Modelling Heat and Mass Transfer in a Cooling Tower under Hot and Humid Conditions

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1 Journl of Advnced Engineering Reserch ISSN: Volume 2, Issue 1, 2015, pp.1-10 Modelling Het nd Mss Trnsfer in Cooling Toer under Hot nd Humid Conditions Dng Trn Tho* nd Dng Quoc Phu School of Het nd Refrigertion Engineering, Hnoi University of Science nd Technology, Vietnm *Corresponding uthor emil: Tel: ABSTRACT A model for estimte of outlet ter temperture under hot nd humid condition in mixed counter-flo cooling toer s developed. With n ssumption tht the cooling toer rected s n dibtic continuous nd stble system, the ter outlet temperture s theoreticlly estimted s function of climte conditions nd structure of the cooling toer. A complete set of experimentl dt on the ter outlet temperture in lb-scle cooling toer operting under the sme climte conditions ere tken for comprison tht hve shon good greement ith the predicted results. Keyords - Cooling, Cooling toer, hot nd humid, het nd mss trnsfer, modeling. 1. INTRODUCTION Cooling toer (CTW) is idely used in mny pplictions, especilly in refrigerting nd ir conditioning systems, here there is need to relese the het from hot ter flo into cooler tmosphere. As mixed het exchnger, the het trnsfer tking plce in CTW is obviously ssocited ith the mss trnsfer beteen the hot ter nd cool ir moving inside the CTW. As result, the cooling toer efficiency depends on the evportion of ter into the ir, hich in turn vries not only ith the climtic conditions under hich the CTW is employed but lso its on structure [1]. So fr, ttempt to study energy performnce of CTW s mde by mny reserchers orldide. Hoever, most ork ere conducted in cold nd dry climte. Under these conditions, het exchnge effectiveness of CTW is normlly high. Min operting vribles investigted re the nturl evportion in CTW ithout pcked-bed [2]; the height nd structure of CTW used in poer plnts [3]; the ir flo direction [4]; the ind direction nd ind shedding objects [5]; the life spn of CTW shell [6]. In ddition, improvements of therml nlysis nd clcultion method for CTW performnce ere lso ttempted bsed upon Merkel s theory [7,8,9]. In hot nd humid climte, mbient temperture nd ir reltive humidity re normlly high, reltively lo het cpcity nd cooling efficiency of CTW used under such conditions re normlly observed. This pper dels ith modelling of CTW performnce by tking into considertion the effect of some operting prmeters (i.e ir humidity nd temperture, ter-toir flos rtio) s ell s its on structure (i.e. specific surfce re, height of the pcked bed of the CTW). Comprison beteen the modelling results nd the experimentl ones hich ere erlier crried out on lb-scle CTW is then mde tht shos pretty good greement. 2. THEORY 2.1 Building differentil eqution system describing het nd mss trnsfer in cooling toer Het nd mss trnsfer in CTW is influenced by mixing beteen the cooling ir nd hot ter inside the CTW. Once the ir reches its sturted stte, het exchnge beteen the ir nd the ter ould decrese. The mount of ter evported into the ir t this stge is negligible. As result, cooling efficiency of CTW depends on ho het exchnge process tkes plce hen the ir is still t under sturted stte [10, 11]. Let s denote da surfce re element of CTW (see Fig 1). Assuming tht the CTW rects s n dibtic system nd het nd mss trnsfer tking plce in the CTW is of continuous nd stble process [10,11], if t > t, het nd mss trnsfer tking plce in da cn be represented by some fundmentl equtions s belo: Het trnsfer by convection from ter to ir in da: dq cv =.(t - t ).da =.t.da (1) Het trnsfer by evportion beteen ter nd ir: Let s denote β mss trnsfer coefficient hich is defined s mount of ter evported into the ir per Reserch Article 1.jeronline.com

