Production of Chilled Air by Melting Ice in Cool-Thermal Discharge Systems

Transcription

1 amkang Jornal of Science and Engineering, Vol., No. 2, pp (2 87 Prodction of Chilled Air y Melting Ice in Cool-hermal Discharge Systems Wen-Pen Wang and Chii-Dong Ho 2 Department of Chemical Engineering, Kwang-W Institte of echnology aipei, aiwan 2, R.O.C 2 Department of Chemical Engineering, amkang University, amsi, aipei aiwan 2, R.O.C. Astract A mathematical model of cool-thermal discharge systems with melt removal has een developed and stdied theoretically to simlate the otlet temperatre of the chilled air prodced dring on-peak power-consmption hors. Eqations have een derived for estimating the thickness of the airflow velocity, the thickness of melted ice and the total amont of cool thermal flx dring the operating process with a specified inlet air temperatre or otlet air temperatre. Nmerical examples have een illstrated in which either the inlet air temperatre or otlet air temperatre was specified, and the reslts of cool-thermal discharge flxes have een also discssed. Key Words: Cool hermal Discharge, Chilled Air, Moving Bondary. Introdction he cool-thermal storage and discharge systems are the processes to prodce ice dring off peak period in the evening and to otain chilled air in the daytime peak, respectively, with air flowing over melting ice. herefore, the electric tility dring nighttime off-peak period can e tilized sfficiently so as to increase the economic enefit of power generation facilities. In addition, power spply companies offer a cheaper rate to encorage energy consmer dring off peak hors, the danger of power shtdown de to insfficient spply of electricity cold hence e avoided as well as lots of the electricity expense cold e saved. Recently, several researchers proposed the cool-thermal storage system of the vacm freezing method to increase oth the electricity tility profitaility and energy efficiency [2,,2,8]. Althogh there are only a few of literatre on applications of cool-thermal storage and discharge systems exists [,,,7,9,,,,7,9], the theoretical analysis on a new device of cool-thermal storage [2,2] and cool-thermal discharge [22] has een stdied. Moreover, the cool-thermal discharge system with convective ondary conditions [2] also has een developed. he adjstale otlet temperatre in cool-thermal discharge systems with melt removal for the space cooling is highly expected. Here a new model proposed is a cool-thermal discharge system with otlet temperatre adjsted so as to facilitate the practical application in or daily life. he ice layer temperatre is at the melting point initially, and the melt was removed immediately once the ice melting occrs with the amient air flowing throgh the open dct, as shown in Fig.. herefore, the airflow rate mst e reglated continosly to prodce the desirale otlet temperatre as well as to afford more flowing air in the dct de to the removal of melt as the operation proceeds.

2 88 Wen-Pen Wang and Chii-Dong Ho Air W (t, W f, f,i x X(t L inslated plate Ice Figre. Schematic diagram of a cool-thermal discharge system. 2. Airflow Velocity he cool-thermal discharge system, as shown in Figre, is the ice layer with infinite thickness, length L and width B. he depth from the ice layer srface to the inslated plate (or the height of the open dct is of W (<<L. he ice layer was assmed to e initially at its melting point s with no temperatre gradient. Constant physical properties and no density change on melting were assmed. he air of velocity flowing throgh the open dct with the inlet and otlet temperatres are and, respectively. he flx of energy asorption or the flx of cool thermal discharge at the free srface of the ice layer varies horly dring the discharging period de to the changing of the removal of melt and the thickness of the open dct as fnctions of time. By taking a differential energy alance within the open dct, the system is governed y the following eqation: d h s + = dz ( ρwc p he conditions are: ( z = = (2 ( z L = = ( integration of Eq. ( with the se of Eqs. (2 and ( yields hl = ( pw in which s s = = ( s s s s he following correlation for flly developed trlent flow of air etween two parallel plates with one side heated and the other side inslated, can e derived from Kays data [2]: 8. N m =. 8Re, Re > 2. ( he Reynolds nmer is defined as ρ De ρ ( 2W Re = = (7 µ µ and D denotes the eqivalent diameter of the air e passage, D e = 2W. Sstittions of Eqs. ( and (7 into Eq. ( give or W = ρ.2 c.7kl p µ.8 W.2 kl.7 = Cool hermal Discharge (8 (9 he total amont of cool-thermal discharge flx reqired to ice melting can e calclated from dx pbw = ρiceqmbl ( dt where dx dw dw d = = ( dt dt d dt Differentiating Eq. (9 with respect to, one may otain dw.7kl 7 = (2 d Sstittions of Eqs. (9, ( and (2 into Eq. ( give 2 d p = ( dt ρiceqml Integration Eq. (2 from t = to t = t, gives the time history of the airflow rate as follows: ρ iceqml = (, i ρc p t + ρ iceqml Note that, i, the initial velocity of the airflow rate, is otained from Eq.(8 with W = Wi.7kL, i = ( Wi

