1、International Journal of Heating,Ventilating, Air-conditioning and Refrigerating Research I Volume 7, Number 1, January 2001 American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc. International Journal of Heating, Ventilating, Air-conditioning and Refrigerating Research Edit
2、or John W. Mitchell, Ph.D., P.E. Professor of Mechanical Engineering, University of Wisconsin-Madison, USA Associate Editors James E. Braun, Ph.D., P.E., Associate Professor, Ray W. Henick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA Alberto Cavalli
3、ni, Ph.D., Professor, Dipartmento di Fisicia Tecnica, University of Padova, Italy Arthur L. Dexter, D.Phil., C.Eng., Reader in Engineering Science, Department of Engineering Science, University of Oxford, United Kingdom Leon R. Glicksman, Ph.D., Professor, Departments of Architecture and Mechanical
4、Engineering, Massachusetts Institute of Technology, Cambridge, USA Ralph Goldman, Ph.D., Chief Scientist, Comfort Technology, Inc., Framingham, Massachusetts, USA Anthony M. Jacobi, Ph.D., Associate Professor and Associate Director ACRC, Department of Mechanical and Industrial Engineering, Universit
5、y of Illinois, Urbana-Champaign, USA Jean J. Lebrun, Ph.D., Professor, Laboratoire de Thermodynamique, Universit de Lige, Belgium Reinhard Rademacher, Ph.D., Professor and Director, Center for Environmental Energy Engineering, Department of Mechanical Engineering, University of Maryland, College Par
6、k, USA Keith E. Starner, P.E., Engineering Consultant, Architecture, Building Loads, Energy, and Weather, York, Pennsylvania, U.S.A. Jean-Christophe Visier, Ph.D., Head, Centre Scientifique et Technique du Btiment Energy Management Automatic Controller Division Mame La Valle, France Policy Committee
7、 Lee W. Burgen, chair Jack B. Chaddock Ken-Ich Kimura John W. Mitchell Editorial Assistant Publisher ASHRAE Staff Jennifer A. Haukohl W. Stephen Comstock Jeanne Baird. Associate Handbook Editor Frank M. Coda W. Stephen Comstock Scott A. Zeh, Publishing Services Manager Nancy F. Thysell, Typographer
8、Reviewers Professor Jeffrey D. Spiller, P.E. Oklahoma State University Cliff Federspiel. Ph.D. University of California-Berkeley John E. Sem Johnson Conuols Professor Moms Grenfell Davies University of Liverpool Professor Marcus Preissner University of Maryland Professor Klaus Sommer Nachtigallenstr
9、asse 2 1 Professor William P. Goss University of Mass-Amherst Chao Zhang Visteon Dr. Jeff Darabi University of Maryland Eric Brodsky Research Products Dr. Erhard Mayer Fraunhofer Institut fr Bauphysu Mark Kedzierski NIST Professor Robert Bittle Texas Christian University Dr. Willem de Gids MO-Bouw D
10、r. Claudio Melo Federal Univ. of Santa Catarina Dr. Yunho Hwang University of Maryland Mahesh Valiya Naduvath. Ph.D. York International Prof. Dr Ing. Juergen Werner Ruhr Universiiaet Professor Lynn Schlager University of WI-Platteville Professor Jamal Seyed-Yagoobi Texas A nor may any part of this b
11、ook be reproduced, stored in a reaieval system. or hansmitted in any form or by any means-electronic. photocopying. recording, or other-without permission in writing from ASHRAE. AbstractsAbstracted and indexed by ASHRAE Abstract Center; Ei (Engineering Information. Inc.) Ei Compendex and Engineerin
12、g Index; IS1 (Institute for Scientific Information) Web Science and Research Alert; and BSRIA (Building Services Research fluid temperature, 10.3“C; liquid density, 10.2%; tube depth, *0.4%; static pressure, *OS%; and measured peak bubble pressure, 11.0%. For pure water, the expectation was that the
13、 measurements would agree with the published surface tension value, obtained from ASHRAE (1991), to within the experimental uncertainty. Small amounts of contamination would most often lead to a measurement that is lower than the published value. Three of the measurements in Table 1 fall slightly ou
14、tside the estimated uncertainty range of 11.2%, which indicates that there may have been other factors leading to greater measurement uncertainty. One source of error could have been caused by some liquid adhering to the inside of the capillary tube, which would likely have affected the bubble shape
15、. Insufficient cleaning of the vessel or any of the components, especially the bubble tube, could also affect the results. Controlling or remedying these sources of error were deemed unnecessary since all of the measurements were within the desired engineering accuracy of 12%. Presented in Table 2 a
16、re the results for 99.8% methanol at near ice point and room temperature conditions. Interestingly, these results showed better agreement with the published values, obtained from Long and Nutting (1942), than for water, even though the estimated measurement uncertainty was 11.4%. This is slightly hi
17、gher than that for water due to the larger hydrostatic com- ponent of the measured bubble pressure. Various bubble interval times were explored from as low as 5 seconds up to about 45 seconds, but there was no discernible trend of surface tension with bub- ble interval that extended beyond the uncer
