A liquid velocity sensor based on the hot-wire principle

Sensors and Actuators A, 37-38 (1993) 693-697

693

A liquid velocity sensor based on the hot-wire principle A J van der Wlel, C Llnder and N F de ROOIJ Instrtute of Mtcrotechnology, Untversrtyof NeuchGzel,Rue Breguet 2, CH-2000 Neuchdtei (Swttzerlandj

A Bezlnge Ascom Mwoelectronrcs, CH-2022 Bevarx (Swrtzerland)*

Abstract This paper reports on modehng and charactenzation of a &con hqmd velocity sensor fabncated by usmg an mdustnal bipolar process combmed with rmcromachmmg For apphcatlons m the blomecbcal field, mmlature sensors are needed for measurmg flow velocities m the range up to 2 m/s In order to measure such small veloaties, we have developed a sensor which IS sensitive to vanations of a forced heat flow modulated by the hqmd veloety As a large temperature gradient wll change the properties of blologxal hqmds, this sensor uses small temperature differences of about 1 to 10 “C A high average sensitivity of 10 mV/(m/s) has been measured The overall dnnensions of the chip are 2 0 mm x 1 6 mm x 0 4 mm

Introduction

Over the last ten years many articles have been reportmg on the development of gas flow sensors [l-3], but only few on hqmd flow sensmg However, low-cost hqmd flow sensors are of mcreasmg Importance m several domains such as m the blomedical field Since the stenhzation of used me&Cal eqmpment 1s expensive, there 1s a strong demand for cheap disposable sensors Furthermore, m LXUO blood flow measurement IS a challengmg field where small-sized sihcon sensors mounted on catheter tips could be applied Another nnportant domain is the automotive industry For optunal performance it 1s necessary to measure the fuel flow, and low-cost s&con flow sensors could posably represent an adequate solution A third example 1s the application of inexpensive liquid flow sensors m household apparatus such as m dishwashers, washmg machines or water-supply systems m hollers For most applications mentioned above, rather small hqmd velocities have to be measured Usual mdustnal flow sensors, hke vortex meters, paddle wheel sensors and dBerentla1 pressure sensors (ordice plates), often measure high velocltles only Furthermore the measurmg range, more precisely the ratio between the highest and lowest value which can be measured, 1s smaller than 10 to 1 Our work focuses on small hqmd velocities up to about 2 m/s This IS possible by using a wrttten

*Present address TESA SA, CH-1020 Renens, Sultzerland

0924-4247/93/$6 00

thermal measurement method which IS also promlsmg for large measurement ranges Two thermal prmclples can be dlstmgmshed [ 51. (1) Hot-wire anemometry, and (n) calonmetnc flow measurement With the first principle the heat loss from the sensor mto the flmd 1s measured at the spot where the sensor 1s placed m the flow Therefore, sensors based on this prmciple measure local fluid velocities Calibration for total flow IS posstble only If the velocity profile in the measurement channel 1s independent of the flow The calonmetnc prmclple has been wdely used for mass flow controllers m which a heater m the middle of a relatively long measurement tube gves a certain temperature distnbutlon This temperature dlstnbutlon is modulated by the mass flow and accurately detected In this case the total mass flow IS measured instead of the local fluid velocity at a certam point The objective for our project is to reahze a low-cost sensor for zn uzuo blood flow measurement, compatible with a h@ volume production Smce mtroducmg a rmcroscale calonmetnc measunng tube m a vein 1s rather delicate, a small chip based on the hot-me pnnclple has been designed and fabricated In this paper a short descnptlon of the design and fabrication of the chip 1s given Then a heat-flow model 1s developed m order to get an optnnal sensor design and to explain the sensor response The model predicts the sensor properties and gves an optnnal heater size for maximum sensitivity Measurement results are compared wth those predicted by the heatflow model

