Building and Environment 42 (2007) 1142–1150
Scale model study of airflow performance in a ceiling slot-ventilated
enclosure: Non-isothermal condition
Hsin Yu
a, Chung-Min Liao
b,, Huang-Min Liang
b, Kuo-Chih Chiang
baDepartment of Civil Engineering, National Ilan University, Ilan 260, Taiwan ROC
bDepartment of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan ROC
Received 16 August 2005; accepted 4 December 2005
Abstract
Scale-model study of a non-isothermal ceiling slot-ventilated enclosure was investigated in both airspeed and thermal fields. Results of airflow pattern, centerline velocity and centerline temperature decay, velocity and temperature profile, airflow boundary layer and thermal boundary layer growth, floor velocity, and floor temperature difference were analyzed to establish semi-empirical prediction equations. Results also compared with previous researches to validate the physical behavior of air-jet. Data of centerline velocity decay showed similar airflow characteristics as isothermal air-jet with Archimedes number ðArÞo0:004, which performed as pseudo-isothermal airflow. Air-jet fell on entry with Ar40:018. A single circulation airflow existed at 0:004oAro0:011 and two-circulation airflow occurred at 0:011oAro0:018. The centerline velocity decay was fitted well as similar form of an isothermal condition. The centerline temperature decay was fitted well as the form of centerline velocity decay in both ceiling and floor regions. Both the velocity and temperature profiles agreed with results obtained from literature. Both airflow boundary layer and thermal boundary layer growths increased with traveling distance of air-jet. Maximum floor velocity and floor temperature difference were fitted well with different parameters. Analysis of airflow performance in a non-isothermal condition makes progress in predicting air quality inside the enclosures and guides the design concepts of ventilation system for an indoor environment.
r2006 Elsevier Ltd. All rights reserved.
Keywords: Airflow characteristics; Slot-ventilated; Ventilation; Non-isothermal; Archimedes number
1. Introduction
Airflow characteristics inside room affect the air distribution, the thermal environment, and the contami-nant concentrations. It also determinates the distribution of thermal energy, moisture, and fresh air into a room. Airflow characteristics are dominated by the behavior of inlet air-jet. Air-jet is used to mix inlet air with room air in most mechanically ventilated enclosures. The theoretical and experimental investigations of confined plane wall jet is much more difficult than the free plane wall jet[1]. On the other hand, the study of non-isothermal airflow in a ventilated enclosure is more close to the reality than in isothermal condition.
The purpose of this study is to analyze air-jet character-istics in non-isothermal slot-inlet ventilated enclosures by experimental processes. Measurements of airspeed and temperature fields associated with airflow trajectory visualization have been investigated in scale-model. The centerline velocity and centerline temperature decays, growths of airspeed and temperature profiles, velocity and temperature profiles as well as flow velocity and temperature distribution were analyzed through experi-mental determination and compared with theoretical results from literature. Semi-empirical equations were established to describe the airflow characteristics in a non-isothermal condition. Performance of a non-isother-mal air-jet in ceiling slot-ventilated enclosure would be predicted by the analysis of airflow characteristics and offer a suggestion of design guidelines of ventilation system for controlling indoor environment.
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Corresponding author. Tel.: +886 2 23634512; fax: +886 2 23626433. E-mail address: cmliao@ntu.edu.tw (C.-M. Liao).
2. Theoretical background 2.1. Airflow pattern
Representations of the separation distance of linear jet or impingement distance from inlet wall were related to Archimedes number Ar ¼ bghðTfTdÞ=U2d [2–5]. Air-jet
penetration has been used to express airflow patterns quantitatively. Adre and Albright [6] defined air-jet penetration (Lp) as the distance from the inlet wall where
the wall jet separated from the ceiling. Kaul et al. [7]
defined air-jet penetration as the distance from the inlet wall on the floor where the incoming air-jet impinged (Lpn).
