1、4704 Analysis and Validation of a Psychrometric Apparatus Joo Batista Dias ABSTRACT This article uses the analysis ofvariance as a tool to vali- date a calibration apparatus for temperature and relative humidity sensors. The validation procedure establishes the operational ranges for measurement of
2、the dry-bulb (tdb) and wet-bdb (twb) temperatures andofthe relative humidity of air (RH) for this particular apparatus. Analyses are carried out testing twb as afunction of air speed ranging from I. 25 to 5.00 m/s and twb as afunction of RHand also compares two envi- ronments to calibrate tdb: eithe
3、r in thermostatic bath or in the airjlow of a test section. The results show that air speed on wet covered semors within the tested range of I. 25 io 5. O m/s does not change the measured twb, thus widening the range suggested in ASHRAEStandard41.1-1974. Howevecfor rela- tive humidity of air within
4、the studied range, significant differ- ences are found, and these are close to the 2-3% indicated range. The use of different calibrated sensorsfor tdb result in different calculated RHc values in a controlled environment. INTRODUCTION Data presented by the manufacturers of some electronic temperatu
5、re sensors show that some ofthem have high thermal dissipation. Some semiconductor sensors present a power dissipation of approximately 4.4 mW 15 V. The use of a sensor covered with a cotton sock to obtain relative humidity of air (RH), which provides the measure of the wet-bulb temperature (twb), i
6、ntroduces a superficial thermal resistance in the sensor, and this may interfere in the process of heat transfer between the air and the sensor. This fact indicates that the sensor must be calibrated again. Therefore, it was found that a calibration apparatus should be built in order to test this co
7、nditions. Paulo Smith Schneider, Ph.D. Member ASHRAE This article presents a calibration apparatus, based on ASHRAE standard41 .l-1974, using the method of analysis of variance (ANOVA) as a validation tool (Dias 2001). CALIBRATION APPARATUS The apparatus basically consists of three subsystems, as sh
8、own in Figure I. Subsystem I is the airflow circuit. Air temperature and humidity are controlled by a conditioning chamber subsystem 21. Subsystem 3 is the test section, where calibration by comparison is carried out. Description of the Apparatus Subsystems Closed Ventilation Circuit-Subsystem 1. Th
9、is consists of piping, a fan, and a flow variator. Piping is made of conventional 100 rnm diameter PVC plastic, which is used in buildings and thermally isolated by a sheet of aluminum- coated polystyrene foam, which is commonly used to cover building roofs. The centrifugal fan is the same as those
10、used in Figure 1 General vision of the calibration apparatus. Joo Batista Dias is a doctoral student and Paulo Smith Schneider is a mechanical engineer at the Federal University of Rio Grande, Porto Alegre, Rio Grande do Sul, Brazil. 02004 ASHRAE. 117 RAC air-conditioners, and the flow variator was
11、built with a plate restricting the the flow cross-sectional area. The subsystem is provided with a micro-manometer with a pitot tube, as shown in Figure 2. Air-conditioning Chamber-Subsystem 2. The function of this subsystem is to supply air at controlled temperature and humidity in order to carry o
12、ut the tests. The chamber consists of a sensitive heat exchange circuit and a vaporizer. Air temperature control is obtained only by heating, depending on environmental conditions. The sensitive heat exchange device consists of an automatic thermostatic bath, which supplies heated water to a heat ex
13、changer placed inside the chamber. The exchanger is a room air conditioner (RAC) evaporator with 2.2 kW (7500 Bhdh) capacity. A water vaporizer is also placed inside the chamber. Vapor injection into the chamber is controlled by a PPC (programmable process controller), connected to a capacitive sens
14、or, whose only function is to measure relative humidity levels and therefore supply control signal information. The structure of the chamber consists of an expanded polystyrene box, internalIy covered with a galva- nized steel plate aimed at protecting the chamber if it is exposed to high air temper
15、ature and humidity. Test Section-Subsystem 3. The test section shown in Figure 3 is part of the piping, where the sensor elements are placed for testing. It consists of reference and test temperature sensor elements, a sock humidifier, a distilled water reservoir, and other accessories. The sensor e
16、lements are placed on the testing section transverse to airflow. The calibration procedure employs comparisons, where the different tested sensors are compared to a reference thermometer. The testing section ensures that the air that flows throughout the system is under the same conditions. The posi
17、tions ofthe reference and the test sensors follow the recommendations of ASHRAE Standard 41.1-1 974. Also according to this standard, the sensors must penetrate the piping up to its circumference center. The sensors for measuring wet-bulb temperature must have a cotton fabric sock or other hygroscop
18、ic material on the sensi- tive part. The sock must cover the sensor element, which must be at a minimal distance of 25.4 mm (1.0 in.) of the levei of water of the sock humidifier, considering that the diameter of air outflow piping is 100 mm (3.93 in.). Taking into consideration that minimum and max
19、imum air speed within the pipe is 1.25 mis and 5.00 mis (246.06 and 984.25 ftlmin), respectively, the Reynolds number varies between 8600 and 34400, assuming an air density of 1.225 kg/ m3 (0.07647425 lb,/ft3), air absolute viscosity of 1.78110 kg/ms (7.18110 Ib,/fimin), and temperature of 15C (59F)
20、. These results, which are higher than the critical Reynolds number (Re,=2300), indicate turbulent flow. There- fore, the position of the sensors must be within a minimal distance of 10 diameters from any accessory, such as curves or restrictions (Hansen 1974). The diameter of the piping used was O.
