doi:10.1016/j.biosystemseng.2006.01.001 SE—Structures and Environment
Similitude Criteria for a Two-dimensional Wall Jet in an Isothermal Mechanically
Ventilated Enclosure
Hsin Yu1,; Li-John Jou2; Huei-Tau Ouyang1; Huang-Min Liang3; Chung-Min Liao3
1Department of Civil Engineering, National Ilan University, Ilan 26041, Taiwan, ROC;
e-mail of corresponding author:yuhsin@niu.edu.tw
2
Department of Biomechatronic Engineering, National Ilan University, Ilan 26041, Taiwan, ROC
3Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
(Received 15 April 2005; accepted in revised form 5 January 2006; published online 7 March 2006)
A scale model experiment is an important method to study ventilation airflow pattern inside buildings that affects indoor air quality. The similitude criteria are the decision factors to guarantee using the result of model study to predict actual airflow of prototype. It is important to decide the similitude criteria between scale model and prototype. The aim of this project focuses on deciding the similitude criteria of a two-dimensional wall jet between the model and prototype to establish same airflow pattern in an isothermal mechanically ventilated enclosure. The parameters of the Reynolds number, Euler number, and jet momentum ratio proposed by previous researchers are investigated to find which parameter is the similitude criterion for a two-dimensional wall jet in isothermal condition. Experiments were conducted in two geometrically similar scale models. The similitude criteria were verified by comparing latent parameters with airspeed distribution following the kinematic similitude, whereas the airflow pattern following the dynamic similitude between the model and prototype. Experimental results indicate that the Euler number is not the similitude criterion, but the jet momentum ratio related to inlet airspeed is the similitude criterion of a two-dimensional wall jet in an isothermal mechanically ventilated enclosure. Reynolds number may be used as the similitude criterion only for flows at low Reynolds numbers. Our results are useful for the researcher to decide the parameters and boundary conditions of scale model study for the prediction of prototype performance of a two-dimensional wall jet in an isothermal mechanically ventilated enclosure.
r2006 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd
1. Introduction
Ventilation is an important technique to regulate the room environment and produce an appropriate micro-climate for the occupant’s thermal comfort and indoor air quality. The behaviour of ventilated airflow inside an enclosure influences the air distribution, thermal envir-onment, and contaminant concentration. In most mechanically ventilated rooms, air-jets are used to mix inlet air with room air. The air-jet performance determines the distribution of thermal energy, moisture, and fresh air in a room (Awbi, 1991).
The characteristics of an enclosed air-jet have been studied by using prototype buildings, scale-models, and numerical simulation. However, a precise mathematical
model is impossible for the extremely complex micro-structure of room airflow (Moog, 1981). Model tests will always be required if the prototype building is not available and no precisely mathematical–physical pre-diction model is established. Model studies are practical for simulating the behaviour of a prototype and can be used to validate a numerical simulation. Similitude, or the relation between a model and prototype, is an important issue when using model studies (Yu, 1996).
The similitude criterion between a model and proto-type is important to guarantee that the experimental results of the model can be used to predict the behaviour of the prototype building. Complete similitude of the isothermal airflow field between the model and proto-type must satisfy the geometric similitude, kinematic
1537-5110/$32.00 415 r2006 Silsoe Research Institute. All rights reserved
similitude, dynamic similitude, and all boundary condi-tions (Shepherd, 1965;Baturin, 1972;Szucs, 1980;Awbi, 1991; Zhang et al., 1991). Only partial similarity between the model and prototype could be satisfied because most of the dimensionless parameters affecting airflow performance have equal importance in most of the realistic problems.
Reynolds number Re has been widely used as the similitude criterion for an isothermal airf1ow in an enclosure (Pattie & Milne, 1966; Smith & Hazen, 1968; Albright, 1976;Timmons & Baughman, 1981;Timmons, 1984; Yao et a1., 1986; Jin & Ogilvie, 1992), but experimental results do not always show that the Reynolds number is the appropriate similitude criterion (Zhang et al., 1991; Adre & Albright, 1994; Yu & Hoff, 1994, 1999).