18、tainty of the measurement. This is to be expected since there should be no difference between the dynamic and static surface tensions of pure liquids. Test results for pure R-134a are presented in Table 3. In order to ensure the purity of the refrigerant, a careful procedure was followed to charge t
19、he vessel. As always, the vessel was first cleaned and rinsed with distilled water and acetone and then heated to drive off any mois- ture. After assembly, the apparatus was evacuated to a very low pressure (0.6 kPa) and par- tially immersed in an ice bath to cool the bottom of the vessel. The sampl
20、e bottle, li, was connected to the fill tube (4) via valve V8), and immersed in a warm water bath and placed on a scale that was set to tip after about 280 mL of fluid had transferred from the bottle. The shut-off valve (V8) was slowly opened to allow the refrigerant to evaporate from the sample bot
21、tle and condense in the bottom of the vessel. Valve V8) was shut off when the sample bottle tipped the balance at the pre-determined weight, and filling was thus complete. The sample bot- tle was then disconnected from the fill tube and re-connected to the bubble tube at valve (V6) to be used as a p
22、ressure source for blowing the bubbles. The bath in which it was immersed was always kept about 5C warmer than the vessel contents to provide a low pressure source for eas- ier control of bubble intervals. Figure 5 is a sample of the output signal from the differential pressure transducer for the ca
23、se of R-134a measurement. The regular sawtooth waveform shown in this figure is characteristic of the process of bubble formation, whereby the gradual increase in pressure coincides with bubble growth, while the sudden drop in pressure coincides with bubble detachment. The peak of the sawtooth wavef
24、orm is the differential pressure measurement that is desired for surface tension calculations. The surface tension results presented in Table 3 show close agreement with the published values, which were obtained from ASHRAE (1991), and are within the estimated measurement uncertainty of 11.7%. No di
25、scernible trend in surface tension values was observed with respect to bubble intervals, which for these tests ranged from 5 to 30 seconds. VOLUME 7, NUMEIER 1, JANUARY 2001 13 The measurement results for the potentially contaminated sample of R-134a are shown in Table 4. For these measurements, the
26、 refrigerant was drawn into the vessel from the liquid side of the storage container. The results show some scatter about the published value, but only one is more than the estimated measurement uncertainty of hl .7%. Therefore it was established that, since the measured surface tension of this samp
27、le of R- 134a was not significantly different from that of the pure sample, the contamination visible in the sample had no significant effect on its surface tension. The nature of the contamination was not known. However, based upon the past usage, it was suspected that dissolved lubricating oil and
28、 grease were the primary contaminants. DISCUSSION While surface tension values are available in the technical literature for a wide variety of flu- ids, these only apply to those liquids in their pure form, and contamination can significantly affect this value. This paper presents the development an
29、d operating procedure of an apparatus that can measure the surface tension of a volatile fluid with reasonable engineering precision under ordinary laboratory conditions. The apparatus performed very well, the measured surface tension results for pure fluids being within oUl C2UI cw O 0.7891 0.3735
30、-0.3735 -0.78913 1 -18.8339 -2.5132 2.5132 18.8335 0.1432 0.1432 2 -13.4565 -4.1956 4.1956 13.4565 -0.000059 -0.000059 3 -0.0932 0.0307 -0.0307 0.0932 O O VOLUME 7, NUMBER 1, JANUARY 2001 23 Figure 4. Environmental variables Figure 5. Heat Fluxes via soi-air temperature (Note that the corresponding
31、curves for RF, CTF and WF methods overlap each other) Table 3. Conduction Transfer Functions for the Reference Wall ce. . j Chj C&jl CfU.1 4.il C40UI QIUI CC O 20.5252 -2.4331 2.4331 -20.5252 1 -14.3785 -4.2744 4.2744 14.3785 O. 1432 0.1432 2 0.7685 -0.2073 0.2073 -0.7685 -0.000059 -0.000059 3 -0.00
32、0194 -0.000036 0.000036 0.000194 The weighting factor method gives values of heat fluxes at time kA corresponding to tempera- ture pulses applied at time (k + 1)A. This differs slightly from the other methods. Following the current ASHRAE method, the sol-air temperature is used for the surface tem-
33、perature of the exterior wall, Two, and the interior air temperature is used for the interior surface temperature, Twi, in Equations (6), (8) and (9). Figure 5 shows plots of values of heat fluxes of exterior and interior walls from the 3 methods. All methods give almost identical results. ENERGY BA