Randall and Battams[8]conducted stability criteria for airflow patterns in livestock buildings using a prototype building with heated cylinders simulating pigs. They proposed an inlet corrected Archimedes number Arc¼
CdgwhWHðW þ HÞðTfTdÞ=ðð546 þ TfþTdÞQ2Þ) to
de-scribe the relative influence of buoyant forces on the air-jet. Their results showed that the air-jet remained horizontal for Arcless than 30 and fell immediately to the floor when
it was greater than 75. Wang and Ogilvie [9]investigated airflow patterns in slot-ventilated rooms under non-isothermal conditions using a test room where the room height was varied. A wall jet Archimedes number Arw¼
bgðTf TdÞHL=ðhU2dÞ was defined and proposed as the
criterion describing airflow patterns. The Arwwas about 40
before the air-jet extended to the midpoint of the room and was about 110 for fully rotary airflow. A significant lag phenomenon was found in the study where once a fully rotary airflow pattern was created; the inlet velocity could be decreased significantly without changing the airflow pattern with the Arw increased to about 240.
Zhang [10] described this lag phenomenon in a study of the relation between the horizontal air-jet penetration and the diffuser air velocity for non-isothermal airflow. It concluded that extra momentum was needed to overcome the existing airflow pattern before a new flow pattern could be formed. The critical Ar defined as the condition where the air-jet fell on entry was found for non-isothermal airflow.
2.2. Centerline velocity decay and centerline temperature decay
The expression of centerline velocity decay in a non-isothermal enclosure had similar form as in an non-isothermal condition[3,4,11,12]. The normalized extreme airspeed was reverse related to the normalized distance from diffuser as Um=Ud/
ffiffiffiffiffiffiffiffi h=x p
, where the related coefficient between the two variables was usually referred to as the throw constant
[13]or velocity decay constant [4], and the value varied in Nomenclature
Ar Archimedes number
Arc corrected Archimedes number
Arw wall jet Archimedes number
Cd diffuser discharge coefficient
g gravitational acceleration rate ðm s2)
h diffuser width (m)
H room height (m)
J jet momentum number defined asQUd
gV
K1 airspeed decay constant
K2 temperature decay constant
L room length (m)
Lp penetration distance defined by Adre and
Alb-right [6](m)
M momentum of jet defined as rhU2d per unit length of diffuser ðN m1)
Pr Prandtl number defined asa n
Q ventilation rate ðm3s1Þ
Re Reynolds number, defined as hUd
n
Rm inlet jet momentum ratio defined as hU2d=ðL þ HÞðm2s2Þ
T mean temperature ðCÞ
DT temperature difference between floor and out-door ðCÞ
U mean air velocity ðm s1Þ w diffuser length (m)
W room width (m)
x horizontal distance from inlet wall (m) y vertical distance from floor (m)
y0:5t location where TrT ¼ ðTrTmÞ=2ðmÞ
y0:5v location where U ¼ Um=2ðmÞ
Greek letters
a thermal diffusion coefficient ðm2s1Þ
b thermal expansion coefficient defined as
1 ðTfþTdÞ=2ðK 1Þ Zt ratio of y to y0:5t Zv ratio of y to y0:5v n kinematic viscosity ðm2s1Þ Subscripts d diffuser f floor
m maximum of inertia flow
r room, ambient
rm maximum of reverse flow t terminal value
different literature. Hassani et al. [3] found that the K1
value in the equation of centerline velocity decay was not significantly different between isothermal and non-isother-mal jets and did not depend on temperature.
The expression of centerline temperature decay [3,4,12]
had the similar form as of centerline velocity decay, that was ðTrTmÞ=ðTrTdÞ /
ffiffiffiffiffiffiffiffi h=x p
. The related tempera-ture decay constant ðK2Þdominated the variation between
normalized temperature difference and the normalized distance from opening. Hassani et al.[3]pointed out that the temperature decay constant was less than the velocity decay constant as K20:85 K1.
2.3. Velocity profile and temperature profile
The expression of velocity profile for plane wall jet in a non-isothermal enclosure [12,14,15] was different with those described in an isothermal condition [16]. The variables of these equations were related to the ratio of y=y0:5tðZtÞor y=y0:5vðZvÞalong vertical distance in different studies. The equations of temperature profile for plane wall jet in a non-isothermal enclosure expressed similar form as of velocity profile[12,14,15]. Yet the value of coefficient or exponential power was different.
