Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

Flowrate

Experimental methods E181101 EXM5

Some pictures and texts were copied from www.wikipedia.com

RotameterTurbine Vortex flowmetersNozzles Venturi, orificePitot tube (multihole tube)UltrasoundCoriolisThermalLaser Doppler

Flowrate measurement EXM5

Rotameter, floater and conical glass pipe. Position 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?

)(2

3

fD

gfDQ

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 street

Nozzles, Venturi, orifice use the Bernoulli Equation to calculate the fluid flow rate by measuring the pressure difference through obstructions in the flow

Vortex, orifice EXM5

uD

Srf

p

ku

2

Strouhal’s number Sr=0.21 for cylinder of diameter D (holds for Re>10000)

p p p

1% accuracy, low pressure drop 2%, pressure drop large (vena contracta)

Ultrasound flowmeters EXM5

Transit time (without particles) expensive, accurate

2221221 cos

cos2,

cos,

cos uc

Lutt

uc

Lt

uc

Lt

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.

c

u

f

f cos2

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:

http://biomechanika.cz

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 flowmetersEXM5

BuqF

Lorentz force acting on ion (charge q) moving with velocity u in magnetic field (magnetic induction B).F

B

u

electrode

Lorentz force is in balance with electromotive force

EqF

Coriolis flowmetersEXM5

umF 2Coriolis 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.

uF

-phase shift

fcm

[kg/s] f-frequency of oscillation

]1)[( 2 f

fk empty [kg/m3] density from

eigenfrequencyElmag.induced oscillations

Detectors of position

Thermal flowmetersEXM5

mbai 2

Thermal mass-flowmeters heated wire/hot film anemometers electr.current is controlled so that the temperature of wire (resistance) is constant.

Rm

i-source

Um=0 controller

i-current is adjusted so that the Rm will be the same as the fixed resistors in the bridge.

DPower necessary to maintain constant temperature of heated wire depends upon flow velocity

Thermal flowmetersEXM5

)()( 2fluidwirewirem TTDLiTR

Hot wire anemometer simplified theory

Heat generated in wire

Heat transferred to fluid by convection

D

uDD

Nu 04.0Pr)Re06.0Re04.0( 3/23/2

uciRm 2

Thermal flowmetersEXM5

)( 22 TTcm

Differential anemometers – heater + 2 thermocouples symmetrically located

T1 T2

Heater

Correlation flowmetersEXM5

dttTtTR )()()( 2112

Cross-correlation of stimulated or random signal detected at two locations (technically it can be a heater and thermocouples)

T1 T2

Heater

Correlation flowmetersEXM5

dttTtTR )()()( 2112

Example calculated by MATLAB

Heater

Random signal shifted by 100 time steps