Building and Environment 38 (2003) 1271–1279
www.elsevier.com/locate/buildenv
Scale model study of air#ow performance in a ceiling slot-ventilated
enclosure: isothermal condition
Hsin Yu
a, Chung-Min Liao
b;∗, Huang-Min Liang
baDepartment of Civil Engineering, National Ilan Institute of Technology, Ilan 260, Taiwan ROC bDepartment of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan ROC
Received 26 November 2002; received in revised form 23 April 2003; accepted 6 May 2003
Abstract
The purpose of this study was to investigate experimentally air#ow performance of wall-jet in ceiling slot-ventilated enclosure under an isothermal condition. Airspeed 6eld measurement associated with air#ow trajectory visualization was conducted in a scale model. Centerline velocity decay, airspeed pro6les, jet penetration on the ceiling, jet impingement on the #oor, air#ow pattern, and airspeed of occupied zone were analyzed via experimental data and compared with literature theoretical expressions. Semi-empirical equations were derived to describe the wall-jet performance. The study of air#ow characteristics is helpful to predict an isothermal wall-jet performance occurred in a ceiling slot-ventilated enclosure. The results provide the design guidelines of ventilation system for regulating and controlling the indoor environment.
? 2003 Elsevier Ltd. All rights reserved.
Keywords: Air#ow performance; Air#ow characteristics; Slot-ventilated; Ventilation
1. Introduction
Wall-jet has been extensively studied due to their impor-tance in mechanical ventilation systems. The wall-jet that di;uses from a ceiling slot into a ventilated enclosure is de-6ned as a plane wall jet because it is bounded by a #at sur-face on one side and is parallel to the sursur-face. The plane wall jet has two-dimensional characteristics for the slot inlet aspect ratio (inlet length to inlet height) is larger than 20 [1] or conservatively 40 [2]. The plane wall jet supplied into a ventilated room is a;ected by opposite wall to produce re-verse #ow created by the wall-jet itself. The air#ow pattern, wall-jet trajectory, and airspeed 6eld of a plane wall jet are a;ected by the physical con6nement.
The purpose of this paper is to investigate experimen-tally the air#ow performance of plane wall jet in ceiling slot-ventilated enclosure under an isothermal condition. Air-#ow 6eld and airAir-#ow trajectory visualization was measured in both ceiling and #oor regions. Centerline velocity de-cay, airspeed pro6les, jet penetration on the ceiling, jet ∗Corresponding author. Tel.: 23634512; fax:
+886-2-23626433.
E-mail address:cmliao@ccms.ntu.edu.tw(C.-M. Liao).
impingement on the #oor, air#ow pattern, and airspeed of occupied zone were analyzed via experimental data and compared with theoretical expressions of literature. Semi-empirical equations were established to describe the performance of wall-jet. The results of model study com-pared with the theory and results from previous studies may identify the reality of wall-jet performance in a con6ned enclosure.
2. Theoretical background 2.1. Jet expansion zones
Rajaratnam [3] pointed out that potential core, character-istic decay, and terminal regions were formed after plane wall jet exiting from an opening to a smooth plate. Potential core region is created immediately at a short length down-stream of the opening where mixing of wall-jet boundary layer on wall side and shear layer of ambient room air on free boundary is not complete. The length depends on the type of opening and the turbulence of the air supply. Gener-ally, for a slot-type di;user, the length extends 5–10 equiv-alent air di;user diameters or width. The maximum velocity 0360-1323/03/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved.
