evaluation of the performance characteristics of a thermal transient anemometer

7
Experiments in Fluids 15, 10 16 (1993) Experiments in Fluids ,~ Springer-Verlag 1993 Evaluation of the performance characteristics of a thermal transient anemometer J. L. Bailey ~, J. Vresk ~ and M. Acharya 2 Argonne National Laboratory, Argonne, IL 60439, USA 2 Illinois Institute of Technology, Chicago, IL 60616, USA Received: 15 May 1991/Accepted: 26 June 1992 Abstract. This paper describes and evaluates a thermal transient anemometer, a novel fluid flow (mass flux) measuring device having a thermocouple probe which is utilized to measure the change in temperature over a period of time to provide a measure of fluid flow velocity. The thermocouple probe (sensor) is periodically heated by the application of an electrical pulse and its rate of cooling between pulses is related to the local mean flow velocity. The theory of operation, device description, comparison with other similar fluid flow devices, and laboratory tests including measurements under different turbulence levels and different fluid temperatures are pre- sented and discussed. 1 Introduction Classical thermal anemometer design is typically charac- terized by the utilization of a steady-state energy balance around a heated sensor located in the flow stream. Using the measured or controlled parameters of heat loss from the sensor and the temperature difference between the sensor surface and fluid bulk, a thermal convective bound- ary coefficient is determined and then correlated to the local fluid velocity over the sensor. Inherent to this ap- proach are the functional requirements of accurately measuring electrical power supply to the sensor and si- multaneously measuring or controlling the temperature differential between the probe and the fluid bulk. Often these requirements result in design and implementation difficulties associated with complex and fragile sensors, necessity of compensation for lead wire resistance, excess- ive electrical power consumption, need for independent measurement of fluid temperature and radiant heat trans- fer correction. The thermal transient anemometer (TTA) is based on established thermal anemometer principles in that the convective boundary coefficient at the probe is deter- mined and then correlated to the local fluid velocity. However, by applying a transient heat transfer method in the determination of the convective coefficient, the measurement (or control) of electrical power supply to the sensor that is required for conventional anemometers is replaced by time measurements which are easier and more accurately obtained. Hence, the TTA minimizes or avoids many of the above design difficulties. In this approach, the sensor is periodically heated by the application of an electrical pulse, and the rate at which the sensor is cooled between pulses is related to the local mean flow velocity. Perhaps the single most important advantage to the TTA is that a standard sheathed thermocouple may be used effectively as a flow sensor probe. This paper describes one possible TTA system using sheathed thermocouple probes and presents the theoret- ical background along with test results and a performance evaluation of the system. 2 Theory of operation A typical sheathed thermocouple probe is shown in Fig. 1. Selection of a sheathed thermocouple as the TTA sensor permits the probe to be modeled as an infinitely long homogeneous solid cylinder with a constant convective boundary. Hence, well established transient heat transfer theory can be applied directly. The temperature decay of the thermocouple junction, following a heating pulse, is characterized by the curve shown in Fig. 2a. Initially, at time to the junction has some arbitrary temperature, To, above the bulk fluid temper- ature and the initial radial temperature profile (in the probe) is described by some arbitrary temperature func- tion,f(r). Modeling the probe as an infinitely long homo- geneous solid cylinder, the temperature distribution as a function of radius r and time t is described by Carslaw and Jaeger (1959) as the series solution of Eq. (1): T(r,t)=22 ~ e k~ 2t fl ,=x (hZ +~ a) rf(r)d~ (l)

Upload: j-l-bailey

Post on 06-Jul-2016

213 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Evaluation of the performance characteristics of a thermal transient anemometer

Experiments in Fluids 15, 10 16 (1993)

Experiments in Fluids ,~ Springer-Verlag 1993

Evaluation of the performance characteristics of a thermal transient anemometer

J. L. Bailey ~, J. Vresk ~ and M. Acharya 2

Argonne National Laboratory, Argonne, IL 60439, USA 2 Illinois Institute of Technology, Chicago, IL 60616, USA

Received: 15 May 1991/Accepted: 26 June 1992

Abstract. This paper describes and evaluates a thermal transient anemometer, a novel fluid flow (mass flux) measuring device having a thermocouple probe which is utilized to measure the change in temperature over a period of time to provide a measure of fluid flow velocity. The thermocouple probe (sensor) is periodically heated by the application of an electrical pulse and its rate of cooling between pulses is related to the local mean flow velocity. The theory of operation, device description, comparison with other similar fluid flow devices, and laboratory tests including measurements under different turbulence levels and different fluid temperatures are pre- sented and discussed.

