS on the carrier ring 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio β 14
FLOW NOZZLE Installation Flow Nozzle 1. It measures the pressure drop before and after a contraction of the cross section of the pipe. 2. It measure ΔP by means a differential manometer. 3. It is easy to be replaced in piping with flow nozzles having a more wide range because it can assume different values of β 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 15
VENTURI METER Venturi meter consists of a converging and a diverging sections. The decrease in the section of the pipeline, due to the inverse proportionality that links the velocity to the section of the pipeline, determines, at constant flow, an increase in velocity (continuity equation). 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 16
VENTURI METER • The Venturi meter shape allows the homogeneity and the axial symmetry of the vena contracta. In improves the local flow regime of the fluid and the pressure meaurements from which depends the precision of the flow rate measure. • The variation of the inner contour of the Venturi meter, the small imperfection and roughness of the internal surface on the Venturi meter and the installation eccentricity are negligible and they don't have much influence on the measurements. • Venturi meter shows a better repeatability of the measurement with time because of the few scratches produced by the small solid particles transported by fluid do not influence the instrument indications. • With the same contract ratio with the other contraction-based devices Venturi meter has greater accuracy and lower pressure drop than the other contraction flow rate sensors but it is more expensive. NOTE: It is fundamental to take into account cavitation in the design and the construction of a Venturi meter. The pressure in vena contracta must not be lower the vapor pressure of the liquid. Cavitation can produce considerable damage to the sensor and to the pipeline. 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 17
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 18
ROTAMETER VARIABLE AREA VOLUMETRIC FLOWMETER • It consists of a transparent tapered pipe, slightly conical, placed vertically with an upward fluid. • A graduated scale is reported externally. • A body (“float”) having a greater density than fluid is located internally. • The float is made on different shapes, as spherical and conical, depending on the application and the fluid. • The flow rate measurement is performed by the observation of the position of the float on the graduated scale. The position is taken on the lowest section flow, corresponding to the section of the diameter for a sphere and of the base for a cone. • A higher volumetric flow rate through a given area increases flow speed and drag force, so the float will be pushed upwards. • The cross section available to the fluid increases when the float is raised, i. e. to increase the flow rate. • A hard-set in placed on the top of the column to avoid severe impact with the upper zone of the rotameter. • A spring is placed at the bottom of the rotameter in order to prevent damage of the instrument for abrupt interruption of the flow. • Pipes made of steel are used for rotameter performing at high pressure. In this case the external indicator is coupled with an electromagnetic float. 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 19
ROTAMETER When the float is stable on a specified position, an equilibrium of forces occurs. Readings are directly performed on the graduated scale of the flowrate on the transparent column 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 20
ROTAMETER 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 21
ROTAMETER VARIABLE AREA VOLUMETRIC FLOWMETER video Rotameter. avi 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 22
ROTAMETER Hypotheses • For a generic float we can indicate: the bottom position of the float (1), when the sectional area for the fluid flow becomes to reduce the position of minimum sectional area for the fluid flow (2), with the subscript “ 0” the quantity referred to the float. • Spherical float (2) • Steady state (1) • Constant ρ • Section area S 2<<S 1 • z 2 - z 1 V 0/A 0; (where: V 0 is the volume of the float, A 0 is the projected area of the float) • Local and Distributed Pressure drops are negligible • z v ≠ f(r) • Surface for pressure forces = Projected area 09. 06. 12 → A 1 = A 2= A 0 Process Instrumentation and Control - Prof M. Miccio 23
ROTAMETER Flow equation Force balance (scalar) equation on the float (a) P 1 A 1 - P 2 A 2 - ρ 0 V 0 g = 0 where: P 1 : fluid pressure in position (1); P 2: fluid pressure in position (2) (with P 2<P 1 for the Bernoulli’s principle) P 1 A 1 = upstream force exerted by the fluid pressure on the float P 2 A 2 = downstream force exerted by the fluid pressure ρ0 V 0 g= weight of the float Since the hypothesis: A 1=A 2=A 0 (b) (2) (1) P 1 A 0 - P 2 A 0 - ρ 0 V 0 g = 0 Bernoulli’s equation For section (1) and (2) and considering a constant density, we have: (c) Continuity equation (d) where S 1>>S 2 e v 2>>v 1 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 25
ROTAMETER Flow equation Equation (c) becomes: (e) From the force balance eq. (b) we obtain: (f) From the previous assumption : (g) where V 0 is the volume of the float NOTE: The assumption (g) is dimensionally correct, but is not properly exact for a sphere. 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 26
ROTAMETER Flow equation Replacing eqs. (f) and (g) in (e) we obtain: By simplification it becomes: Considering the continuity equation: Factorizing in v 2: 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 27
ROTAMETER Flow equation and solving for v 2 we obtain: The flow coefficient for a contraction γ is: And multiplying by S 2 the right and the left hand sides we have the final equation: NOTE: S 2 is a linear function of the position of the float due to the conical shape of the pipe The mass flow rate can be calculated from the volumetric flow rate as: 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 28