21、 10 m (3.93 in.), which leads to a minimal distance of 1 .O rn (39.36 in:). thmnostic bah- 1.63 m (49.21 in) Re sensor flow vuiator W air conditioning- chamber ZJ vaporizer Figure 2 Design of the calibration apparatus. Figure 3 Testing section. FUNDAMENTALS Psychrometry A psychrometer is an instrume
22、nt capable of determining relative air humidity from dry and wet-bulb temperatures. When a wet bulb is exposed to an airflow, water evaporates from the tissue, determining an equilibrium temperature called wet-bulb temperature (twb). This process is not an adiabatic saturation process, which defines
23、 the thermody- namic wet-bulb temperature, but rather simultaneous heat and mass transfers in the wet bulb (ASHRAE 1994). In order to avoid saturation of the environment surrounding the sensor, a small fan is added on the wet sensor to promote the aspiration of air flowing over it. Calculated relati
24、ve humidity of air (RHc) in YO is defined by Equation 1, obtained from the sequence of calculations proposed by ASHRAE (1 997). 118 ASHRAE Transactions: Research wherep is total atmospheric pressure (Pa);pws/db is the partial pressure of water vapor in saturation at tdb (Pa), and p is the degree of
25、saturation. ASHRAE Standard 41.6-1994 proposes Equation 2, known as the dry-bulb and wet-bulb psychrometer equation. In the present study, this equation was used to determine the psychrometer coefficient (A), in K- or OC“. where pw is the atmospheric partial pressure of water vapor (Pa), andpwsmb is
26、 the partial pressure of water vapor in satu- ration at twb (Pa). Deriving Equation 2, as a function of tdb and twb, and replacing their derivatives in the Kleine and McClintock equa- tion (Holman 1996) gives Equation 3, which determines the propagated uncertainty of measurement of the relative humi
27、d- ity of air wrc in %, within the testing section. where Ax=Ap lpwstdb, wr,db is the uncertainty of the measurement of tdb f (“C), and wrbVb is the uncertainty of the measurement of twb (OC). Analysis of Variance The method of analysis of variance (ANOVA) (Box et al. 1 978; Barros et al. 1995) for
28、multiple groups was employed in a situation of a single variable (one-way ANOVA). The exper- iment always involves one response variable and a controlla- ble factor in several levels. The aim is to identify if there are differences among the means or the variances of a response variable, measured at
29、 various levels. The tested hypotheses are: HO: there are no significant differences among groups; H1: there are significant differences among groups. The test compares the value ofthe F-factor, calculated by the method with the Fc value (critical value) found in tables of F distribution. If the val
30、ue calculated by the method is higher than the value found in the table, the HO hypothesis is rejected and hypothesis H1 is accepted, that is, there are significant differences among group means. VALIDATION OF THE CALIBRATION APPARATUS The method of analysis of variance was used to validate the test
31、s. The validation procedure establishes the operational ranges for measurement of the dry-bulb and wet-bulb temper- atures and of the relative humidity of air for this particular apparatus. Tests of wet-bulb temperatures as a function of air speed within the range of 1.25 to 5.00 m/s (246.06 to 984.
32、25 ft/min) and as a function of the relative humidity of air were performed. Also, the comparison between two calibration environments, one in the water of a thermostatic bath and the other in the air of the testing section, were analyzed. Some different assays were performed in order to verify the
33、apparatus operation and its ranges of validity. Some of these tests aimed to confirm some standard prescriptions. Type-K thermocouples, PT100 thermoresistance thermome- ters, AD592 semiconductor sensors, and mercury-in-glass thermometers were used in different tests. Apparatus Stability in Terms of
34、Temperature and Relative Air Humidity It is important and necessary to check a system in order to understand the limitations ofthe equipment and the stability in terms of temperature and relative humidity of air. It is also necessary to check the behavior of sensors submitted to an environment with
35、variable temperature, relative humidity, and air speed. Figure 4 illustrates the stability behavior of dry-bulb (tdb), wet-bulb (mb), and room air (tenv) temperatures as a function of time (t). tdb O 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 Time of observation, t (min)
36、 Figure 4 Stability curves of tdb and twb in the testing section and tenv as a function of time (0. ASHRAE Transactions: Research 119 0 1 2 3 4 5 6 7 8 9 1011 121314151617181920212223242526272829303132 Tim of observation, i (min) t (min) Figure 5 Stability curves of calculated relative humidity (RHc
37、) in the testing section and of environmental relative humidity of air (RHenv) as a function of time (t). RHc (YO) wrc *(YO) A (“C-) t (min) RHc (YO) wrc * (YO) A (OC-) Table 1. Results of RHc, wrc, and Psychrometer Coefficient (A), Determined in the Testing Section as a Function of Time (f) O 1 64.