@ 1993- Elsevler Sequoia All nghts reserved

694

Design and fabrication Flgnre 1 shows a sketch of the chp wluch has been fabncated using an mdustnal bipolar process combined with amsotroplc s&on etchmg The chip consrsts of a heater thermally isolated from the rest of the chip by a membrane The temperature increase caused by the heater 1s measured as a voltage difference between two strings of diodes connected m series One strmg 1s placed at the center of the heater, the other one on the thck nm of the sensor Figure 2 shows the pnnciple of the chip If there 1sno flow, the power dlsslpated by the heater causes a conductive heat flow mto the flmd and mto the membrane When hqmd passes, a convective heat flow 1s added which drops the temperature of the heater Hence, the temperature difference between the heater and the rest of the chop 1s a measure for the fluid velocity The 15 pm thick membrane measures 600 pm x 600 pm and results from KOH etchmg The heat reslstor 1s a high-doped enutter n+ dtiuslon and has a resistance of typically 130 n With the use of the fimte element modeling program ANSYS, the resistor has been designed m such a way that a square m the nuddle of the membrane IS heated uniformly The resistor forms a nng vvlth a varymg urldth around the temperature sensing diode stnng m the rmddle of the membrane (see Fig 1) The square formed by thus resistor represents 27% of the membrane surface which gves the largest possible sensltlvlty (see next section) Bipolar trannstors, connected as diodes, are used for temperature measurement smce the temperature behavior of diodes 1s almost mdependent of the fabncatlon process, contrary to diffused or unplanted resistors Transistors are used since they show better stability than single pn-

membrane

Rg I Schematic view of the hqmd flow sensmg chip wth Its mam parts

FQ 2 Cross section of the clup showmg the conductwe and convectwe heat flows and the dfierentml temperature measurement

Junctions The two diode strings have the same layout and consist of four base to collector connected bipolar transistors Each 1s supplied mth a constant current of 100 pA and the temperature difference 1smeasured mth a sensitivity of 7 00 mV/“C The transistors of a strmg are placed m such a way that their emitters form the corners of a square In this way first order temperature and first order electnc field effects are compensated Bondmg pads are located downstream on the clup to insure that the necessary electrical connections do not affect the flow profile over the heater area (see Fig 1 )

Heat flow model An analytical heat flow model has been denved for the sensor The hot-mre prmciple 1s apphed to the chip to relate the dissipated power of the heater Hrlth the velocity of the fluid passing over the heater Connderatton of the power balance of the sensor results m an expression that has the form of Kmg’s law The model provides an optimal heater surface as a function of the membrane surface For the power balance three heat flows are important as 1s indicated m Fig 2 (1) the forced convective heat 4Con”that flows from the membrane into the fled, (11) the conductive heat qcondlfrom the membrane mto the fluid and, (m) the conductive heat qcona from the heater mto the substrate For the total dissipated power Pbs we find

pdlss= kmdl + &and2+ qc‘eonv(w) The conductive heat flows are iirst approxnnated and represent the static part of the model The convective heat flow or the dynamic part of the model, is denved afterwards In Fig 3, the important geometrical dnnensions are gven L mdlcates the membrane length, b the length of the heated area, n the &stance from the sensor edge to the heater, d the membrane thickness and H the distance from the membrane to the tube wall assumed to be a liquid temperature A conductive heat flow q from a lirst isotherm S, to a nearby second isotherm S,+,+ 1s expressed by qdr=-kSdT

(2)

where, k IS the thermal conductlvlty of the matenal (W/m K) and T the temperature (K) Note that dr/(kS) 1s an expression for the thermal resistance between two isotherms To find an expression for q, the surface S has to be- wntten as a function of the vector r Figure 4 shows a cross section for an isotherm S,, The nuddle of the membrane is heated to a temperature difference AT urlth respect to ambient temperature The assumption 1s made that no heat 1s transferred from the chip to the flmd outside the heater area From

695

qconaz1s found m a smular way Figure 3 mdzates that the membrane can be dmded by the Qagonals m four sectors The surface S,,,, for one sector at a distance a from the heated surface 1s then d(b + 2~2)or 4d(b + 2~) for four sectors Note that the approxnnated isotherms are contmuous from one section to another Substitution of SaPP_ m eqn (2) and integrating x from x = 0 to x = L/2 - b/2 &Ives b’cd2

Ftg 3 Geometwal dlmenslons for the heat flow model, L mdlcates the membrane length, b the length of the heated area, l the distance from the sensor edge to the heater, d the membrane thickness and H the distance from the membrane to the tube wall

the heated area the heat d&fuses away through the matenal above the heater Therefore, the isotherms have a curvature snnllar to d&slon contours I)lrectly above the heater the contours are approxnnately flat and Just beside the heat source the ratio between the honzontal and the vertical dnnenslon of the curvature IS about 3 to 4 (venfied Hrlth the tite element modeling program ANSYS) In order to obtam an analflcal expression, it IS assumed that heat only flows m between the dotted lines m Fig 4 The hatched areas are chosen to be equal, to insure that the thermal resistance of the volume m&cated by the lower hatched area 1s approxnnately equal to the thermal resistance of the upper one Hence the dotted hnes are chosen at an angle of 45” wth respect to the heated surface In this way the isotherms are expressed as a function of z only For qmndland the surface S,,,,, at a &stance a from the heated surface can be wntten as (b + 2a)2 Substltutlon of this surface m eqn (2) and integrating z from z = 0 to z = H pves %mdl

