EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2 Department f Architecture, Tky Plytechnic University, Atsugi, Japan 2 Department f Architecture, Tky University f Science, Tky, Japan 3 Department f Architecture, Kant Gakuin University, khama, Japan 4 Department f Architecture, The University f Tky, Tky, Japan ABSTRACT Variatin f discharge cefficients with wind directin and pening psitin is ne f the main factrs debasing accuracy f crss-ventilatin flw rate predictin. The lcal dynamic similarity mdel was develped t slve this prblem, and previus studies had validated it fr inflw penings. In the present study, tw experiments were carried ut t investigate its validity fr utflw penings. The experiments shwed that the relatinships between the discharge cefficient and a dimensinless rm pressure P R *, which was riginally defined by the mdel, were independent f wind directin and pening psitin, althugh they were dependent n whether r nt the utflw pening was in a recirculatin flw regin. It was thus cncluded that the lcal dynamic similarity mdel was valid fr utflw penings as well as inflw penings. KEWORDS Crss-Ventilatin, Discharge Cefficient, Wind Tunnel Experiment, Outflw Opening INTRODUCTION Crss-ventilatin is an energy-efficient technlgy that is adpted t reduce energy cnsumptin fr ventilatin and cling in buildings. Fr successful design f crss-ventilatin, its perfrmance must be predicted prperly. The CFD technique has been imprved and prvides rather accurate predictins. Hwever, it is still imprtant t imprve ventilatin flw rate predictin using a cnventinal netwrk mdel, because s many cnditins need t be evaluated fr effective crss-ventilatin and the netwrk mdel seems t be the mst feasible methd fr sme design phases. Many researchers had demnstrated prblems that debase the predictin accuracy f the netwrk mdel. One f the main prblems is that the dynamic pressure f airflw thrugh an inflw pening smetimes des nt dissipate and is preserved at an utflw pening (Ishihara 969, Murakami et al. 99). Anther is that discharge cefficients, which relate wind pressures t ventilatin flw rates, vary with wind directin and pening psitin althugh they are fixed as cnstants in the cnventinal mdel (Katsuta and Sekine 96, Vickery and Karakatsanis 987). In rder t slve the latter prblem, Kurabuchi and Ohba et al. (24) develped a lcal dynamic similarity mdel that explains the variatin f discharge cefficients, and validated it fr inflw penings in their previus studies. In the present study, tw wind tunnel experiments were carried ut t investigate the variatin f discharge cefficients f utflw penings. The validity f the lcal dynamic similarity mdel fr utflw penings is discussed n the basis f the results. Crrespnding Authr: Tel: + 8 46 242 9637, Fax: + 8 46 242 9548 E-mail address: gt@arch.t-kugei.ac.jp
LOCAL DNAMIC SIMILARIT MODEL (LDSM) Figure shws the pressures in the vicinity f an inflw pening. It is pssible t cnsider that the pressure field at the inflw pening is represented by three pressures: dynamic pressure nrmal t the pening (P n ), dynamic pressure tangential t the pening (P t ) and ventilatin driving pressure (P r ). The lcal dynamic similarity mdel assumes that the P n, which is directly related t ventilatin flw rate (Q), is uniquely determined by P t and P r, and that there are dynamic similarities n the relatinships amng the three pressures when the ratis f P r t P t are cincident. As shwn in Table, the discharge cefficient (C d ) and the inflw angle (β) are described by the ratis f P n t P r and P t t P n, respectively. If the abve assumptins are true, these are uniquely determined by the ratis f P r t P t. Kurabuchi and Ohba et al. (24) defined the rati f P r t P t as dimensinless rm pressure (P R *), and verified the mdel fr inflw penings by wind tunnel experiments. P S P t Pn + PS PW P n Pr = PR PW β P W P P P R Figure Definitins f pressures in vicinity f inflw pening Table Fundamental frmulas f lcal dynamic similarity mdel r = PR PW () Q = A Pr (2) n C d = (3) Pr P t β (4) Pn = tan 2 ρ P P = r R * (5) Pt Figure 2 shws the pressures in the vicinity f an utflw pening. Here, P t is defined at the external side f the pening, and static pressure (P S ) at the utflw pening is cnsidered t equal the wind pressure (P W ), while P S +P n is cnsidered t equal P W at the inflw pening. The discharge cefficient (C d ), the utflw angle (β) and the dimensinless rm pressure (P R *) are defined by the same equatins as thse fr the inflw penings. Hwever, P R * fr the utflw pening is always psitive while that fr inflw pening is always negative. P R Ps P W P s Pr = PR PW P W P n β P t Figure 2 Definitins f pressures in vicinity f utflw pening DISCHARGE COEFFICIENT, STATIC PRESSURE AND EXTERNAL AIRFLOW The first experiment was cnducted t reveal the mechanism f the variatin f discharge cefficient fr an utflw pening. This experiment was carried ut in an Eiffel-type wind tunnel (width: 2 mm, height: mm) at
