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6. Flow and Humidity Sensors
Flow sensors
Venturi tube
turbine flowmeter
ultrasonic flowmeters
laser flowmeter
thermal flowmeters, anemometer
correlation flowmeter
miniature flowmeters
Humidity sensors
piezoresistance - type
resistance - type
capacitance - type
gravimetric
SAW
dew-point
1
Flow sensors
Flow sensors can be divided into two groups:
• mass flowmeters registering the mass flow rate dm/dt
• volume flowmeters registering the volume flow rate dV/dt
Flow rate
Mass flow rate for a cross section A
 dV 
 dm 





 vA
 dt 



A  dt A
For a pipe of a cross section A:
dm
dV

   v dA   v av A
dt
dt A
In general there exists a distrubution of velocity v(r) in a pipe cross-section, what has
to be taken into account in the design of flowmeters (one determines the local value
or average for a certain area).
Depending on the magnitude of Reynolds number we have:
a) laminar flow (Re < 2300)
  r 2 
v  v m 1 -   
  R  
R – radius of a pipe
b) transition flow (critical), for 2300<Re<104
c) turbulent flow, dla Re > 104
r

v  v m 1 - 
 R
Reynolds number: Re 
2R v av 

1
n
n - dep. on Re and roughness of a pipewall
η – coeff. of viscosity
ρ - density
Velocity profiles for different kinds of flow
1 – laminar flow
2 – turbulent flow
(rough pipewalls)
3 – turbulent flow
(smooth pipewalls)
Narrow channel sensors
One measures the differential pressure existing during transfer of a fluid
through the narrow channel.
Sensors with Venturi tube
v 2w
v 2n
 pw 
 pn
2
2
vwAw  vvAn
Bernoulli’s law
continuity equation
Solving the equation system one obtains:
vn 
1
A 2n
1- 2
Aw
2(p w - p n )

v n  p
Volume flow rate:
dV
 v v A n  A n p
dt
Mass flow rate:
dm
  A n p
dt
Turbine flowmeter
Frequency of rotations depends
linearly on medium velocity.
Time rate of change of a pulse
number at the magnetic coil output
is prop. to the volume flow rate.
Precise measurements are obtained
for liquids of small viscosity.
Ultrasonic flowmeters
Applied essentially for measurements of volume flow in liquids.
Transit time method
Transit time for a down-stream direction:
t1 
s
c  v s cos 
c – velocity of sound in a fluid
vs – average fluid velocity
Transit time for an up-stream direction:
t2 
A, B – transmitters/receivers
s
c - v s cos 
Fluid velocity:
vs 
s 1 1
 - 
2 cos   t 1 t 2 
The local value of liquid velocity v(r) can be also measured
t1 
l
c  v( r )
t2 
l
c - v( r )
down-stream direction
up-stream direction
t  t 2 - t 1 
2 v( r )
c 2 - v( r ) 2
In order to avoid the influence of temperature on sound
velocity c one determines:
t
2 v( r )

t1t 2
l
Volume flow rate:
dV
 K   R 2  vx
dt
where K depends on r/R and vx is a given velocity
Doppler flowmeter
Developed first of all for measurements
in inhomogeneous liquids, e.g. containing
solid particulates or gas bubbles.
If the transmitted wave frequency is f, then
due to scattering on moving particles one
observes also f1 and f2.
Scattering by escaping particles gives:
f1  f
c - vx
c
Scattering by particles moving in reverse direction gives: f 2  f
Velocity v is determined from relation:
f 2 - f1 2v x 2v cos 


f
c
c
c  vx
c
Doppler flowmeter, cont.
Doppler flowmeters enable also the determination of velocity profile.
The ultrasonic pulses lasting 0.1 – 1 ms are emitted and the distance from
which they are received is changed by selection the instant of time of receiver
opening.
By this method the variations of velocity profile of blood in aorta are
determined.
Laser Doppler flowmeter
fD - Doppler shift
Thermal flowmeters
These flowmeters give the mass flow rate.
The mass flow rate is equal:
dm dQ / dt
dQ / dt


