a cfd analysis of room aspect ratio on the effect of ... · a cfd analysis of room aspect ratio on...

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 paperUDC: 697.12/.13

BIBLID: 0354-9836, 11 (2007), 4, 79-94

Com fort con di tions in air-con di tioned rooms re quire that tem per a ture inthe oc cu pied zone should not vary by more than 1 °C and ve loc ity, ev erywhere 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 pro vid ing ef fec tive in su la tion and mak ingleak tight build ings are con sid er ably re duced the cool ing load re quire ments and the sup ply air flow rates. Ob tain ing uni form tem per a ture dis tri bu tionwith 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 inthe 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, 0.1-0.25 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 thebuild ings are de signed ac cord ingly. From a com pu ta tional per spec tive, airflows in therooms 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-scaleflow 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 themean flow mo tion. The pres ence of walls cre ates so called near wall re gions, where thetur 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 calcom 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 roomadds to the com plex ity of the flow. Due to these char ac ter is tics, airflows in room pres enta 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 ablyre duced. Hence, lam i nar and low Reynolds num ber turbulent flows modelling aregaining increasing importance.

DOI:10.2298/TSCI0704079T 79

Literature review

Terai [1] made the first at tempt for the nu mer i cal cal cu la tion of in door air flowfor 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 oftwo-di men sional lam i nar room airflows. Many au thors have re ported a closely re latedtopic of nat u ral con vec tion in par ti tioned en clo sures and it has been re viewed in a re centpa per by Hsu et. al. [5]. Lee et al. [6] have ap plied fi nite el e ment method to study thechar ac ter is tics of forced and mixed con vec tion in an air-cooled room for both lam i narand 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 andge 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] havede scribed a nu mer i cal model to as sess the ther mal com fort tak ing into ac count the in doorair mois ture and its trans port by the air flow within an en clo sure. Eftekhari andMarjanovic [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 tionsys tems where ther mal buoy ancy is the dom i nat ing driv ing force. Bin et al. [17] havepro posed a sim pli fied sys tem based on a new air sup ply open ing model and a nu mer i calmethod 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 beenfound by solv ing Navier Stokes equa tions and en ergy equa tion nu mer i cally by SIMPLEand SIMPLEC algorithms.

Non-dimensionalization

The in let ve loc ity Uin let and in let open ing W1 are taken as char ac ter is tic ve loc ityand length, re spec tively. The dif fer ence be tween wall tem per a ture Tw and in let tem per a -ture Tin let is used for non-dimensionalization of tem per a ture. The non-dimensionalization scheme is as fol lows:

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THERMAL SCIENCE: Vol. 11 (2007), No. 4, pp. 79-94

Uu

UV

v

UX

x

W

Yy

WP

p

U

T T

= = =

= =-

inlet inlet

inlet2

inlet=

1

1 nrq

T T

TW U W C

K

w inlet

inlet pGr

gPr =

-

= =b

n n

mD 13

2

1Re

where Pr is the Prandtl number, Re is the Reynolds number, and Gr is the Grashofnumber. Non-dimensional form of conservation equations are:

Conservation of mass (continuity equation)

¶

¶

¶

¶

U

X

V

Y+ = 0 (1)

Conservation of X-momentum

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( )

Re

UU

X

VU

Y

P

X X

U

X Y

U

Y= = - +

æ

èç

ö

ø÷ +

æ

èç

ö1

ø÷

é

ëê

ù

ûú (2)

Conservation of Y-momentum

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( )

Re

UV

X

VV

Y

P

Y X

V

X Y

V

Y+ = - +

æ

èç

ö

ø÷ +

æ

èç

ö1

ø÷

é

ëê

ù

ûú +

Gr

Re 2q (3)

Energy conservation equation

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( )

Re Pr

U

X

V

Y X X Y Y

q q q q+ =

æ

èç

ö

ø÷ +

æ

èç

ö

ø÷

é

ë

1ê

ù

ûú (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 airmove ment in the room has been ana lysed for var i ous as pect ra tios at dif fer ent val ues ofGrashof num ber. Three dif fer ent as pect ra tios have been con sid ered as shown in figs.

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Tripathi, B., Moulic, S. G., Arora, L. R. C.: A CFD Analysis of Room Aspect Ratio on ...