Tky Plytechnic University, using a blw-type ventilatin mdel shwn in Figure 3. The ventilatin mdel had tw rms, and a rund plate was attached arund it. A blw fan was cnnected t the ventilatin mdel t simulate varius ventilatin flw rates, and a partitin with small hles was installed between the tw rms t dissipate the dynamic pressure f the airflw frm the fan. The rund plate attached t the building had multiple pressure taps t measure the static pressure distributin near the utflw pening. The utflw pening was in cntact with the rm flr, and the rund plate and the rm flr were set flush. The mdel with the rund plate was lifted t a height f 25mm frm the wind tunnel flr, and the experiment was perfrmed under a unifrm apprach flw f. The incident angle f the apprach flw was varied as shwn in Figure 4. Under sme incident angles, the wind pressure was psitive at the pening despite the utflw. Hwever, this situatin is pssible, e.g. when penings are lcated in bth walls adjacent t a windward crner f a building, r when an pening is lcated in a rf as well as a windward wall f a building. In rder t bserve the discharge cefficient, rm pressure was measured at different cntrlled ventilatin flw rates. The rm pressure was measured at pressure taps n the ceiling, and the rm pressure measured withut ventilatin (Q = ) was cnsidered t be wind pressure. Internal/external static pressures n the flr (P f ) and external air velcities arund the pening were als measured under different cntrlled ventilatin flw rates. The air velcities were measured with a split film type ht-wire anemmeter that discerned 3D velcity vectr cmpnents. We defined the discharge cefficient under stagnant cnditins as the basic discharge cefficient (C ds ). The C ds f the utflw pening used in the experiment was determined t be.66 by a pre-experiment withut an apprach flw. 68 2 Opening (2x4) 84 Wing wall 25 Fan Thermal flw meter Figure 3 Schematic f first experiment 35 O 2.5 O 9 O 9 O 67.5 O 45 O (a) Withut wing wall (b) With wing wall Figure 4 Test cases f first experiment Figure 5 shws the relatinships between C d and P R * btained fr all incident angles f the experiment. P t t determine P R * was evaluated frm tangential air velcity measured 5mm frm the external side f the pening under the n-ventilatin cnditin (Q = ). As shwn Figure 5, the relatinships shwed tw different trends. Where the utflw pening was in a recirculatin flw regin behind the mdel, i.e.
9 O, 2.5 O and 35 O, C d increased gradually by P R * = 5, and was almst cnstant at the same level f C ds when P R * was greater than 5. Where the utflw pening was nt in the recirculatin flw regin, i.e. 45 O, 67.5 O and 9 O with a wing wall, C d increased rapidly by P R * = 2, and reached a cnstant beynd C ds when P R * was greater than 2. There were a few irregular data arund P R * = fr 35 O, which seemed t be due t measurement errrs. Figures 6 and 7 shw sme results (67.5 O and 2.5 O ) f the internal/external static pressure (P f ) distributins and external airflw patterns arund the pening. Frm the airflw patterns fr bth 67.5 O and 2.5 O, it was fund that the curse f the airflw diffusing frm the pening was narrwer when the C d was smaller. Therefre, it was cnsidered that the decrease f C d was caused by cntractin f the utflw. The cntractin f the utflw greatly depended n the strength f the external crss flw. Thus, the lcal dynamic similarity mdel reasnably explains the variatin f discharge cefficient f the utflw pening..8.6.4.2 5 5 2 2 4 6 45 67.5 袖壁あり 9 with 9 wing wall 9 2.5 35 P R* Figure 5 Relatinships between C d and P R * btained in first experiment (P f P W )/P >.2 (P f P W )/P <.2 (P f P W )/P <.2 (P f P W )/P >.2 (P f P W )/P <.2 (P f P W )/P <.2 -. -. -. -.6 -.9 -.8 -.7 (a) Q= (P R *=, C d =) (a) Q= (P R *=, C d =) -.5.2 -.2 -.4 -.7 -.6 -.8 -.7 (b) P R *=.53, C d =.59 (b) P R *=2.9, C d =.62.4 3 2 -.4 -.8 3 2 -.6 - -.4 -.2 (c) P R *=6., C d =.77 Figure 6 Internal/external static pressure (P f ) distributin and external airflw pattern arund pening in case f 67.5 O (Numbers in left figures are Pf/P. Airflw vectrs in right figures are at mm abve the flr.) (c) P R *=46, C d =.66 Figure 7 Internal/external static pressure (P f ) distributin and external airflw pattern arund pening in case f 2.5 O (Numbers in left figures are Pf/P. Airflw vectrs in right figures are at mm abve the flr.)
