A CFD ANALYSIS OF ROOM ASPECT RATIO ON THE EFFECT OF BUOYANCY AND ROOM AIR FLOW

Transcription

1 A CFD ANALYSIS OF ROOM ASPECT RATIO ON THE EFFECT OF BUOYANCY AND ROOM AIR FLOW by Brajesh TRIPATHI, Sandipan Ghosh MOULIC, and Late R. C. ARORA Original scientific paper UDC: /.13 BIBLID: , 11 (2007), 4, Com fort con di tions in air-conditioned rooms require that temperature in the oc cu pied zone should not vary by more than 1 C and ve loc ity, ev ery where in the room, should be less than 0.15 m/s so that oc cu pants do not feel draft. Re cent de vel op ments in providing effective insulation and making leak tight build ings are con sid er ably re duced the cool ing load re quire ments and the sup ply air flow rates. Obtaining uniform temperature distribution with re duced air vol ume flow rates re quires care ful de sign of air dis tri bu - tion sys tem. This study aims to find ve loc ity and tem per a ture dis tri bu tion in the room to wards this end. Key words: aspect ratio, room airflow, buoyancy, comfort Introduction A dry-bulb tem per a ture of 25 C, 50% rel a tive hu mid ity, m/s air ve loc - ity and ap pro pri ate air pu rity are con sid ered as com fort able sum mer con di tions, and the build ings are de signed ac cord ingly. From a com pu ta tional per spec tive, airflows in the rooms are very com plex. The flow is fully tur bu lent in the sup ply air ducts, HVAC out lets /in lets and down stream of the edges of the ob sta cles. Else where, the flow is more likely to be lam i nar or weakly tur bu lent and un steady with a wide range of small to large-scale flow struc tures where mo lec u lar trans port is im por tant. In the con text of cool ing (or heat - ing in cold cli mates), these flows are buoy ant and in some cases, buoy ancy drives the mean flow mo tion. The pres ence of walls cre ates so called near wall re gions, where the tur bu lent transport is significantly influenced by a solid surface. In prac ti cal ap pli ca tions, the ob struc tions within the room cre ate geo met ri cal com plex ity. In re al ity, most room airflows are in her ently three-di men sional and un - steady. Shear lay ers on the pe riph ery of sup ply air jet and recirculation within the room adds to the com plex ity of the flow. Due to these char ac ter is tics, airflows in room pres ent a great chal lenge for the avail able nu mer i cal codes and mod els. Now a days, very ef fec tive in su la tion ma te ri als are be ing used in air-con di tioned build ings, which have con sid er ably re duced the cool ing/heat ing loads and thereby the air sup ply rates have also con sid er ably re duced. Hence, lam i nar and low Reynolds num ber turbulent flows modelling are gaining increasing importance. DOI: /TSCI T 79

2 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp Literature review Terai [1] made the first at tempt for the nu mer i cal cal cu la tion of in door air flow for the case of two-di men sional buoy ant flow. Tsuchiya [2], Nomura and Kaizuka [3], and Yamazaki et al. [4] have made im por tant con tri bu tions to wards un der stand ing of two-di men sional lam i nar room airflows. Many au thors have re ported a closely re lated topic of nat u ral con vec tion in par ti tioned en clo sures and it has been re viewed in a re cent pa per by Hsu et. al. [5]. Lee et al. [6] have ap plied fi nite el e ment method to study the char ac ter is tics of forced and mixed con vec tion in an air-cooled room for both lam i nar and tur bu lent re gimes. Ed ward et al. [7] have ex per i men tally in ves ti gated the ef fect of air move ment on dif fer ent hu man sub jects within a room. Sherman [8] and Srebric et al. [9] have stud ied air flow and air qual ity for res i den tial build ings. Costa et al. [10] have in ves - ti gated the tur bu lent air flow with two jet heat ing sys tem for dif fer ent room as pect ra tios. Sinha [11] has in ves ti gated the ef fect of in clined jet on room air cool ing. Gobeau and Saunders [12] have in ves ti gated the ef fect of in let con di tions and ge om e try on a tur bu lence model. Yi and Qingyan [13] have in ves ti gated buoy - ancy-driven sin gle-sided nat u ral ven ti la tion with large open ings. Catalin et al. [14] have de scribed a nu mer i cal model to as sess the ther mal com fort tak ing into ac count the in door air mois ture and its trans port by the air flow within an en clo sure. Eftekhari and Marjanovic [15] have de vel oped a fuzzy con trol ler for nat u rally ven ti lated build ings. Andersen [16] has given a re li able tool for an a lyz ing and de sign ing nat u ral ven ti la tion sys tems where ther mal buoy ancy is the dom i nat ing driv ing force. Bin et al. [17] have pro posed a sim pli fied sys tem based on a new air sup ply open ing model and a nu mer i cal method of solv ing the dis crete al ge braic equa tions to ac cel er ate and sim plify the con ver - gence pro ce dure of pre dict ing air dis tri bu tion in ven ti lated rooms. Problem formulation In this in ves ti ga tion two-di men sional, steady, in com press ible, lam i nar flow un - der Boussinesq s ap prox i ma tion has been con sid ered. The phys i cal prop er ties are as - sumed to be con stant. The ve loc ity and tem per a ture dis tri bu tions in a room have been found by solv ing Navier Stokes equa tions and en ergy equa tion nu mer i cally by SIMPLE and SIMPLEC algorithms. Non-dimensionalization The in let ve loc ity U in let and in let open ing W 1 are taken as char ac ter is tic ve loc ity and length, re spec tively. The dif fer ence be tween wall tem per a ture T w and in let tem per a - ture T in let is used for non-dimensionalization of tem per a ture. The non-dimensionalization scheme is as fol lows: 80

