Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 Flowrate Experimental methods E EXM5 Some pictures and texts were copied from

 Rotameter  Turbine  Vortex flowmeters  Nozzles Venturi, orifice  Pitot tube (multihole tube)  Ultrasound  Coriolis  Thermal  Laser Doppler Flowrate measurement EXM5

 Rotameter, floater and conical glass pipe. P osition of floater is determined by the balance of forces: weight of floater = fluid forces. The higher is floater, the wider is the gap, therefore the lower are velocities and viscous friction. This flowmeter can be used not only for liquids, but also for gases (or inviscid fluids). In this case the fluid forces are not viscous, but inertial and can be derived from Bernoulli’s equation.  Turbine (detector of pulses – flowrate proportional to frequency) Rotameter, Turbine EXM5 What do you think is the purpose of these inclined grooves? f -frequency. g -viscous correction

 Vortex flowmeters utilize the vortex shedding principle. The fluid strikes a bluff body, generating vortices (eddies) that move downstream. The vortices form alternately, from one side to the other. A piezoelectric sensor housed in a sensor tube directly downstream of the bluff senses the pressure zones created by the vortices. The sensor generates a frequency directly proportional to the vortices (flow). Look at more details about von Karman vortex streetKarman vortex street  Nozzles, Venturi, orifice use the Bernoulli Equation to calculate the fluid flow rate by measuring the pressure difference through obstructions in the flow Nozzles Vortex, orifice EXM5 Strouhal’s number Sr=0.21 for cylinder of diameter D (holds for Re>10000) pp pp pp 1% accuracy, low pressure drop 2%, pressure drop large (vena contracta)

Ultrasound flowmeters EXM5 Transit time (without particles) expensive, accurate Doppler effect (reflected wave by particles). Doppler frequency shift Measurements are made by sending bursts of signals through a pipe. Sound waves travelling in the direction of flow of the fluid require less time than when travelling in the opposite direction. The difference in transit times of the ultrasonic signals is an indication for the flow rate of the fluid. Since ultrasonic signals can also penetrate solid materials, the transducers can be mounted onto the outside of the pipe.  L-length of beam, u-flow velocity, c-speed of sound (1500 m/s in water) Doppler ultrasonic flowmeters operate on the Doppler shift principle, whereby the transmitted frequency is altered linearly by being reflected from particles and bubbles in the fluid. The net result is a frequency shift between transmitter and receiver frequencies that can be directly related to the flow velocity. Doppler meters require a minimum amount of solid particles or air in the line to achieve measurements. 

UVP monitor (Ultrasound Velocity Profile) EXM5 Ultrasound Doppler effect for measurement velocity profiles 1.Piezotransducer is transmitter as well as receiver of US pressure waves operating at frequency 4 or 8 MHz. 2.Short pulse of few (  10) US waves is transmitted (repetition frequency 244Hz and more) and crystal starts listening received frequency reflected from particles in fluid. 3.Time delay of sampling (flight time) is directly proportional to the distance between the transducer and the reflecting particle moving with the same velocity as liquid. 4.Received frequency differs from the transmitted frequency by Doppler shift Δf, that is proportional to the component of particle velocity in the direction of transducer axis. PROBLEMS: 1.What is spatial resolution of velocity, knowing speed of sound in water (1400 m/s) and sampling frequency 8 MHz ? 2.Calculate flowrate in a circular pipe from recorded velocity profile (given angle  )

Magnetic flowmeters (electromagnetic or induction flowmeters), obtain the flow velocity by measuring the changes of induced voltage of the conductive fluid passing across a magnetic field. A typical magnetic flowmeter places electric coils around the pipe of the flow to be measured and sets up a pair of electrodes across the pipe wall. If the targeted fluid is electrically conductive, i.e., a conductor, its passing through the pipe is equivalent to a conductor cutting across the magnetic field. This induces changes in voltage reading between the electrodes. The higher the flow speed, the higher the voltage. Electromagnetic flowmeters EXM5 Lorentz force acting on ion (charge q) moving with velocity u in magnetic field (magnetic induction B). electrode Lorentz force is in balance with electromotive force

Coriolis flowmeters EXM5 Coriolis force in a rotating pipe Rotation is substituted by vibration in an actual design of flowmeter. The flow is guided into the U-shaped tube. When an osillating excitation force is applied to the tube causing it to vibrate, the fluid flowing through the tube will induce a rotation or twist to the tube because of the Coriolis acceleration acting in opposite directions on either side of the applied force. This twist results in a phase difference (time lag) between the inlet side and the outlet side and this phase difference is directly affected by the mass passing through the tube. A more recent single straight tube design is available to measure some dirty and/or abrasive liquids. Vibration of Coriolis flowmeters has very samll amplitude, usually less than 2.5 mm, and the frequency is near the natural frequency of the device, usually around 80 Hz. The vibration is commonly introduced by electric coils and measured by magnetic sensors. Resonant frequency depends upon density – therefore not only flowrate but also density is measured.  - phase shift [kg/s] f-frequency of oscillation [kg/m 3 ] density from eigenfrequency Elmag.induced oscillations Detectors of position

Thermal flowmeters EXM5 Thermal mass-flowmeters heated wire/hot film anemometers electr.current is controlled so that the temperature of wire (resistance) is constant. RmRm i- source U m =0 controller i-current is adjusted so that the R m will be the same as the fixed resistors in the bridge. D Power necessary to maintain constant temperature of heated wire depends upon flow velocity

Thermal flowmeters EXM5 Hot wire anemometer simplified theory Heat generated in wire Heat transferred to fluid by convection D

Thermal flowmeters EXM5 Differential anemometers – heater + 2 thermocouples symmetrically located T1T1 T2T2 Heater

Correlation flowmeters EXM5 Cross-correlation of stimulated or random signal detected at two locations (technically it can be a heater and thermocouples) T1T1 T2T2 Heater

Correlation flowmeters EXM5 Example calculated by MATLAB Heater Random signal shifted by 100 time steps