1 Introduction

Classical thermal anemometer design is typically charac- terized by the utilization of a steady-state energy balance around a heated sensor located in the flow stream. Using the measured or controlled parameters of heat loss from the sensor and the temperature difference between the sensor surface and fluid bulk, a thermal convective bound- ary coefficient is determined and then correlated to the local fluid velocity over the sensor. Inherent to this ap- proach are the functional requirements of accurately measuring electrical power supply to the sensor and si- multaneously measuring or controlling the temperature differential between the probe and the fluid bulk. Often these requirements result in design and implementation difficulties associated with complex and fragile sensors, necessity of compensation for lead wire resistance, excess- ive electrical power consumption, need for independent measurement of fluid temperature and radiant heat trans- fer correction.

The thermal transient anemometer (TTA) is based on established thermal anemometer principles in that the convective boundary coefficient at the probe is deter- mined and then correlated to the local fluid velocity. However, by applying a transient heat transfer method in the determination of the convective coefficient, the measurement (or control) of electrical power supply to the

sensor that is required for conventional anemometers is replaced by time measurements which are easier and more accurately obtained. Hence, the TTA minimizes or avoids many of the above design difficulties. In this approach, the sensor is periodically heated by the application of an electrical pulse, and the rate at which the sensor is cooled between pulses is related to the local mean flow velocity. Perhaps the single most important advantage to the TTA is that a standard sheathed thermocouple may be used effectively as a flow sensor probe.

This paper describes one possible TTA system using sheathed thermocouple probes and presents the theoret- ical background along with test results and a performance evaluation of the system.

2 Theory of operation

A typical sheathed thermocouple probe is shown in Fig. 1. Selection of a sheathed thermocouple as the TTA sensor permits the probe to be modeled as an infinitely long homogeneous solid cylinder with a constant convective boundary. Hence, well established transient heat transfer theory can be applied directly.

The temperature decay of the thermocouple junction, following a heating pulse, is characterized by the curve shown in Fig. 2a. Initially, at time to the junction has some arbitrary temperature, To, above the bulk fluid temper- ature and the initial radial temperature profile (in the probe) is described by some arbitrary temperature func- tion,f(r). Modeling the probe as an infinitely long homo- geneous solid cylinder, the temperature distribution as a function of radius r and time t is described by Carslaw and Jaeger (1959) as the series solution of Eq. (1):

T(r,t)=22 ~ e k~ 2t fl ,=x (hZ +~ a) rf(r)d~ (l)

Page 2: Evaluation of the performance characteristics of a thermal transient anemometer

JUNCTION ~ / T H E R M O C O U P L E ~ / ~ S I N O PROBE

FLUID ~ "-q [[ V

I I I " 1 ~ TH ERM OCOU PLE

PU LSING I REFI I

\ I PERPO J

/ I [RECORD L I _ ~ [ m~ I VOLTAOE

vs. TiME

Fig. l. TTA system schematic

~ ~ D E C A Y CURVE

To

t o t 1 t 2 a

T/T -e-ka2(t- tl)? / 1 - -

r~

I I TIME tl t 2

b

Fig. 2a and b. Temperature decay of thermocouple junction

where

T = temperature at given radius and time (with the assumption that T.ULK=0)

r = radius a --outer radius of cylinder t = time h = H / K k = K/pc H = convective heat transfer coefficient at cylinder

surface K =thermal conductivity within the cylinder p =density of cylinder c = specific heat of cylinder Jo = Bessel function of order zero.