dt
c w T c w (T2 - T1 )
By keeping T constant (change of mass requires change of a heat):
dm dQ

dt
dt
In order to keep constant T an appreciable power is required.
Placing a heater on a pipe (at low flows) decreases the power consumption.
A bypass can be also applied for this purpose.
Anemometers
At a staeady state the power of heating is equal to the power
of heat dissipation for a wire resistor
(Tw – resistor temp., Tf – fluid temp.)
coeff. of heat loss
From above equations one obtains the fluid velocity vf
wire: PtRh, W, Pt
diameter: 4 – 10 mm
length: 1 mm
layers: Ni, Pt
Anemometers, cont.
Constant temperature condition (Tw and Rw constant):
Constatnt current condition:
Anemometers in a measurement system
Constant current bridge
(R2 - initial balance setting,
source resistor – initial
temperature setting)
A bridge with constant temperature
sensor
Uwyj ~ vgaz
Correlation flowmeter
The system realizes the correlation function
T
1
R xy ()  lim
y( t ) x ( t - ) dt


T  2T - T
Rxy attains maximum for:

Having L and  one calculates velocity.
Miniature flowmeters
Humidity sensors
Moisture – the amount of water contained in a liquid or solid.
Absolute humidity – the mass of water vapour per unit volume.
Relative humidity (RH) – the ratio of actual vapour pressure (pw - partial pressure
of water vapour) to the saturation vapour pressure ps at the same temperature.
RH 
pw
100
ps
Dewpoint temperature – the temperature at which RH is 100%.
At dewpoint condensation droplets appear (at low teperature below O0C
the moisture can freeze).
Piezoresistance sensors
Hygroscopic layer of
polyimid swells causing
modulation of a
technological stress in a
membrane and change
in resistance of 4 p+ Si
piezoresistors (details
on the following page).
Piezoresistance sensors, cont.
4 piezoresistors at the
membrane edge (2 parallel
and 2 perpendicular to the
edge).
The voltage UA at a bridge
output is a linear function
of the difference between
stress σL in a perpendicular
resistor and stress σQ in a
parallel resistor.
π44 – piezoresistance coeff.
of Si (100) in direction <110>
UA  -
44
U SS (  L - Q )
2
R. Buchhold et al. Sens.&Act.B 53 (1998) 1-7
Integrated resistance sensors
Integrated resistance sensor in CMOS-MEMS
technology.
Polysilicon resistor RS changes its resistance
due to water vapour absorption by the WO3
surface layer.
Vout = - RS/R1 ·Vin
C.L. Dai i in. Sens.&Act.B123 (2007) 896
Integrated resistance sensors, cont.
Porous sensitive layer as
WO3 nanowires.
Integrated humidity sensor in 0,35 μm
technology (outside view).
C.L. Dai i in. Sens.&Act.B 123 (2007) 896
Manufactured op amp
Resistance - capacitive sensors
Measurement of impedance Z
Au
Equivalent circuit of a pore and
its environment
Rs
Ro
Al2O3
CB
Co
RB
Al
Anodized Al
R0, C0 – layer of aluminum oxide
RS – pore wall
RB, CB – area between the pore bottom
and Al electrode
Capacitive sensors
A capacitive thin flm humidity sensor.
The electrodes form interdigitized pattern.
The dielectric layer can be CVD SiO2 or CVD PSG (phosphosilicate glass).
When humidity increases, the distributed resistance drops and equivalent
capacitance increases.
Capacitive sensors, cont.
Capacitive sensors with different
electrode configuration:
interdigital,
spiral,
grid.
Nonlinear behaviour of
capacitance as a function of RH
Cs   w 
  