3 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... u v x U V X U inlet U inlet W1 y p T T Y P q = W U 2 1 nr inlet Tw T gbdtw U W C inlet p m Gr Re Pr = n2 n K where Pr is the Prandtl number, Re is the Reynolds number, and Gr is the Grashof number. Non-dimensional form of conservation equations are: inlet inlet Conservation of mass (continuity equation) U X V 0 (1) Y Conservation of X-momentum ( UU ) ( VU ) P 1 X Y X Re X U X U Y Y (2) Conservation of Y-momentum ( UV ) ( VV ) P 1 X Y Y Re X V X V Y Y Gr Re 2 q (3) Energy conservation equation ( U q ) ( V q ) 1 q q X Y Re Pr X X Y Y (4) Geometry and boundary conditions A rect an gu lar room 6 m long and 3 m high has been con sid ered. For sim plic ity, the aero dy namic block age due to var i ous items in the room has been ne glected. The air move ment in the room has been ana lysed for var i ous as pect ra tios at dif fer ent val ues of Grashof num ber. Three dif fer ent as pect ra tios have been con sid ered as shown in figs. 81

4 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp No-slip and impermeability bound ary con di tions have been used on all walls ex - cept at in lets and out lets. The bound ary con di tions are: at the left, right, top, and bot tom walls U = 0, V = 0, q = 1 Figure 1. Room geometry (A) at the in let U = 1, V = 0, q = 0 at the out let f 0, f U, V, q n Figure 2. Room geometry (B) Neumann con di tions have been set for the flow vari ables as above. Where n is the di rec - tion nor mal to the out flow bound ary. In ad di - tion, mass con ser va tion has also been sat is - fied at the out let. Numerical solution procedure The com pu ta tional do main shown in fig. 1 has been di vided into non-over lap ping con - trol vol umes. Fine grids have been cho sen near the walls, in let, and out let. These have been slowly ex panded to coarse grids in the in te rior of room. Grid points are lo cated at the cen ter of the con trol vol umes where the sca lar vari ables such as pres sure, den sity and tem - per a ture are de fined. Grid points are also lo - Figure 3. Room geometry (C) cated on the bound aries for con ve nience of spec i fy ing the bound ary con di tions. In this case, the room has been di vided into grids in x-y di rec tion. The discretized equa tions are ob tained by in te grat ing Navier-Stokes and en ergy equa tions over the con trol volumes. As sum ing fa mil iar ity with the SIMPLE al go rithm due to Patankar [18] and SIMPLEC al go rithm due to Van Doormaal et al. [19], the de tails are omit ted. The nu mer i cal so lu tions were com pared with bench mark ex per i men tal re - sults re ported by Niel sen [20]. The in let and out let were slots ex tend ing through out the width of the room. In let and out let were lo cated on top of the left wall and bot tom of the right wall, re spec tively. 82