1-3. No-slip and impermeability bound arycon di tions have been used on all walls ex -cept at in lets and out lets. The bound arycon di tions are:– at the left, right, top, and bot tom walls

U = 0, V = 0, q = 1

– at the in let

U = 1, V = 0, q = 0

– at the out let

¶

¶

ff q

nU V= =0, , ,

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 sennear the walls, in let, and out let. These havebeen slowly ex panded to coarse grids in thein 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 -cated on the bound aries for con ve nience ofspec i fy ing the bound ary con di tions. In this

case, the room has been di vided into 80 ´ 92 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 rithmdue 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 thewidth of the room. In let and out let were lo cated on top of the left wall and bot tom of theright wall, re spec tively.

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Figure 1. Room geometry (A)

Figure 2. Room geometry (B)

Figure 3. Room geometry (C)

Fig ure 4 shows a com par i son ofthe 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 thecen tral plane where the two-di men -sional nu mer i cal pre dic tions can becom pared with the mea sured data ofthree-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 lentflow. 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 tainsvari a tions on a much wider range oflength and time scales than the lam i -nar flow. There fore, it can be con -cluded that the so lu tions of lam i narflows 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 tratedin figs. 5 to 22 for the case of cool ing (in let near the ceil ing on left wall and out let near tofloor 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/Re2 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 Coandaef 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 mesdown along the wall togo out or stoops down -wards, at ta ches with thefloor and then goes outde pend ing upon Gr.Fig ure 5 shows that atRe = 2000 and Gr/Re2 == 0.01, it stoops down -wards. As buoy ancy in -creases fur ther, thepoint of at tach ment onfloor moves to wards the in let as seen in fig. 11.Two cir cu la tion zones

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Figure 4. Velocity (U) profile at X/H = 2

Figure 5. Streamlines for Re = 2000, Gr/Re2 = 0.01 for case (A)

are ob served due to en train ment. The ex tent of cir cu la tion in creases with in creases inGrashof 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 floormoves 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

84


Figure 6. Isotherms for Re = 2000, Gr/Re2 = 0.01 for case (A)

Figure 7. Streamlines for Re = 2000, Gr/Re2 = 0.01 for case (B)

recirculatory cell is ob served in the top right cor ner due to warm air ris ing along the rightwall. The point of at tach ment moves to wards the in let with in crease in buoy ancy.

85


Figure 9. Streamlines for Re = 2000, Gr/Re2 = 0.01 for case (C)

Figure 8. Isotherms for Re = 2000, Gr/Re2 = 0.01 for case (B)

The flow pat tern has been found to be sim i lar in all the cases of dif fer ent as pectra tios. Both the left and right walls are at higher tem per a ture then in let. There fore, thesec ond ary flow rises up along both the walls in the nat u ral con vec tion bound ary layer due

86


Figure 10. Isotherms for Re = 2000, Gr/Re2 = 0.01 for case (C)


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/Re2 = 0.1 for as pectra tios of 2.0, 5/3, and 4/3, re spec tively. It is ob served that as Grashof num ber in creasesthe point of at tach ment on the floor moves to wards the left wall since the in ten sity of

87




recirculation cell near left wall in creases. The flow at as pect ra tio of 4/3 also at ta cheswith the floor as seen in fig. 15. Iso therms re veal that tem per a ture vari a tion is con fined towall bound ary layer. There is some vari a tion in tem per a ture near stag na tion zones asshown in figs. 12, 14, and 16.

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Fig ures 17-22 shows sim i lar re sults for Gr/Re2 = 0.2. The in ten sity of clock wiserecirculation con tin ues to in crease and its size con tin u ous to de crease with in crease inGr/Re2 for all as pect ra tios. The ef fect of buoy ancy seems to be more pro nounced at

89




smaller as pect ra tios. For as pect ra tio of 4/3 at Gr/Re2 = 0.2 the clock wise recirculationcell 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/Re2

in creases. At Gr/Re2 = 0.2, two more coun ter ro tat ing cells ap pear near the ceil ing in themid dle of the room. These are more pro nounced for larger as pect ra tio. Recirculatorycells make ap pear ance at both the cor ners on the floor also.