Frm the static pressure distributins fr 67.5 O, a large pressure drp ccurred at the leeward side f the pening. This must have been because the external flw alng the wall was separated frm the wall by clliding with the utflw at the windward side f the pening. It was als fund that the curse f the utflw was in the regin with the pressure drp. Therefre, the static pressure in the curse f the utflw was cnsidered t be lwer than P W. This means that the ventilatin driving pressure was greater than P R -P W. This explains why C d fr 67.5 O became greater than C ds as shwn in Figure 5. Hwever, the static pressure fr 2.5 O was nt much different frm P W. This must be because there was riginally a large negative pressure dwnstream f the airflw acrss the pening, and the airflw acrss the pening was relatively weak. The ther cases in the recirculatin flw regin and nt in the recirculatin flw regin shwed the same characteristics as fr 2.5 O and 67.5 O, respectively. Thus, the mechanisms that caused the differences in the relatinships between C d and P R * were als cnfirmed fr thse cases. APPLICABILIT OF LDSM TO OUTFLOW OPENINGS The secnd experiment was cnducted t investigate the applicability f LDSM t utflw penings under mre cmplicated cnditins than the first experiment. The experiment was carried ut in the same wind tunnel as the first experiment, and the same ventilatin mdel withut the rund plate was used and installed n the flr f the wind tunnel. The apprach flw was a bundary layer flw with a pwer-law index f.25, and the reference velcity was kept at at the mdel s upwind edge. The incident angle f the apprach flw was varied frm 45 O t 8 O, and the pening psitin was varied frm A t E as shwn in Figure 8. P R, P W, P t and Q were measured in the same way as in the first experiment. C ds f the utflw pening used in the experiment was determined t be.68 by a pre-experiment. 2.5 O 35 O 57.5 O 8 O 4 2 4 9 O A 6 4 C 34 4 34 E 4 6 67.5 O 45 O 4 B D 4 2 2 3 4 6 4 3 4 Figure 8 Schematic f secnd experiment Figure 9(a) shws the relatinships between C d and P R * btained with pening C (center). Under the bundary layer flw cnditin, the trends were the same as in the unifrm apprach flw. Increase f C d t P R * was mre rapid where the utflw pening was nt in a recirculatin flw regin than where it was in a recirculatin flw regin. Besides, C d that was nt in a recirculatin flw regin increased beynd the basic discharge cefficient. Hwever, it was fund that the relatinships between C d and P R * fr 9 O and 35 O were different. In these cases, there were reattachment pints within r very clse t the pening area, as shwn in Figures (b) and (d). Thus, the ventilatin airflws were mre cmplicated than fr the ther cases, and it was difficult t describe this effect by the LDSM. The directins f the external flw alng the wall fr 2.5 O, 57.5 O and 8 O were different. The directins were almst vertical fr 57.5 O and 8 O, while it was mre hrizntal fr 2.5 O. Hwever,
there were n substantial differences with directins. Figures 9(b), (c) and (d) shw the relatinships between C d and P R * fr different pening psitins fr 67.5 O, 9 O and 2.5 O. The relatinships at all pening psitins were basically the same as thse btained at pening C (center), and culd be distinguished int the tw trends mentined abve. There were exceptins fr pening A fr 67.5 O and 9 O, and pening B and C fr 9 O. Frm Figures (a) and (b), they were cnsidered t be due t the separatin r reattachment f the external airflw within the pening area..8.6.4.2 5 5 2 45 67.5 9 2.5 35 57.5 8.8.6.4.2 5 5 2 A B C D E PR* (a) Opening C PR* (b) Apprach flw 67.5 O.8.6.4.2 A B C D E.8.6.4.2 A B C D E 5 5 2 5 5 2 PR* PR* (c) Apprach flw 9 O (d) Apprach flw 2.5 O Figure 9 Relatinships between C d and P R * btained in secnd experiment 5 5 2 X 2 4 (a) Apprach flw 67.5 O 5 5 2 X 2 4 (b) Apprach flw 9 O X 2 5 5 2 4 X 2 5 5 2 4 X Figure (c) Apprach flw 2.5 O (d) Apprach flw 35 O External airflw patterns measured with sealed mdel (n pening)