Nomenclature
A area (m2)
A0; A1; A2 constant
C peak velocity decay coeFcient C0:5 jet spread gradient
Cd di;user discharge coeFcient
Cw throw constant of plane wall jet
g gravitational acceleration rate (m s−2)
h di;user width (m)
H room height (m)
I0 jet momentum function de6ned as
U2
dh=LH (kg m−2s−2)
J jet momentum number de6ned as QUd=gV
K centerline velocity constant
Krm ratio of maximum velocity at reverse #ow
to maximum velocity at end wall
L room length (m)
Lmax maximum penetration distance from inlet
(m)
Ljt wall-jet throw (m)
Lp penetration distance from inlet (m)
Lpn impingement distance from inlet wall (m)
GP pressure di;erence through the inlet (Pa) Q ventilation rate (m3s−1)
Re Reynolds number de6ned as hUd=
Rm inlet jet momentum ratio de6ned as hU2
d=(L + H) (m2s−2)
U mean air velocity (m s−1)
V The volume of the ventilated space (m3)
W room width (m)
x horizontal distance from inlet wall (m)
x sum of the distance that jet traveled from ceiling
to vertical wall and extended to the #oor. x0 distance between virtual origin and inlet (m)
xf distance from inlet which the e;ect of opposite
wall is not detectable (m) y vertical distance from #oor (m) y0:5 location where U = Umax=2 (m)
Greek symbols
boundary layer thickness (m)
non-dimensional parameter de6ned as hAfanGP=( g)(WL)2
angle between wall-jet direction and horizontal y=y0:5 density of air (kg m−3) Subscripts d di;user f #oor fan fan
max maximum of inertia #ow mean mean of #oor region rm maximum of reverse #ow t terminal value
L distance of room length
within this region remains unchanged and equal to di;user velocity.
A fully developed #ow of characteristic decay region is established beyond potential core region with the shear layer penetrating to the core of the wall-jet. The extent of this re-gion depends on, among other factors, the type of opening, aspect ratio, and initial #ow turbulence. Terminal region is a zone of rapid di;usion where the velocity pro6le degener-ates and disappears within a few equivalent diameters. The potential core and characteristic decay regions dominate the performance of plane wall jet in a con6ned enclosure. 2.2. Centerline velocity decay
The centerline velocity decay for a plane wall jet in the characteristic decay region can be described as [3]
Umax
Ud = Cw
h
x; (1)
where Cwis referred to as the throw constant [2] and given by Adre and Albright [4]
Cw=√2CCd; (2)
where C is the peak velocity decay coeFcient for a plane free jet and is estimated to be 2.7 [5] and Cd is the
dif-fuser discharge coeFcient that depends on the inlet con6g-uration. Tuve [6] demonstrated that the maximum velocity of the plane wall jet was greater than that of a plane free jet by a factor 21=2. The values of Cw vary from 2.20 to 3.68
depending on di;erent studies [3,4,7–10]. ASHRAE [11] suggested another expression of the centerline velocity de-cay of a wall-jet with ceiling linear outlet type as
Umax Ud = Kh x ; (3) where K= 5:5. 2.3. Velocity pro:le
Rajaratnam [3] derived the dimensionless velocity pro6le of a plane wall jet from the empirical expression by Verho; [12],
U
Umax = 1:48
where = y=y0:5 and y0:5= 0:068(x + 10h). Schwarz and
Cosart [13] expressed the pro6le of plane wall jet as U
Umax = exp[ − 0:937( − 0:14)
2]: (5)
Awbi [2] pointed out that Eq. (4) gives a good agreement with experimental data for ¿ 0:14.
2.4. Air=ow boundary layer growth
The spread gradient of position at y0:5 of the maximum
airspeed of plane wall jet at ceiling is dy0:5=dx = C0:5where
C0:5 ranges from 0.065 to 0.1 [3,7,9,13,14]. Launder and
Rodi [15] derived a theoretical formula of y0:5 as y0:5=
0:073(x + x0). Schwarz and Cosart [13] gave the boundary
layer thickness () as = 0:068(x + 11:2h). Albright [7] derived a formula of y0:5as y0:5= =0:14. The spread angle
of the plane wall jet ranges from 10◦ to 12◦, which is half
value of a free wall jet [16]. 2.5. Floor velocity
The desired near-#oor airspeed in adult animal hous-ing was 0.2–0:4 m s−1 [17]. The average airspeed in the
occupied zone for human comfort has been speci6ed as 0:15 m s−1in winter and 0:25 m s−1in summer [2,11].
Experiments con6rmed that jet momentum number (J) correlated well with #oor air speed (Umean) and maximum
air velocity in the return #ow (Urm) for various building
con6gurations as [18–21]
Umean= A0+ A1JA2 (6)
or
Urm=mean= A0JA2: (7)
Inlet jet momentum ratio (Rm) correlates well with Urm
in an isothermal condition as [19,21]
Urm= A0Rm0:5: (8)
A dimensionless parameter, , which can also be used to characterize the #oor velocity by the following form [18]:
Umean= A0A1; (9)
where = hAfanGP=( g)(WL)2.