Jet momentum ratio Rm, which is defined as the ratio
of inertia force (inlet jet momentum) and total drag (momentum loss) due to viscous shear at the walls of the enclosure (Adre & Albright, 1992), has been validated as an appropriate similitude criterion through recent experiments (Adre & Albright, 1994;Yu & Hoff, 1994, 1999), but Rmin m2/s2is a dimensional parameter and is
not a valid criterion since a similitude parameter must be dimensionless (Murphy, 1950;Szucs, 1980). Jet momen-tum number J was proposed byBarber et al. (1982)and has been verified as an improper similitude criterion between the model and prototype by experimental validation (Timmons, 1984;Adre & Albright, 1994).
Liu et al. (1995) compared three ventilation criteria (Reynolds number, jet momentum number, and jet momentum ratio) analytically under isothermal condi-tions. Reynolds number was found to be the correct similitude criterion based on a dimensional analysis and the Navier–Stokes equations. They concluded that previous research which showed the inappropriateness of Reynolds number as the similitude criterion might be the results of experimental errors, such as the failure of similarity in turbulent boundary conditions between the model and prototype. Using Rm as the similitude
criterion will result in the same inlet airspeed udin m/s in
both the model and prototype. The same values of udfor
the model and prototype leading to the conclusion that a turbulent flow in the prototype will be similar to a laminar flow in the model was questioned.
Rousseau and Albright (1996) stated an anomaly in the use of Reynolds number as the kinematic similitude criterion for scale modelling of slot-ventilated enclo-sures. Reynolds number has a negligible effect on the governing equations of fluid dynamics when compared to that of Euler number Eu which becomes an alternative kinematic similitude criterion instead of Re. The conclusion of similarity analysis indicates that the possible similarity parameters for the isothermal airflow in an enclosure are geometry, Froude number, Euler number, jet momentum ratio, and Reynolds number between the model and the prototype (Yu, 1996). The Froude number is important for compressible flow and Notation
a air-jet acceleration, m/s2 Cw throw constant
d slot outlet height, m Eu Euler number H enclosure height, m h slot inlet height, m J jet momentum number L enclosure length, m Lj jet throw, m
L0 length of exhaust plenum of the test
cham-ber, m
P pressure, N/m2 Q airflow rate, m3/s
R2 coefficient of determination Re Reynolds number
Rm inlet jet momentum ratio, m2/s2
t time, s
u air-jet velocity, m/s
ui air-jet velocity along the X axis, m/s
uj air-jet velocity along the Y axis, m/s
ut terminal velocity of the air-jet, m/s
ud air-jet velocity at diffuser, m/s
u ma-x
maximum velocity of the air-jet at specific distance from the inlet wall, m/s
W enclosure width, m w slot inlet width, m
x horizontal distance from the inlet wall, m xi distance along the X axis, m
xj distance along the Y axis, m
y vertical distance from floor, m DP pressure difference, N/m2 r density of air, kg/m3 Subscripts d diffuser m model p prototype
for motion with free liquid–vapour surfaces in the flow (Schlichting, 1979). The isothermal airflow in a confined space is considered as a homogeneous fluid without free liquid–vapour surfaces, thus the Froude number could be neglected (Zhang, 1991). The remaining similarity parameters require higher inlet airspeed in the model based on Re but the same inlet airspeed between the model and prototype based on both Eu and Rm.
The objective of this study is to investigate similitude criteria of a two-dimensional wall jet airflow between a scale-model and a prototype confined enclosure for isothermal conditions. The sub-objectives are to validate the Reynolds number, jet momentum ratio, and Euler number that proposed by previous researches as the similitude criteria for isothermal condition. The ultimate purpose of this research is to develop guidelines when using scale-models for assessing proto-type behaviour of a two-dimensional wall jet airflow patterns in confined spaces. The desire is to predict airflow patterns and airspeed distribution, especially within the animal occupied zone in the prototype building.
2. Methods and materials
Two geometrically similar scale models representing a scale-model and a prototype with ratio of 1:2 were used to study airflow similitude criteria. The ratio of
geometry between the scale-model and prototype is defined from the previous literatures (Smith & Hazen, 1968; Adre & Albright, 1994; Yu & Hoff, 1994). The airflow patterns and variation in velocity fields were measured by airspeed measurements. The test chambers used are shown in Fig. 1. The slot inlet width w in m was the same as the width of the enclosure W in m. The inlet aspect ratio was much larger than 20, and as a result, the airflow was treated as a two-dimensional wall jet without the effect of side walls (Forthmann, 1934).