34、LANCE METHOD As illustrated in Figure 1 the energy balance (Pederson, 1998) at the exterior surface of the wall gives the relation between absorbed solar radiation, convection, long-wave radiation, and conduction: At the interior surface, a similar equation can be written as -ab+ l)+hCiTWj(k+ l)-Ti(
35、k+ l)1+hJTWi(k+ l)-TJk+ i) = qi(k+ 1) (12) 24 HVAC&R RESEARCH Substituting qO(k+ 1) from relationships such as Equation (8) and similar relationship for qi(k + i), and re-arranging gives L where b,(k+ 1) = bi(k+ 1) = a+ 1) = q,n(k) = a+ 1) = and rn n n -abrl(k+ 1)-hCiTi(k+ l)-hriTsi(k+ 1) m n n Solu
36、tion to Equation (13) can be written in the form where E = 1“ “j e21 e22 In Equation (14), El is the inverse of the coefficient matrix in Equation (13). In this form, the new values of surface temperatures of the wall are computed from the new environmental vari- ables (a, and ai) and the previous v
37、alues of heat fluxes and temperatures (qon and sin). The pro- cedure of energy balance has rendered temperature variables state variables. The computation procedure can be implemented by first computing qon and qin using previous values of heat fluxes and temperatures, which may be a set of initial
38、values. Then the new Two and Twi are computed, to be followed by use of Equation (6) for the new values of heat fluxes for the FW method, or Equations (8) or (9) for the WF and CTF methods respectively. The following values were used for heat transfer coefficients: At the exterior surface - h, = 8 W
39、m-2K-1, and h, = 4 wm-2K-1, VOLUME 7, NUMBER 1, JANUARY 2001 -50 - -15 1 3 5 7 9 11 13 15 17 19 21 23 25 Time (hour) -W(W -9IiWI -qdCTF) -NCTFl . . * . .TMw) . . * . . TNRF) . . * Tm(CTF) O -Tw(ClF) Figure 6. Wall surface temperatures and heat fluxes computed via energy balance: RF and CTF methods f
40、or the reference wall 300 300 - 200 - 100 E s! 0- - Io g io -100 -200 Figure 8. Wall surface temperatures and heat fluxes computed via energy balance: WF method for the reference wall 25 O 2 4 8 8 10 12 14 16 18 20 22 24 Time (hour) -CsO(soi-Air) -. 0 . qi(CoMir) -qo(E-bal) . - o. . qi(E-bal Figure
41、7. Heat fluxes via sol-air temperature and energy balance: RF method for the reference wall 30 3 15 - -4 I“ O -15 O 2 4 6 8 10 12 14 16 18 20 22 24 -CNWFI -Cqi(wF) . . +. ,Tvio(WFJ . . * ,Tm(WO Time (hour) Figure 9. Wall surface temperatures and heat fluxes computed via energy balance: WF method for
42、 the light wall For the reference wall, the RF and the CTF methods produce identical results as shown in Figure 6. The values of the wall surface temperatures obtained differ from the sol-air tempera- 26 HVAC&R RESEARCH Figure 10. State-space model for heat transfer through a wall considering the en
43、ergy balance at wall surfaces ture. Figure 7 shows that the resulting values of heat fluxes also differ substantially from those computed using sol-air temperature. However, when the energy balance procedure is applied with the WF method to the reference wall, the recursive calculation diverges, as
44、can be seen from Figure 8. This divergence is not inherent in the WF method, as can be seen in the results of the compu- tation using sol-air temperature. The recursive steps of the energy balance procedure cause the divergence. When the energy balance procedure is applied with the weighting factor
45、method to a light wall with identical environmental variables, heat transfer variables, and the same thermal properties except that p = 700 kgm-3 and k = 0.1 Wm-K-l, the recursive calculation converges. The results are shown in Figure 9. However, even for this light wall, there is an apparent evi- d
46、ence of the instability problem. ANALOGOUS DYNAMIC SYSTEM FOR THE ENERGY-BALANCE METHOD Figure 10 shows the block diagram of the realization of an analogous dynamical system for the procedure implied by Equation (8) or (9), (10) and (14). The procedure used in obtaining new values of Two, Twi, go an
47、d qi by using qOn and qin in Equation (13) is tantamount to using feedback of past values of state variables in conjunction with new values of environmental variables. Note that in this configuration, the temperature VOLUME 7, NUMBER 1, JANUARY 2001 27 o/o o I . o/ : :I O00 I .: I ojo o 1 . o/o o o
48、. I , . /I: : : : 01 O00 010 o o . . I:,: I: j . /. ,/: . Figure 11. State equation of the analogous dynamic system resulting from the energy balance method variables are also state variables. The state equations for the dynamic system shown in Figure 10 are given in Figure 11. The analogous dynamic
49、 system can be used to examine if the recursive calculation of a given problem will diverge. The convergence or divergence of the recursive calculation is analogous to the stability of the state variables in the dynamic system. Thus, the stability of the dynamic system can be examined to determine the convergence of the recursive calculation procedure. From system theory, such linear, time-invariant, discrete-time dynamic system is stable if and only if the magnitudes of the eigenvalues of the state transition matrix are all smaller than one (Kuo, 1992). State tr
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