An expression of maximum #oor airspeed was expressed as [19]
Urm= A0UdA1hA2: (10)
The ratio of Urmto the wall jet velocity at a distance x = L
from the opening (UL) was derived as [22] Urm
UL = Krm; (11)
where Krm is a weak function of room and inlet geometry
and is estimated to be 0.7 [23]. Combined Eq. (1) with x replacing by x + x0, the resulting expression of centerline
velocity is Umax Ud = Cw h x + x0: (12)
The maximum #oor airspeed can then be expressed as
Urm= CwKrmUd
h
L + x0; (13)
which is related to the centerline velocity of wall-jet at dis-tance L.
2.6. Air=ow pattern and jet penetration
Jin and Ogilvie [24] used three air#ow zones: the stagnant zone (the mean velocity at #oor less than 0:1 m s−1), the
stable rotary #ow (air#ow pattern was fully rotary along the room perimeter and was independent with change of inlet height and inlet velocity), and the intermediate #ow pattern (any #ow patterns between the stagnant and stable #ow pattern) to represent di;erent types of air#ow pattern under an isothermal condition.
Threshold values of parameter to maintain fully rotary air#ow pattern have been identi6ed in many studies. The threshold parameter is de6ned as the value of the parame-ter where an unchanging fully rotary air#ow patparame-tern is es-tablished. Kaul et al. [25] concluded that air#ow patterns are related to the inlet jet momentum (J ) and the min-imum inlet-jet momentum function (I0) that produced a
stable three-dimensional eddy (rotary #ow) in a condition of I0¿ 0:01 kg m−2s−2.
Timmons et al. [26] suggested the air#ow pattern was independent of Reynolds number (Re) above a threshold value of about 3800. Timmons [27] showed that the value of a threshold Re was di;erent for di;erent enclosures and there was a proportional relationship between the required threshold Re and the physical size of the ventilated enclo-sure. Adre and Albright [4] and Yu and Ho; [28] reported that a threshold Rm existed between model and prototype where the air#ow pattern remained unchanged for increas-ing air#ow rates in three di;erent enclosures.
Wall-jet penetration has been used to express air#ow pat-terns quantitatively. Adre and Albright [4] de6ned wall-jet penetration as the distance from the inlet wall where the wall jet separated from the ceiling. Kaul et al. [25] de6ned wall-jet penetration as the distance from the inlet wall on the #oor where the incoming wall-jet impinged. ASHRAE [11] de6ned the wall-jet throw as the distance from the sup-ply where the centerline velocity in the wall-jet decreased to 0:25 m s−1for most di;users except for slot-type air
The throw of plane wall jet could be derived from Eq. (1) as Ljt= Ud 0:5 2 C2 wh: (14)
Adre and Albright [4] employed a inlet jet Rm to charac-terize wall-jet penetration distance for the isothermal air#ow in a ceiling slot-ventilated enclosure as
Lp
L =
Lmax=L
A0exp(−A1√Rm) + 1: (15)
Yu and Ho; [28] derived a similar description of penetra-tion distance as a funcpenetra-tion of Rm in a ceiling slot-ventilated enclosure. Threshold inlet-jet momentum ratio reaching maximum jet penetration (Lmax=L) was presented in both
studies. Awbi and Setrak [29] suggested a theoretical ex-pression of extreme wall-jet penetration in a ventilated room in#uenced by the surrounding solid boundaries as
xf h = 0:52 L h 1:09 ; (16)
where xf is the distance from inlet opening of wall-jet that the
e;ect of the opposite wall is not detectable. The expression, xf, is similar to the maximum wall-jet penetration, Lmax,
de6ned by Adre and Albright [4] when the air#ow pattern beyond threshold of fully rotary pattern.
Karimipanah [30] stated that the jet travel length begins to be a;ected by the opposite wall at 0:7L of the room. The in#uenced region remained as 0:7L even the room length is varied. Nielsen [22] indicated that the maximum air velocity in the return #ow (occupied zone) might occur at a distance of 2=3L from the inlet in ceiling slot-ventilated enclosures. The position of the maximum reverse velocity is also de6ned as the impingement point [25].