The ~, are obtained as the roots of

~J'o(a~) + hJo(a~) = 0 (2)

After a sufficient decay time, t o - tl , the initial temper- ature conditions in the probe (cylinder) relax and all terms in the above series approach zero except the first. Hence, the temperature decay after time tl can be approximated

11

by

T(r, t) = A 1 e- k~,~, (3)

with

2~2 Jo(:q r) f~ A s = a2 (h2 +~21) j2(~la) . j . r f (r )Jo(~lr)dr ,

where A1 is a constant for fixed initial conditions, flow conditions and radial position, r; and ~1 is the smallest root (eigenvalue) of Eq. (2).

A semilogarithmic plot of the temperature variation after time tl, normalized by T1, is shown in Fig. 2b. The slope of this curve is constant and is given by

ln(Tz/T1) k ~ =S (4)

t z - - t l

Significantly, the initial conditions do not enter this ex- pression and, therefore, the slope is independent of the power pulse shape, duration, and magnitude. From a knowledge of 0~ 1 and K, the heat transfer coefficient H may be obtained from Eq. (2).

For low Blot numbers (< 0.1, typical in air flows), the slope in Eq. (4) can be expressed as

s = l n ( T 2 / T x ) _ H A s t2 - tl pc V (5)

by approximating the root of Eq. (2) using an explicit function for :r

In the above equation, As is the surface area, V is the volume, and pc is the heat capacity of the probe. For a cylindrical probe geometry, of length l,

A~ ndl 4

V - n(d/2) 21 - 3 (6)

4H so that S = pcd (7)

From fluid dynamic considerations, the convective heat transfer coefficient at the surface of the probe can be approximated using a correlation for a cylinder in cross flow, in the form of Eq. (8). 1

Nu = ORe" (8)

where

Nu = H d (Nusselt number) KI

Re = vd (Reynolds number) V

1 Equation (8) is taken from Kreith (1973) and was empirically developed for gas flows; however, for liquid flows, the equation is corrected by multiplying the equation by 1.1 Pr ~ where Pr is the Prandtl number of the fluid. The exponent, n, is independent of fluid properties

Page 3: Evaluation of the performance characteristics of a thermal transient anemometer

12

d = 2a=outside diameter of cylinder v =local fluid velocity K I = thermal conductivity of the fluid v =kinematic viscosity of the fluid,

and C and n are known empirical constants over large ranges of Re numbers.

Using Eqs. (8) and (7), the following dimensionless relationship can be obtained:

Sd 2 - - = - 4 C R e " (9) KI/pc

which describes the expected "universal" transient behav- ior of such a probe.

By using the definition of Reynolds number and grouping the terms into mass flow, probe, and fluid prop- erty terms, the slope can be expressed as:

P cdT'534 Kf

(mass flux) (probe properties) (fluid properties)

(10)

where for 40 < Re < 4000, n = 0.466. Such a representation reveals clearly the expected variation in the slope S with each of these groups. The flow velocity can be computed from a knowledge of the slope, probe, and fluid properties. A subsequent section will examine the actual trends de- scribed by Eqs. (9) and (10) and compare those with the prediction of this theory.

For conditions where the internal thermal resistance cannot be neglected (Blot number >0.1, typical in water flows), Eq. (5) is not valid and Eq. (4) must be used. The slope in Eq. (4) can be determined from measured temper- ature values, T1 and 7"2, and hence the local fluid velocity, v, can be calculated using Eqs. (2), (4), and (8).

The basic distinction between all prior work in this field and the TTA presented in this paper is the selective use of the natural mode of temperature decay of the probe. The approach taken by Calvet (1970) and Boegli (1985) is typical of the earlier work. They consider only the energy balance across the convective boundary between probe surface and fluid. In doing so, no knowledge or insight of the local heat transfer within the probe is realized.

The invariance of the slope with respect to shape, duration, and magnitude of the power pulse, as well as to the temperature sensor location, is the key factor which allows standard sheathed thermocouples to be used as TTA flow sensor probes. More specifically, the fact that the deposition of the heat within the probe during the power pulse and the location of the heating and sensing elements within the probe do not affect the calibration of the probe allows for large tolerances in the manufacture of the probes. Hence, the probes can be made using standard thermocouple fabrication techniques where the location

of the wires within the sheath cannot be accurately con- trolled.