5 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... Fig ure 4 shows a com par i son of the hor i zon tal ve loc ity (U) at the ver - ti cal cross-sec tion of the room. These ex per i men tal re sults are at the cen tral plane where the two-di men - sional nu mer i cal pre dic tions can be com pared with the mea sured data of three-di men sional case. The agree - ment is ob served to be good in the re - gion of lam i nar or weakly tur bu lent flow. It is not sat is fac tory in the re - gion of main stream near the ceil ing, where the tur bu lent flow con tains vari a tions on a much wider range of length and time scales than the lam i - Figure 4. Velocity (U) profile at X/H = 2 nar flow. There fore, it can be con - cluded that the so lu tions of lam i nar flows can be used for quick, eco nomic and ap prox i mate pre dic tions for room air dis tri bu - tion. Results and discussion The com puted dis tri bu tions of stream lines and iso therms in room are il lus trated in figs. 5 to 22 for the case of cool ing (in let near the ceil ing on left wall and out let near to floor on right wall) at dif fer ent as pect ra tios and for Reynolds num ber, Re = 2000 and dif - fer ent val ues of Gr/Re 2 rang ing from 0.01 to 0.2. It has been ob served that the cold pri - mary air en ters in the room near the ceil ing and at ta ches with the ceil ing due to Coanda ef fect. It moves along the ceil ing for some dis tance and then ei ther moves to wards the op - po site wall and co mes down along the wall to go out or stoops down - wards, at ta ches with the floor and then goes out de pend ing upon Gr. Fig ure 5 shows that at Re = 2000 and Gr/Re 2 = = 0.01, it stoops down - wards. As buoy ancy in - creases fur ther, the point of at tach ment on floor moves to wards the in let as seen in fig. 11. Two cir cu la tion zones Figure 5. Streamlines for Re = 2000, Gr/Re 2 = 0.01 for case (A) 83

6 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp are ob served due to en train ment. The ex tent of cir cu la tion in creases with in creases in Grashof num ber. Fig ures 6 and 12 show that tem per a ture vari a tion is con fined to ther mal bound - ary lay ers on the walls. The tem per a ture be comes more uni form in the re cir cu lat ing re - gion. As the as pect ra tio de creases to 5/3 in case (B), the point of at tach ment on the floor moves to wards the right wall as shown in fig. 7. The flow touches the right wall as the as - pect ra tio fur ther de creases to 4/3 in the case (C) as shown in fig. 9. A small anticlockwise Figure 6. Isotherms for Re = 2000, Gr/Re 2 = 0.01 for case (A) Figure 7. Streamlines for Re = 2000, Gr/Re 2 = 0.01 for case (B) 84

7 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... Figure 8. Isotherms for Re = 2000, Gr/Re 2 = 0.01 for case (B) Figure 9. Streamlines for Re = 2000, Gr/Re 2 = 0.01 for case (C) recirculatory cell is ob served in the top right cor ner due to warm air ris ing along the right wall. The point of at tach ment moves to wards the in let with in crease in buoy ancy. 85

8 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp Figure 10. Isotherms for Re = 2000, Gr/Re 2 = 0.01 for case (C) The flow pat tern has been found to be sim i lar in all the cases of dif fer ent as pect ra tios. Both the left and right walls are at higher tem per a ture then in let. There fore, the sec ond ary flow rises up along both the walls in the nat u ral con vec tion bound ary layer due Figure 11. Streamlines for Re = 2000, Gr/Re 2 = 0.1 for case (A) 86

9 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... Figure 12. Isotherms for Re = 2000, Gr/Re 2 = 0.1 for case (A) to buoy ancy. The tem per a ture is ob served to be uni form in both the recirculation zones. Fig ures 11, 13, and 15 shows the stream lines for Re = 2000 and Gr/Re 2 = 0.1 for as pect ra tios of 2.0, 5/3, and 4/3, re spec tively. It is ob served that as Grashof num ber in creases the point of at tach ment on the floor moves to wards the left wall since the in ten sity of Figure 13. Streamlines for Re = 2000, Gr/Re 2 = 0.1 for case (B) 87

10 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp Figure 14. Isotherms for Re = 2000, Gr/Re 2 = 0.1 for case (B) recirculation cell near left wall in creases. The flow at as pect ra tio of 4/3 also at ta ches with the floor as seen in fig. 15. Iso therms re veal that tem per a ture vari a tion is con fined to wall bound ary layer. There is some vari a tion in tem per a ture near stag na tion zones as shown in figs. 12, 14, and 16. Figure 15. Streamlines for Re = 2000, Gr/Re 2 = 0.1 for case (C) 88

11 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... Figure 16. Isotherms for Re = 2000, Gr/Re 2 = 0.1 for case (C) Figure 17. Streamlines for Re = 2000, Gr/Re 2 = 0.2 for case (A) Fig ures shows sim i lar re sults for Gr/Re 2 = 0.2. The in ten sity of clock wise recirculation con tin ues to in crease and its size con tin u ous to de crease with in crease in Gr/Re 2 for all as pect ra tios. The ef fect of buoy ancy seems to be more pro nounced at 89

