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THE THERMAL TRANSIENT ANEMOMETER

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THE THERMAL TRANSIENT ANEMOMETER Powered By Docstoc
					THE THERMAL TRANSIENT ANEMOMETER Authors and Addresses Foss, J.F.,* Schwannecke, J.K.,* Lawrenz, A.R.,* Mets, M.W.,* Treat, S.C.,* Dusel, M.D.** *Turbulent Shear Flows Laboratory, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824; (Foss Telephone: 517-355-3337; Fax: 517-353-7179; foss@egr.msu.edu) **Digital Flow Technologies, Inc., 2353 Sapphire Lane, East Lansing, MI 48823 Short Title The Thermal Transient Anemometer

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Abstract Applications, that require the measurement of the spatially averaged velocity over a given area segment, can be addressed by the Thermal Transient Anemometer (TTA). The operating principle can be characterized as: i) elevate the temperature of the zigzag patterned sensor – that appropriately

samples the area of interest – to an initial overheat condition, ii) allow the sensor to cool by the heat transfer of the passing fluid (plus end

conduction effects), iii) execute a calibration such that the exponential decay of the sensor resistance can

be characterized by the time constant:  , and iv) infer the spatially averaged velocity <U>  or the spatially averaged density-

velocity product <U>  from the relationship (1/  ) = A+B<U>n. where A, B, n are defined by the calibration data. A description of the enabling electronics, demonstration measurements in a calibration air stream and the post-processing strategy to account for ambient temperature changes between calibration and test data are presented in order to characterize this instrument.

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1.0

Introduction “Anemos”, the Greek word for “wind”, has as its logical extension, “anemometer” as the

measurement of air velocity magnitude (speed: L/t, where L=a length dimension and t=time). Anemometer, in the context of this paper, refers to the measurement of the spatially averaged velocity magnitude over a designated area that is termed a “cell” herein.. If the vector velocity values are normal to the area of interest (the condition for the present motivation) then the spatially averaged velocity can be related to the volume flow rate (L3/t) for the measurement area. If the vectors are not perpendicular to the area, then the yaw response: Ueffective= U f (cos ) – where  is the angle between the velocity vector and the sensor in the plane that is normal to the plane of the TTA array – would have to be considered. This additional complexity is not considered in the present communication. Each cell will be calibrated in an air stream of uniform and known velocity and temperature. If the application involves a different ambient temperature, then the measurement is understood to recover the averaged density () velocity (U) product for the cell. The basic TTA features will be described for the isothermal condition. Adjustments for non-isothermal effects are then described. There exists a myriad of applications in which this measurement is required. These include HVAC (heating, ventilating, air conditioning), respiration, combustion processes, etc. in addition to the motivating problem of determining the velocity and temperature distribution at the downstream face of an automotive radiator. The novel device described herein gains the anemometer function by first elevating the temperature of the sensor to a value well above ambient and then allowing the sensor to cool following the cessation of the heating current. The measured resistance, Rs(t), of the sensor can be related to the (assumed steady for the time period

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of the measurement) cooling velocity: U  or, if the measurement is made with an ambient temperature that is different from the ambient temperature during the sensor‟s calibration, U. Since U or U are inferred from the rate at which the sensor is cooled, the present device is termed the “Thermal Transient Anemometer” or “TTA”. The present paper will consider the motivation provided by the flow distribution through an automotive radiator. Specifically, the influence of various upstream obstruction elements (condenser, transmission oil cooler, crash members, grill work, etc.) on the flow distribution through the radiator was of interest. With this motivation, the complete area of the radiator was subdivided into sixteen rectangular sections of the same aspect ratio as that of the radiator. That is, the “local” flow rates, and temperatures, and not simply the total flow rate of the cooling air, or the temperature rise that could be inferred from the “heat balance around the radiator,” were determined. These local flow rate values provide the “signatures” of the upwind disturbance elements and they provide important information regarding the performance of the cooling package as a system. (Since nominally one-third of the energy released in the combustion process must be rejected through the radiator in a typical automotive engine, the importance of quantifying the cooling air distribution is considered to be apparent.) 2.0 2.1 The TTA Measurement Strategy Basic Considerations The flow field, downstream of a radiator, is both a challenging measurement environment and one that highlights the interest in an „area-averaged flow speed”. The complexity is easily recognized near the exit face of the radiator. The tubes and the fins will produce strong local wake effects with the attendant non-uniformities of the velocity field. Sufficiently far