C0   d 
n
J.G. Korvink i in., Sens. Mater. 4 (6) (1993)323-335
Capacitive sensors, cont.
Microsystem technologies
Membrane with a buried n-Si heater
for regeneration, surface gold meshtype electrodes and porous silicon (PS)
layer absorbing humidity.
G.M. O`Halloran et al., Delft Univ. Press
(1999) 1919
Bulk-type humidity sensor with a
surface heater and temperature
detectors.
Porous Si sheet is covered by meshtype electrodes.
Z.M. Rittersma i in., Sens. Mater.
12 (1) (2000) 035
Gravimetric sensors
Oscillating element, e.g. quartz, is covered with a humidity absorbing layer.
Change in oscillator’s mass causes a change in its resonance frequency:
f -m

f0
m
For a quartz plate with AT cut, 35o15’ versus its z-axis,
one obtains:
f  -2,3 106 f 02
m
A
Large fo is therefore beneficial.
the units are:Δm [g], A [cm2 ], f [MHz]
Gravimetric sensor in an oscillator circuit
Typical parameters for a quartz microbalance
(QMB) sensor are as follows:
f0 = 10 MHz, Δfmin = 0,1 Hz, Δfmax = 1 – 10 kHz.
In this case it is possible to detect the change of a
mass at the level of 0,1 ng/cm2.
When measuring with computer, one can use the frequency/voltage converter and
the output voltage is passed to the measurement card for data aquisition.
Gravimetric sensors, cont.
A resonant cantilever humidity sensor
with a piezoelectric PVDF
(polyvinyl –difluorene) layer
and Al electrodes.
Expanding or contraction of the
piezoelectric foil forces the cantilever
into vibracions which are influenced
by the change of mas of the adsorbed
water vapour.
A. Gluck i in. Sens.&Act.B 18/19 (1994)554
Sensors based on Surface Acoustic Waves (SAW)
Surface wave in a piezoelectric medium.
Rayleigh wave consists of two components:
a longitudinal wave and shifted in phase by π /2 transversal
wave.
These waves disappear completely at the depth of order two
wavelengths.
SAW sensors
Interdigitated electrodes on
the piezoelectric substrate
forming a transducer
with period L and aperture W.
The condition for resonance
frequency is:
f0 
v


v
L
v – velocity of a sound
Changing the period L of a transducer one can generate SAW waves in a wide
frequency range.
For a quartz substrate one obtains frequencies in the range from ca. 30 MHz
to 1 GHz. In this case the resonance frequency is not connected with a thickness
of the quartz plate.
SAW resonator
SAW resonator with a hygroscopic
layer.
SAW resonator in a resonance is
equivalent to the series connection
of RLC elements with a parallel
capacitance C0.
SAW sensors, cont.
Measurement of phase
shift in a differential
configuration of delay
lines. One delay line is
covered with a humidity
absorbing layer, the other
serves as a reference.
Detection system of frequency shift
for two SAW resonators in a
differential configuration.
As small frequency changes as 10-8
are detected.
SAW sensors, cont.
Practical solution of a system
based on measurement of frequency
change for differentially connected
resonators.
The change in frequency is caused
by absorption of humidity by
a hygroscopic polimer PVA.
M. Penza et al. Sens.& Act.B 68 (2000)300-306
Psychrometric sensor
Temperature difference ΔT = T1 – T2 is a function
of relative humidity RH.
Dew point sensors – optical type
The dew point is determined by temperature at which the water
vapour and the liquid are in equilibrium. The mirror covers with
water droplets and a diffusive reflectivity appears (instead of specular).
The dew point temperature determines RH, once the pressure is known.
Dew point sensors – optical type, cont.
Condensing water vapour changes the amplitude
and polarization of an incident optical signal.
S. Lomperski et al. Meas. Sci. Technol. 7 (1996) 742-745
Dew point sensors – capacitive type
Capacitive-type dew point
sensor
R. Jachowicz et al. Sens.& Act. A
85 (2000)75-83
Intersection of a membrane - the smallest
repeatable fragment of capacitive detector
(not to scale).