EXPERIMENTAL TECHNIQUE
A THERMISTOR ANEMOMETER FOR
MEASUREMENT OF LOW FLUID VELOCITIES DONALD E. M U R P H Y ' A N D ROBERT E. SPARKS Chemical Engineering Science Division, Case Western Reserve University, Cleveland, Ohio 44106 Development and calibration of a low speed, self-heated thermistor anemometer are discussed. Temperature gradients in the fluid can b e tolerated, since temperature compensation is accomplished by a second measurement of the sensor. Threshold values of the velocity measurement are 0.1 cm. per second in air and 0.02 cm. per second in water. Natural convection causes anemometer readings to depend on the direction of fluid flow. TUDY
of the spatial velocity distribution in packed beds at
S the low velocities in gas chromatographic and ion exchange columns requires an instrument which can accurately measure air velocities below 5 cm. per second and water velocities below 1 cm. per second. Several instruments, based on some form of heated element which is cooled by the moving fluid, have been developed for measuring low fluid velocities. Clayton and Farmer (1963) used a heated thermopile to measure air velocities down to 45 cm. per second and water velocities down to 3 cm. per second. Although the sensitivity of the instrument was not exceptional, it was rugged and hence less susceptible to damage than is the standard hot wire. Simmons (1949) reported an anemometer consisting of twinbore silica tubing with an electrically heated 8-mil Nichrome wire in one bore and a thermocouple sensing element in the other bore. When the wire was placed horizontal and transverse to a horizontal air stream, the thermocouple response passed through a maximum at 4 cm. per second. Apparently, the maximum was caused by the changing direction of the heated wake as velocity increased from zero. LVhen the wire was mounted vertically, the response decreased continuously with increasing velocity. I n this position, the sensitivity of the instrument increased appreciably below 10 cm. per second. At these low velocities, a decrease in velocity causes the thermocouple to be warmed by the decrease in convective cooling of the wire and by the heating effect of the wake as it develops an upward velocity component. The instrument was sensitive down to 1 cm. per second. Proper placement of the cold junction gave adequate temperature compensation a t low velocities. Kumazawa (1965) measured velocities down to 1 cm. per second in a vertical air stream using externally heated nickel wire and thermistors as sensing element. He compensated for ambient temperature changes by means of an unheated sensor having a temperature coefficient of resistance equal to that of the anemometer. Veprek (1963) was able to measure velocities down to 2 cm. per second in air and 0.02 cm. per second in water using a selfheated bead thermistor. Broer et al. (1957) measured air velocities down to 3 cm. per second using an externally heated rod thermistor. The major disadvantage of these anemometers, most of which have the required sensitivity, is the requirement of a constant bulk fluid temperature. This is a stringent requirement when extreme sensitivity is desired. An anemometer element which could also be used as a resistance thermometer Present address, E. I. du Pont de Nemours and Co., Inc., Wilmington, Del. 642
l&EC FUNDAMENTALS
Table I . Thermistor Specifications Shape Elliptical Leads Platinum (90%), iridium (10%) . Lead length (unmounted) 5 / 1 6 inch 0,001 inch Lead diameter Nominal diameter 0 . 0 1 inch Minor axis 0.013 inch Maior axis
Dissipation constant (still air) Time constant Nominal resistance (25' C.) Temperature coefficient of resistance (25' C.) R us. T relationship
0.017 inch 0 . 1 mw./O C. 1 . O second 2000 zk 50 ohms
68 ohms/' C.