The scale models were made from 127 mm thick plywood. The inner surfaces of the models were sanded and painted black. The front wall was made of Plexiglas to accommodate airflow visualisation. A portion of the top ceiling was fabricated with Plexiglas, which extended along the length of both models for illuminating purposes. Both models had an exhaust plenum between the test room and exhaust duct to reduce the effect of exhaust airflow from the slot outlet. Exhaust fan with circular duct was provided on the outlet wall. A 150 mm diameter duct was used for both models. Calibrated orifice plates were used within duct to select desired airflow rates through each model. A micro-manometer transducer was used to measure the pressure difference across the orifice to determine airflow rate.
Airspeed was measured with hot-film anemometers (model 8455 and 8475; TSI, Inc., USA) which were mounted on an traverse system automatically controlled
Exhaust plenum
Outlet pipe diameter = 150 mm Slot outlet
height d = 100/50 mm
Plexiglas
Outlet airflow to exhaust fan
Orifice plate diameter = 100 mm Test room Slot inlet height h = 20/10 mm L = 2000/1000 mm L′ = 1000/500 mm W = 2000/1000 mm H = 1000/500 mm Plexiglas
Fig. 1. The scheme and dimensions (prototype/model) of test chambers used in this study: H, enclosure height; L, enclosure length; W, enclosure width; L0length of exhaust plenum of the test chamber
with a programmable logic controller. A portable data acquisition system (model CR10; Campbell Scientific Inc., USA) was used to collect data. The sampling frequency was set at 16 Hz. The sampling period was fixed at 180 s per collection point to ensure accurate time-averaged results for turbulent airflow (Thorshauge, 1982). This sampling period was much longer than was used in previous similar studies (Zhang, 1991; Adre & Albright, 1994). The average value over time, at a point, was used for analysis and presentation. The wall jet peak velocity was measured at values for x of 025L, 05L, and 075L in both the model and prototype, where x is the specific distance in m from inlet wall and L is the length of the enclosure in m. Each peak velocity was determined from the vertical jet velocity profile at specific distance from the inlet wall.
3. Results and discussion
The ranges of airflow rates with corresponding values of Re, Rm, Eu and udused to investigate airflow
performances in an enclosure are shown in Table 1. Typical vertical velocity profiles of a plane wall jet at values for x of 025L, 05L, and 075L with inlet airspeed of 341 and 356 m/s for the model and prototype respectively are shown inFig. 2. The peak velocity of the two-dimensional wall jet at a specific distance is determined from the above vertical velocity profile. The peak velocity of the air-jet decreases with the increased distance from the inlet wall because of the raised entrainment compensates the initial momentum of the air-jet from the inlet.
The normalised wall jet peak velocities related to the normalised distances from the inlet wall are shown in
Table 1
Test conditions of airflow rates without corresponding values of parameters for isothermal airflow
Test Airflow rate (Q),
m3/s Air-jet velocity at diffuser (ud), m/s Reynolds number (Re) Inlet jet momentum ratio (Rm) Euler number (Eu) Prototype Minimum 00403 101 1347 001 0427 Maximum 01420 355 4746 008 0323 Model Minimum 00175 175 1170 002 0047 Maximum 00763 763 5101 039 0032 0.55 0.60 0.65 0.70 0.80 0.85 0.90 0.95 1.00
Normalised distance from the inlet wall x / L
Normalised height y / H 0.75 0.50 0.25 0 1.00 u = 5 m /s 0.75
Fig. 2. The vertical velocity profile of a plane wall jet at distance x of 025L, 05L, and 075L from the inlet wall at specific inlet airspeed as 341 and 356 m/s of the model and prototype respectively: , prototype; , model; x, horizontal distance from the inlet
Fig. 3. All the specific distances of 025L, 05L, and 075L are within the range of values for x between 10 h to 100 h which belongs to the characteristic decay region of a plane wall jet (Awbi, 1991). The normalised peak velocity of a plane wall jet in the characteristic decay region is proportional to the square root of the ratio between the slot height h in m and the stream-wise distance of the air-jet from the inlet wall x as (Awbi, 1991;Yu & Hoff, 1999): umax ud ¼Cw ffiffiffi h x r (1)
where: umax is the maximum velocity of the air-jet at
specific distance from the inlet wall in m/s; udis the
air-jet velocity at diffuser in m/s; and Cw is the throw
constant.