=

k&2 + b/H) AT (w)

urlth kfl the thermal conductmty T \

a _ m

b

(3) (W/m K) of the flmd

.I. a

=

%,W(W

AT

(w)

(4)

urlth k,, the thermal conductmty of the membrane (slhcon) The static behavior of the sensor predlcted by the eqns (3) and (4) are m good agreement wth snnulatlons carned out mth the fimte element modelmg program ANSYS Dependmg on the mesh of the model, ANSYS Bves values a few percent larger or smaller than the formula’s above A dynamic analysis can be done by using the boundary-layer theory m order to calculate the convective heat flow An m-depth study of this theory can be found m [6-81 Fmte element modeling of heat transfer m hqmd flows 1s not possible mth our faclhtles smce it demands the computation capacity of very large computers In this paragraph only relevant formulas are introduced urlthout refemng to that theory For both lammar and turbulent flow the convective heat qmav can be described as qmnv= h,b2

AT

(w)

(5)

wrth h,, the average heat-transfer coetlicient (W/m’ K), b* the heater surface and AT the temperature difference between the heater and the fled For a hot plate the local heat-transfer coefficient k, 1s given as function of the fluid velocity u (m/s) as well as X, the coordmate m the dmzction of the flow and the ongn at the front of the hot plate (see Fig 3) [6] h, = 0 332k&PrL13Re ‘I2 or

0 332k,Pr 113(u/v)1/2x-‘/2 (W/m2 K)

(6)

Mth Pr the Prandtl number, Re the Reynolds number and v the fluid vlscoslty (m2/s) However, this formula 1s only valid for a plate mth a constant temperature If there 1s an unheated area of length, l, from the leadmg edge to the heated area (see Fig 3), the heat transfer starts at a &stance r from the startmg pomt of the velocity boundary layer In our study the unheated length 1; is taken into account Therefore eqn (6) is expanded for respectively lammar and turbulent flow m the followmg way [6] h, = 0 332& Pr “‘(u/v) 1/2x1/2 x (1 - ([/x)“‘~)-‘/~

Fig 4 Sketch of a cross se&on of a real isotherm S,, and an approxunated Isotherm S,,,,,

Re c 2300

h, = 0 0296k, Pr 1/3(u/v)4’5x- I’5 x (1 - ([/~)~‘~o)-‘/~

Re > 5 x IO5

(7)

696

No satisfying formula 1s known for Reynolds numbers m the range of 2300 to 5 x lo5 Now the following integral expresses h,, Normally this factor 1s calculated by numerical approxnnation ttb h,

h, dx

= l/b

(W/m’ K)

(8)

5

r Substitution of eqn (8) m eqn (5) gives then the followmg expression for qconv C+b 4conv= b AT

I c

k dx

WI

(9) Experimental

The conductive heat flows and the convective heat flow are linear functions of AT as stated by Kmg’s law For lammar flow Kmg’s law 1s then expressed as Phss = (A + BJ;;) AT wth A = kflb(2 + b/H) + Sk,,d/ln(L/b) 3 = 0 332kflbPrL’3(l/v)“2 i+b x-w(1

X

-(~/x)y-113

&

(10)

s 5

where, A expresses the conductive thermal heat conductance, and B& the convective thermal heat conductance For optimal sensor behavior B has to be as large as possible unth respect to A In Fig 5 the function B/A

B/F

04

0515

06

b/L

O8

Fig 5 The ratlo B/A, the ratlo of convective and conductive heat as function of b/L, the heater length dwlded by the membrane .