+
In R = A B/T ( A , B = constants over limited temperature range)
would eliminate the need for a constant temperature environment and increase the utility of the instrument. This paper discusses the development of such an anemometer. The requirements of the device are high temperature coefficient of resistance, high heat capacity to minimize Joule heating when used as a thermometer, small time constant to minimize the time lag between measurement of velocity and ambient temperature, and small volume to permit approximate measurement of point velocities. No single element can satisfy completely all four requirements, since reducing the size of the element also reduces its heat capacity. A glass-coated bead thermistor (Veco 32A7) was selected as the sensing element because it came closest to meeting all requirements (Table I). Theory
The steady-state heat balance around a self-heated thermistor placed in a moving fluid stream is
Ri2 = UA(T
- T,)
+ QL
where the heat transfer coefficient, U , is a function of the fluid velocity, u, and the ambient temperature, T,. Q L is the heat loss through the leads. The heat balance for a stagnant fluid is
The heat loss into the leads may be expressed as a form of Newton's law of cooling. QL
=
ULAL(T- Tu)
(3) (4)
Equations 1 and 2 can now be rearranged into a more convenient form.
(5) 2.0
FLUID-AIR ORIENTATION -VERTICAL CURRENT=I.O MlLLlAMP
I
lJY
P
0
Since the heat loss thro'ugh the leads is small compared to the heat loss from the b0d.y of the thermistor, its velocity dependence can be neglected without incurring serious error. This lead heat loss can then be eliminated by subtracting Equation 6 from Equation 5.
n-.
'0 x
21;g I
4/
zt 3
J
(U-Uo) will be a unique function of the fluid velocity, u, only if there is no free convection heat transfer. This can be approximated by operating a t a small "temperature loading" (T-T,). The temperalure loadings in this study were approximately 4' and 13' C. Equation 7 shoirs that calibration of the anemometer requires knoivledge of the resistance-temperature relationship for the thermistor. The gmeral functional form of this relationship for thermi ,tors is In l? = A
+ B/T
(8)
Equation 8 was verified from resistance measurements made in a controlled-temperature bath. A and B were found to be constant over the temperature range of 22' to 40' C. used in the anemometer calibration. Equation 8 can now be combined with Equation 7.
u) ( CM /SEC)i
Figure 1. Comparison of heat transfer equation with experimental data
The heating current is shut off, the null-meter sensitivity increased, and the meter zeroed. R, is measured by balancing the bridge with temperaturesensing current on. Both R and R, could be measured in approximately 40 seconds. The ambient temperature change during this interval was negligible. Additional information concerning the apparatus and procedures is given by Murphy (1967). Results
A valid assumption for small temperature loadings is
B
__
Tor,
B M
~
TTa
M
constant
(10)
and Equation 9 can be put in the form
Experimental
The anemometer \vat; calibrated a t the center line of a parabolic velocity profile in a 0.954-inch i.d. tube with the thermistor mounted on a Flow Corp. Model HTYP-A probe. The upstream pressure was held constant by a Cartesian manostat, and the volumetric flow rate of air was measured by a Meriam laminar-flow element. A five-place Tfheatstone bridge was used to measure the resistance of the thermistor. A 50-volt regulated d.c. power supply, in series with a clropping resistor, provided a constant current supply. The bridge unbalance was measured by a Leecls 8r Northrup d.c. guarded-null detector with continuously adjustable current sensitivity. T h e negative side of the bridge and the null detector chassis were grounded to stabilize the null-meter zero. A thermistor current of 2.5 Wa. was used in the measurement of R,. At zero velocity this current produced a maximum change of 0.1 ohm in thermistor resistance because of Joule heating. Thermistor c u i ~ e n t sof 1.0 and 0.5 ma. were used for the measurement of R
Calibration in a Vertical Air Stream. T h e value of Ro/log(Ro/R,) was measured periodically during the course of the anemometer calibration and did not exhibit any dependence upon ambient temperature at 22' to 25' C., the range employed during this investigation. The average value of Ro/log (Ra/Ro)was 6124 i 32 ohms. Figure 1 is acalibration curve showing the resistance term of Equation 9 plotted against
l/u. Ample literature exists supporting this functional form for spheres (McAdams, 1954; Ranz and Marshall, 1952) and bead-type thermistors (Tsubouchi and Sato, 1960). T h e square-root dependence holds down to 4 cm. per second, corresponding to a Reynolds number of 0.90. The threshold of the anemometer is approximately 0.1 cm. per second. Several investigators (Bowman et al., 1961; Kronig and Bruijsten, 1951 ; Yuge. 1956) have proposed theoretical equations for heat or mass transfer from spheres or bead thermistors for R e < 1. ,411 these equations can be put in the form of a power series
- R- log
Ra --
R
Ro = constant x(U R log 3 RO
=
Au
+ Bu2 +
,
.,
(12) For u 54 cm. per second, the heat transfer data of this study could be fitted by a third-order polynomial:
The experimental procedure for anemometer calibration a t a known velocity is outlinesd below.