2 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), 1-10 unit time per unit re if difference in the differentil pressure of the evportion surfce nd tht of ir is 1 Pscl. The mount of evported ter into ir cn be thus clculted s follos. d =.(p vplt - p vp ).da =.p.da =.d(d) (2) Here: - p vplt is the differentil vpor pressure of the ir on the ter-to-ir interfce nd t ter temperture t. Of course, p vplt = p s (t ), in P. - p vp is the differentil vpor pressure of the ir t ir temperture t, in P. - d(d) is differentil vrition of moisture content in ir, in kg ter/kg dry ir. +d h + dh d +d(d) h +dh Combining Equtions (3), (4), (6) nd (7), the energy blnce eqution for da is s follo: dq dq k n dq dq dl dl dq dq tc tc (8) By replcing Equtions (1), (2), (3), (4) into Eqution (8) nd ith some mthemticl modifictions, system of to differentil equtions describing het nd mss trnsfer process in under-sturted ir zone cn be obtined s belo. dt dt d(d) dt [ α.δt ( β.δp [ α.δt β.δp α.δt ( β.δp r C r lt lt C i i ).(C ] pvp. t).c pd d.c pvp ) ] (9), h dq cv da dq mt h, d The equtions system (9) expresses the vrition of ir temperture nd tht of ir moisture content s function of ter temperture. To solve this differentil eqution system, prt from its initil nd boundry conditions, it is necessry to define some intermedite prmeters s follos. Fig 1. Het nd mss trnsfer in da From Eqution (2), het exchnge beteen ter nd ir by mss trnsfer cn be estimted s belo. dq mt = d.r lt =.p.r lt.da (3) here r lt is the ltent het of ter vpor hich is determined by the ltent het of ter vpor t 0 C nd its specific het C pvp. r lt = C pvp.t + r 0 (4) Assuming ir is still t under-sturted stte, the energy blnce eqution hs the folloing form: dq = dq = dq (5) From the ter side: dq =.dh + h.d (6) From the ir side: dq =.dh (7) 2.2 Determine intermedite prmeters Vrition of moisture content in ir Moisture content in ir cn be estimted s belo. p ( t ) s d 0,622., kgter/kg dry ir (10) p. p ( t ) s here P s (t ) is the sturtion pressure of ter vpor in moist ir Wter to ir flo rtio As ter evportion lys tkes plces inside CTW during its opertion, the rtio / chnges ith vrition of moisture content in ir. Bsed upon the mss blnce for the element da, this rtio cn be defined s belo. 2.[ 1.( d d )] (11) 1 2. t Chrcteristic coefficient of cooling toer. P Reserch Article 2.jeronline.com

3 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), 1-10 The estimte of het nd mss trnsfer coefficients for mixed het exchngers ppers complicted s coefficients nd depend on mny fctors. By pplying Leis Theorem, reltionship beteen these to coefficients cn be expressed s belo [14]. C p (12) The bove expression cn be hoever pproprite only under dibtic conditions. On the other hnd, by ssuming het conduction nd diffusion processes being of the sme nture, reltionship beteen het nd mss trnsfer coefficients cn be represented s follos [15] α β.c p 0,9085. ξ 1 (13) ln ξ In this study, by combining Equtions (1) nd (7), het trnsfer by convection cn be expressed s belo. dq cv =.(t - t )da =.t.da =.C p.dt (14) Also, het trnsfer by evportion cn hve nother expression s fololos In some cses, moisture content in ir t the outlet of CTW (d 2 ) is knon. From Equtions (9) nd (17), e obtin the system of differentil equtions to estimte the ter nd ir temperture s functions of moisture contents in ir. d(t ) Δt d(d) d d(t ) d(d).[ C p Δt. rlt d C i ] (21) The bove differentil eqution systems (20) nd (21) cn be solved by numericl methods. 3. EXPERIMENTAL WORK 3.1 Experimentl set-up An experimentl ork s crried out on T123D lbortory equipment currently vilble t Hnoi University of Science nd Technology [1]. Its schemtic digrm is presented in Figure 2 [14]. dq mt =.d(d).r lt = =.[d.c pvp.dt + (r 0 + t.c pvp ).d(d)] (15) By combining Equtions (4) nd (15) one cn get d.c pvp.dt = (C pvp.t - t.c pvp ).d(d) = C pvp.t.d(d) (16) or: dt d ( d ) t d (17) Similrly, by combining Equtions (14) nd (3), one cn obtin:. t C. P p dt dd By combining Equtions (17) nd (18) e hve:. t C. P p t d C p P. d (18) (19) By substituting Eqution (19) into Eqution system (9), e finlly receive ne differentil equtions system s follos: Fig 2. Schemtic digrm of the experimentl set-up Legend nd notes: B: Cooling toer: The toer hs squre cross section, toer shell is mde of orgnic glss. Configurtion of the pcked-bed inside the toer cn be chnged during experiment; C: Centrifugl fn ith flo control vlve; D: the ir heter; d ( t ) d ( t ) d ( d ) d ( t ).[ ( C.[ C p p C. t ( r d. C. t ( r. t lt lt i i ). d ] ). d ] ) (20) F: Over-flo trough-type distributor of ter. Hot ter is pumped into the distributor here it runs off through smll holes nd squirt ll over the pcked-bed; Reserch Article 3.jeronline.com