.

length

is plotted as function of b/L III arbitrary umts From the graph an optimal ratio B/A 1s found for b/L = 0 515 Therefore, we conclude that the surface of the heater should represent 27% of the membrane surface for optlmal sensor senstlvlty It can be shown easily that ths value 1s also vahd for turbulent flow Now the heat flow model 1s given by eqn (10) which describes the sensor behavior as a function of the fluid velocity and the sensor properties Also the optimal heated membrane area IS found for maxlmum convection with respect to the conductive heat flow

In this part the measurement setup used to characterize the sensor behavior IS described Basically it consists of a 20 mm wide tube m which a delomzed water flow of 5 to 30001/h can be regulated This results m an average velocity of 0 005 to 2 65 m/s The chip, mounted on top of a wmg shaped ceramic, 1sposltloned exactly parallel to the water flow m the nuddle of the tube m order to disturb the flow as httle as possible For two other measurements the cerarmc 1s slightly tilted by 2” and 5” m order to have a thinner boundary layer over the &up The heat resistor (130 Q) on the membrane is supplied with a constant voltage of 5 V which results m a temperature daerence between the heater and the rnns of the chip of about 10 “C Since the chip nms are heated up to 4 “C m comparrson with the water temperature, this effect IS taken mto account m the calculations For lammar flow, the velocity m the rmddle of the tube 1s twice the, average velocity However, above 0 15 m/s (Re. > 2300) the flow 1s not larmnar anymore and the velocity becomes less than twice the average velocity [8] This effect has to be taken into account also For the thermal conduct&y of slhcon a value of 100 W/(m K) 1s taken, smce the membrane 1s heavdy doped v&h boron Doping silicon decreases the thermal conductlvlty as the boron atoms disturb the heat transport m the slhcon lattice substantially [9] With a gven flow, both the diode voltages are measured 250 times wlthm 40 s by a scannmg multlmeter and the average value difference 1s calculated by a computer to which the multnneter 1s linked Averagmg is necessary smce the sIgna vanes strongly because of turbulences m the flow With maxlmum flow the noise 1s 60 dB (I) higher than for zero flow as measured wth a spectrum analyzer connected to the sensor The noise spectrum showed that the turbulences cause a constant noise level over a wde frequency range This measurement was hnuted by the thermal time constant of the sensor which 1s about 5 ms The measured responses and the predicted lammar response of the chip are demcted m FE 6 I

691

vlscoslty, smce these parameters can affect the sensor sensitivity

Conclusions

100

1000

Reynolds

10000

100000

number

Fig 6 Sensor response and calculated lammar response as funcbon of the Reynolds number For a 20 &n urlde measurement tube, these Reynolds numbers correspond to average veloatles that range from 0 to 2 65 m/s

A small-sized liquid velocity sensor has been developed urlth highly sensitive response (10 mV/(m/s)) for small velocltles up to 3 m/s over a range of three decades An analytic model has been derived which predicts the sensor behavior over that range within a few percent The sensor 1s fabricated by using standard mdustnal processes and therefore well suited for large volume productlon Our ObJective m the near future IS to improve the sensor response with adequate signal treatment and dedicated packaging

Acknowledgements Discussion graph It can be seen that the response predicted by the lammar theory (eqn ( 10)) are in good agreement v&h expernnental results for Reynolds numbers up to 8000 This means that for our measurement setup (wth 20 mm tube diameter) and usmg the equation for the Reynolds number I& = U.&/V the model 1s vahd for velocities up to 0 4 m/s Furthermore the sensor 1s sensltlve over almost three decades of flow velocity The upper curve, measured with the sensor placed completely parallel to the flow, shows a peak for Reynolds numbers of about 2000 This peak 1s explained by the fact that the surface and the edges of the ceramic are not completely smooth, which causes local turbulences decreasmg the heat transfer However, if the sensor IS tilted a little, the flow profile over the sensor IS more stable and the heat transfer mcreases smce the boundary layer gets thinner Hence, the graph shows no peaks for the tilted positions and the sensltlvlty IS a httle higher than that predcted by the theory However, for practical apphcatlons some conslderatlons have to be taken into account As expected from theory, it IS observed that the velocity profile of the flow changes with mcreasmg veloclhes Therefore, special attention has to be gven to the design of the measurement tube to relate the sensor signal to total flow For this reason a conic measurement tube has been installed recently Accuracy IS affected strongly by noise, therefore noise has to be reduced Hence dedicated cucmtry to dnve the sensor with a constant temperature &fference and a chopped feedback IS m study Special attention has to be &ven to the fled temperature and fluid From

the

The authors urlsh to thank Ascom Mlcroelectromcs Bevalx, Switzerland for fabricating the sensor and Mr J J Vudleumler for reallnng the measurement setup Furthermore we wish to thank Mr C Gossweder and Mr H Verdegaal of the Turbulentmachinery Laboratory ETH, Zurich, for their helpful discussions We especially acknowledge the financial support of the Comnuttee for Promotion of Apphed Scientific Research, Switzerland

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