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downstream, these wakes (and the jets) will merge to a nominally uniform flow. However, underhood systems often do not permit “far enough” given typical packaging requirements. In the present realization of the TTA, a nominal distance of 6 mm or 0.6 tube spacings or 6 fin spacings was used as the measurement location. Figure 1a shows a TTA array as a freestanding unit and Figure 1b shows the same array mounted behind a DaimlerChrysler (minivan) radiator. The 16 units are defined by the

rectangular circuit board elements that support the zigzag (or multi-X) 50  m tungsten wires which form the sensor elements of the TTA. This first generation TTA assembly has been replaced by a more robust stainless steel cell frame with Teflon plugs that serve as the tether points for the 50  m sensor wire. In the automotive applications, the frame size is adjusted to fit the area occupied by the radiator‟s fins. The control-electronic circuit, Fig. 2, delivers electrical current to the 50m wires of a TTA module until a preset level (Rhot) of the cell‟s resistance is reached. Namely, Rhot= Rcold (1+OHR) =  Tcold (1+OHR), (1)

where  is the temperature coefficient of resistance of the thermal sensor. (TH is established to be less than the oxidation temperature.) The circuit then transitions from heating to sensing in which a small (10 ma) current is used to record the resistance of the sensor wire as a function of time. Each segment (x ) of the tungsten wire will lose energy by convection to the passing air and either gain – or lose – energy by conduction along its length. These effects have been modeled by numerous authors. The analytical description by Morris and Foss (2003) provides a useful reference for the present considerations. Namely, the sensor, between the supported ends,

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can be subdivided into short length segments: x, and each element can be described by the thermal balance equation:

T    q axial  q convection  I 2 R  (x ) s cA s t  n
where I2Rn is the power released in the nth x segment,
q axial ] n  (x )KA s  2T   x 2  n

(2)

(3)

and

q conv ]n  h n Ds x[Tn  Tamb ].

(4)

The subscript “s” refers to the sensor wire. The convection coefficient: hn, can be modeled in terms of the Nusselt number, Reynolds number, Prandtl number expression:

N u  0.42Pr ]0.26  0.57Pr ]0.33 R e ]0.45 f f f

(5)

from Brunn (1995). (Note that hDs/kfNu and [UDs/ ]  R e where Ds is the diameter of the sensor wire). The [ ]f term signifies a “film temperature” for the evaluation of the thermodynamic
T  Tamb   properties  Tf  n . 2  

The initial temperature distribution: T(x) for t<0 would derive from (2) with the steady state heating condition (T / t  0) and with the boundary conditions that Tsensor = Tsupport where the sensors are supported at their “tether points.” The full equation (2) would then be used to describe the “temperature decay” following the cessation of the heating current (I=0).

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The measured sensor resistance: Rs, can be described as the summation of the resistance values for each segment “n,” of the sensor wire. From (1), and using the ambient condition as the reference for the linear variations of R with respect to T, Rn = {  (TnTamb)+Ramb} and
Rs   Rn
n 1 N

(6)

(7)

for the N individual segments of the sensor. 2.2 First Order Response and Corrections If the convection effects in (2) dominate the conduction effects and if this condition holds “on average” for all x elements, and if the convection coefficient h (from (5)) were constant, then the simplified equation:

d Ts  (1 / )[Ts  Tamb ] , dt

(8)

where Ts is the average sensor temperature would lead to the exponential decay of the sensor temperature as
 Ts ( t )  Ts ()      exp(  t / )  Ts (0)  Ts () 

(9)

where T() is the ambient temperature. The time constant: , represents the constants of the problem including the reciprocal of h from (4). The utility of (9) is that it represents, with reasonable accuracy, the experimental data as shown below. Second order effects are present in the temperature dependence of h as identified in (5). Characteristic temperature values for T(0) and T() are required to assess these second order effects.

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In order to avoid oxidation effects, T(0) will be established as 510oK. The initial film temperature depends, therefore, on T(). The relevant h values are obtained from (5) with the condition that <ambU> is factored out from the Re term
h  /   kf [0.42Pr ]0.26  0.57Pr ]0.33  f amb [ amb U]0.45 f f Ds  f 

(10)

A simplified statement of (10) is
k h f Ds
0.45   1    0.33  (0.57 Pr ]f    amb U  0.45        f  amb   

(11)