2.4. Airflow boundary layer growth and temperature boundary layer growth
The expressions of airflow boundary layer growth were of the form as dy0:5v=dx ¼ C, where C ranged from 0.065 to 0.1 [16,17]. The spread angle of the plane wall jet was about 10–12 that is half value of a free wall jet [18]. All
results were derived from research of isothermal condition because of that no airflow boundary layer growth in non-isothermal condition was found depending on the efforts in this project. Wilson et al.[14] derived a simple expression of thermal boundary layer growth that was related to the traveled length of jet and Ar. The regression equation of C in Wilson et al.[14]was derived by this project to find the variation of coefficient in different Ar.
2.5. Floor velocity
Zhang et al.[11]derived averaged reverse flow velocity of occupied zone related with Ar when Reynolds number Re remains constant. Wang and Ogilvie [9] showed that the mean floor velocity and maximum floor velocity can be expressed related to momentum ratio (Rm) and HDT in two different configurations of scale model, which is inlet and outlet at same wall and the other is at opposite wall. The results also showed that the floor velocity measured in the case of inlet and outlet at opposite wall is lower (20% less) than that measured in the case which inlet and outlet at same wall. When the air-jet passed over the outlet area, the inner layer of the airflow would be affected by the suction effect and cause significant jet momentum loss[9].
3. Materials and method
Airflow performance and thermal characteristics of plane wall jet in ceiling slot-ventilated enclosure under a non-isothermal condition was investigated by experimental measurement. A scaled model of 1:3 representing a prototype building was used to study airflow performance in a confined enclosure. Anemometer and temperature instruments measured the airflow characteristics of velocity fields and thermal fields inside an enclosure. The config-uration and dimensions of the test chamber used is shown inFig. 1. Slot inlet width (w) is the same as width of the enclosure (W). As a result of the inlet aspect ratio been much greater than 20, resulting the airflow was treated as a two-dimensional wall jet without the effect of sidewalls
[19]. The scale model was constructed of 12.7 mm thick plywood. The inner surfaces were sanded and painted black. The front wall was made of Plexiglas to accom-modate airflow visualization. Access holes were placed on the top ceiling between inlet wall and end wall at intervals of 20 mm, except for the area between the inlet and a distance of 33 h from the inlet where a continuous access slot was constructed to discretize air-jet development near the inlet.
Ductwork was constructed and fitted between the circular exhaust hole and an exhaust fan (Model 3C507A; Dayton Electric MFC, Co.). Calibrated orifice plates were used to select desired airflow rates through model. A micro-manometer (Model 1430; Dwyer Instru-ments, Inc.) was used to measure the pressure difference across the orifice to determine airflow rate. The orifice plates used in the pressure measurements were calibrated by a standard Venturi flow meter. The calibration curve showed good correlation with r240:99. The floor of model
was fitted with insulated silicone rubber heat panels (Model SRFG 442/2 and 1242/2; OMEGA Engineering, Inc.) that occupied 58% of the floor area to simulate occupied surface temperature. The power density was 3875 ðW m2Þ and was controlled by miniature microprocessor tempera-ture controllers (Model CN9000; OMEGA Engineering, Inc.) with an accuracy of 0:5C using a PID control
Air inlet = 50 mm Inlet airflow h=12.7mm Metal slot H=900mm L=1830mm W=2420mm
Outlet with 150mm diameter Slot inlet
12.7mm plywood test model Plexglas
mode. The maximum operating temperature of the heaters was 120C.
Airspeed was measured using an omni-directional hot-film anemometer (Model 8470; TSI, Inc.) that was calibrated by the manufacture. The % error was below 3%. A portable data acquisition system (Model CR10; Campbell Scientific, 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 fixed to 180 s and the sampling frequency was set at 16 Hz to ensure accurate time-average results for turbulent airflow
[20]. The temperature field was measured using T-type thermocouples connected to the same data acquisition system as the airspeed measurements. Both the inertia and buoyant forces affect the airflow pattern in a non-isothermal enclosure. Several airflow rates were chosen to encompass the anticipated stable and unstable airflow zones. Table 1lists the test conditions for quantifying the airflow pattern.