The throw constant in the model and the prototype are estimated as 389 and 384 respectively, and the average value is 387. The similar value of throw constant between the model and prototype indicates that the normalised peak velocity of a plane wall jet at comparable distance from the inlet wall is analogous between the model and prototype.
The normalised peak velocities of the air-jet at distances of 025L, 05L, and 075L from the inlet wall
versus Re, Rm, Eu, and udare shown inFig. 4. The plots
of the normalised wall jet peak velocity at specific distance from the inlet wall related to the different parameters are invariable because the self-similarity of the peak velocity. If the normalised travel distance of the air-jet from the inlet wall x/h is defined, the normalised peak velocity of the air-jet only depends on the throw constant according to Eqn (1) and is independent on the parameters of Re, Rm, Eu, and ud.
The plots of peak velocities at specific distances from the inlet wall varied as a function of Re, Rm, Eu, and ud
are shown inFig. 5. The plots of peak velocities against Re and Eu [Fig. 5(a) and (c)] fall in different curves between the model and prototype. Only the plots against Rmand ud[Fig. 5(b) and (d)] fall in the same curve with
data from different models. The equations of regression lines in both models with Re, Rmand udat values for x
of 025L, 05L, and 075L are shown in Table 2. All regression lines indicate appropriate correlation with coefficient of determination R2 greater than 097. The plot of peak velocities of the air-jet with Eu shows irregular curves in both the model and prototype.
The peak velocities of the air-jet at comparable positions are similar in both the model and prototype only when same ud or Rm is employed. It is shown
that the same ud or Rm will result in the same peak 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 10 100
Normalised distance from the inlet wall x / h
Normalised peak velocity
umax
/ u
d
Fig. 3. Normalised peak velocity at different normalised specific distance from the inlet wall: , at 025L of prototype; , at 05L of prototype; , at 075L of prototype; ,at 025L of model; , at 05L of model; , at 075L of model; , regression line; umax, the maximum velocity of air-jet at specific distance from inlet wall; ud, the air-jet velocity at diffuser; x, specific distance from the
velocities of a plane wall jet at comparable positions between the model and prototype. The normalised, Reynolds-averaged Navier–Stokes equation of momen-tum balance for an elemental portion of fluid at position x and time t in s is qui qt þuj quj qxj þquiuj qxj ¼ Eu 2 qP qxi þ 1 Re q2ui qxiqxj (2)
where: ui, uj are the air-jet velocities in the X direction
and Y direction, respectively, in m/s; xi, xjare distances
in the X direction and Y direction, respectively, in m; and P is pressure in N/m2.
By using the method of order of magnitude, it confirms that above a certain threshold value 1/Re becomes infinite and the Re can be neglected comparing to that of Eu (Rousseau & Albright, 1996). However, 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 1000 2000 3000 4000 5000 6000 Reynolds number Re
Normalised peak velocity
umax / u d 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Normalised peak velocity
umax / u d 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Euler number Eu 0.0 0.3 0.5 0.8 1.0 0.00 0.25 0.50 Rm umax / ud 0.0 0.3 0.5 0.8 1.0 0 2 4 6 8 ud, m/s umax / ud (a) (c) (b) (d)
Fig. 4. The normalised peak velocity of a plane wall jet related without (a)Reynolds number Re; (b) jet momentum ratio Rm; (c) Euler number Eu; and (d) air-jet velocity at diffuser udat distance of 025L, 05L, 075L from the inlet wall: , at 025L of prototype; , at 05L of prototype; , at 075L of prototype; , at 025L of model; , at 05L of model; , at 075L of model; L,
the viscosity term should not be neglected for low Reynolds number flow because of the expansion of the air-jet is caused by the insignificant airspeed and viscous effects in this region. Thus the possible similitude criterion might be Re at low Reynolds number flow (laminar inlet flow), and Rmwhich related
to ud at high Reynolds number flow (turbulent
inlet flow) of a particular range. The implementation of using Rm (or ud) as the similitude criterion in a
slot-ventilated enclosure under isothermal condition is in agreement with the results of Adre and Albright (1994).