12 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp Figure 18. Isotherms for Re = 2000, Gr/Re 2 = 0.2 for case (A) Figure 19. Streamlines for Re = 2000, Gr/Re 2 = 0.2 for case (B) smaller as pect ra tios. For as pect ra tio of 4/3 at Gr/Re 2 = 0.2 the clock wise recirculation cell is small est in size and has larg est in ten sity com pared to that at large as pect ra tios. The recirculation cell due to Coanda ef fect tends to dis ap pear for as pect ra tio of 4/3 as Gr/Re 2 in creases. At Gr/Re 2 = 0.2, two more coun ter ro tat ing cells ap pear near the ceil ing in the mid dle of the room. These are more pro nounced for larger as pect ra tio. Recirculatory cells make ap pear ance at both the cor ners on the floor also. 90

13 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... Figure 20. Isotherms for Re = 2000, Gr/Re 2 = 0.2 for case (B) Figure 21. Streamlines for Re = 2000, Gr/Re 2 = 0.2 for case (C) 91

14 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp Figure 22. Isotherms for Re = 2000, Gr/Re 2 = 0.2 for case (C) Conclusions The cold fluid has a ten dency to flow down wards due to buoy ancy while the hot fluid rises up. Coanda ef fect, ef fect of buoy ancy and wall bound ary lay ers has been ob - served in this in ves ti ga tion. The Coanda ef fect is ob served in all the cases of lam i nar flow ex cept at large Gr/Re 2 and small as pect ra tio. If cold fluid en ters in the room near the ceil - ing, the flow at ta ches with the ceil ing for dif fer ent val ues of Gr. For small val ues of Gr, it con tin u ous along the ceil ing co mes down along the right wall and goes out from out let. With in creases in Gr/Re 2, that is, as the buoy ancy in creases, it stoops down to - wards the floor in the mid dle of the room, flows along the floor and goes out. For small as pect ra tio of room, it stoops down to wards the floor at larger val ues of Gr/Re 2. Once it at ta ches with the floor, the room air flow con sists of a clock wise cir cu lat ing cell near left wall and an anticlockwise cir cu lat ing cell near right wall. The in ten sity of recirculation of both the cells in creases with in crease in Gr/Re 2. The rate of in crease is more pro nounced at smaller as pect ra tios. Tem per a ture vari a tion is con fined to a nar row re gion near the ceil ing and in bound ary lay ers on the walls. The tem per a ture is more or less uni form through out the room ex cept for the re gion near the stag na tion point. The uni for mity of tem per a ture in - creases as the value of Gr/Re 2 in creases. The ef fects of Re, Gr/Re 2, and as pect ra tio has been in ves ti gated. 92

15 Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on... Nomenclature Gr g Grashof number (= gbdtw 3 1 /n 2 ), [ ] acceleration due to gravity, [ms 2 ] K ther mal con duc tiv ity, [Wm 1 K 1 ] Pr Prandtl num ber (= C p mk 1 ), [ ] p pressure of fluid, [Nm 2 ] Re Reynolds number (= U inlet W 1 /n), [ ] T temperature of fluid, [K] T inlet inlet temperature of fluid, [K] T w wall temperature, [K] DT dif fer ence be tween in let and wall tem per a ture, [K] u x component of velocity, [ms 1 ] U inlet inlet velocity in x-direction, [ms 1 ] v y component of velocity, [ms 1 ] W 1, W 2 inlet and outlet widths, respectively, [m] x, y rectangular Cartesian co-ordinates, [ ] Greek symbols b coefficient of thermal expansion, [K 1 ] m absolute viscosity of fluid, [kgm 1 s 1 ] n kinematic viscosity, [m 2 s 1 ] r reference density of the fluid, [kgm 3 ] References [1] Terai, T., In door Ther mal Con vec tion, Trans ac tion of Ar chi tec tural In sti tu tion of Ja pan (in Japanese), l (1959), 4, pp [2] Tsuchiya, T., Ap pli ca tion of Me te o ro log i cal Nu mer i cal Cal cu la tion Method to In door Airflows, Trans ac tion of Ar chi tec tural In sti tu tion of Ja pan (in Jap a nese), 4 (1973), 2, pp [3] Nomura, T., Kaizuka, M., Nu mer i cal Cal cu la tion Method of Air Dis tri bu tion, Trans ac tion of Ar chi tec tural In sti tu tion of Ja pan (in Jap a nese), 4 (1973), 3, pp [4] Yamazaki, H., Urano, Y., Nashida, M., Watanabe, T., Com par i son of Nu mer i cal Cal cu la tion and Vi su al iza tion Ex per i ments of Two-Di men sional Flows, Trans ac tion of Ar chi tec tural In - sti tu tion of Ja pan (in Jap a nese), 6 (1976), 3, pp [5] Hsu, T. H., Hsu, P. T., How, S. P., Mixed Con vec tion in a Par tially Di vided Rect an gu lar En - closure, Nu mer i cal Heat Trans fer, Part A, 31 (1997), 6, pp [6] Lee, S. C., Cheng, C. Y., Chen, C. K., Fi nite El e ment So lu tions of Lam i nar and Tur bu lent Flows with Forced and Mixed Con vec tion in an Air-Cooled Room, Nu mer i cal Heat Trans fer, Part A, 31 (1997), 5, pp [7] Ed ward, A., Tengfang, X., Katsuhiro, M., Zhang, H., Foun tain, M., Bauman, F., A Study of Oc cu pant Cool ing by Per son ally Con trolled Air Move ment, En ergy and Build ing, 27 (1998), 1, pp [8] Sherman, M., In door Air Qual ity for Res i den tial Build ings, ASHRAE Jour nal, 27 (1999), 5, pp