0.007~2- 0.001~3 (13)
R
is measured by balancing the bridge with the heating current on.
- U,)
with a n average deviation of ztO.06 cm. per second. VOL. 7
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0.4
I-
I
FLUID-AIR ORIENTATION-VERTICAL
5
ib0.5 MA
$
i.i.0 MA
0.3-
0.2-
0
Figure 2. sitivity
Effect of heating current on anemometer sen-
.9 -
; i
5 0 ag
n-
3
.8-
FLUID-AIR ORIENTATION -HORIZONTAL CURRENT=I.O MlLLlAMP
.7.6-
Figure 5. Fenwol glass - encapsulated b e a d thermistor for water velocity meosurement
I
v
.I-
O
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
"-FLUID-WATER CURRENT-3.0MILLIAMPS
I
u:(CM/SECli
Figure 3. Comparison of heat transfer equation with experimental data
1 0.30
A
FLUID-AI ORlENTAl
O
Figure 6. equation
O
k
E
ComK
Calibration in
u,(CM/SECI Figure 4. tivity
Effect of heating current on anemometer sensi-
An attempt was made to increase the sensitivity of the anemometer at velocities 5 3 cm. per second. To reduce the amount of heat transferred hy free convection, the thermistor current was reduced to 0.5 ma,, reducing the temperature loading to approximately one third. The calibration curves for the two heating currents are compared in Figure 2, indicating that there is no significant effect of heating current on anemometer sensitivity. Equation 11 is therefore valid for this flow situation. 644
lhEC FUNDAMENTALS
___
study was condu ..... -.. . . -......... effect of buoyancy on the sensitivity of the anemometer. A thermistor similar to the one used in the previous study was mounted on a Flow Corp. Model HWP-CS probe. T h e anemometer was calibrated as before at the center line of a I
For this orientation, heating current affected sensitivity as shown in Figure 4. T h e free and forced convection forces act in mutually perpendicular directions; hence, a change in current causes a chang: in the resultant wake angle. Since the thermistor is not symmetrical in the cross section about which the wake is shifting, It is not surprising that the calibration curves a t different currents are not alike. The calibrations also would vary strongly ivith current if the anemometer were used with the air stream floliing counter to the force of gravity. A maximum in temperature would be expected for this case, since the inertial and buoyant forces act in opposite directions on the heated fluid. Calibration in Water. A preliminary determination was made of the sensitivity of the thermistor in water. T h e thermistor used was a l~enwalbead-type glass probe thermistor (GB32P38) having both the bead and the leads encapsulated in glass (Figure 5). The thermistor was sealed inside a Swagelok 300-R-6 brass fitting with silicone RTV adhesive sealant. Calibration was carrietl out a t the center line of the parabolic velocity developed in a 0.934-inch i.d. Plexiglas tube, which was inclined a t a 15” angle u i t h the horizontal to keep the tube filled Lvith water for at least 7 inches beyond the thermistor. IVater was fed a t a known flow rate by gravity from a constant head tank. The average value of R,/log(R,/R,) was 2784 + 5 ohms. is plotted against The value of R/log(R,,/R) -R,/log(R,/R,) in Figure 6 for a thermistor current of 3 ma. The squareroot relationship is valid down to u = 0.1 cm. per second, and the instrument is capable of measuring to 0.02 cm. per second.