Using Rm as the similitude criterion results in the
design condition of scaling law between the model and 0 1 2 3 4 5 6 0 1000 2000 3000 4000 5000 6000 Reynolds number Re Peak velocity umax , m/s 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Euler number Eu Peak velocity umax , m/s 0 2 4 6 0.0 0.1 0.2 0.3 0.4 0.5 umax , m/s umax , m/s ud, m / s 0 2 4 6 0 2 4 6 8 Rm (a) (b) (c) (d)
Fig. 5. The peak velocity of a plane wall jet related without (a)Reynolds number Re; (b) jet momentum ratio Rm; (c) Euler number Eu; and (d) air-jet velocity at diffuser udat distance of 025L, 05L, 075L from the inlet wall: , at 025L of prototype; , at 05L of prototype; , at 075L of prototype; ,at 025L of model; , at 05L of model; , at 075L of model; , regression line; L,
prototype (denoted by subscripts m and p) as hu2 d L þ H m ¼ hu 2 d L þ H p (3) where H is the enclosure height in m.
As h L þ H m ¼ h L þ H p , then: u2d m¼ u 2 d p (4) or ud;m¼ud;p (5)
Using Eu as the similitude criterion will result in the same design condition as using Rm when the pressure
difference is identical in both the model and prototype: 2DP ru2 d m ¼ 2DP ru2 d p (6) where: DP is the pressure difference in N/m2; and r is the density of air-jet in kg/m3. If the same working fluid and the same pressure difference were implemented, then, u2d m¼ u 2 d p (7) or ud;m¼ud;p (8)
The plot ofFig. 5(c)shows that values of Eu concentrate at 011 and 088 in the model and prototype, respec-tively. The parameter DP equals the pressure difference between the inlet and outlet of the enclosure in the analysis. The results of experiments indicate that DP is
proportional to the inertia force of the air-jet as ru2 d=2;
and the values of Eu in a specific model approach to a constant value even the inertia force of the air-jet varied. As the loss of total energy of the air-jet varies in different geometry model, the value of Eu concentrates to different value in dissimilar scale models. The results of experiments are opposed to the conclusion that the similar airflow is defined with the same Eu byRousseau and Albright (1996).
Jin and Ogilvie (1990) derived the change of airflow patterns in an enclosure under isothermal conditions as four stages (Fig. 6). In stage 1, the incoming jet velocity is very low and cannot reach the sidewall [Fig. 6(a)]. The mean air velocity at the floor region is less than 01 m/s. As the inlet velocity increases, the air-jet reaches the sidewall and flows along the wall towards the floor as stage 2 [Fig. 6(b)]. The mean air velocity at the floor region is greater than 01 m/s. If the inlet velocity continues to increase, the air-jet reaches the floor and travels along the floor as stage 3 [Fig. 6(c)]. Further increase of inlet air velocity will result in the fully rotary flow as stage 4 [Fig. 6(d)]. Any further increase of the inlet air-jet velocity will not change the airflow pattern inside the enclosure but increase the velocity of the rotary airflow. Distinguish of the airflow pattern inside an enclosure under isothermal condition depends on the length of the trajectory that the air-jet can travel along. A plane wall Jet is diffused from a slot-inlet and is terminated when the peak velocity of the air-jet is 05 m/s (ASHRAE, 1993). The distance from the diffuser to a point where the peak velocity in the cross stream section of the air-jet reduced to the terminal velocity is the jet throw. The jet throw also represents the air-jet trajectory which creates the airflow pattern inside the enclosure. The jet throw Lj in m can be derived from Eqn (1) Table 2
Regression equations of peak velocity of the air-jet umax at specific distance from inlet wall in the model and prototype against Reynolds numberRe, jet momentum ratio Rm, and air-jet velocity at diffuserud
Parameters Position (x) Chamber type Equations R2
Re 025L Model umax¼00011Re 09966
Prototype umax¼00006Re 09873
05L Model umax¼00009Re 09963
Prototype umax¼00004Re 09909
075L Model umax¼00007Re 09944
Prototype umax¼00003Re 09785
Rm 025L Model and prototype umax¼94444R05145m 09914
05L Model and prototype umax¼75004R05217m 09945
075L Model and prototype umax¼63206R05525m 09845
ud 025L Model and prototype umax¼0739ud 0993
05L Model and prototype umax¼05782ud 09963
075L Model and prototype umax¼04542ud 09936
in both the ceiling region and the floor region because the wall-jet at the floor region behaves like a plane wall jet after the reverse air-jet has impinged on the floor (Jin & Ogilvie, 1990; Yu et al., 2003): Lj ¼ Cwud ut 2 h (9)
where utis the terminal velocity of the air-jet in m/s.