3. Experimental methods
A scaled model of 1:3 representing a prototype building, measuring L × W × H = 1:83 × 2:42 × 0:9 m3, was used to
study air#ow performance in a con6ned enclosure. The slot height was 0:0127 m with slot width of 2:42 m. Due to the inlet aspect ratio being much greater than 20, resulting the air#ow was treated as a two-dimensional wall jet without the e;ect of sidewalls [1]. The scale model was constructed by 0:0127 m thick plywood. The inner surfaces were sanded and painted black. The front wall was made of Plexiglas to accommodate air#ow visualization. Access holes were placed on the top ceiling between inlet wall and end wall at intervals of 0:02 m, except for the area between the inlet and a distance of 33h (h = 0:0127 m in the scale model) from the inlet where a continuous access slot was constructed to observe clearly the wall-jet development near the inlet.
Ductwork was constructed and 6tted between the cir-cular exhaust hole and an exhaust fan (Model 3C507A; Dayton Electric MFC, Co.). Calibrated ori6ce plates were
Table 1
Test conditions of air#ow performance under an isothermal condition
Test Q Ud GT Re Rm (m3s−1) (m s−1) (◦C) IP1 0.097 3.14 0 2512 0.0460 IP2 0.067 2.18 0 1745 0.0222 IP3a 0.046 1.50 0 1203 0.0105 IP4 0.033 1.08 0 863 0.0054 IP5a 0.024 0.77 0 614 0.0027 IP6 0.017 0.54 0 435 0.0014 IP7 0.009 0.29 0 234 0.0004
aMeasurements on ceiling region only.
used to select desired air#ow rates through model. A micro-manometer (Model 1430; Dwyer Instruments, Inc.) was used to measure the pressure di;erence across the ori-6ce to determine air#ow rate. The oriori-6ce plates used in the pressure measurements were calibrated by a standard Venturi #ow meter. The calibration curve showed a good correlation (r2¿ 0:99).
Airspeed was measured using an omni-directional hot-6lm anemometer (Model 8470; TSI, Inc.), which was calibrated by the manufacture. The percentage of error was below 3%. A portable data acquisition system (Model CR10; Campbell Scienti6c, Inc.) was used to collect data. The average over time, at a point, was used for analysis and presentation. The acquiring period for each point was 6xed to 180 s and the sampling frequency was set at 16 Hz to ensure accurate time-average results for turbulent air#ow [31]. Several air#ow rates were chosen to encompass the anticipated stagnant and fully rotary air#ow zones. The test conditions used are summarized in Table1.
4. Results and discussion 4.1. Centerline velocity decay
The centerline velocity decreased with the extent of wall-jet travel along the ceiling. The normalized centerline velocity pro6les at ceiling behave similarly when air#ow rates beyond threshold value of fully rotary #ow (Fig.1A). The maximum #oor velocity occurred at the impingement point of reverse #ow and the jet traveled forward to the inlet-opening wall at #oor surface as a plane wall jet. The impingement points at #oor from inlet opening wall were about 0:6L–0:7L in di;erent air#ow rates (Fig. 1B). This value agrees with Nielsen [22] of 2=3L from the inlet wall. The representations of di;erent airspeed pro6les in both ceiling and #oor regions could be illustrated in normalized and log-transformed coordinates along perimeter of enclo-sure (Fig. 2). The region of ceiling length below 10h was the potential core, where the centerline velocity maintained constant and approximated to Ud. The centerline velocity
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 x /L U ma x /U d 0.097cms 0.067cms 0.033cms 0.017cms 0.009cms (A) 0 0.1 0.2 0.3 0 0.2 0.4 0.6 0.8 1 x /L Umax /U d (B)
Fig. 1. Centerline velocity varied along (A) ceiling and (B) #oor in di;erent ventilation rates ranged from 0.009 to 0:097 m3 s−1.
0.01 0.1 1 10 1 10 100 1000 x / h U ma x /U d 0.097 0.067 0.033 Rajaratnam [3] Albright [7] ASHRAE [11]
Regression line of this study
C haracte ristic de cay Te rminal re gion Pote ntial core Floor re gion L H
Fig. 2. Normalized centerline velocity decays along perimeter of enclo-sure in di;erent ventilation rates ranged from 0.033 to 0:097 m3 s−1. A
comparison of the 6tted results with the other studies is also shown.
region in that the 6tted equation of airspeed decay had the form as Umax Ud = 2:87 h x: (17)
The estimated throw constant Cw of 2.87 was within the
ranges between 2.35 and 3.5 of other studies [3,7,11].