3 Prodction of Chilled Air y Melting Ice in Cool-hermal Discharge Systems 89 Sstittion of Eq. (8 into Eq. ( yields the thickness of melted ice dx dw = dt dt.9 L k = ( ρ ice Qm c W Also, the time history of the height of open dct was calclated y integrating Eq. ( from t = to t = t W = X + W i L = ( k t+ Wi (7 ρiceq m (,, c f i f o herefore, time history of the cool-thermal discharge flx ( q is also calclated from Eq. ( as follows: q = = ρ ice Q m dx dt L k.9 c W. Nmerical Examples (8 We consider three cases for the amient temperatres, 2, and C, and three cases for the otlet air temperatre, 2, 2 and 2 C. Here, we assign the following nmerical vales: t = h, s = 27 K, p = atm, D e = 2 W =.2 m, L = m. he physical properties of air at atm and 2 o C are []: ρ =.kg m c kj kg K, p =. 8, k=.9kj/m-h-k and µ =. kg m h. he physical properties oce at atm and o C are Q kj kg []: m = and ρ = ice 97 kg m. Sstitting these vales into the appropriate eqations, reslts for, X and q have een calclated and those of, X and q are shown in Figs he calclation procedre will e descried riefly as follows. First, the Reynolds nmers Re were estimated from Eq. (7. Next, the height of the open dct was calclated from Eq. (7. Finally, the total amont of cool-thermal discharge flx q reqired with, or specified from Eq. (8.. Discssion and Conclsion he mathematical formlation of cool-thermal discharge systems with melt removal from ice melting has een developed, and the airflow velocity and the total amont of cool-thermal discharge flx were calclated with the analysis of energy alances in the air flowing dct. he present stdy is to estimate how large airflow velocity,, is needed nder specified inlet air temperatre,,, or otlet air temperatre,, which is adjsted for cool-thermal discharge systems to prodce the chilled air. he airflow velocity in the open dct and the thickness of melted ice in the ice layer may e estimated from Eqs. ( and (7, respectively, while the total amont of cool-thermal discharge flx is calclated from Eq. (8. he most important assmptions in this work are that the ice layer is initially at its melting point and that the volme changed de to ice melting is neglected. Moreover, according to the standard defined in Central Weather Brea, aiwan, R.O.C., wind velocity less than. m s is of no wind. It is not applicale to real systems in the laminar regime of the airflow velocity eing less than.2 m s, then the trlent regime was assmed in this stdy with the se of Eq. (. Figres 2- show that the airflow velocity, the thickness of melted ice and the total amont of cool-thermal discharge flx taken as illstrations with the se of the inlet air temperatre, as a f o parameter for a specified, while Figs. -7 show those nmerical reslts with otlet air f o temperatre, as a parameter for a specified.

4 9 Wen-Pen Wang and Chii-Dong Ho 8 f,o =2, L=m f,o =2, L=m f,i =2 f,i =2 2, m/sec f,i = q(t, kj/m 2 -h 8 f,i = 2 f,i = f,i = t/t Figre 2. ime history of the airflow velocity with inlet air temperatre as a parameter t/t Figre. ime history of the cool thermal flx with inlet air temperatre as a parameter. f,o =2, L=m 7 f,i=, L=m.2 f,i =2 f,o=2.2 f,i = X, m. f,i =, m/sec f,o=2. 2 f,o= t/t Figre. ime history of the thickness of melted ice with inlet air temperatre as a parameter Figre. ime history of the airflow velocity with otlet air temperatre as a parameter t/t

5 Prodction of Chilled Air y Melting Ice in Cool-hermal Discharge Systems 9 X, m f,i =, L =m f,o =2 f,o =2 f,o = t/t Figre. ime history of the thickness of melted ice with otlet air temperatre as a parameter q(t, kj/m 2 -h f,i =, L =m f,o =2 f,o =2 f,o = t/t Figre 7. ime history of the cool thermal flx with otlet air temperatre as a parameter In the present stdy, we considered the variation of air temperatre decreasing from to along the flow channel. he logarithmic-mean vales, Eq. (, were taken for estimating the rate of convective heat transfer etween the flowing air and the free srface oce layer. It is shown in Figs. 2 and that the cooling passage keeps expanding with time as the operation proceeds, and then the airflow velocity decreases with time. hese reslts can e checked y Eq. (8 as well as y Eq. (. It is also fond in Fig. 2 that the airflow velocity increases as the inlet air temperatre decreases for a specified. he higher inlet air temperatre, the longer residence time of air inside the cooling passage for a specified otlet air temperatre. Under sch an operation condition, larger temperatre differences were achieved, and hence the airflow velocity wold e even lower for a specified otlet air temperatre. However, the higher inlet air temperatre associated with the smaller airflow velocity reslts in the lower mean convective heat transfer coefficient. herefore, the thickness of melted ice decreases with increasing inlet air temperatre, as shown in Fig.. he total amont of cool-thermal discharge flx is also calclated from Eq. (8 with the se of X (t. he reslt of the total amont of cool-thermal discharge flx with the se of the inlet air temperatre as a parameter for a specified, as shown in Fig., decreases with increasing inlet air temperatre accordingly. It may e seen from Figs. -7 that the airflow velocity, the thickness of melted ice and the total amont of cool-thermal discharge flx increase with otlet air temperatre for a specified. he temperatre difference of otlet air temperatre and inlet air temperatre increases with decreasing otlet air temperatre for a specified inlet air temperatre, and hence the airflow velocity increases with the otlet air temperatre for a shorter residence time inside cooling passage. In other words, for otaining lower otlet air temperatre nder the same inlet air temperatre, lower airflow velocity (longer residence time is needed. Besides, the average convection heat transfer coefficient decreases with the airflow velocity, therefore, the ice melting thickness and cool thermal discharge flx decrease