DISCUSSIONS The present experiments have shwn that the LDSM reasnably explains the variatin f discharge cefficients f utflw penings, which were fund t be a functin f dimensinless rm pressure P R *. Thus, the discharge cefficients and ventilatin flw rates can be predicted mre precisely by the cupled simulatin f the netwrk mdel with the LDSM, if P t and the relatinships between C d and P R * are knwn. Hwever, it must be nted that the relatinships between C d and P R * fr the utflw penings depended n whether the utflw pening was in the recirculatin flw regin r nt. The LDSM culd nt predict the precise C d where the separatin r reattachment pint was within r very clse t the pening area. Nevertheless, it is cnsidered t be useful even fr these cases, because it at least captures the trends f the varying C d. P t in this study was determined at a distance f 5mm (/8 f the pening width) frm the external side f the pening. Althugh the distance was decided prvisinally, there were n substantial prblems in the present experiments. Further study will investigate whether the /8 f the pening width is generally apprpriate. CONCLUSION The lcal dynamic similarity mdel was fund t be valid fr utflw penings. Hwever, the relatinships between C d and P R * fr utflw penings depends n whether the utflw pening is in a recirculatin flw regin r nt. Increase f C d t P R * is mre rapid where the utflw pening is nt in a recirculatin flw regin than where it is. Besides, C d that is nt in a recirculatin flw regin increases beynd the basic discharge cefficient. ACKNOWLEDGEMENT This study was partially funded by the Ministry f Educatin, Culture, Sprts, Science and Technlgy, Japan, thrugh the 2st Century Center f Excellence Prgram f Tky Plytechnic University. NOMENCLATURE A pening area C d discharge cefficient C ds basic discharge cefficient Q ventilatin flw rate P f static pressure n flr P n dynamic pressure nrmal t pening P dynamic pressure f reference velcity (=ρu 2 /2) P R rm pressure P r ventilatin driving pressure (=P R -P W ) P R * dimensinless rm pressure P S static pressure at pening P t dynamic pressure tangential t pening P W wind pressure U reference wind velcity at rftp (=) β inflw/utflw angle ρ air density REFERENCES. M. Ishihara (969) Building ventilatin design, Asakura-shten. (In Japanese) 2. S. Murakami, S. Kat, S. Akabayashi, K. Mizutani and. D. Kim (99) Wind tunnel test n
velcity pressure field f crss-ventilatin with pen windws, ASHRAE Transactins, Vl.97, pp.525-538 3. S. Katsuta and T. Sekine (96) Experimental study n ventilatin thrugh penings n building envelpe, Part : Pressure lss cefficient and wind pressure cefficient, Transactins f Architectural Institute f Japan, N.68, pp.6-2 (in Japanese) 4. B.J. Vickery and C. Karakatsanis (987) External wind pressure distributins and induced internal ventilatin flw in lw-rise industrial and dmestic structures, ASHRAE Transactins, Vl.93, Part 2, pp.298-223 5. T. Kurabuchi, M. Ohba, T. End,. Akamine, F. Nakayama (24) Lcal dynamic similarity f crss-ventilatin, Part Theretical framewrk, Internatinal Jurnal f Ventilatin, Vl.2, N 4, pp37-382. 6. M. Ohba, T. Kurabuchi, T. End,. Akamine, M. Kamata, A. Kurahashi (24) Lcal dynamic similarity f crss-ventilatin, Part 2 Applicatin f lcal similarity mdel, Internatinal Jurnal f Ventilatin, Vl.2, N 4, pp383-393.