If similar airflow patterns between the model and prototype are proposed, then the normalised jet throws Lj/h will also be the same as
Lj h m ¼ Lj h p (10) Substituting Eqn (9) to Eqn (10) gives
Cwud ut 2 m ¼ Cwud ut 2 p (11) and because Cw;m¼Cw;p; then:
ud ut 2 m ¼ ud ut 2 p (12) or ud ut m ¼ ud ut p (13)
As the terminal velocity utof a plane wall jet in both the
model and prototype is 05 m/s, thus
ud;m¼ud;p (14)
The similar inlet airspeed in both the model and prototype will result in the same jet throw which creates similar airflow pattern inside the enclosure.
Complete similitude of the airflow field between the scale-model and prototype requires geometric simili-tude, kinematic similisimili-tude, dynamic similisimili-tude, and all boundary conditions in isothermal conditions. Geo-metric similarity requires that the model and prototype have the same shape, and all the linear dimensions of the model are related to the corresponding dimensions of the prototype by a constant scale factor (Fox et al., 2004). Kinematic similarity exists between the model and prototype when the streamline pattern is the same and corresponding velocity ratios between velocity of the model um and of the prototype up (um/up) and
acceleration ratios between acceleration of the model am
and of the prototype ap(am/ap) are constant throughout
the flow field, where am, apare the air-jet acceleration for
the model and prototype, respectively, in m/s2. If the ratio of forces in the model and prototype to be the same, we have dynamic similarity between the model and prototype (Young et al., 2004).
(c) (a)
(d) (b)
Fig. 6. Four-stage airflow patterns visualised in a prototype slot-ventilated enclosure; (a) stage 1, the incoming jet velocity is very low and cannot reach the sidewall; (b) stage 2, the air-jet reaches the sidewall and flows along the wall towards the floor; (c) stage 3,
From the setting of experiments, geometric similarity is validated by proposing the same shape and scaling the linear dimensions by a constant ratio between the model and prototype. The similar peak velocities of the air-jet at comparative positions will result in the corresponding velocity ratio between the model and prototype. Thus the kinematic similarity in the model and prototype is achieved. The airflow pattern of a two-dimensional wall jet inside an enclosure is the result of integrated effects between relevant forces acted on the air-jet. The similar jet throw of the plane wall jet causes analogous airflow pattern in an enclosure. The same inlet airspeed of a plane wall jet in both the model and prototype will result in the corresponding jet throw which cause similar airflow pattern and gives dynamic similarity in the model and prototype.
4. Conclusions
From above discussion, Reynolds number Re may be validated as similitude criterion only at low Reynolds number flow, and the threshold value to discriminate the boundary of laminar flow still needs to be studied. Euler number Eu may not be the similitude criterion for a two-dimensional wall jet in mechanically ventilated spaces under isothermal condition based on the experimental results. On the other hand, the jet momentum ration Rm,
which related to the inlet velocity ud, indicates consistent
peak velocity in comparable distance between different models is the similitude criterion for a two-dimensional wall jet in mechanically ventilated spaces under iso-thermal condition. The dilemma of using the dimen-sional parameter as similitude criterion is based on the physical performance of the plane wall jet inside an enclosure. The air-jet will vanish when the peak velocity of the air-jet decreases to the terminal velocity which is a constant value in both the model and prototype. It requires that the inlet air-jet velocity also is identical in both the model and prototype to get the similar air-jet throw and airflow pattern by self-similarity of the air-jet velocity.
These results provide evidence that the similar airflow in geometrically alike mechanically ventilated confined spaces under isothermal condition can be achieved by using Rm (or ud) as similitude criterion, and are in
agreement with the results presented in the literature.
Acknowledgements
This study is officially supported by the funding from National Science Council of the Republic of China under the grant NSC-89-2313-B-197-016.
