1、I n t e r n at ion a 1 Jo u i-n a 1 of Heat in g ,Ve n til at in g, Air-conditioning and Refrigerating Research Volume 5, Number 1, January 1999 American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc. International Journal of Heating, Ventilating, Air-conditioning and Refrige
2、rating Research Editors Raymond Cohen, Ph.D., P.E., John W. Mitchell, Ph.D., P.E. Professor of Mechanical Engineering and Herrick Professor of Engineering Purdue University, USA Rofessor of Mechanical Engineering University of Wisconsin-Madison, USA Associate Editors James E. Braun, Ph.D., P.E., Ass
3、ociate Professor, Ray W. Herrick Laboratories, Arthur L. Dexter, D.Phil., C.Eng., Reader in Engineering Science, Department of Leon R. Glicksman, Ph.D., Professor, Departments of Architecture and Ralph Goldman, Ph.D., Senior Consultant, Arthur D. Little, Inc., USA Hugo Hens, Dr.Ir., Professor, Depar
4、tment of Civil Engineering, Laboratory of Building Physics, Katholieke Universiteit, Belgium Anthony M. Jacobi, Ph.D. Associate Professor and Associate Director ACRC, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana-Champaign, USA Ken-Ichi Kimura, Dr. Eng., Profess
5、or, Department of Architecture, Waseda University and President, Society of Heating, Air-conditioning and Sanitary Engineers of Japan, Japan Horst Kruse, Dr.-Ing., Professor Emeritus, Institut fr Kltetechnik und Angewandte Wrmetechnik, Universitt Hannover, Germany Jean J. Lebrun, Ph.D., Professor, L
6、aboratoire de Thermodynamique, Universit de Lige, Belgium Reinhard Radermacher, Ph.D., Professor and Director, Center for Environmental Energy Engineering, Department of Mechanical Engineering, University of Maryland, College Park, USA School of Mechanical Engineering, Purdue University, West Lafaye
7、tte, Indiana, USA Engineering Science, University of Oxford, United Kingdom Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA Policy Committee Lynn G. Bellenger, chair Mario Costantino Hans O. Spauschus John W. Mitchell Frank M. Coda . W. Stephen Comstock Jennifer A. Hauk
8、ohl Editorial Assistant Publisher W. Stephen Comstock ASHRAE Editorial and Publishing Services Staff Robert A. Parsons, Handbook Editor Scott A. Zeh, Publishing Services Manager Nancy F. Thysell, Typographer 01999 by the American Society of Heating, Refrigerating and Air-Con- ditioning Engineers. In
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10、 of his bwk be reproduced. stored in a retrieval system. or Abstracts-Abstracted and indexed by Engineering Information. Inc. Available electronically on Compendex Plus and in print in Engineer- ing Index. Information on the contents are also presented in the follow- ing IS1 products: SciSearch. Res
11、earch Alert, and Current Contents/ Engineering, Computing, and Technology. Disclaimer-ASHRAE has compiled this publication with care, but ASHRAE has not investigated, and ASHRAE expressly disclaims any duty to investigate, any product. service. process, procedure, design, or the like which may be de
12、scribed herein. The appearance of any techni- cal data or edirorial material in this publication does not constitute endorsemeng warranty. or guaranty by ASHRAE of any product, ser- vice, process. procedure, design, or the like. ASHRAE does not warrant that the information in this publication is fre
13、e of errors, and ASHRAE does not necessarily agree with any statement or opinion in this publica- tion. The entire risk of the use of any information in this publication is assumed by the user. Postmaster-Send form 3579 to: HVAC John W. Mitchell and William A. Beckman are professors of Mechanical En
14、gineering at the University of Wisconsin-Madison. 3 4 HVAC or cf = 1.067f;: , where vstd is in m/s (3) The heat transfer coefficient between the inner fluid and the tube wall was based on the Sieder-Tate equation (Incropera and DeWitt 1990). In a manner similar to that for Equation (i), the relation
15、 for the heat transfer coefficient-area product inside the tubes was modified to be The exponent on the Reynolds number was taken as a constant of 0.8 since this exponent is valid over a wide range of Reynolds numbers. However, for tubes that have turbulators, the Rey- nolds number exponent was chan
16、ged from 0.8 to 0.7 (Kaka et al. 1987). Because the fluid inside the tubes is a liquid, the property effect was expressed as the viscosity ratio. The values of the three characteristic heat transfer parameters Cl, C, and C, need to be fit using catalog data points. For the dry coil analysis, the two
17、 convection coefficient-area products were combined into an overall heat transfer coefficient-area product. The effectiveness-Ntu method was then used to predict the performance of the coil. The wet coil model uses the convection coef- ficient-area products in conjunction with specific heats to calc