4 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), 1-10 : Control pnel here mjor experimentl dt re displyed; H: Mke-up ter tnk; I: Hot ter tnk tht includes ter try, ter collector, flot vlve to djust the ter level inside the tnk, nd n electric ter heter; L: Wter circulting pump ith mximum flo rte V mx of 3.26 m 3 /h; Q: Flo meters; t 1, t 2 : ter temperture t the inlet nd outlet of toer, respectively; t 3, t 4 : dry ir thermometer temperture t the inlet nd outlet of the toer, respectively; t 8, t 9 : et bulb ir thermometer temperture t the inlet nd outlet of the toer, respectively; t 5, t 6, t 7 : mbient temperture, temperture of the ter tnk, nd temperture of the ter collector, respectively; P 1, P 2 : sttic pressures inside the pcked-bed of CTW; Dp2: pressure drop through the pcked-bed of CTW 3.2 Experimentl procedure nd instrumenttion Hot ter from the hot ter tnk I is pumped up into the over-flo distributor F locted on top of the CTW. From there, ter is spryed onto the pcked-bed surfce. By floing donrds, ter is cooled by flo of ir tht moves uprds from fn (C). A mixed het nd mss trnsfer from the ter to ir then tkes plce on the pcked-bed surfce. The cooled ter is collected t the bottom of the CTW, preheted in the hot ter tnk I nd gin is pumped bck on the top of CTW. Mke-up ter is regulrly mde due to loss of ter evported during the ter-to-ir het nd mss trnsfer process. Under sttic conditions, reduction in the volume of ter in the mke-up ter tnk should equl to the mount of ter evported in the CTW tht leds to n increse in humidity of the ir going out from the CTW. bed to its entire volume, f: 0 m 2 /m 3, 25 m 2 /m 3, 64 m 2 /m 3, 125 m 2 /m 3, 160 m 2 /m 3, 250 m 2 /m 3 nd 300 m 2 /m 3 ; Height of the pcked-bed, H: 150mm, 300mm, 450mm, 600mm nd 750 mm. For ech experiment, only one operting prmeter is vried t time hile the others re kept unchnged. During ech experiment, mesurement of ter nd ir tempertures nd flo, pressure drop in the pcked bed nd ir humidity ere crried out ith the help of TESTO 400 (ermn product) nd Dyer (USA product) ith high ccurcy. 4. COMPARISON BETWEEN THE EXPERIMENTAL AND PREDICTED RESULTS In this ork, the Runge-Kutt numericl method s used to solve the differentil eqution systems (20) nd (21) ith the boundry conditions being stted in ccordnce ith the rnge of the experimentl ork [1]. On the other hnd, totl of 181 runs ere conducted on the bove described CTW set-up. Detiled experimentl dt nd results ere nlyzed in [1] hile the effects of some min operting vribles on the energy performnce of the CTW ere erborted in [15]. All the experimentl nd predicted results of the ter temperture t the outlet of the CTW re given in Tble 1. Figure 3 shos comprion beteen the experimentl nd predicted results. From this figure, the positions of the points t2-ex re fluctuted round nd focus on the min digonl, ith the lrgest nd verge devitions being 4.65% nd 1.4%, respectively. For this study, the folloing re min operting prmeters ith their respective selected vlues. Wter temperture t the inlet of the CTW, t 1 : 35 o C, 40 o C, 45 o C; Air temperture in the CTW, t 1 : 25 o C, 30 o C, 35 o C; Air humidity in the CTW, 1 : 55%, 60%, 65%, 70%, 75%, 80%, 85% nd 90 %; Specific re surfce of the pcked-bed tht is estimted s the rtio of surfce re of the pcked Fig 3. Comprison beteen the experimentl nd predicted results Reserch Article 4.jeronline.com

5 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), 1-10 ter temperture t the outlet of the cooling toer Tble 1. Experimentl nd predicted results for the ter temperture t the outlet of the cooling toer t 1 [ o C] μ f [m 2 /m 3 ] H [mm] t 1 [ o C] φ 1 [%] t 2 [ o C] φ 2 [%] t 2ex [ o C] t 2pre [ o C] Reserch Article 5.jeronline.com

6 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), Reserch Article 6.jeronline.com

7 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), Reserch Article 7.jeronline.com

8 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), Reserch Article 8.jeronline.com