6 92 Wen-Pen Wang and Chii-Dong Ho with for a specified, as shown in Figs. and 7. Nomenclatre B cooling channel width (m c specific heat of air ( kj kg K p D the eqivalent diameter of cooling passage e (m h average convective heat transfer coefficient ( kj h m K k thermal condctivity of air ( kj h m K L cooling channel length (m N Nsselt nmer ( hd m e k Pr Prandtl nmer ( µ ρα Q m heat of melting ( kj kg Re Reynolds nmer ( ρ De µ, the inlet temperatre of air ( K f o, the otlet temperatre of air ( K ice temperatre at the free srface ( K s defined y Eq. ( t time (h t total operating time per day (h gas flowing velocity ( m s W the height of the cooling passage (m X thickness of the water layer (m Greek letters ρ air density ( kg m ρ ice density ( kg m ice µ air viscosity ( kg m h References [] Carslaw, H. S. and J. C. Jaeger, Condction of Heat in Solids, 2nd edn, Oxford Univ. Press, New York, (99. [2] David, H. H., DDC and Ice hermal Storage Systems Provide Comfort and Energy Efficiency, ASHRAE J., March, (99. [] Dorgan, C. E. and J. S. Elleson, ASHRAE s New Design Gide For Cool hermal Storage, ASHRAE J., May, 29 (99. [] Eckert, E. R. G. and R. M. Drake Jr., Analysis of Heat and Mass ransfer, McGraw-Hill, New York, (972. [] Geankoplis, C. J., ransport Processes and Unit Operations, Allyn and Bacon Inc., Boston, (98. [] Goodman,. R., he eat-balance Integral and Its Application to Prolems Involving a Change of Phase, rans. ASME, 8, (98. [7] Groer, H., S. Erk, and V Griqll, Fndamentals of Heat ransfer, McGraw-Hill, New York, (9. [8] Ho, C. D., H. M. Yeh and W. P. Wang, Cool hermal Discharges with ime-velocity Variation of Flowing Air in sit Contact on Water Srface, J. Chin. Inst. Engrs., 29, 29 (998. [9] Incropera, F. P. and D. P. DeWitt, Fndamentals of Heat and Mass ransfer, hird Edition, John & Sons, New York, pp , (99. [] Incropera, F. P. and D. P. Dewitt, Fndamentals of Heat and Mass ransfer, hird Edition, John & Sons, New York (99. [] Ingersoll, L. R. and J. Zoel, Mathematical heory of Heat Condction, Univ. of Wisconsin Press, Madison, WI, (9. [2] Jekel,. B., J. W. Mitchell and S. A. Klein, Modeling of Ice-Storage anks, ASHRAE ransactions: Symposia, (99. [] Kays, W. M. and M. E. Crawford, Convective Heat and Mass ransfer, McGraw-Hill, New York, (98. [] Landa, H. G., Heat Condction in A Melting Solid, Q. Appl. Math., 8, 8 (9. [] Mercer, W. E., W. M. Pearce, and J. E. Hitchcock, Laminar Forced Convection in the Entrance Region Between Parallel Flat Plates, J. of Heat ransfer, 89, 2 (97. [] Penner, S. S. and S. Sherman, Heat Flow throgh Composite Cylinders, J. Chem. Phys.,, 9 (97. [7] Roerts, L., On he Melting of A Semi-Infinite Body of Ice Placed in A Hot Stream of Air, J. Flid Mech.,, (98. [8] Stovall,. K. and J. J. omlinson, Laoratory Performance of A Dynamic Ice

7 Prodction of Chilled Air y Melting Ice in Cool-hermal Discharge Systems 9 Storage System, ASHRAE ransactions: Symposia, 79 (99. [9] Yao, L. S. and J. Prsa, Advances in Heat ransfer, Academic Press Inc., San Diego, California, (989. [2] Yeh, H. M. and C. Y. Cheng, Cool hermal Storage y Vacm Freezing of Water, Energy-he International Jornal,, (99. [2] Yeh, H. M. and C. Y. Cheng, Cool hermal Storage y Vacm Freezing of Water with Constant Volme Rate of Slimation, Energy Convers. Mgmt.,, (992. [22] Yeh, H. M. and C. D. Ho, Cool hermal Discharges from Ice Melting with Specified Heat Flxes on he Bondary, Energy-he International Jornal, 2, (99. [2] Yeh, H. M., C. D. Ho and W. P. Wang, Cool hermal Discharges Otained with Air Flowing over Melting Ice, Energy-he International Jornal, 2, 279 (998. Accepted: Jn. 2, 2