4;
ture. Temperature compensation is accomplished by switching the anemometer to a temperature-sensing mode. Calibration shows the anemometer to be sensitive down to 0.1 cm. per second in air, and preliminary results indicate a sensitivity in water down to 0.02 cm. per second. The anemometer response is proportional to the square root of velocity at all but the lowest velocities, as expected from reports in the literature. The sensitivity of anemometer response is a function of heating current when free and forced convection do not act in the same direction. literature Cited
Bowman, C. I$’., IYard, D. M., Johnson, A . I., Trass, O., Can. J . Chem. Eng. 39, 9 (1961). Broer, L. J. F., Hoogendoorn, C. J., Kortleven, A., Appl. Sci. Res. A7. 1 (1957). Clayton, B . R., Farmer, E. G., J . Sei. Instr. 40, 579 (1963). Kronig, R., Bruijsten, J., AB$. Sei. Res. A2,439 (1951). Kumazawa, S., “Investigation of Hot-Element Anemometry at Very Low Velocity,” M. S. thesis, Chemical Engineering Science Group, Case Institute of Technology, Cleveland, Ohio, 1965. Mc.\dams, L$’. H., “Heat Transmission,” 3rd ed., p. 266, McGrawHill, New York, 1954. Murphy, D. E., ‘‘A Study of Low Speed Momentum Transfer in Packed Beds,” Ph.D. dissertation, Chemical Engineering Science Group, Case Institute of Technology, Cleveland, Ohio, 1967. Ram, \$‘. E., Marshall, I+‘. R., Chem. Eng. Progr. 48 (3), 141; (4), 173 (1952). Simmons, T. F. F., J . Sei. Instr. 26, 407 (1949). Tsubouchi, T., Sato, S., Chem. E n g . Progr. Symp. Ser. 56 (30), 285 (1960).
Veprek,’J. .4., J . Sei. Instr. 40, 66 (1963). Yuge, T., Rept. Inst. H i g h Sjeed Mechanics, Tohaku Univ. 6 , 143 (1956). RECEIVED for review May 15, 1967 ACCEPTED July 1, 1968
Summary
A lowspeed, self-heated thermistor anemometer has been developed which does not require constant bulk fluid tempera-
Investigation supported by the U.S. Atomic Energy Commission through Contract AT(11-1)-1605.
MEASUR,EMENT OF ENTHALPY DIFFERENCES WITH A FLOW CALORIMETER J . P. DOLAN, B. E. E A K I N , AND
Institute of Gas Technology, Chicago, Ill.
R . F. B U K A C E K
60676
A flow calorimeter has been developed for determining enthalpy differences of natural gases in the range 100” F. for pressures up to 2000 p.s.i.a. Provisions for measurement of integral isothermal, of - 320” to
+
integral isobaric, and total enthalpy differences are included. Measurements are made by heat transfer between a reference fluid and/or heaters and the test material stream. Operating capability and an accuracy characteristic as a function of test stream energy throughput were established from runs on nitrogen.
u
or overdesign of chemical processing plants is costly. One factor contributing to design errors is the uncertainty in the values of the physical properties of the many different materials Processed. The experimental d a t a available are insufficient to produce correlations of general application or to evaluate the accuracy of correlations. Many investigations, both experimental and analytical, are being made to reduce this deficiency. The calorimeter described in this paper is part of an experimental investigation of the physical properties of natural gases. NDER-
Three major goals were stressed in the design of the calorimeter: T o define the enthalpy-pressure-temperature field of a fluid of known composition writhout reference to the measurements of other investigators. T o provide for cross checks on the data by alternative measuring techniques. T o measure enthalpy differences with an uncertainty of not than lyo,
A design satisfying these goals is described. Trial runs on VOL. 7
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