3 General description and operation of a TTA system

The TTA system consists of a probe located in the flow of interest and externally located support electronics. A sche- matic is shown in Fig. 1. The operation cycle of the probe is divided into a power pulse and decay period as shown in Fig. 3. The procedure is as follows:

(1) At time t_l, a constant, relatively high voltage (5-15 V) is applied directly across the thermocouple wires for a time ( t0 - t 1). Hence, the thermocouple junction temperature is raised (typically 8 ~ to 15 ~ above the fluid bulk temperature by resistive heating. This power pulse (voltage) does not have to be accurately controlled or measured.

(2) At time to, the power pulse is switched off and the temperature distribution in the thermocouple begins to relax.

(3) At time tx, an instantaneous junction temperature, T1 (i.e., the thermocouple emf voltage reading across the wires) is recorded.

(4) At time t2, a second instantaneous junction tem- perature, Tz, is recorded.

(5) Using the measured values T1 and T2, the prepro- grammed microprocessor calculates the corresponding flow velocity.

(6) At time t3, the power pulse is reapplied and the cycle is repeated. Temperatures T 1 and T3 need not be the same.

Typical values for the power pulse phase t o - t 1 are 0.25 to 2 s. Time required for initial conditions to decay, tl - t o , ranges from 0.25 to 0.5 s and can be determined either experimentally or analytically. Analytically, t l is determined such that the second largest term, in the sum of the Eq. (1), i.e., when n=2, becomes negligible. The decay period t z - t l can range from 0.25 to 5 s.

T0 " - -

T~

[ V t ~ t o t 1 t 2 t 3 TIME

~ _ P O W E R ~ D E C A Y __~l P U L S E / C U R V E

Fig. 3. Temperature cycle of the probe

Page 4: Evaluation of the performance characteristics of a thermal transient anemometer

4 Laboratory tests and results

Laboratory tests were conducted in both air and water. The air flow tests were performed using a 1.6 mm-dia thermocouple probe inserted into a round duct, and the flow rate was measured using a calibrated orifice. Opera- tion cycle of the probe was as described in Section 3.

Tests were run using 6- and 12-Volt pulses for the follow- ing two conditions:

(1) The junction temperature was allowed to decay to the bulk temperature of the fluid prior to initiation of the next power pulse.

(2) Another power pulse was initiated before the junc- tion temperature decayed to that of the fluid. Normalized plots of junction temperature vs time were generated for each flow case. A typical plot for several flow rates is shown in Fig. 4.

These plots and a series of similar graphs derived from additional tests substantiated the following:

(1) The experimental temperature decay curves were exponential, i.e., curves were linear on the semilogarithmic plot, as theoretically predicted, and the values of the slopes calculated from these experimental curves were in good agreement with theoretical calculations.

(2) The slopes remained invariant with respect~ to 6- and 12-Volt power pulses. Also, the slopes remained the same whether or not the junction temperature was al- lowed to decay to the bulk fluid temperature before re- pulsing.

(3) The repeatability of these tests was within 5% for all flow cases, which is within the accuracy of the calib- rated orifice plate used.

(4) The flow measurements were stable, repeatable, and confirmed that such a flow measurement device is feasible and practical.

1 . 0 LtJ " " 0 . 8 2

0 . 6 k ~ Q_

~ 0.4 Z ~ - ~

S ~

,s 0 . 2 N

0 Z I I

0 " 1 0 1 2

~i .~:~ . . . . . . . . ~ . . . . ~ . - . . . . . . . . . 0. m/s

% ~ \ ' ~ . "---..~..__

% ~ . "~ "- ' -- . 31 m/s

�9 \ �9 ~...5.7 m/s ~ : \ \ . \ : \ ~'\

\ ' \ ..~e m/s

7 . 0 m ~ / s ~ : \ ' 5 . 5 m / s I I I I I I I I I I

3 4 5 6 7 8 9 10 11 12

T I M E ( s )

Fig. 4. Normalized temperature decay for 1.6 mm diameter probe in ambient air flow

13

Prototype tests using water were conducted with both 1.6 mm dia and 0.33 mm dia probes. In general, these test results were as good as the air flow tests. Normalized plots for the water tests were similar to that shown in Fig. 4; however, the time responses were substantially faster.