ROTAMETER Relationship between Flowrate and Height of the float 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 29
ROTAMETER Relationship between Flowrate and Height of the float 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 30
ROTAMETER Calibration The volumetric flow rate of a rotameter is expressed as normal-liters per hour for the calibration conditions. If the instrument is used in a different condition than the calibration conditions the measurement needs a correction as: where: ρn is the calibration density; is the corrected measure; is the actually read flow rate. 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 31
ROTAMETER Calibration Volumetric flow rate: For an ideal gas: If P = constant the correction becomes: On the other hand, if T = constant 09. 06. 12 we have: Process Instrumentation and Control - Prof M. Miccio 32
ROTAMETER Accuracy: 1% of the measurement at 100% of the flow rate (3 10)% of the measurement at 10% of the max flow rate Measuring range: up to 30 kg/s (H 2 O), up to 1 kg/s (air) Advantages • • Linear relation flow rate – float position Constant pressure drop across the float Easy to read Easy to install and to use in laboratories and pilot plants Disadvantages • • • A proper calibration is needed for each fluid at specific temperature and pressure Correction formulas when it is used in condition different from calibration It is not an electrical transducer Only vertical installation Requires "reinforced" model or non-transparent tube for high working pressures 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 33
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 34
FLOWMETERS based on measurement of velocity Name Principle Application Intrusive Transducer VORTEXSHEDDING frequency of vortices formation liquids at low viscosity, gas and clean vapors YES liquids and gases YES liquids (also emulsion or suspension, no gas) with electrical conductivity (C 5 S/m) NO YES YES SWIRL METER frequency of vortices formation ELECTROMAGNETIC Faraday. Neumann-Lenz law TIME-OFTRAVEL ultrasonic wave liquids DOPPLER ultrasonic wave Liquids with NO particles or Process Instrumentation and Control - Prof M. Miccio bubbles 09. 06. 12 YES 35
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 36
CORIOLIS METERS Working principle They use the Coriolis effect. The measuring element is subjected to a vibration “simulating” the rotation of it; the Coriolis effect produces a force TOP VIEW depending on the mass flow rate. The measurement is independent from both the flow regime and a possible variation of fluid properties. SIDE VIEW 09. 06. 12 from Magnani, Ferretti and Rocco (2007) Process Instrumentation and Control - Prof M. Miccio 37
CORIOLIS METERS 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 38
CORIOLIS MASS FLOWMETER Vibrating tube configuration 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 39
CORIOLIS MASS FLOWMETER Direct measurement of mass flow rate [kg/s] Recommended to measure flow rate for liquids and fairly dense gases. Measuring range (liquids) Accuracy Repeatability Rangeability Installation from 0. 001 kg/s to 20 kg/s 0. 25% of the measurement 0. 15% of the measurement 100: 1 No restrictions (vertical installation is better) Advantages Small pressure drop Disadvantages Expensive 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 40
ELECTRONIC THERMAL MASS FLOWMETER Thermal Mass Flow Meters (and Controllers) make use of the heat conductivity of fluids (gases or liquids) to determine mass flow. Three implementations: Ø for gases, by-pass principle Ø for gases, inline principle Ø for liquids, inline principle ] following the anemometric principle flowz. flv 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 41
ELECTRONIC THERMAL MASS FLOWMETER for gases, by-pass principle The sensor is mounted as a by-pass to the main channel, where a patented flow resistance splitter takes care of proportional flow division, also under varying process conditions. A part of the gas stream flows through the sensor, and is warmed up by heaters RHT 1 and RHT 2. Consequently the measured temperatures T 1 and T 2 drift apart. The temperature difference is directly proportional to mass flow. Electrically, temperatures T 1 and T 2 are in fact temperature dependent resistors RHT 1 and RHT 2. This laminar flow element consists of a stack of stainless steel disc with high-precision etched flow channels, having similar characteristics as the flow sensor. http: //www. bronkhorst. com 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 42
ELECTRONIC THERMAL MASS FLOWMETER 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 44
ELECTRONIC THERMAL MASS FLOWMETER 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 45
ELECTRONIC THERMAL MASS FLOWMETER 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 46
ELECTRONIC THERMAL MASS FLOWMETER for gases, inline principle http: //www. bronkhorst. com Mass Flow Meters with inline sensor (no by-pass) consist of a straight flow channel, into which two stainless steel probes protrude; a heater probe and a temperature sensor probe. A constant temperature difference (ΔT) is created between the two probes and the energy required to maintain this ΔT is proportional to the mass flow rate (CTA: Constant Temperature Anemometry). Mass flow can be measured with low pressure drop. Compared to traditional thermal MFMs and MFCs with by-pass, they are less sensitive to humidity and contamination. 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 47
ELECTRONIC THERMAL MASS FLOWMETER Advantages • Direct measurement of mass flow rate [kg/s] • Accuracy up to: Ø εa = 0. 75% Ø εf = 0. 25% • Rangeability from 10: 1 to 100: 1 Other characteristics • Recommended for “very clean” gas • Adjustable to measurement of flow rate for liquids with special and expensive devices 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 48
