de Bree, H.E.

Elwenspoek, Michael Curt

Korthorst, M.T.

Leussink, P.J.

English

A novel flow sensing principle will be presented which combines the advantages of both the anemometer and the mass flow sensor. The sensor consists of two elements which are used as both sensor and heater. For small flows a qualitative model of sensitivity and frequency response as well as measurements will be presented

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THE TWO SENSOR µ -FLOWNA N  I M P R O V E D  F L O W  S E N S I N G  P R I N C I P L EHans-Elias de Bree, Peter Leussink, Twan Korthorst, Miko ElwenspoekMESA Research Institute, University of Twente, PO Box 217, 7500 AE Enschede, The NetherlandsPhone: X-31-53-4894438; Email: H.E.deBree@el.utwente.nl; Secr: X-31-53-4892751; Fax: X-31-53-4309547A novel flow sensing principle will be  presented which combines the advantagesof both the anemometer and the mass flow sensor. The sensor consists of twoelements which are used as both sensor and heater. For small flows a qualitativemodel of sensitivity and frequency response as well as measurements will bepresented.INTRODUCTIONFlow sensors commonly are used in, for example,micro liquid handling systems or for measuring gasflows. One example is a gas flow sensor used as amicrophone: the Microflown [3]. This sensor isdesigned to measure particle velocity, very smallflows in a frequency range up to twenty kilo Hertz.While the signal to noise ratio is a very importantparameter of the microflown an innovativemeasuring principle is optimised with respect to thesignal to noise ratio.To measure small air flows, mass flow sensors(MFS) are commonly used. This type of sensorconsists of a heater and two temperature sensorsequally spaced around this heater. The flow altersthe temperature distribution around the heater. Thisis measured by the sensors and the temperaturedifference quantifies the flow.Another principle to measure a flow is ananemometer. This sensor consists of one heated wirewhich acts like a sensor at the same time. The heatloss, which is dependent on the air flow, ismeasured.A disadvantage of the anemometer is the lowsensitivity for small DC flows [1]. The direction ofthe flow can not be obtained while for both positiveand negative flows the heat loss is the same.The new proposed sensor, the Two SensorMicroflown (TSM), consists of two heated elementswhich are used as both sensor and heater (like theanemometer) and uses the differential temperatureas a representation of the flow (like the MFS). Usingonly hot sensors (and no heater) will lead to aneasier to make sensor, an improved signal to noiseratio and a larger dynamic range, as will be shownin this article.THE MODEL OF THE TWO SENSOR MICROFLOWNFirst only one heated wire will be observed. Thiswire is heated by an electrical current. At the sametime the electrical resistance of this wire ismeasured to determine the temperature. When aflow is applied, the temperature of the wire willdrop because the convective heat loss increases.This effect can be described by observing the heatbalance for a hot wire (Fig. 1).Fig. 1: The various heat losses of a hot wire.Heat is generated electrically in the wire and lostnot only by convection to the fluid but also byconduction to the bulk and radiation to thesurroundings. In addition, there is heat storage in thewire. An energy balance yields for the followingdifferential equation for the heat balance in a hotwire sensor (eq. 1):AxkTxIAcATtdh T T d T Tss r ss f s sur∂∂∂∂ρρ∂∂π π σε+ − − − − − =24 4 0( ) ( )Here ks is the coefficient of thermal conductivity forthe sensor material, Ts the sensor temperature, I theelectrical current, ρr the resistivity of the sensormaterial, ρ the density of the sensor material, c thespecific heat, t the time, h the coefficient ofconvective heat transfer, Tf the temperature of thefluid, σ the Stefan-Boltzmann constant, ε theemissivity of the sensor and Tsur the temperature ofthe surroundings. The first part of eq. 1 representsthe heat transfer by conduction in the wire, thesecond part the electrical heat generation, the thirdpart the heat storage, the fourth the convection lossand the last part the emission loss. The last part isnormally neglected while the emission loss isassumed very small [5].In order to develop an expression for thefrequency response of a heated wire sensor the heatbalance is used. If the sensor is assumed longenough (i.e. a high aspect ratio) for the temperatureprofile to be constant and the heat loss by radiationis neglected, eq. 1 will be:IAcATtdh T Tr s s f2ρρ∂∂π= + −( ) (2)The coefficient of convective heat transfer is givenby [1]:h A B U= + (3)A and B are arbitrary constants and U represents thefluid velocity. For a cylinder shaped wire theseconstants are known as:A B UkdUdfd d+ = +0 42 0570 2 0 33. .. .