4. Results and discussion 4.1. Airflow pattern
Airflow patterns were observed by visualization of centerline velocity trajectory as represented by various airflow rates with dT ¼ 40C (Fig. 2). The airflow
penetration distance was decided when the centerline of air-jet fall to the height of 0:9H.Fig. 3presents the results of normalized penetration distance of air-jet versus Ar. The critical values measured and used to distinguish the behavior of non-isothermal air-jets are shown in the plot. At critical Aro0:004 ðArco27Þ, a single-circulation airflow
pattern with fully rotary existed and the airflow pattern was governed by the isothermal behavior. At critical Ar40:018 ðArc4110Þ, buoyant force dominated airflow
performance and air-jet fell immediately after diffused on the entry. Critical values to distinguish the airflow pattern are similar to Randall and Battams [8]in the fully rotary Table 1
Test conditions of experimental measurement for non-isothermal airflow
Test Q (cms) Udðm s1Þ TdðCÞ TfðCÞ DT ðCÞ Re Rm Ar Arc NP1 0.153 4.97 61.5 21.5 40 3976 0.115 0.0006 4 NP2 0.104 3.39 61.5 21.5 40 2708 0.053 0.0014 8 NP3 0.071 2.30 57 17 40 1842 0.025 0.0030 18 NP4 0.050 1.61 57.5 17.5 40 1284 0.012 0.0062 37 NP5 0.034 1.10 54.5 14.5 40 882 0.006 0.0133 80 NP6 0.027 0.90 55.5 15.5 40 716 0.004 0.0201 121 NP7 0.025 0.81 62.77 22.77 40 649 0.003 0.0239 144 NP8 0.055 1.78 82.33 22.33 60 1424 0.015 0.0072 44 NP9 0.039 1.28 79.37 19.37 60 1025 0.008 0.0141 85 NP10 0.034 1.12 81.94 21.94 60 898 0.006 0.0182 110 NP11 0.028 0.90 79.56 19.56 60 723 0.004 0.0283 170 0 0.1 0.2 0.3 0.4 0.5 0.6 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 ymx /H 0.153 cms 0.104 cms 0.071 cms 0.050 cms 0.034 cms 0.027 cms
0.025 cms Appr. iso. airflow Sing-circ. airflow
Two-circ. airflow
Fig. 2. Normalized peak airspeed trajectory in a non-isothermal enclosure at DT ¼ 40C. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Ar Lp /L Two-circulation zone Single-circulation zone Fully rotary zone
Jet fall on entry
Fig. 3. Critical values to distinguish non-isothermal airflow patterns based on normalized air-jet penetration distance versus Archimedes number ðArÞ.
condition (i.e., Arco30Þ, and similar to Zhang[10] in the
jet fall on entry (i.e., Arc4113Þ.
For intermediate range ð0:004oAro0:018Þ, the air-jet was unstable with single-circulation or two-circu-lation airflow type. The critical value to distinguish them is about Ar ¼ 0:011 ðArc¼72Þ when the air-jet
penetra-tion distance beyond x ¼ 0:5L. The penetrapenetra-tion distance of intermediate range was fitted linearly as following (Fig. 4): Lp¼0:0341 1 Ar 2=3 ; ðr2¼0:81Þ. (1)
The expression is more similar to that of Rodahl[21]than that of Li et al.[4]and Grimitlyn and Pozin[12].
4.2. Centerline velocity decay and centerline temperature decay
The centerline velocity decay of air-jet was unstable when the airflow pattern was dominated by buoyancy or in an intermediate airflow condition (i.e., Ar40:004). The experimental data were fitted well in both ceiling and floor regions at Aro0:004 when fully rotary air-flow was dominated by inertia force as in a pseudo-isothermal condition (Fig.5). The centerline velocity decay of ceiling region in characteristic decay and terminal regions for non-isothermal plane wall jet can be simu-lated with same decay equations for an isothermal condition [22]. The equations were derived as following, respectively: Um Ud ¼2:87 ffiffiffi h x r , (2) Um Ud ¼2744 ffiffiffiffiffi h2 x2 s . (3)
The characteristic decay region was between the distance of x ¼ 10 and 100h. Beyond this distance, centerline velocity vanished rapidly in the terminal region. The decay of normalized centerline velocity has similar form as in previous studies[16,17,23].
