ASHRAE-4593-2002.pdf
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1、4593 (RP-986) Uncertainty Analysis of the Experimental Results Investigating the Effects of Turbulence Intensity on the Performance of Rotating Vane Anemometers B. Terry Beck, Ph.D. Member ASHRAE Dawn M. Bardot Mohammad H. Hosni, Ph.D. Member ASHRAE ABSTRACT The experimental results o f an investiga
2、tion of the influ- ence o f various levels o f turbulence intensity on the ability o f rotating vane anemometers to accurately measure average air speed have beenpresented in a companion paper: Results were given for two different sizes of rotating vane anemometers detailing the error in rotating va
3、ne measurement. The two rotating vane anemometers were each tested at six different air speeds-1 OOfpm, 200fpm, 500fpm, I OOOfpm, 2500fpm, and 5000 fpm-through a range of nominal turbulence intensities from 0.5% to 20%. The results suggest that turbulence intensity gives rise to signijkant errors o
4、f as much as 20% to 25% in vane anemometer performance, and that significant differ- ences exist in the relative influence of turbulence intensity on the two different sizes o f anemometers tested. Because of its importance in quantitatively assessing the signijicance o f the experimentally determin
5、ed influence of turbulence intensity, this paper gives a detailed analysis of the uncertainty bands that were presented along with the previ- ously presented experimental results. A description of the design o f the statistical sampling procedure utilized in conducting this research project is given
6、. Included in this paper is a detailedevaluation of the uncertainty of the resulting vane anemometer erro 3600 . Therefore, the minimum effec- tive sample size was selected as 3600. Determining the Sampling Frequency. If two values are correlated, it means that knowledge of one gives some informatio
7、n about the other. If the selected sample rate yields correlated data, then the statistics may understate the true value. Ideally, if the data are random over the entire sampling interval, every sample is uncorrelated. The auto- correlation function R d c ) and the autocovariance function C T ) were
8、 used to determine the minimum sampling interval that yields uncorrelated data. These functions char- acterize the duration over which V(t) is correlated with itself, and they are defined by RvdX2) = V(t)V(t+T), (27) From Equation 17, it follows that CVV(2) = V(t)V(t+z)-?, (28) (25) This experiment
9、investigated turbulence intensities, TZ, . There- fore, combining Equations 18,24, and 17 yields the following approximation to the uncertainty in the turbulence intensity: where, for a stationary random process, it follows that TI = 2-. VH Jij 2 CVv(7 -+ O) = oV = variance of V(t), ranging from 0.0
10、05 to a maximum of 0.2, uvH C uU CVV(2+W) = o. VH So, the ideal minimum estimated sampling interval, beyond which the data are not correlated, is zY, where ASH RAE Transactions: Research 437 -,-,- TABLE I Initial Implementation of the Selected Data Acquisition Parameters to Verify the Statistical Re
11、sults Data Set 1 2 r Independent Hot-Film Data (N= 8192,A = 100 Hz) Mean Velocity Iiirbulence (fmin) Intensity (fmin) 1670.08 73.80 1673.15 73.33 3 Mean 1673.04 72.16 1672.09 73.10 0 - 50Hz. 1 fs = - = - - T“ 0.02s 1.7374 0.8415 Selected Data Acquisition Parameters. Based on the statistical estimate
12、s above and data collection options in the thermal anemometry software, the following data acquisition parameters were selected: N = 8192 f , = 100 Hz In practice,- 438 ASHRAE Transactions: Research bration had bias associated with the curve fit and the measure- ment equipment used to calibrate the
13、probe. The potential sources of error included the following: 1. 2. 3. 4. 5. 6. 7. Bridge voltage measurement Application of the offset and gain A/D conversion Removal of the offset and gain Temperature correction Probe calibration Calibration curve Velocity standard Pressure correction Measurements
14、lCaIcuIationslUncertainties Bridge Voltage Measurement. Since the IFA- 100 measures the bridge voltage from a Wheatstone bridge, the bridge output voltage, EB, is given by EB = Ei(%), Rl where EB ranges from -1.3 to -2.2 V and the bridge resis- tances have approximately the same nominal values ofR,-
15、 R, - 10 ! 2 The input voltage, Ei, is also nominally about 2 V. The manufacturers specifications list the tolerance on Ei to be -10.4 mV and M.002 Q on RH and RI. From Equation 13, the relative uncertainty in the bridge output is bias, EB = (30) where, from Equation 2, and Therefore. 2 2 2 uB = kA(
16、0.02) +(O.OZ) +(0.02) = I0.035%. (33) Application of the Offset and Gain. The voltage was conditioned by an offset and gain so that the output signal, E, range was close to +5 VDC peak to peak. Ec = G(E-Eofiset) (34) The gain, G, ranged from 1 to 900 and had a *0.15% manufacturers uncertainty specif
17、ication. The offset, Eoffser ranged from 0-9 VDC in 1-volt increments with a -10.15% manufacturers uncertainty specification. Applying Equation 11 to evaluate the uncertainty of Equation 34 yields, for the absolute uncertainty of the output signal, 1 The relative uncertainty is thus given by The nom
18、inal values of physical parameters in the above expression for relative uncertainty include Eoffset = lV, EB = 2V, and EB - EOffset = 1 V. In addition, Eoffset is in 1 -volt incre- ments and EB ranges from 0.5 to 2 V. Evaluating the separate contributions to the relative uncertainty given in Equatio
19、n 36 yields - - EB . - - L. 0.035% = *0.070%, EB -Eoffset EB -Eoffset EB 2 - 1 ! ! ! ? = uG = *0.15%, G The resultant relative uncertainty is then given by u E, = +/(0.15%)2 + (0.070%)2 + (0.15%) = *0.22%. (37) A/D Conversion. Once the voltage signal was scaled to a range of k5 VDC peak to peak, a 1
20、2-bit A/D converter digi- tized the signal. The uncertainty of this conversion process was +0.01% of reading *?h bit. Thus, the uncertainty of the sampled voltage becomes U 10 v ES 4096 = IO.01% of reading f - = f0.01% of reading f0.00244 V. (3 8) Since the signal was always scaled to achieve 2 5 VD
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- ASHRAE 4593 2002
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