References
Adre N; Albright L D (1992). Criterion for establishing similar airflow patterns in slotted-inlet ventilated enclosure. ASAE Paper No. 92-4530, St Joseph, MI
Adre N; Albright L D (1994). Criterion for establishing similar airflow patterns (isothermal) in slotted-inlet ventilated enclosures. Transactions of the ASAE, 37(1), 235–250
Albright L D (1976). Airflow through hinged baffle slotted inlets. Transactions of the ASAE, 19(4), 728–735
ASHRAE (1993). ASHRAE Handbook: Fundamentals. American Society of Heating, Refrigeration and Air-Conditioning Engineers, Atlanta, GA
Awbi H B (1991). Ventilation of buildings. Chapman & Hall, London
Barber E M; Sokhansanj S; Lampman W P (1982). Stability of airflow patterns in ventilated airspaces. ASAE Paper No. 82-4551, St Joseph, MI
Baturin V V (1972). Fundamentals of Industrial Ventilation, 3rd Edn. Pergamon Press, Oxford, UK
Forthmann E (1934). Turbulent jet expansion. National Advisory Committee for Aeronautics, Technical Memor-andum No.789
Fox R W; McDonald A T; Pritchard P J (2004). Introduction to Fluid Mechanics, 6th Edn. John Wiley & Sons, Inc., New York, NY
Jin Y; Ogilvie J R (1990). Near floor air speeds from center slot air inlets in swine barns. ASAE Paper No. 90-4004, St Joseph, MI
Jin Y; Ogilvie J R (1992). Airflow characteristics in the floor region of a slot ventilated room (isothermal). Transactions of the ASAE, 35(2), 695–702
Liu Q; Hoff S J; Bundy D S (1995). A comparison of three proposed ventilation criteria. ASAE Paper No. 95-4642, St Joseph, MI
Moog W (1981). Room flow tests in a reduced-scale. ASHRAE Transactions, 87(4), 1162–1181
Murphy G (1950). Similitude in Engineering. Ronald Press Co., New York, NY
Pattie D R; Milne W R (1966). Ventilation airflow patterns by use of models. Transactions of the ASAE, 9(5), 646–649
Rousseau A N; Albright L D (1996). An alternative kinematic similitude criterion for slot-ventilated enclosures. Transac-tions of the ASAE, 38(6), 1887–1889
Schlichting H (1979). Boundary-Layer Theory. McGraw-Hill, Inc., New York, NY
Shepherd D G (1965). Elements of Fluid Mechanics. Brace & World, Harcourt, NY
Smith M R; Hazen T E (1968). Similitude study of ventilation-inlet configuration. Transactions of the ASAE, 11(2), 218–225,235
Szucs E (1980). Similitude and Modeling. Elsevier Scientific Publishing Co., Amsterdam, Netherlands
Thorshauge J (1982). Air-velocity fluctuations in the occupied zone of ventilated spaces. ASHRAE Transactions, 88(2), 753–764
Timmons M B (1984). Use of physical models to predict the fluid motion in slot-ventilated livestock structures. Transac-tions of the ASAE, 27(2), 502–507
Timmons M B; Baughman G (1981). Similitude analysis of ventilation by stack effect from an open ridge livestock structure. Transactions of the ASAE, 14, 1030–1034
Yao W Z; Christianson L L; Muehling A J (1986). Air movement in neutral pressure swine buildings-similitude theory and test results. ASAE Paper No. 86-4532, St Joseph, MI
Young D F; Munson B R; Okiishi T H (2004). A Brief Introduction to Fluid Mechanics, 3rd Edn. John Wiley & Sons, Inc., New York, NY
Yu H (1996). Air mixing criteria foe ceiling slot-ventilated agricultural enclosures. Unpublished PhD Dissertation, Iowa State University , Ames, IA
Yu H; Hoff S J (1994). Validation of the momentum ratio concept for isothermal airflow similarity in a ceiling slot-ventilated enclosure. ASAE Paper No. 94-4582, St Joseph, MI
Yu H; Hoff S J (1999). Airflow pattern similitude criteria for ceiling slot-ventilated agricultural enclosures under
isothermal conditions. Transactions of the ASAE, 42(2), 459–469
Yu H; Liao C M; Liang H M (2003). Scale model study of airflow performance in a ceiling slot-ventilated enclosure: isothermal condition. Building and Environment, 38, 1271–1279
Zhang J S (1991). A fundamental study of two-dimen-sional room ventilation flows under isothermal and non-isothermal conditions. Unpublished PhD Disserta-tion, University of Illinois at Urbana-Champaign, Urbana, IL
Zhang J S; Christianson L L; Riskowski G L (1991). Effect of diffuser air velocity profiles on scaling methods for predicting room air motion. ASAE Paper No. 91-4558m St Joseph, MI