Normalized centerline velocity in floor region was fitted well when the reversed air-jet traveled through floor surface as plane wall jet. Airspeed decay equation in characteristic decay region was expressed as
Urm Ud ¼5:19 ffiffiffi h x r . (4)
The throw constant in a non-isothermal condition was less than the value in an isothermal condition (i.e., 3.73)[22]. It may result from that stronger buoyancy affects the decay rate in a non-isothermal floor region.
Data of centerline temperature decay in both ceiling and floor regions were fitted well (Fig.6(A)). The temperature decay of ceiling region (Fig.6(B)) in different airflow rates were fitted well within the characteristic decay region according to the form of previous studies [4,15,24] as following: TrTm TrTd ¼2:44 ffiffiffi h x r . (5)
The temperature decay constant was chosen as K2¼
0:85K1(i.e., 2:44 ¼ 0:85 2:87) from Hassani et al.[3]. The
normalized temperature difference decreased with the increasing normalized air-jet traveling distance. The cool diffused air-jet became warm when the hot entrainment of ambient room air mixed with the air-jet.
The centerline temperature decay within the terminal region had similar form as the centerline velocity decay as
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Ar Lp (m) Experimental data Regression line of data Li et al. [4] Rodahl [21]
Grimitlyn and Pozin [12]
Lp=0.0341 Ar(-2/3)
Fig. 4. Penetration distance of non-isothermal enclosure versus Archi-medes number ðArÞ.
0.01 0.1 1 10 1 10 100 1000 x/h Um /U d 0.153 cms 0.104 cms 0.071 cms Rajaratnam [16] Albright [17] ASHRAE [24] Yu et al. [22] Characteristic decay Terminal region Potential core Floor region L Um/Ud=2.87(h/x) 0.5 Um/Ud=2744(h/x)2 Urm/Ud=5.19(h/x)0.5 H
Fig. 5. Normalized centerline velocity decay along perimeter of non-isothermal enclosure.
following: TrTm TrTd ¼2561 h x 2 . (6)
The variation of temperature decay for different airflow rates was not significant through floor region and can be
fitted by the similar form of ceiling region as following (Fig. 6(C)), TrTm TrTd ¼6:57 h x . (7)
The heat exchange between cool inlet air and hot room air was mixed thoroughly when the air-jet impinged the floor region. The floor heater established much thermal capacity in the floor region that caused insignificant variation of temperature decay. The fitted equations of temperature decay in floor region were not approached to the form as of Albright and Scott[15]because their model is used in the ceiling region, but were similar to other studies.
4.3. Velocity profiles and temperature profiles
Normalized velocity profile of non-isothermal plane wall jet are conducted from different position (i.e., x ¼ 0:3, 0.5, and 0:7L) with airflow rate of 0:185 cms and DT ¼ 40C as
0.01 0.1 1 10 1 10 100 1000 x/h (T r -T m )/( Tr -T d ) 0.153 cms 0.104 cms 0.071 cms 0.050 cms Regression line of data 0.153 cms-Albright and Scott [15] 0.104 cms-Albright and Scott [15] 0.050 cms-Albright and Scott [15] Li etal. [4]
Characteristic decay Terminal region
Potential core Floor region L H L (Tr-Tm)/(Tr-Td)=2.44(h/x) 0.5 (Tr-Tm)/(Tr-Td)=2561(h/x) 2 (Tr-Tm)/(Tr-Td)=6.57(h/x)0.5 (A) 0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 120 140 160 x/h (T r -T m )/( Tr -T d ) 0.153 cms 0.104 cms 0.050 cms Regression line of data 0.153 cms-Albright and Scott [15] 0.104 cms-Albright and Scott [15] 0.050 cms-Albright and Scott [15] Shepelev [24] and Liet al. [4]