The wall-jet terminal region collapsed rapidly at distance beyond 100h, where the region begins to be a;ected by the opposite wall. The 6tted equation of maximum airspeed in the terminal region had the form as
Umax
Ud = 2744
h2
x2: (18)
Fig.2shows that the wall-jet at the #oor region behaves like plane wall jet at ceiling after the reverse #ow impinged on #oor. The 6tted airspeed decay equation in characteristic decay region was obtained as
Urm
Ud = 3:73
h
x; (19)
where xis sum of the distance that jet traveled from ceiling
to vertical wall and extended to the #oor. The results show that the behavior of wall-jet at #oor could be identi6ed as plane wall jet after the reverse #ow impinged on #oor surface (Fig.2).
4.2. Jet pro:les and air=ow boundary layer growth Experimental results indicate that both the isothermal jet airspeed and #oor airspeed pro6les have a better agree-ment with results obtained from Rajaratnam [3] than that
Isothermal jet airspeed profile Q =0.046 m3s-1 scale=1:3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 y /( y0.5) U /U max X=0.3L X=0.5L X=0.7L Schwarz an d C osart [13] Rajaratn am [3 ]
(A) Isothermal floor
airspeed profile 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 y /( y0.5) U /U max (B)
Fig. 3. Normalized airspeed pro6les of plane wall jet along (A) ceiling and (B) #oor with air#ow rate Q = 0:046 m3 s−1. The pro6les located
in the positions of x = 0:3L; 0:5L, and 0:7L from the inlet wall are equals to 43h, 72h, and 101h in both ceiling and #oor regions.
0 5 10 15 20 25 30 0 20 40 60 80 100 120 140 x/h y 0.5 /h Experimental data of y0.5 /h Sigalla[9] Rajaratnam[3] Liu et al.[32] Albright[7]
Fig. 4. Half the maximum wall-jet airspeed position measured along enclosure ceiling.
obtained from Schwarz and Cosart [13] in both ceiling and #oor regions (Fig.3). Experimental results also reveal that the maximum airspeed of wall-jet at y0:5=h under air#ow
rate of 0:046 m3s−1 have a better agreement with that of
Rajaratnam [3] than that of Albright [7], Sigalla [9], and Liu et al. [32] (Fig.4).
4.3. Floor airspeed
Floor airspeed in an enclosure for an isothermal con-dition was 6tted well with di;user velocity (r2 = 0:99)
(Fig.5A). The coeFcient of determination was greater than that of Nielsen [22] when x0 is neglected (Table2). A
re-gression analysis for Urmand Rm shows that the coeFcient
of determination fell between the results of Jin and Ogilvie [19] and Wang and Ogilvie [21] (Fig. 5B, Table2). The
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Ud (m s-1) U rm (m s -1) (A) 0 0.2 0.4 0.6 0.8 1 0 0.02 0.04 0.06 Rm U rm (m s -1) (B) 0 0.2 0.4 0.6 0.8 1 0 0.005 0.01 J U rm (m s -1) (C)
Fig. 5. Maximum #oor velocity (Urm) 6tted with (A) di;user velocity (Ud), (B) inlet jet momentum ratio (Rm), and (C) jet momentum number (J).
Urm6tted with J having the same 6tting results of Urmand
Umean6tted with J by Wang and Ogilvie [21] and Jin and Ogilvie [19], respectively (Fig.5C, Table 2). There exists a large discrepancy between Umean6tted with J (r2= 0:67)
by Ho; [18] and Urm6tted with J (r2= 0:99) in this study.
The di;erence may result from the variance of con6guration of test room.
4.4. Air=ow pattern
Air#ow pattern in the scale model was de6ned by the measurement and visualization of wall-jet trajectories with varied discharge rate (Fig.6). The trajectory is the position of centerline velocity along the wall-jet.