For the conditions considered, U=1m/sec and T() = 400oK provide the largest disagreement between (10) and (11); specifically, 0.7 %. This is considered to be sufficiently small such that (11) will be used to infer <ambU> when T()]calT()]test. Two ambient temperature values: 300 and 400oK and three representative velocities: 1, 5, 10 m/sec, are used to represent h(Tamb, U); see Figure 3. The property values, to evaluate the terms in (11), were obtained from Table C.1 of Johnson (1998). The somewhat irregular h(U, Tamb) values are ascribed to round-off effects in the tabulated values and the small range of the values shown in Figures 3a and 3b. Given the objective to obtain <U> for an isothermal condition (test cf calibration) or <U> for Tamb(test)Tamb(calibration), Fig. 3 can be used to identify the conditions for which h is nominally constant as shown on the figure h/h(0)=1%. For Tamb=300oK, this range is bracketed by 510360oK. With these same temperature limits, h/h(0) is 0.6% if Tamb=400oK. Hence, the operational condition that the data will be utilized in the range: 510oK360oK is established for the subsequent processing. Imposing a uniform approach velocity and recording Rs(t) provides an empirical solution to the “completely accurate governing equation and boundary conditions” boundary value

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problem discussed above. Using representative experimental data, a “fitting template” has been created that operates in the temperature range: 360510oK, for the sensor where the convection term is dominant and the signal-to-noise levels are relatively large. Also, the large value of “sensor length to sensor diameter” – here nominally equal to 2000 for the reported measurements – is also responsible for the dominance of the convection term, rhs of (2). These features are demonstrated in the next section. 3.0 3.1 Demonstration Measurements Calibration Data and Isothermal-Flow Measurements A single TTA cell was fabricated using a stainless steel frame and Teflon tether disks; see Fig. 4. This cell was mounted in a subatmosphere chamber at the exit plane of a delivery conduit from a low disturbance plenum; see Fig. 5. A calibrated Venturi meter was used to determine the flow from this chamber and the known density () and inflow area(A) allowed the spatially

 averaged velocity at the cell to be known in terms of the measured m (mass flux) value as:
 <U>= m / A

(12)

The response of the cell, operating as a TTA, was determined for nine <U> values that are typical of the velocities to be expected in an automotive cooling circuit. Three of these velocities were selected to demonstrate the TTA features. Equation (6) allows the temperature ratio of (9) to be written as the time varying sensor resistance values in non-dimensional form; namely
 R ( t )  R s ( )  R*   s .  R s (0)  R s () 

(13)

Three representative velocities: 1.58, 3.08, 9.21, provide the R*(t) values presented in Fig. 6. The data of Fig. 6 were utilized in the range

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1  R*  0.2 86

given the ambient temperature of 21oC and the limit of 1% variation in h described above. Excellent agreement with an exponential decay is evident in the data representation of Fig. 7. The best fit (least squares) relationship yields the indicated  values for the expressions
ln R*   t /  ( U )

(14)

The complete set of experimental data can be evaluated in terms of the expected functional form:

1  A  B  U n 

(15a)

where the left-hand side of (12) is of the form expected for the solution to (2) with I2R=0 and h=constant. The agreement demonstrated between (12) and the data for the discrete velocity values (see Fig. 8), gives confidence that a calibrated TTA can provide an accurate   U  transfer function in its calibrated range. Specifically, the standard deviation between the fitted relationship (12) and the experimental data is 0.008m/sec. 3.2 Measurement of the Density-Velocity Product <U> Consider that the basic TTA response is established via calibration and the A, B, n coefficients are established at the ambient temperature: Tamb)1. If the measurements were to be made at a different ambient temperature: Tamb)2, the basic heat transfer relationships: (2), (4), (11), that rely on the value of h, can be utilized to determine the <U> product experienced by the sensor. From (2), (4) and (11), it is apparent that the direct effect of Tamb)2 Tamb)1 is included in the [T(t)T()] term that represents the “driving” effect for the heat transfer. The indirect effects on h are represented by the temperature dependencies of the Nuselt Number which, as

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described in Section 2.2, vary by less than 1% for Tamb)test>Tamb)cal when T=360oK is used as the lower bound for the evaluation of  and Tamb)cal  300oK. Hence, as shown by (11), the measured  value can be used to infer the <U> product and (15) can be rewritten as

1  A  B  U  n 
where A=A and B=B/(Tamb=Tcal).

(15b)

It is instructive to observe that this product: <U>, is of primary interest given the presence of an elevated Tamb. Specifically, if the local velocity and density magnitudes vary over the sampled area, then their spatial variations can be described as U=<U>+U and =<>+ (16b) (16a)

with ( ) as the deviation from the spatial average. The true mass flux will be described as (for the cell area: Ac) Ac<U>=Ac{<><U>+<U>} (17)