90




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Conclusions

The cold fluid has a ten dency to flow down wards due to buoy ancy while the hotfluid 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/Re2 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, itcon 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/Re2, 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 smallas pect ra tio of room, it stoops down to wards the floor at larger val ues of Gr/Re2. Once itat ta ches with the floor, the room air flow con sists of a clock wise cir cu lat ing cell near leftwall 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/Re2. The rate of in crease is more pro nouncedat 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 inbound ary lay ers on the walls. The tem per a ture is more or less uni form through out theroom 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/Re2 in creases. The ef fects of Re, Gr/Re2, and as pect ra tio hasbeen in ves ti gated.

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Nomenclature

Gr – Grashof number (= gbDTW13/n2), [–]

g – acceleration due to gravity, [ms–2]K – ther mal con duc tiv ity, [Wm–1K–1]Pr – Prandtl num ber (= CpmK–1), [–]p – pressure of fluid, [Nm–2]Re – Reynolds number (= UinletW1/n), [–]T – temperature of fluid, [K]Tinlet – inlet temperature of fluid , [K]Tw – 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]Uinlet – inlet velocity in x-direction, [ms–1]v – y component of velocity, [ms–1]W1, W2 – 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–1s–1]n – kinematic viscosity, [m2s–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 (inJap a nese), l (1959), 4, pp. 63-78

[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 doorAirflows, Trans ac tion of Ar chi tec tural In sti tu tion of Ja pan (in Jap a nese), 4 (1973), 2, pp.172-187

[3] Nomura, T., Kaizuka, M., Nu mer i cal Cal cu la tion Method of Air Dis tri bu tion, Trans ac tion ofAr chi tec tural In sti tu tion of Ja pan (in Jap a nese), 4 (1973), 3, pp. 31-39

[4] Yamazaki, H., Urano, Y., Nashida, M., Watanabe, T., Com par i son of Nu mer i cal Cal cu la tionand 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. 240-248

[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 -clo sure, Nu mer i cal Heat Trans fer, Part A, 31 (1997), 6, pp. 655-683

[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 lentFlows 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. 529-550

[7] Ed ward, A., Tengfang, X., Katsuhiro, M., Zhang, H., Foun tain, M., Bauman, F., A Study ofOc cu pant Cool ing by Per son ally Con trolled Air Move ment”, En ergy and Build ing, 27(1998), 1, pp. 45-59

[8] Sherman, M., In door Air Qual ity for Res i den tial Build ings, ASHRAE Jour nal, 27 (1999), 5,pp. 26-30

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[9] Srebric, J., Chen, Q., Glickman, L. R., A Cou pled Air flow and En ergy Sim u la tion Pro gramfor Indoor Ther mal En vi ron men tal Stud ied, ASHRAE Trans ac tions, Part I, 106 (2000), 1, pp. 465-476

[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.327-343

[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. 569-578

[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, 8th In ter na -tional Con fer ence Air Dis tri bu tion in Rooms, Roomvent 2002, Co pen ha gen, pp. 697-700

[13] Yi, J., Qingyan, C., Buoy ancy-Driven Sin gle-Sided Nat u ral Ven ti la tion in Build ings withLarge Open ings, In ter na tional Jour nal of Heat and Mass Trans fer, 46 (2003), 6, pp. 973-988

[14] Catalin, T., Raluca, H., Gilles, R., Monika, W., Nu mer i cal Pre dic tion of In door Air Hu mid ityand Its Ef fect on In door En vi ron ment, Build ing and En vi ron ment, 38 (2003), 5, pp. 655-664

[15] Eftekhari, M. M., Marjanovic, L. D., Ap pli ca tion of Fuzzy Con trol in Nat u rally Ven ti latedBuild ings for Sum mer Con di tions, En ergy and Build ings, 35 (2003), 7, pp. 645-655

[16] Andersen, Karl T., The ory for Nat u ral Ven ti la tion by Ther mal Buoy ancy in One Zone withUni form Tem per a ture, Build ing and En vi ron ment, 38 (2003), 11, pp. 1281-1289

[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. 543-552

[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. 147-163

[20] Niel sen, P. V., Spec i fi ca tion of a Two-Di men sional Test Case, En ergy Con ser va tion inBuild 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. AroraDepartment of Mechanical Engineering,Indian Institute of Technology, Kharagpur,West Bengal, 721302, India

Corresponding author B. TripathiE-mail: [email protected]

Paper submitted: October 24, 2006Paper revised: March 5, 2007Paper accepted: October 19, 2007

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