(Tr-Tm)/(Tr-Td)=2.44(h/x) 0.5 (Tr-Tm)/(Tr-Td)=1.7(h/x) 0.5 (Tr-Tm)/(Tr-Td)=0.587Re 0.224(x/h)(-3/5) (B) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 215 235 255 275 295 315 335 355 375 x/h (T r -T m )/( Tr -T d ) 0.153 cms 0.104 cms 0.071 cms Regression line of data 0.153 cms-Albright and Scott [15] 0.104 cms-Albright and Scott [15] 0.071 cms-Albright and Scott [15]
(Tr-Tm)/(Tr-Td)=6.57(h/x)0.5
(Tr-Tm)/(Tr-Td)=0.587 Re
0.224(x/h)(-3/5)
(C)
Fig. 6. Normalized centerline temperature decay (A) along perimeter, (B) along ceiling region, and (C) along floor region of non-isothermal enclosure. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.50 1.00 1.50 2.00 2.50 3.00 y/y0.5 (T r -T )/( Tr -T m ) (Tr-T)/(Tr-Tm)@0.3L (Tr-T)/(Tr-Tm)@0.5L (Tr-T)/(Tr-Tm)@0.7L Wilson et al. [14] Albright and Scott [15] Grimitlyn and Pozin [12]
(Tr-T)/(Tr-Tm)=exp(-0.8(y/y0.5t-0.1) 1.4 ) (Tr-T)/(Tr-Tm)=exp(-(y/y0.5t)Ln2) (Tr-T)/(Tr-Tm)=exp(-0.7Pr(y/y0.5v)) 2 (B) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 y/y0.5 U /U m U/Um@0.3L U/Um@0.5L U/Um@0.7L Wilson et al. [14] Albright and Scott [15] Grimitlyn and Pozin [12]
U/Um=(exp(-0.8(y/y0.5t-0.2) 1.4))2 U/Um=exp(-(y/y0.5v) 2Ln2) U/Um=exp(-0.7(y/y0.5v)) 2 (A)
Fig. 7. (A) Normalized velocity profiles and (B) normalized temperature profiles of non-isothermal plane wall jet in ceiling region.
shown inFig. 7(A). The predicted curves were derived from previous research which based on different variables of Zv or Zt. Zt is calculated from vertical distance of thermal boundary layer spread index (y0:5t)[15], and Zv was based on the vertical distance of jet spread index (y0:5v)[12,14]. The plots suggested better agreement with results obtained from Wilson et al. [14] than that obtained from other studies.
Normalized temperature profile of non-isothermal plane wall jet in different positions (i.e., x ¼ 0:3, 0.5, and 0:7L) with airflow rate of 0.185 cms and DT ¼ 40C are
presented in Fig. 7(B). Both the predicted expressions of Wilson et al. [14] and Albright and Scott [15] showed similar agreement for experimental data than that of Grimitlyn and Pozin[12]. The shape of temperature profile is similar as velocity profile.
4.4. Airflow boundary layer growth and thermal boundary layer growth
The position data of half the maximum airspeed of air-jet with various airflow rates in both isothermal and
non-isothermal conditions are described inFig. 8(A). The root mean-square error (RMSE) between experimental data and Rajaratnam’s prediction was 2.45, which was less than that of Sigalla (3.96), Liu et al. (5.86), and Albright (4.55). The experimental data had the best agreement with Rajaratnam
[16] compared with other studies [17,25,26] that all the predicted expressions were derived from an isothermal air-jet. The growth of thermal boundary layer, which indicated by the vertical distance where the temperature difference is half of the extreme temperature difference, is shown inFig. 8(B). Both the predicted curves from Albright and Scott
[15]and Wilson et al.[14]fitted well with the experimental data and the RMSE were 3.63 and 3.13, respectively. The rate of growth decreased when the air-jet traveled close to the opposite wall inside an enclosure.