Another set of tests was conducted in a special air-jet facility where the mean velocities and turbulence inten- sities could be varied in a controlled manner, the latter by the use of interchangeable grids placed at the jet exit. Thermocouple probes of 1.6 mm dia and 0.5 mm dia were used for these tests.

During the tests, the fluid velocities (determined using a constant temperature hot-wire anemometer) and the TTA temperature decay slopes were measured and, based on these results, calibration curves of slope vs velocity were developed. The tests were performed over a range of flow velocities of 5 to 20 m/s at various turbulence inten- sities from 0.5% to 18%, and at ambient temperature (20 oc).

In addition, heated flow tests of fluid velocity (as determined by Pitot-tube measurements) vs. slope (as de- termined by TTA measurements) were conducted using the 1.6 mm O.D. probe. These tests were performed at a turbulence intensity of approximately 2% for a fluid temperature range of 23 ~ to 55 ~ The test results are shown in Figs. 5-8 and are discussed hereafter.

A V E R A O E ERROR = 0 . 2 6 5 9 5

STANDARD DEViATiON = 0 . . 3 7 6 8 5 0 . 2 7 - �9 " - ":- - �9 - - ' �9 - " �9 ":" �9 -:" �9 ":" �9 ": . . . . .

0 . 2 5

oo Y

O9

L J El_ 0

0.15

0.09~ - 4- 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 V E L O C I T Y ( m / s )

Fig, 5. Calibration curve, slope versus flow velocity, for 1.6 mm diameter probe in ambient air flow

Page 5: Evaluation of the performance characteristics of a thermal transient anemometer

14

1.1

1.0

0 .9 >o

>~ 0.8-

0 .71

" " x ~- ~ V o : 4.8 m / s

" . . . . .

" --~ V o : 21.5 m/"s

0 .6 0 I'0 2'0

TURBULENCE INTENSITY (%)

Fig, 6. Effect of turbulence intensity on TTA calibration for the 1.6 mm diameter probe

0.14, 0.12 .

L~ 0.10-I /.~"

J o

0.08t . J " 4s.s~ o.o6 , 5: . . . . . . s4."~ ~ ' ,

4 6 8 10 12 14 16 VELOCLTY (m/s @ 21.1~

Fig. 7. Calibration curve, slope versus flow velocity, for heated air flow

901 ,%

8 0 ,,~t" PROBE .# d i .6mm

" ~ 4o-

PROBE d=O.Smm ~

S ~

,,o |

e

2 0 1 0 0 0 2 0 ' 0 0

REYNOLDS N U M B E R

Fig. 8. Universal calibration curve, as defined by Eq. 9

F igu re 5 shows the ca l i b r a t i on curve for the 1.6 m m

p r o b e at approx . 2 % tu rbu l ence in tens i ty and a m b i e n t

fluid t e m p e r a t u r e wi th a d a t a acqu i s i t i on ra te of 100

samples /s . The s lopes in Fig. 5 were ca lcu la ted us ing

a decay time of 3 s. Decay times of 1.5 and 6 s were also used to calculate the slopes, however, the decay time of 3 s provided the best least squares fit.

Similar calibration curves were developed using 0.5 mm probe and decay time of 1.0 s, at a sample rate of 200 s 1. Decay times of 0.75 and 0.5 s were also evaluated, however, the 1 s decay time provided the best least squares fit.

During the tests it was established that the calibration of the 1.6 mm probe was significantly affected by the length of the probe that was exposed to the cross-stream flow. This sensitivity indicates that there is significant axial heat conduction within the probe. In order to elimin- ate this effect during actual testing, an insulating sleeve was installed along the probe, allowing only a short length to be exposed to the air cross stream. The inherent design of the 0.5 mm probe eliminated the need for such insula- tion.