18、ulate an overall enthalpy transfer coefficient similar to the conductance-area product for sensible heat exchangers (Braun et al. 1989). The heat exchanger analogy method allows the performance of the wet coil to be predicted using the effectiveness-Ntu method based on enthalpy. Selection of Catalog
19、 Data Points The number of catalog data points required for a good fit and the means by which these points are chosen are important to obtaining a good fit. For a chilled water cooling coil, the air flow rate, entering dry-bulb/wet-bulb temperature combination, entering water temperature, and water
20、tem- perature rise are the four input properties usually given in a catalog. In this study the parameters were evaluated for a number of different heat exchangers using data sets with the number of points varied from eight to up to sixty. It was found that sixteen performance values, chosen to cover
21、 all combinations of high and low values of the four input properties, provided a good fit to the catalog values (Rabehl 1997). The parameter estimation procedure and the accuracy of the technique are illustrated using a proprietary coil with face dimensions of 3.0 m by 1.2 m (120 in. by 48 in.), ei
22、ght tube rows and 262 aluminum fins per metre (80 findfoot). The characteristic heat transfer parameters were determined by minimizing the sum-of-squares of the difference between the model estimates for heat transfer and the catalog heat transfer values. The temperatures were then computed using th
23、e model relations and compared to those given in the catalog. The results of the parameter estimation are shown in Figure 1 where the calculated heat transfer rate is plotted as a function of the catalog heat transfer rate in Figure l(a), the calculated leaving dry-bulb temperature against the catal
24、og value in Figure 1 (b), and the calculated leaving wet-bulb temperature against the catalog value in Figure l(c). The filled triangles indicate the catalog points 6 HVAC&R RESEARCH 20 u 15 - c Ld f 10 rl 5 Figure 1. Comparison of performance predicted by model to catalog data Filled triangles are
25、catalog points used to determine Characteristic parameters. Open circles are values predicted by fitted characteristic parameters. (a) Heat transfer (b) Leaving dry-bulb temperature (c) Leaving wet-bulb temperature used to determine the characteristic parameters, and the open circles represent perfo
26、rmance values predicted by the fitted characteristic parameters. As shown, the data points used in the fit cover the entire operating range. The root-mean-square (RMS) error in the heat transfer rate is about 5.8% of the median value of the heat transfer. The RMS error in the leaving dry-bulb temper
27、ature is 0.6“C, and the RMS error in the leaving wet-bulb temperature is 0.4“C. An important aspect of the modeling approach described here is the ability to use the fitted characteristic parameters to estimate the performance with other heat transfer fluids. Because fluid transport properties are r
28、etained as separate quantities within the model correlations, the fit- ted characteristic parameters are functions only of geometry. Therefore, the characteristic param- eters fitted with catalog data for a given tube fluid are expected to be applicable to the operation of the same cooling coil with
29、 a different tube fluid. This is an extremely useful attribute since a catalog may present performance using water as the tube fluid but another fluid such as ethylene glycollwater, propylene glycollwater, or calcium chloridelwater may be used in the tubes. To test the ability of the approach to pre
30、dict coil performance with other fluids, a data set was compiled from the catalog for operation of the same coil butwith a solution of 50% ethylene gly- col/water flowing in the tubes. The same characteristic heat transfer parameters as found with 16 data points using water as the tube fluid were th
31、en used to predict performance for ethylene gly- col/water in the tubes. The calculated heat transfer rate as a function of the catalog heat transfer VOLUME 5, NUMBER 1, JANUARY 1999 7 20 15 10 5 20 n 2 -i a 3 10 o 15 Figure 2. Comparison of performance predicted by model to catalog data for 50 % et
32、hylene glycowater (a) Heat transfer (b) Leaving dry-bulb temperature (c) Leaving wet-bulb temperature rate for the 50% ethylene glycol/water data is shown in Figure 2(a), the calculated leaving dry-bulb temperature as a function of the catalog value is shown in Figure 2(b), and the calculated leavin
33、g wet-bulb temperature as a function of the catalog value is shown in Figure 2(c). Compar- ison of Figures 2(a) to 2(c) with Figures l(a) to i(c) shows that the model predicts coil perfor- mance with comparable accuracy for both water and 50% ethylene glycol/water as the tube fluid. The errors in to
34、tal heat transfer rate, leaving dry-bulb temperature, and leaving wet-bulb tem- perature that result from using the characteristic heat transfer parameters fit with operating points using water as the tube fluid are given in Table 1. The relative errors in the heat transfer are the difference betwee