The separate <> value can be obtained from the barometric pressure: p(abs), and <T> as obtained from T() in the measurement process. This will allow <U> to be determined under the assumption that <U>=0. However, an estimate of the true mass flux is available from the measured <U> product as shown in (15b). 4.0 Summary

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A novel airflow measurement device: the Thermal Transient Anemometer, has been described and representative experimental data – that certify its capability to evaluate the spatially averaged velocity in a given TTA cell – have been presented. The utilization of the TTA for automotive cooling circuit applications has been identified. This automotive application, however, does not circumscribe its potential contributions. The TTA can provide flow rate information for one or more cells in numerous applications. Acknowledgements The TTA was developed with the technological motivation and financial support provided by the DaimlerChrysler Challenge Fund. The support provided by C. Mesa, B.

Chapman, M. Zabat, and J. Schmitt are gratefully acknowledged. References Brunn, H.H. (1995) Hot-Wire Anemometry – Principles and Signal Analysis, New York, Oxford University Press. Johnson, R.W. ed. (1998) The Handbook of Fluid Dynamics, CRC Press, Boca Raton. Morris, S.C. and Foss, J.F. (March 2003) “Transient thermal response of a hot-wire anemometer”, Meas. Sci. and Tech., 14, pp. 251-259. Figure Captions Figure 1a: The TTA frame and zigzag patterned 50 m Tungsten sensor wires. (Note, each cell is individually heated and monitored for Rs(t).) The Mark I TTA (Fig. 1a) installed on the downwind side of a radiator. A schematic representation of the TTA control electronics. The normalized heat transfer coefficient: h(T)/h(T=510oK). a) Tamb=300oK; U=1, 5, 10 m/sec. b) Tamb=400o; U=1, 5, 10 m/sec. The single TTA cell used for the experimental data of Figs. 5, 6, 7. Note the Teflon tether discs that were installed in the stainless steel frame.

Figure 1b: Figure 2: Figure 3:

Figure 4:

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Figure 5: Figure 6: Figure 7: Figure 8:

The experimental facility in which the calibration velocity data were obtained. Time varying sensor resistance values. Logarithmic display of sensor resistances. Representative calibration 1/   A  B  U  n . data that support the analytic expression

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(a)

(b) Figure 1

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Overheat Sense Cell 1 Decay Sense
Heating Voltage Source Sensing Current Source

Cell 16

DSP Based Control Unit

PC (RS-232 link) for control and display

Figure 2

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1.0000

0.9950

h(T) / h(T(0)=510)

0.9900

0.9850

Tamb=300, U=1 m/s Tamb=300, U=5 m/s Tamb=300, U=10 m/s Poly. (Tamb=300, U=1 m/s) Poly. (Tamb=300, U=10 m/s) Poly. (Tamb=300, U=5 m/s)

0.9800 300

350

400

450

500

Temperature (K)

(a)
1.0020

1.0000

0.9980

h(T) / h(T(0)=510)

0.9960

0.9940

0.9920

Tamb=400, U=1 m/s Tamb=400, U=5 m/s Tamb=400, U=10 m/s Poly. (Tamb=400, U=1 m/s) Poly. (Tamb=400, U=10 m/s) Poly. (Tamb=400, U=5 m/s)

0.9900

0.9880 300

350

400

450

500

Temperature (K)

(b) Figure 3

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Teflon tether plug

Figure 4

17

Figure 5

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Wire Resistance vs. Time

1

0.8

0.6

Exponential decay region evaluated for curve fit

R*

0.4

v1 = 1.58 m/s v2 = 3.08 m/s v3 = 9.21 m/s

0.2

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

time (s)

Figure 6
Evaluated Region
0

-0.25

Note: ln(R*) = -t/ V1: = 93.4 ms, = 576 s,  = 6.17e-3 V2: = 72.3 ms, = 312 s,  = 4.32e-3 V3: = 47.6 ms, = 225 s,  = 4.73e-3

-0.5

ln(R*)

-0.75

v1 = 1.58 m/s v2 = 3.08 m/s v3 = 9.21 m/s

-1

-1.25 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

time (s)

Figure 7

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Calibration Results
25

20

15

-1 1 (s )
10

a = 3.663 s-1 b = 5.768 sn-1/mn n = 0.4981 = 0.009

5

0 0 1 2 3 4 5 6 7 8 9 10

Velocity (m/s)

Figure 8

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