The trajectory of jet at air#ow rates ranging from 0.033 to 0:097 m3s−1was classi6ed as fully rotary #ow that
trav-eled through perimeter of enclosure in both ceiling and #oor regions (Fig.6). Wall-jet separated from ceiling be-fore the jet reached the extreme length, which is a;ected by the opposite wall, was treated as a stagnant #ow under the air#ow rate ranging from 0.009 to 0:024 m3 s−1. The
trajectory of air#ow rates between 0.024 and 0:033 m3s−1
is experienced as an intermediate #ow and results in the re-verse #ow ascended far from the inlet wall.
The positions of maximum airspeed attached to the ceiling when the wall-jet remained as plane wall jet until opposite wall forced the wall-jet to detach from ceiling. The distance of wall-jet separation from ceiling shown in Table 3 is based on the visualization of jet trajectories (Fig.6). The jet throw representing penetration of wall-jet was derived from Eq. (14) with terminal velocity of 0:25 m s−1.
The ultimate wall-jet penetration distance is suggested to be 1.28–1:32 m when the air#ow rate beyond a critical value in that the air#ow pattern is fully rotary #ow. The ultimate penetration distance is consistent with the wall-jet
Table 2
Comparisons of 6tted equation of #oor velocity with other studies
Our studya Other studies Con6guration of test room (L × W × H m3) Reference
Urm= 0:26Ud Urm= 0:17Ud 0:27 × 0:09 × 0:09 [22,23] (r2= 0:99) (r2= 0:97) Urm= 4:14 Rm0:53 Urm= 4:56 Rm0:50 4:9 × 3:8× (2.6–3.2) [21] (r2= 0:99) (r2= 0:98) Urm= 3:33 Rm0:52 4:8 × 4 × 3 [19] Urm= 13:56J0:56 Urm= 19:33J0:50 4:9 × 3:8× (2.6–3.2) [21] (r2= 0:99) (r2= 0:97) Umean= 15:02J0:52 (r2= 0:96) 4:8 × 4 × 3 [19] Umean= 1652:43J1:76 (r2= 0:67) 10:6 × 29:3 × 2:3 [18]
aCon6guration of our test room is 1:83 × 2:42 × 0:09 m3.
0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x/L y/H ¡º 0.097 ¡¼ 0.067 ¡³ 0.046 ¡µ 0.033 ¡´ 0.024 ¡Ï 0.017 X 0.009 0 0.1 0.2 0.3 0.4 0.5 x/L y/H ¡º 0.097 ¡¼ 0.067 ¡³ 0.046 ¡µ 0.033 ¡´ 0.024 ¡Ï 0.017 X 0.009 (A) (B) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fig. 6. Trajectory of wall-jet measured in both ceiling and #oor regions in di;erent ventilation rates ranged from 0.009 to 0:097 m3 s−1for (A)
y=H = 0–0.5 and (B) y=H = 0:7–1.0.
that reached the end of characteristic decay region at 100h = 0:7L = 1:27 m. The normalized penetration distance at ceiling is 6tted with Rm as (Fig.7)
Lp
L =
0:72
196:82 exp(−117:22Rm) + 1 (r2¿ 0:91): (20)
Ultimate penetration distance is 0:72L and is closed to the result of 0:64L from Adre and Albright [4] with the similar con6guration of scale model.
Awbi and Setrak [29] derived the maximum penetration of wall-jet blocked at the distance from the supply of plane wall jet as xf= 0:52h L h 1:09 = 0:8L = 149 cm: (21)
The discrepancy between xf and departure penetration
dis-tance (Lp) may result from xf that was derived from the
wall-jet boundary separated from enclosure ceiling, and Lp
that was derived from the centerline velocity position de-parted from ceiling (Fig.6).
In the present study, the critical value derived from the wall-jet penetration throw with terminal velocity of 0:25 m s−1 was used to de6ne the penetration distance.
Therefore, it was assumed that transition from stagnant zone to intermediate and fully rotary zones occurred at Ud= 0:25=Cw(0:7L=h)1=2= 0:87 m s−1, where the air#ow
rate is 0:027 m3 s−1 (Re = 690) for the scale model. The
critical discharge to distinguish intermediate #ow and fully rotary #ow in the model was found to be 0:034 m3s−1
(Re = 880) that was derived from Eq. (19) in that the peak #oor velocity decreases to 0:25 m s−1as traveling through
ceiling, vertical wall and #oor region as Ud=0:253:73
0:7L + H + 0:7L
h = 1:11 m s−1; (22)
where the length of wall-jet traveled through ceiling, vertical wall, and #oor are about 0:7L; H, and 0:7L, respectively. The length that wall-jet traveled through #oor is 0:7L according to the visualization and measurement of wall-jet trajectory (Fig.6).