4.5. Floor velocity and floor temperature
The maximum floor velocity was fitted well with jet momentum ðMÞ, jet momentum number (J), and inlet jet
(A) 0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 0 20 40 60 80 100 120 140 160 180 x (cm) y0.5 v (cm) Isothermal data of y0.5v Sigalla [25] Rajaratnam [16] Liu et al. [26] Albright [17] Non-isothermal data of y0.5v (B) 0 10 20 30 40 50 60 70 80 90 100 120 140 160 180 x (cm) y0.5 v (cm) Experimental data of y0.5v Albright and Scott [15] Wilson et al. [14]
Fig. 8. Position of (A) half of the extreme airspeed and (B) half of the extreme temperature difference along enclosure ceiling.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 M (Nm-1) Urm (ms -1) dT=40C dT=60C (A) Urm = 0.41M0.42 R2 = 0.96 0 1 2 0.00 0.01 0.02 0.03 J Urm (ms -1) (B) Urm = 8.3J0.42 R2 = 0.96 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Rm Urm (ms -1) dT=40C dT=60C (C) Urm = 3.96Rm0.42 R2 = 0.96 0 1 2 0.00 0.01 0.02 0.03 Ar Urm (ms -1) (D) Urm = 0.09Ar-0.38 R2 = 0.92
Fig. 9. Maximum floor velocity (Urm) fitted with (A) jet momentum (M),
(B) jet momentum number (J), (C) inlet jet momentum ratio (Rm), and (D) Archimedes number ðArÞ.
momentum ratio (Rm) (Figs.9(A–C)). All the parameters relating to the inertia force resulted in same coefficient of determination ðr2 ¼0:96Þ. The maximum floor velocity also fitted well with Ar that was the ratio of buoyancy to viscosity (Fig.9(D)). An expression followed the results of Wang and Ogilvie[9]was fitted as following:
Urm¼4:71
ffiffiffiffiffiffiffi Rm
p
þ0:0023ðHDT Þ; ðr2¼0:98Þ. (8) The results of maximum floor velocity related to inertia force with different temperature environment were not recognized because of the temperature difference was not significant in the experiments (i.e., DT ¼ 40 and 60C).
The maximum floor velocity related to Ar[11]or HDT [9]
is reasonable because the consideration of thermal envir-onment. The temperature difference between maximum jet temperature on the floor and room temperature was fitted well with jet momentum ðMÞ, jet momentum number (J), and inlet jet momentum ratio (Rm), and Ar (Figs.10(A–D)). Ar relating to buoyancy and viscosity has better correlation with temperature difference than other parameters relating to inertia force only.
5. Conclusions
The airflow characteristics of plane wall jet diffused from ceiling slot-inlet into a non-isothermal enclosure were investigated through the scale-model study. The results showed that the air-jet behavior was similar as an isothermal plane wall jet while the airflow rate beyond a critical value (i.e., Aro0:004) and inertia force dominate airflow pattern as pseudo-isothermal air-jet. When the airflow condition below a critical condition (i.e., Ar40:018), air-jet fell on entry immediately with buoyancy dominate airflow pattern. Intermediate condition includes single circulation air-jet (i.e., 0:004oAro0:011) and two-circulation air-jet (i.e., 0:011oAro0:018). The penetration distance can be fitted well with Ar when Ar40:004. The expression of centerline velocity decay for non-isothermal air-jet in ceiling region has same expression of an isothermal condition. But the rate of centerline airspeed decay in a non-isothermal floor air-jet was less than in an isothermal condition for the buoyancy effect.
The present derived predictive equations can simulate the centerline temperature decay of non-isothermal air-jet well in ceiling region. The temperature decay in the floor region was not significant because of the well-mixed reverse air-jet and the occurrence of floor heat. Both normalized velocity and normalized temperature profiles can be fitted well by predictive equations of Wilson et al. [14]. The growth of airflow boundary layer and thermal boundary layer increased positively with traveling distance of air-jet. The growth rate of airflow boundary layer in non-isothermal air-jet is similar as in the non-isothermal condition. Maximum floor velocity and floor temperature differ-ence can be fitted well with key parameters. Parameters include Ar and HDT are more reasonable for the effect of thermal environment. Our results demonstrate that not only the experimental data fitted well with predictive equations obtained from previous researches but also the present derived semi-empirical equations can predict well the airflow characteristics of plane wall jet in a ceiling slot-inlet ventilated non-isothermal enclosure. Our findings also identify the reality of air-jet performance in a confined enclosure.
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