38、72 0.29 6.391 x 57.19 0.32 6.399 x lo4 17 57.22 0.32 6.399 x loF4 18 65.24 0.30 6.390 2 57.35 0.32 6.399 x lo4 19 65.01 0.30 I 6.390 3 4 57.35 0.32 6.399 x 20 70.36 0.27 6.384 x 57.45 0.32 6.399 x 21 76.56 0.27 6.377 x IO4 5 I 7 I 57.59 I 0.32 I 6.399 lo4 II 24 I 74.15 I 0.27 1 6.380 57.56 0.32 6.39
39、9 x lo4 22 73.31 0.27 I 6.381 x 10-4 6 57.55 0.32 6.399 x IO4 23 73.27 0.27 I 6.381 x I 13 I 64.30 I 0.30 I 6.392 x II 30 I 74.29 I 0.21 I 6.378 x I 8 9 10 57.7 I 0.32 6.399 x 25 74.29 0.27 6.379 x 57.80 0.3 1 6.399 x lo4 26 73.89 0.27 6.379 60.65 0.29 6.396 x lo4 27 73.37 0.27 6.378 10 Stability wa
40、s pursued with tdb as a control variable. Figure 4 shows three stabilization plateaus for tdb: 30.50“C (86.90F), 35.60“C (86.90F), and 44.40“C (1 11.92“F). Following the same time intervals in the stability curve of tdb, twb shows similar behavior, with three stabilization plateaus at 25C (77“F), 27
41、.20“C (80.96“F), and 3 l.lO“C (87.98“F). The tenv also remained virtually constant throughout the test, at approximately 25C (77F) with a 0.40“C (0.72“F) variation during 75 minutes of observation. Data indicated that the apparatus is capable of ensuring stable conditions for the test. Figure 5 pres
42、ents the stability curves of calculated relative 11 12 humidity of air (RHc) in the testing section and environmental relative humidity of air (RHenv) as a function of time (t). Stability was pursued with mb as a control variable. Three stabilization plateaus of RHc of 57.20%, 65.06%, and 74.46% wer
43、e observed. In Table 1, it is observed that the uncertainty measured wrc was within the range of k(0.26 to 0.32) % relative humidity, which was below that expected of zkt(2-3 %) also found in ASHRAE (1 994). Data indicated that the apparatus is capable of ensuring stable conditions for the tests. Ta
44、ble 1 shows the values determined for RHc, the psychrometer coefficient (A) and propagated uncertainty of measure wc calculated by Equations 1,2, and 3, respectively. 67.06 0.29 6.390 x 28 73.84 0.27 6.379 x 67.53 0.30 6.389 29 74.29 0.27 I 6.378 120 14 16 15 ASHRAE Transactions: Research 63.94 0.30
45、 6.392 x 31 74.69 0.26 6.377 x 65.06 0.30 6.391 64.93 0.29 6.391 x 32 74.46 0.26 6.377 x Test 1 I sequence 1 I 29.3 I 29.3 I 29.3 I 29.3 I 31.3 I 1.25 wb C tdb IC I vmm/s) Table 3. Results of ANOVA F-Test: ( twb x wm) Tests F (calculated) d! 0.06451 6129 Table 1 shows the mean value of A (6.381 x C-
46、), which is close to the values suggested by ASHRAE (1994) that are 6.5 x 6.7 x and 6.9 x C-. Temperature and relative humidity of air were ensured within the following ranges: tdb of 30.50 - 44.40 “C (86.90-111.92 OF) with wr withintherangeofk(O.11 -0.19OC) (0.20-0.34F), andMc of 57.20 -74.46 % wit
47、h wrc within the range off (0.26 - 0.32 %), which were the ranges assayed in the present study. Variation of Air Speed Range All standards for relative humidity of air measurement assign values for the crossing airflow through sensor elements. The (twb x vm) test aimed at verifying if the values of
48、wet-bulb temperature (twb) as measured in the testing section were different if air speed vm varied. In order to do so, mercury-in- glass thermometers were placed in the testing section of the apparatus. The airflow speed range for this test was 1.25 to 5.00 m/s (246.06 to 984.25 Wmin), whereas the
49、speed range recommendedbyASHRAE(1994)is 3.0 to 5.0m/s(590.55 to 984.25 fdmin). In test 1, (Table 2), a sequence of four twb and one dry-bulb temperature (tdb) stabilization plateau collec- tions were carried out for each speed. Test 2 followed the same procedure but of a different tdb stabilization plateau. Table 3 presents the results of ANOVA F-factor. In Table 3, it is observed that the F-value (calculated) Fc (critical), and hence H1 hypothesis is considered as true, i.e., there are significant differences among the means of RHc within the teste