It is concluded that if the air#ow rate were greater than threshold inlet Re (880 in this study), wall-jet traveled through perimeter of enclosure could result in a fully rotary air#ow. The threshold Re is less than that derived from
Table 3
Comparisons of jet throw and departure distance of maximum airspeed position
Air#ow pattern Air#ow rate Di;user airspeed Distance of departure Jet throw (Eq. (14)) Normalized Normalized jet Q (m3 s−1) Ud (m s−1) Lp (m)a Ljt(m) departure Lp=h throw Ljt=h
Fully rotary #ow 0.097 3.14 1.32 16.54b 104 1302c
Fully rotary #ow 0.067 2.18 1.32 7.98b 104 628c
Fully rotary #ow 0.046 1.50 1.28 3.79b 101 298c
Intermediate #ow 0.033 1.08 1.28 1.95b 101 154c
Stagnant zone 0.024 0.77 0.92 0.99 72 78
Stagnant zone 0.017 0.54 0.51 0.48 40 38
Stagnant zone 0.009 0.29 0.12 0.14 9 11
aSee Fig.6.
bActual penetration distance is 1.28–1:32 m by the e;ect of opposite wall. cActual penetration distance is 101h–104h by the e;ect of opposite wall.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00 0.02 0.04 0.06 0.08 0.10 Rm L p /L
Fig. 7. Normalized wall-jet penetration distance (Lp=L) as a function of inlet jet momentum ratio (Rm).
Timmons et al. [26], which is Re=3800, due to the di;erent con6guration among experimental models.
When the inlet Re of air#ow exceeds the threshold value of this model, air#ow pattern will be fully rotary #ow and is independent of increased inlet Re. Intermediate #ow oc-curred when inlet Re is between 690 and 880 in that the wall-jet traveled through ceiling and impinged downwardly on #oor, yet the reverse #ow ascended far from the inlet wall. Stagnant #ow is the wall-jet with inlet Re below 690 and separates from ceiling before reaching extreme jet pen-etration that is about 0:7L.
5. Conclusions
The results demonstrate that the centerline velocity decay in both ceiling and #oor regions follow the charac-teristics of plane wall jet proposed by other studies. The velocity pro6les of the wall-jet in both ceiling and #oor re-gions showed a better agreement with Rajaratnam [3] than that obtained from Schwarz and Cosart [13]. The air#ow
boundary layer growth was consistent with that of Rajarat-nam [3]. The #oor airspeeds are 6tted well with di;user velocity, inlet jet momentum ratio (Rm), and jet momen-tum number (J), respectively. The 6tted results are similar to the results obtained from Jin and Ogilvie [19], Nielsen [22], and Wang and Ogilvie [21], respectively.
Air#ow trajectory was distinguished by using jet throw with terminal velocity of 0:25 m s−1. Ultimate penetration
distance at ceiling is about 0.72 of room length and impinge-ment distance at #oor is 0.6–0.7 of room length from inlet wall. Wall-jet penetration may classify the air#ow pattern within an enclosure. The normalized penetration distance 6tted well with inlet momentum ratio. Conclusions of the air#ow patterns were similar to that of Adre and Albright [4], Awbi and Setrak [29], Jin and Ogilvie [24], Karimi-panah [30] and Nielsen [22]. The consistence of wall-jet penetration appears that the estimated wall-jet trajectory and the e;ect of opposite wall can predict the air#ow pattern of isothermal plane wall jet di;used into an enclosure.
The results suggest that air#ow performance from exper-imental measurements can be used to predict the wall-jet behavior in ceiling slot-ventilated enclosure. The studies provide a suggestion for design guidelines of ventilation system for controlling a bioenvironmental enclosure. Fu-ture studies include the measurement of airspeed 6eld in the surface of vertical wall, wall-jet performance under a non-isothermal condition, and the in#uence of real enclo-sure con6gurations of size, shape, and location of inlet and outlet, size of room, etc.
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