Flow rate measurements 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 MASS (m) (kg/s) VOLUMETRIC (V) (L/s) MOLAR (N) (kmol/s) §2.2.1 pag. 9 Magnani, Ferretti and Rocco (2007) 09.06.12 Process Instrumentation and Control - Prof M. Miccio

FLOW RATE METERS CLASSIFICATIONS First classification (by contrast) Volumetric Mass Static Rotary Trasducer Non-Trasducer Intrusive Non-Intrusive 09.06.12 Process Instrumentation and Control - Prof M. Miccio

FLOW RATE METERS CLASSIFICATIONS Second Classification based on measuring principle Differential pressure Variable Area Velocity Direct Mass Measurement Rotary 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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

CONTRACTION-BASED FLOW METERS HYPOTHESES: horizontal position ρ = constant v # f (r ) Δploc= 0 circular pipe 1 2 d1 d2 A1 A2 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) Local pressure drop (vortices formation) where β is the contraction ratio 09.06.12 Process Instrumentation and Control - Prof M. Miccio

CONTRACTION-BASED FLOW METERS Hypotheses: compressible fluid (Gas or Vapor); small (P1 - P2); K = calibration factor [m2] “PI ON TI” CORRECTION 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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

ORIFICE PLATE or ORIFICE METER d1 d2 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. 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio DIAPHRAGMS Examples vent (optional) Φ=2,5mm C.F.R. Internal to the pipe purge (optional) 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ORIFICE PLATE INSTALLATION Re > 500 HORIZONTAL POSITION Undisturbed and straight pipeline 20D upstream and 5D downstream d = orifice diameter D = pipe diameter β = d/D<1 Exploded view drawing 09.06.12 Process Instrumentation and Control - Prof M. Miccio

PRESSURE PROFILE OF A LIQUID IN A CONTRACTION [(P/ρg)+(v2/2g)] Friction loss P Pressure drop due to the orifice Kinetic energy Pressure and potential energy orifice_meter.swf upstream vena contracta downstream 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ORIFICE PLATE POSITIONING OF PRESSURE SENSORS at vena contracta on the carrier ring 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

ORIFICE PLATE POSITIONING OF PRESSURE SENSORS at vena contracta on the carrier ring 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

Process Instrumentation and Control - Prof M. Miccio FLOW NOZZLE Installation Flow Nozzle It measures the pressure drop before and after a contraction of the cross section of the pipe. It measure ΔP by means a differential manometer. 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

Process Instrumentation and Control - Prof M. Miccio 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

Process Instrumentation and Control - Prof M. Miccio 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

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

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

Process Instrumentation and Control - Prof M. Miccio 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

Process Instrumentation and Control - Prof M. Miccio ROTAMETER 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ROTAMETER variable area Volumetric FlowMETER video Rotameter.avi 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio 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 Steady state Constant ρ Section area S2<<S1 z2 - z1  V0/A0; (where: V0 is the volume of the float, A0 is the projected area of the float) Local and Distributed Pressure drops are negligible z v ≠ f(r) Surface for pressure forces = Projected area → A1 = A2= A0 (1) (2) 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ROTAMETER Flow equation Force balance (scalar) equation on the float (a) P1A1 - P2A2 - ρ0V0g = 0 where: P1 : fluid pressure in position (1); P2: fluid pressure in position (2) (with P2<P1 for the Bernoulli’s principle) P1A1 = upstream force exerted by the fluid pressure on the float P2A2 = downstream force exerted by the fluid pressure ρ0V0g= weight of the float Since the hypothesis: A1=A2=A0 (b) P1A0 - P2A0 - ρ0V0g = 0 Bernoulli’s equation For section (1) and (2) and considering a constant density, we have: (c) Continuity equation (d) where S1>>S2 e v2>>v1 (1) (2) 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ROTAMETER Flow equation Equation (c) becomes: (e) From the force balance eq. (b) we obtain: (f) From the previous assumption : (g) where V0 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

ROTAMETER Flow equation Replacing eqs. (f) and (g) in (e) we obtain: By simplification it becomes: Considering the continuity equation: Factorizing in v2: 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ROTAMETER Flow equation and solving for v2 we obtain: The flow coefficient for a contraction γ is: And multiplying by S2 the right and the left hand sides we have the final equation: NOTE: S2 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