The influence of turbulence intensity on the TTA re- sponse was studied by systematically varying the turbu- lence intensity over a range of mean velocities. The turbu- lence intensity was measured using the constant temper- ature anemometer system. The ratio of the actual mean flow velocity, t,a, to the TTA measured mean flow ve- locities, Vo, of 4.8 and 21.5 m/s at different turbulence intensities is plotted in Fig. 6. Similar plots were de- veloped for the 0.5 mm probe.

The tests indicated that turbulence can affect the mean velocity reading by as much as 30% for the 1.6 mm probe and 18% for the 0.5 mm probe, over the range of turbu- lence intensities of 3% to 20% and velocity range of 4 to 20 m/s.

In order to examine the effect of fluid temperature on the TTA response, heated flow tests were performed in the fluid temperature range of 23~ to 55~ These results are shown in Fig. 7. During these tests, it was found that the TTA probe had to be rotated parallel to the flow stream so that the entire length of the probe was heated uniformly in order to avoid axial conduction affects that were ag- gravated by the increased temperature difference between the heated air jet and the surrounding air}

The test results showed that within an uncertainty of 5%, the fluid temperature did not affect the probe re- sponse. This is in agreement with a calculated value of 4% based on the fluid property term of Eq. (10). In the Appen- dix, sample calculations show effects of fluid temperature from 21 "C to 55 '~'C on the fluid property term of Eq. (10). In the above calculations, a coefficient of n = 0.466 [in Eq.

2 Although insulation of the probe eliminated the axial conduction affects when the temperature differences between the air jet and surrounding air were small, at higher temperature differentials the insulation was not adequate and therefore, the probe had to be rotated parallel to the flow stream. Additional insulation probably would have eliminated the problem as well

Page 6: Evaluation of the performance characteristics of a thermal transient anemometer

15

(8)], applicable to cross flow, was used. However, in the test, the probe was positioned parallel to the flow stream and coefficient of n = 0.6, which is applicable to flow over an arbitrary shaped body, Kreith (1973), would be more appropriate. Nevertheless, calculations in the Appendix show that the above variance in coefficient n effects the fluid property term by only 1% and is not significant. It should be noted that the above refers to the effects of probe position on the fluid property term only, and does not include the effects of probe position on the other terms of the Eq. (10).

A universal calibration curve as suggested by Eq. (9) would require that the calibration curves for all probes should coincide. An attempt to determine a universal curve using test data for the 1.6 and 0.5 mm probes, is shown in Fig. 8. The fact that the above curves do not coincide as predicted can be explained by considering that effects of axial conduction are more dominant for larger diameter probes. It can be seen, by inspection of Eq. (9), that larger values of cp for the 1.6 mm diameter probe would move the 1.6 mm diameter probe curve closer to the 0.5 mm diameter probe curve.

5 Discussion

A theory of operation was developed which indicated that there were significant advantages inherent in transient anemometers when compared to the classical steady state anemometers. Laboratory testing showed that the basic theory and resulting equations, which characterized the thermal performance of the probe, were valid and hence such an approach was feasible. The testing also character- ized the overall performance of the TTA in air flows and, in particular, examined the effects of turbulence intensity and fluid temperature. The turbulence effects test results indicated that turbulence intensity levels in the range of 3% to 20% significantly affected the mean flow velocity measurements. Also, the results indicated that the mean velocity flow measurements using the smaller diameter probe were less affected by varying turbulence levels than the larger diameter probe.

The heated flow test results were in good agreement with the theory prediction 3 and indicated that fluid tem- peratures in the range of 23 ~ to 55 ~ had negligible effect on the mean velocity measurements. Also, place- ment of the thermocouple reference junction in the flow stream proved to be a satisfactory method of compensa- ting for the varying fluid temperature.

Possible sources of error include the effects of axial conduction previously discussed in the test results. The error introduced by these effects was particularly ag-

3 Good agreement was seen after compensating for errors introduc- ed by axial conduction effects.

gravated when the temperature of the air jet flow was significantly different than that of the surrounding air. It was found that temperature drift on the order of 5~ between the jet air and room air resulted in substantial calibration drift of the velocity measurement. Adequate insulation of the thermocouple hot junction sheath and reference junction leads appeared to alleviate this prob- lem.