35、n the calculated and catalog values divided by the catalog value. The first line of each section of Table 1 presents the errors that resulted when characteristic heat transfer param- eters fitted with water were applied to a larger set of operating points with water. The second line of each section
36、presents the errors that resulted when these same characteristic heat transfer parameter values were used to predict the performance of the same coil using a 50% ethylene gly- col solution. The third line of each section of Table 1 presents the errors that resulted when char- acteristic heat transfe
37、r parameters fitted with 50% ethylene glycol operation data were applied to the larger set of 50% ethylene glycol operating points. The results in Table 1 indicate that accurate performance predictions can be made for another fluid without the need to determine character- istic parameters for that p
38、articular fluid. 8 HVAC&R RESEARCH Table 1. Errors in Representation for Basic Coil Model Fluid Maximum Average RMS Bias Water 0.153 0.0587 0.0728 -0.0494 50% Ethylene glycollwater (using water to fit) 0.234 0.0478 0.0596 0.0219 (a) Relative Errors for Heat Transfer 50% Ethylene glycollwater O. 163
39、0.0603 0.0750 -0.0512 (b) Absolute Errors for Leaving Dry Bulb, “C Water 1.31 0.458 0.550 0.132 50% Ethylene glycollwater (using water to fit) 2.34 0.639 0.806 -0.606 50% Ethylene glycollwater 1.53 0.443 0.554 0.0761 (c) Absolute Errors for Leaving Wet Bulb, “C Water 0.88 0.33 1 0.393 0.182 50% Ethy
40、lene glycollwater (using water to fit) 2.13 0.437 0.606 -0.350 50% Ethylene glycollwater 1.28 0.358 0.794 0.221 Pressure Drop The pressure drops of the fluid flowing inside the tubes and over the coil surfaces were modeled similar to that for heat transfer. The equation for calculating the air press
41、ure drop as it flows nor- mal to the bank of water tubes is given by (Kays and London 1955). The first grouping of terms inside the brackets of Equation (5) accounts for frictional pressure losses as the air flows across the tube bank. The second grouping accounts for pressure losses due to flow acc
42、eleration resulting from density changes as the air temperature changes, and is usually small relative to the frictional pressure loss (Kays and London 1955). In this study the friction fac- tor was assumed to be apower function of the Reynolds number, and is based on tabulated friction factor data
43、for flow normal to a bank of finned tubes (Kays and London 1955). Neglecting the flow acceleration term, Equation (5) was rearranged to group geometric terms into characteristic air pressure drop parameters resulting in c5 APO = c4($)($ The pressure drop coefficients depend on whether the coil is dr
44、y or wet. The air pressure drop through the proprietary coil is plotted as a function of coil face velocity for both dry and wet coils in Figure 3. For a given coil face velocity, the air pressure drop for a wet coil is greater than that for a dry coil due to differences in the flow area. The conden
45、sate film on the fins results in a slightly smaller flow area for a wet coil than for a dry coil. The decreased minimum free-flow area and accompanying increased velocity result in the greater air pressure drop across a wet coil. The calculation of the air pressure drop requires values for two chara
46、cteristic parameters, C4 and C5 that are different for dry and wet operation. The parameters were obtained using separate sets of catalog data for dry and wet operation of the coil. The resulting pressure drop is presented in Figures 4(a) for the dry coil and 4(b) for the wet coil. There is seen to
47、be good agreement using the characteristic relations and Equation (6). The water pressure drop was calculated assuming fully developed flow and the friction factor. VOLUME 0.8 5, r NUMBER 1, / 0.0 - O12345678 Face Velocity ds Figure 3. Air pressure drop for dry and wet coils from catalog data 9 0.8
48、- 0.0 0.2 0.4 0.6 0.8 1.0 cat Wal (a) 0.3 - 0.0 0.1 0.2 0.3 0.4 Figure 4. Comparison of air side pressure drop predicted by the model to catalog data (a) Wet coils (b) Dry coils AP = f (b)($) (7) where the flow was assumed to be turbulent and Moody friction factor was calculated as (Incropera and De
49、Witt 1990). (8) -0.25 f = 0.316ReD Equation (8) was substituted into Equation (7), terms were manipulated so that the mass flow rate replaced the velocity, geometric terms were grouped into characteristic pressure drop param- eters, and then a viscosity-based correction factor was added. The following equation was devel- oped for the water pressure drop. HVAC&R RESEARCH 160 120 80 40 o - O 40 80 120 160 Figure 5. Comparison of water side pressure drop predicted by the model to catalog data for a cooling coil with turbulators The calculated water pressure drop is compared to