νανα ν(4)Using kf as the coefficient of thermal conductivity ofthe fluid, ν the kinematic viscosity of the fluid andαd the thermal diffusivity of the fluid. If the DCflow is small (smaller than 0.2 m/s in air [7]) thefirst term between the brackets becomes dominantand therefore sensitivity decreases. While forpositive and negative flows the heat loss is the samean AC flow can only be measured with a DC biasflow [8].The value of a resistor is given by:RlAr=ρ(5)And the dependence of the temperature is given by:R R T T Rs f s f f= + −α( ) (6)Using α as the first order temperature coefficient ofresistivity, Tf as a certain reference temperature (inthis case the fluid temperature) and Rf as theresistance of the resistor at the referencetemperature. Substituting the previous relations thefollowing relation yields:I R PcAlRRtdRA B U R Rsfss f20= = + + −ρα∂∂πα( )( ) (7)If now is assumed that all fluctuating quantities canbe expressed by a sum of a mean component and afluctuating component, for example U(t)=U+∆Uand Rs(t)=Rs+∆Rs eq. 7 will alter in the followingfirst order ordinary differential equation (eq. 8):d RdtRcAllkRA B U I RkcAUB U R R Us f ffsfs f∆∆∆+ + − = −αρπαπρ( )( )22The corner frequency of this equation is:fI RcAl R RPcAl T Tcfs f s f=−≈−2 2αρ ρ( ) ( )(9)The latter simplification is justified because forsmall flows P=I2Rs≈I2Rf. The corner frequency isdependent on the sensor temperature and thus of theapplied flow. For relatively small flows the wire willnot cool down significantly and there is a lineardependence between the dissipated power and thesensor temperature, see eq. 12.The DC behaviour can be derived easily usingeq. 7 because the derivative is zero.T TPlk A B Us ff− =+π ( )(10)Even if radiative losses are neglected, thetemperature is not constant over the hot wire.Because of conductive losses to the bulk thetemperature is approximately at ambient level at thebeginning and end of the hot wire. The temperatureprofile can be calculated (assuming it does not varyin time) by solving the following differentialequation (see eq. 1):Ak ld TdxI R dhl T T I Rssf s f f222 2 0+ − − + =( )( )α π (11)To make a constant temperature approximationpossible, the aspect ratio must be very high. This ispossible by using micro machined hot films.Therefore for a high aspect ratio eq. 11 becomes:T TI Rdhls fs− =2π(12)The corner frequency (see eq. 9) for relatively smallflows thus becomes:fhcdc=4ρ(13)The corner frequency (for small flows) is lineardependent on the coefficient of convective heattransfer and inversely dependent on the density ofthe sensor material, the specific heat and thediameter (i.e. the volume) and not of the dissipatedpower and temperature.Now the model of a MFS is observed. The heateris in fact a hot wire and all relations mentionedbefore can be applied to the heater. The temperatureof the heater, Th, is equivalent with Ts.If the influence of the temperature sensors isneglected the model of the mass flow sensor can bederived by calculating the temperature at a certainplace symmetrical around the hot wire.Lammerink et al. [2] presented a static behaviourof the MFS based on a lumped element analysis.The temperature distribution as a function of theflow is given by:T T T T eT T T eT T Tu s h sU U g Xd h sU U g Xd udd− = −= −= −+ +− +( )( ){ }{ }1241242 22 2αααα∆∆∆(14)Using g-1 as an arbitrary surface and ∆X as thespacing between the heater and sensors. The twosensors are labelled by a u (upstream) and d(downstream).To give an impression, the temperaturedistribution for no-flow (solid line) and for a certainflow (dotted line) is shown in Fig. 2. The location ofboth sensors and heater is shown by the letters S andH, the heater has a certain width.Fig. 2: Temperature distribution of a mass flowsensor.As can be seen, the heater temperature is muchhigher as the sensor temperature and the sensitivityis dependant on the no-flow sensor temperature.It’s possible to implement the MFS as a threebeam configuration, one heater and two sensors likeLammerink et al., see Fig. 3A, or as a two beamconfiguration, the heater is distributed and placed onthe same carrier as the sensors. This has been doneby Johnson et al. [6], see Fig. 3B.Fig. 3: Two implementations of mass flow sensorsIn the two beam configuration the no-flow sensortemperature is higher than the no-flow sensortemperature of the three beam configurationresulting in a higher sensitivity. The carrier for thesensor and heater however has to be larger in orderto support two wires, which results in a lower cornerfrequency, see eq. (13).The temperature sensor is normally implementedas a resistor of the same material and having thesame shape as the heater. Including eq. 6 thedifferential temperature (∆T) is measured as:∆RRR RRT Td u s=−= α∆ ( ) (15)With ∆R/R the relative differential