16 THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp [9] Srebric, J., Chen, Q., Glickman, L. R., A Cou pled Air flow and En ergy Sim u la tion Pro gram for Indoor Ther mal En vi ron men tal Stud ied, ASHRAE Trans ac tions, Part I, 106 (2000), 1, pp [10] Costa, J. J., Oliveira, L. A., Blay, D., Tur bu lent Air flow in a Room with a Two-Jet Heat - ing-ven ti la tion Sys tem A Nu merical Study, En ergy and Build ing, 32 (2000), 3, pp [11] Sinha, S. L., Be hav ior of In clined Jet on Room Cool ing, Build ing and En vi ron ment, 36 (2001), 5, pp [12] Gobeau, N., Saunders, C. J., Com pu ta tional Fluid Dy nam ics (CFD) Val i da tion of the Pre dic - tion of Pes ti cide Dis per sion in a Nat u rally-ven ti lated Build ing, Pro ceed ings, 8 th In ter na - tional Con fer ence Air Dis tri bu tion in Rooms, Roomvent 2002, Co pen ha gen, pp [13] Yi, J., Qingyan, C., Buoy ancy-driven Sin gle-sided Nat u ral Ven ti la tion in Build ings with Large Open ings, In ter na tional Jour nal of Heat and Mass Trans fer, 46 (2003), 6, pp [14] Catalin, T., Raluca, H., Gilles, R., Monika, W., Nu mer i cal Pre dic tion of In door Air Hu mid ity and Its Ef fect on In door En vi ron ment, Build ing and En vi ron ment, 38 (2003), 5, pp [15] Eftekhari, M. M., Marjanovic, L. D., Ap pli ca tion of Fuzzy Con trol in Nat u rally Ven ti lated Build ings for Sum mer Con di tions, En ergy and Build ings, 35 (2003), 7, pp [16] Andersen, Karl T., The ory for Nat u ral Ven ti la tion by Ther mal Buoy ancy in One Zone with Uni form Tem per a ture, Build ing and En vi ron ment, 38 (2003), 11, pp [17] Bin, Z., Xianting, L., Qisen, Y., A Sim pli fied Sys tem for In door Air flow Sim u la tion, Build - ing and En vi ron ment, 38 (2003), 4, pp [18] Patankar, S. V., Nu mer i cal Heat Trans fer and Fluid Flow, Hemi sphere Publ. Comp., Wash - ing ton DC, USA, 1980 [19] Doormaal, Van J. P., Raithby, G. D., En hance ment of the SIMPLE Method for Pre dict ing In - com press ible Fluid Flow, Nu mer i cal Heat Trans fer, 17 (1984), 1, pp [20] Niel sen, P. V., Spec i fi ca tion of a Two-Di men sional Test Case, En ergy Con ser va tion in Build ings and Com mu nity Sys tems, An nex 20: Air Flow Pat tern within Build ings, In ter na - tional En ergy Agency, 1990 Authors' address: B. Tripathi, S. G. Moulic, L. R. C. Arora Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, West Bengal, , India Corresponding author B. Tripathi brajesh@mech.iitkgp.ernet.in Paper submitted: October 24, 2006 Paper revised: March 5, 2007 Paper accepted: October 19,