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 49
POSITIVE-DISPLACEMENT METER DEFINITION A fluid (liquid or gas) quantity meter that separates and captures definite volumes of the flowing stream one after another and passes them downstream, while counting the number of operations. 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 50
ROTARY METERS Classification Positive Displacement Momentum transfer The axis is normal to the flow direction The axis is coincident to the flow direction 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 51
ROTARY VANE FLOWMETER from ISA Certified Control Systems Technician (CCST) program http: //www. isa. org Rotation velocity of rotor N. of “units of volume” carried for unit of time fluid volumetric flow rate 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 52
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 53
PADDLE WHEEL FLOWMETER (for liquids) • The paddle wheel flow meter is frequently considered as a low cost alternative to the turbine-type flow meter in applications with less demanding accuracy requirements. • The paddle wheel (rotor with blades) is perpendicular to the flow path, not parallel as in the traditional turbine-type flow meter (Tangential rotor) • The rotor's axis is positioned to limit contact between the paddles and the flowing media to less than 50% of the rotational cycle. This imbalance causes the paddle to rotate at a speed proportional to the velocity of the flowing media. • The fluid transfers a small amount of momentum to the impeller • A sensor is used to detect the proximity of micromagnets imbedded in each of the passing paddle wheel blades. The frequency of the output signal is proportional to the fluid velocity and can be transmitted directly to external remote readout/data acquisition. • It is inherently bi-directional. • It is a transducer http: //www. instrumart. com/pages/227/in-line-turbine-paddle-wheel-flow-meters 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 54
TURBINE FLOWMETER (for liquids) • Axial rotor • Rotation speed is detected magnetically (e. g. , by a magnet fixed on the rotor) • The fluid transfers a small amount of momentum in the turbine • The sensor relates the volumetric flow rate to the rotation speed of the rotor • It is a transducer 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 55
APPENDICE 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 56
SECOND CLASSIFICATION (based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 57
VORTEX-SHEDDING FLOWMETER Vortex sensor Functioning principle: Measure the frequency of vortices formation with: • piezo-electric element which detects local pressure variations associated to vortices; • thermistor, heated with a little electric current, which detects resistance temperature variations due to the different cooling transport phenomena occurring between thermistor and the fluid influenced by vortices formation Bluff body Operating equation: Vortex formation frequency: fv = Kv Shape of the bluff body K constant for different motion condition Volumetric flor rate: Bluff body 09. 06. 12 fv measurement with a thermistor Process Instrumentation and Control - Prof M. Miccio 58
VORTEX-SHEDDING FLOWMETER Characteristics: Recommended for liquids at low viscosity, gas and clean vapors P/T correction for gas and vapors Accuracy: 0. 75% of the measurement for liquids (1% for gas), Rangeability: 10: 1 Measuring range: 0. 2 450 kg/s (H 2 O), 4 3600 kg/s (air) Transducer Intrinsically digital signals (no AC/DC converter) More modern model vortex mass flow rate Limitation • High turbulent flow regime (Re > 30000) • Installation constraints: • L_ = 15 DN; L+ = 5 DN; • Horizontal position 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 59
SWIRL METER • vortices are caused by specific fins at the entrance of the instrument • it uses a piezo-electric element or a thermistor to “sense” turbulence • it measures the volumetric flow rate of liquids and gases Measuring range: – 0, 01 ÷ 500 kg/s liquid – 0. 3 x 10 -3 ÷ 6. 6 kg/s gas 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 60
SWIRL METER vs. VORTEX COMPARISON WITH A VORTEX-SHEDDING FLOWMETER • horizontal and vertical installation • no upstream and downstream straigth line 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 61
ELECTROMAGNETIC FLOWMETER Functioning principle: Faraday’s Law Faraday-Neumann-Lenz law (absolute value) magnetic field B [weber/m 2 = tesla] Liquids (also emulsion or suspension, no gas) with electrical conductivity (C 5 S/m) • • Advantages The output signal is linear to the volumetric flow rate. The flow direction can be inverted. Not intrusive negligible pressure drop They are used in all industrial applications, e. g. : food, waste waters, chemicals, etc. very high accuracy up to <0. 5% rangeability from 50: 1 to 100 : 1 Measuring range from 0. 005 to 30000 kg/s (H 2 O) COIL PIPE ELECTRODES Limitation/Disadvantages STRAIGTH LINE constraint (HORIZONTAL and/or VERTICAL installation) with L_ = 3 DN L+ = 2 DN 09. 06. 12 OUTPUT SIGNAL Process Instrumentation and Control - Prof M. Miccio 62
ELECTROMAGNETIC FLOWMETER Technical features 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 63
ULTRASONIC FLOWMETER 2 types: • Time-of-travel • Doppler effect 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 64
TIME-OF-TRAVEL ULTRASONIC METER 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 65
DOPPLER FLOWMETER 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 66
DOPPLER FLOWMETER (with clamp-on configuration) TRANSMITTER, FREQUENCY ft WEDGE REFLECTING PARTICLES FLOW RECEIVER, FREQUENCY fr Advantages Non intrusive negligible pressure drop 09. 06. 12 Process Instrumentation and Control - Prof M. Miccio 67
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