resistor valuewhich is normally measured by using theWheatstone bridge.Fig. 4: Measuring a differential resistance variation.The signal (differential output voltage due to thedifferential resistance variation uel) equals IR⋅∆R/Rand the thermal noise is given by 4kT R Bws ⋅  (k isthe Boltzmann’s constant and Bw the bandwidth)and therefore the signal to noise ratio is given by:SNIRRRkT R BwP T TkT Bwsss=⋅=⋅∆4 4α∆ ( )(16)The signal to noise ratio is proportional to thesquare root of the dissipated power in the sensors.Instead of heating the sensors with a separateheater, the power of the sensors can be increased sothat the sensors produce heat. This configuration isshown in Fig. 4.Fig. 5: The Two Sensor MicroflownThe heater becomes redundant and an increase ofthe power in the sensors will lead to an increase ofthe signal to noise ratio. The carriers now have thesame size as in the three beam configuration (a highcorner frequency), and the no-flow sensortemperature is the same as in the two beamconfiguration (a high sensitivity).When fabricated in the same technology theanemometer and the MFS heater have the samemaximum allowable temperature. When exceedingthis maximum temperature the wire or heater willbreakdown. In the MFS, the sensors have aprincipally lower temperature as the heater. So whenremoving the heater, the power supplied to thesensors can be increased.For all implementations of the MFS the cornerfrequency will be lower than the corner frequency ofthe hot wire anemometer. This is because thecoefficient of convective heat transfer is smallerthan for one sensor, since a heat source has beenplaced nearby and therefore heat loss decreases.MEASUREMENTSTwo modes of the three beam MFS and the TSMhave been compared in an AC flow, the result isshown in Fig 5. The three resistor values of the MFSare 300Ω and the two resistor values of the TSM are210Ω. The configurations are compared having thetemperature of the hottest element at about 500°C.The current through the sensors in the TSM is 9mAeach. The current through the heater of the MFS is11.5mA, the temperature about 500°C and thesensor currents are 3mA each.While the signal to noise ratio increases when thesensors are fed with a larger current both heater assensors are fed with a current of 6mA.Fig. 6: Sensitivity of the TSM, the MFS with heatproducing sensors and a MFS in normal operation(cold sensors).In Fig. 7 the sensitivity of the TSM and the MFS asa function of the frequency is depicted. While thesensitivity of the MFS with hot sensors is largeronly this mode is compared to the TSM. The noiselevel due to self noise and background noise was30dB PVL re 50nm/s.Fig. 7: Sensitivity of the TSM and the MFS with heatproducing sensors as a function of the frequency.CONCLUSIONBy using qualitative models it shows that byremoving the heater from a mass flow sensor thesignal to noise ratio increases.This rather surprising thought can be understoodby knowing that the sensitivity of a mass flowsensor increases by increasing sensor temperatureand the signal to noise ratio for measuring a resistorvalue is proportional with the square root of thedissipated power.The two sensor microflown (TSM) can be seenas a mixture of an anemometer because it consists oftwo heated elements which are used as both sensorand heater (like the anemometer) and uses thedifferential temperature as a representation of theflow (like the MFS).Measurements are performed for acoustic flowsand show that the TSM performs better than a MFS.The anemometer is not able to distinguish thedirection of the flow and therefore not suitable formeasuring acoustic flows.REFERENCES[1] C.G. Lomas, 'Fundamentals of hot wire anemometry', Cambridge University Press, Cambridge, 1986.[2] T.S.J. Lammerink et al, “Micro Liquid Flow Sensor,”Sensors and Actuators A, pp.37-38, 45-50, (1993).[3] H.E. de Bree et al, “The µ-flown, A novel device measuring acoustical flows”, Transducers ‘95.[4] H.E. de Bree et al, The Wheatstone Gadget, A simple circuit for measuring differential resistance variations, MME, Copenhagen ‘95.[5] R. Aigner et al; SI-Planar-Pellistor: Designs for temperature modulated operation, Transducers ‘95-Eurosensors IX, (1995), 213-PD5[6] R.G. Johnson et al., A Highly sensitive silicon chip microtransducer for air flow and differential pressure sensing appications, sensors and actuators, 63-72, 1987.[7] F.E. jorgensenAn omnidirectional thin-film probe for indoor climate research. DISA Info., 24, 24-29, 1979.[8] S. Baker, An Acoustic Intensity Meter, Journal of the acoustic society of amerika,volume 27, 1955.

The two sensor microflown, an improved flow sensing principle

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The two sensor microflown, an improved flow sensing principle

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