9 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), CONCLUSION The mixed het nd mss exchnge process in CTW under hot nd humid condition ppers complicted. The efficiency of this process depends on the evportion process from ter into the ir floing inside the CTW. In this study, mthemticl model s developed to comprehensively describe such exchnge process tking plce inside the CTW. A good greement beteen the experimentl nd predicted results hs shon tht developed mthemticl model ould be relible tool for the designing, operting nd performnce evlution of the CTW. Temperture nd humidity of ir hve gret influence to the cooling efficiency of CTW. Normlly, CTW produced in the temperte zone, eld zone nd cold countries operted in hot, humid conditions then its orking het cpcity only chieve 40% cpcity s designed (reduces 60%). In CTW het trnsfer by mss trnsfer minly, ith hot nd humid climte conditions, het trnsfer by this Reserch Article 9.jeronline.com

10 Dng Trn Tho nd Dng Quoc Phu / Journl of Advnced Engineering Reserch, 2015, 2 (1), 1-10 mechnism is more thn 80% of the totl het exchnge. NOMENCLATURE Symbol Nme Subscripts C [kj/kgk] Specific het cpcity 1 In d [kgh/kgk] Humidity rtio 2 Out A [m 2 ] Are ev Evportion m [kg/s] Mss flo rte cv Convection H [m] Height of cooling toer pcking vp Vpor h [kj/kg] Enthlpy Air Q [W] Het flux lt Limit t [ o C] Temperture pre Predicted Ltent het of r [kj/kg] Wter evportion [W/m 2 Het convection K] v verge coefficient Mss trnsfer [kg/m 2 mt Mss trnsfer sp] coefficient Reltive humidity of the [%] ex Experimentl ir Rtio of ter nd ir b et bulb [kgw/kga] flos s Sturtion REFERENCES d Dry ir [1] Dng Trn Tho, Theoreticl nd experimentl study on het nd mss trnsfer in cooling toers of refrigerting nd ir-conditioning systems, PhD s Thesis, Hnoi University of Science nd Technology, Vietnm, [2] S.P. Fisenko, A.I. Petruchik nd A.D. Solodukhin, Evportive cooling of ter in nturl drft cooling toer, Interntionl Journl of Het nd Mss Trnsfer, 45 (23), 2002, [3] R. Witsse, J.F. eorgin nd J.M. Reynourd, Nucler cooling toer submitted to shrinkge, behviour undereight nd ind, Nucler Engineering nd Design, 217, 2002, [4] M.A. Al-Nimr, Dynmic therml behviour of cooling toers, Energy Conversion nd Mngement, 39, 1998, [5] Murizio Orlndo, Wind-induced interference effects on to djcent cooling toers, Engineering Structures, 23 (8), 2001, [6] DD. Derksen, T. J. Bender, D. J. Bergstrom nd K. S. Rezkllh, A study on the effects of ind on the ir intke flo rte of cooling toer: Prt 1. Wind tunnel study, Journl of Wind Engineering nd Industril Aerodynmics, 64, 1996, [7] Jmeel-Ur-Rehmn Khn, Bill Ahmed Qureshi nd Syed M. Zubir, A comprehensive design nd performnce evlution study of counter flo et cooling toers, Interntionl Journl of Refrigertion, 27, 2004, [8] Jorge Fco nd Armndo Oliveir, Het nd mss trnsfer correltions for the design of smll indirect contct cooling toers, Applied Therml Engineering, 24, 2004, [9] M.S. Soylemez, On the optimum performnce of forced drft counter flo cooling toers, Energy Conversion nd Mngement, 45, 2004, [10] Dng Trn Tho, A study of the effects of hot nd humid climte on het nd mss exchnger efficiency of cooling toers, Mster s Thesis, Hnoi University of Science nd Technology, Vietnm, [11] Poppe, Wärme-und Stoffübertrgung beider Verdungstungs- kühlung in egen- und Kreuzstrom, VDI-Forschungsheft, Düsseldorf 56. ermny, [12] W. Leis, In The Evportion of Liquid into s. Engineering, Ne York 55. USA [13] F. Bonjkovic, Technische thermodynmik, Dressden, ermny, [14] T123D ctlogs: Bench top cooling toers study unit, Didct, Itli, [15] Dng Quoc Phu nd Dng Trn Tho, A study of energy effectiveness in cooling toer, Proceedings of the Interntionl Conference nd Utility Exhibition 2014 on reen Energy for Sustinble Development (ICUE 2014), Thilnd, Mrch Reserch Article 10.jeronline.com

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