Another source of error was found to be caused by the variance in the orientation of the probe relative to the flow direction. Significantly different calibration correlations were obtained when the probe was oriented parallel to the flow velocity as opposed to when the probe was in the cross flow position indicating that the probe is sensitive to its angle of attack in the flow stream. Hence, error will be introduced in the velocity readings if the probe is not held in the position for which it was calibrated. The correlation can be modified, in principle, to include a term that accounts for the orientation in the flow.

In general, the tests showed that the TTA system has good stability, repeatability, sensitivity, and, generally, is quite workable. Promising applications range from stan- dard commercial/industrial air, water and steam flow measurements to flow measurements in high temperature and/or radiation environments.

Advantages of the thermal transient anemometer over conventional anemometers are as follows:

�9 A simpler, more durable and rugged probe is used, unlike the fragile electrical resistance element required for conventional thermal anemometers.

�9 Flow measurements are a function of time intervals which are easily and accurately determined as opposed to the sensitive steady state electrical power measure- ments required by other types of thermal anemometers.

�9 Radiant heat transfer is negligible; hence no correction for radiant heat transfer is required.

�9 Due to the pulsed type of power supply, the average power requirements are greatly reduced as compared to steady state thermal anemometers, hence extending the practical operating range of the device.

�9 "Off-the-shelf" sheathed thermocouples can be used as the probe sensor.

Work planned for the future includes a more detailed mathematical model which includes axial conduction, ef- fects of turbulence intensity, probe orientation, develop- ment of a universal calibration curve, investigation of more efficient and accurate numerical means for calculat- ing the slope, and repetitive pulsing of the probe. Other probe designs such as the use of thermistors, as well as the application of the transient method to standard hot wire and film probes, should be investigated. Further reduction of the electrical power requirements for probe heating, such as localized heating at the probe tip, should be developed. All the tests have been performed under steady

Page 7: Evaluation of the performance characteristics of a thermal transient anemometer

16

state flow conditions. However, in order to obtain a com- plete evaluation of TTA instrument, tests in time varying flows are planned.

Acknowledgements

We would like to thank Gus Boulios for his competent and enthusi- astic help in the TTA testing and data plotting.

Appendix

Effects of fluid temperature on the fluid property terms of Eq. (10)

0 . 4 6 6 The fluid property term in Eq. (10) is K:/p: . Consider two fluid temperatures, 21 ~ and 55 ~C. Then the ratio of the fluid property terms, which represents the percentage change of the fluid property term over the above temperature range, can be written as

K:(~21cC(p:(~ 55 ~'C~ ~

Using the values for air at atmospheric pressure

K: % 21~ W/mk

K: I~ 55~

~: % 21 -'C= 1.833 x 10 s N s/m 2

/t: (~ 55 C = 1.982 x 10 s N s/m 2

in the above equation yields

0.0256 ( 1.982 x 10- 5~o.466

0.0277 1.833 x l ~ J =0.96

indicating a 4% change over the given temperature range.

(A-l)

Comparison of the Effects of Parallel Flow vs. Cross Flow on the Fluid Property Terms

The value of 0.466 for coefficient n used in Eq. (10) is valid for cross flow over a cylindrical probe. However, for a flow parallel to the same cylindrical probe, coefficient n is equal to 0.6. The effect of using n=0.466 versus n=0.6 on the fluid property term K:/~} can be determined by using n =0.6 in Eq. (A-l) rather than n = 0.466. The above yields deviation of 3% versus 4% deviation calculated in Eq. (A-1); thus actual variance due to variation in n is of the order of 1%.

References

Boegli, J. C. et al. 1985: Immersion thermal exchange parameter determination. U.S. Patent #4,501,145 col. 3 line 25

Calvet, P. J. F. 1970: Apparatus for measuring a physical quantity by the use of pulsed energy. U.S. Patent # 3,498,128 col. 9 & 10, Eqs. (1) (6)

Carslaw, H. S., Jaeger, J. C. 1959: Conduction of Heat in Solids. 2nd Ed., London: Oxford University Press

Kreith, F. 1973: Principles of Heat Transfer. 3rd Ed., New York: lntext Press, 1973