ROTAMETER Relationship between Flowrate and Height of the float The geometric dependence of the surface area of the throttling section S2 on the height of float lifting H is defined according to the scheme in figure is: 𝑆 2 𝐻 =π 𝐷 𝑡𝑔 θ 𝐻+ 𝑡𝑔 θ 𝐻 2 where θ is the angle of the cone-forming line with relation to the pipe axis. For pipes with small conicity (from the order of 1:100) and not long float travel, the expression 𝑡𝑔 θ 𝐻 2 gets insignificant values and it can be ignored. 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ROTAMETER Relationship between Flowrate and Height of the float So we can obtain the relationship between the Volumetric Flowrate and on the height of float lifting H is defined according to the scheme in figure is: V̇= γπ 𝐷 𝑡𝑔 θ 𝑔 ρ 0 ρ −1 𝑉 0 𝐴 0 𝐻 Multiplying the two sides of this equality by the density of the fluid ρ, we will get the generalized characteristic of the rotameter for measuring the mass flow ṁ: ṁ= γπ 𝐷 𝑡𝑔 θ 𝑔ρ ρ 0 −ρ 𝑉 0 𝐴 0 𝐻 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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

ROTAMETER Calibration Volumetric flow rate: For an ideal gas: If P = constant the correction becomes: On the other hand, if T = constant we have: 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio 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 (H2O), 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

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

FLOWMETERS based on measurement of velocity Name Principle Application Intrusive Transducer VORTEX-SHEDDING frequency of vortices formation liquids at low viscosity, gas and clean vapors YES SWIRL METER liquids and gases ELECTRO-MAGNETIC Faraday-Neumann-Lenz law liquids (also emulsion or suspension, no gas) with electrical conductivity (C  5S/m) NO TIME-OF-TRAVEL ultrasonic wave liquids DOPPLER Liquids with particles or bubbles 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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

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 depending on the mass flow rate. The measurement is independent from both the flow regime and a possible variation of fluid properties. TOP VIEW SIDE VIEW from Magnani, Ferretti and Rocco (2007) 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio CORIOLIS METERS 09.06.12 Process Instrumentation and Control - Prof M. Miccio

CORIOLIS MASS FLOWMETER Vibrating tube configuration 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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) from 0.001 kg/s to 20 kg/s Accuracy  0.25% of the measurement Repeatability 0.15% of the measurement Rangeability 100:1 Installation No restrictions (vertical installation is better)  Advantages Small pressure drop  Disadvantages Expensive 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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: for gases, by-pass principle for gases, inline principle for liquids, inline principle ] following the anemometric principle flowz.flv 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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 RHT1 and RHT2. Consequently the measured temperatures T1 and T2 drift apart. The temperature difference is directly proportional to mass flow. Electrically, temperatures T1 and T2 are in fact temperature dependent resistors RHT1 and RHT2. 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

ELECTRONIC THERMAL MASS FLOWMETER 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ELECTRONIC THERMAL MASS FLOWMETER 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ELECTRONIC THERMAL MASS FLOWMETER 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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

ELECTRONIC THERMAL MASS FLOWMETER  Advantages Direct measurement of mass flow rate [kg/s] Accuracy up to: εa =  0.75% 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

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

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

Classification ROTARY METERS 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

rotary vane flowmeter Rotation velocity of rotor 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

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

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

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

Process Instrumentation and Control - Prof M. Miccio APPENDICE 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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

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 the 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 fv measurement with a thermistor 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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 (H2O), 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

Process Instrumentation and Control - Prof M. Miccio 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 0.3x10-3 ÷ 6.6 kg/s gas 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio 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

ELECTROMAGNETIC FLOWMETER Functioning principle: Faraday-Neumann-Lenz law magnetic field B [weber/m2 = tesla]  Liquids (also emulsion or suspension, no gas) with electrical conductivity (C  5S/m) Faraday’s Law (absolute value)  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 (H2O)  Limitation/Disadvantages STRAIGTH LINE constraint (HORIZONTAL and/or VERTICAL installation) with L_ = 3 DN L+ = 2 DN Coil PIPE ELECTRODES OUTPUT SIGNAL 09.06.12 Process Instrumentation and Control - Prof M. Miccio

ELECTROMAGNETIC FLOWMETER Technical features 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio ULTRASONIC FLOWMETER 2 types: Time-of-travel Doppler effect 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Time-of-travel ultrasonic meter 09.06.12 Process Instrumentation and Control - Prof M. Miccio

Process Instrumentation and Control - Prof M. Miccio DOPPLER FLOWMETER 09.06.12 Process Instrumentation and Control - Prof M. Miccio

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