improved calculation of air distribution in an auditorium

NO-94-16- 5

IMPROVED CALCULATION OF AIR DISTRIBUTION IN AN AUDITORIUM M. Tarnopolsky

I

Ph.D.

ABSTRACT

This paper outlines a semi-empirical method for calculating the velocity and temperature fields in airconditioned auditoriums. The method takes into consideration the interaction between the various jets in the auditorium, the boundaries of the auditorium, and the exhaust j10w by adding the momentum flux of all jets at each point alld later correcting the velocity fields for deviations from the equation of continuity. Similarly, the temperature field is calculated so that the heat balance equation is preserved. The effect of the walls is calculated by the mirror method. The results of the calculations are shown to be in good agreement with Ttlp(,surements in scaled models. Several examples of desiSil ba.~ed on this procedure are then discussed.

1991; Trox 1991). However, experience shows that very large deviations from these calculations are / possible, as confined jets will usually have lower ve.!9Pityand temperature differences, a shorter trajectory, and a greater ability to heat (or cool) than free jets. To overcome this inability, a calculation procedure was developed by the author and his colleagues at a laboratory in Moscow. This procedure was later improved and used successfully in the design of several large indoor spaces (Tarnopolsky 1992). This paper describes this calculation procedure and compan.s typical calculations with the results of the tests in physical models, presents the basic concepts for improving the performance of large air-conditioned spaces, and presents examples to illustrate the validity and advantages of this design concept and procedure.

INTRODUCTIO~

ANALYSIS

Engineers are making a conSIderable effort to achieve high standards of air conditioning in large theaters, concert halls, gymnasiums, £wimming pool arenas, and department stores using optunized and ecoD.olnica! air-conditioning systems. In spite of this effolt 2nd the large investments in both equipment and operating costs, the results are not always satisfactory .. Large nonuniforrc;ties in comfort conditions are found in many auditonur'.ls, and air quality standards are not always met. The main reason for these deficiencies is the engineer's basic inability to accurately predict the complex temperature and velocity fields induced by a large number of nonisothermal jets in a large space bounded by nonuniform boundary conditions. It should he recalled that these boundary conditions include area a!.d point sources and sinks of heat and humidity and that the turbulent motion induced in such a space is often drastically affected by a complex nonlinear interactio'" between the different nonisothermal jets and boundaries. The problem is common for spaces of all sizes, from individual rooms to very large auditoriums. Here, the author focuses on the performance of large auditoriums. Conventional calculations of air distribution in rooms are usually based on seII.t..i-empiricalequations that describe the velocity, temperature, &!1dtrajectory of free jets, sometimes takin:::into consideratio;] the Coanda effect (ASHRAE

Our analysis assumes that the hall is air-conditioned using a series of jets supplied from rectangular outlets in one of the walls. It also assumes that the cross section of the hall is rectangular (Figure 1). The analysis is performed in two stages. Initially, the effect of the side walis, ceiling, and floor is taken into consideration by the mirror metb.od(ignoring friction in the boundary layer). The velocity profiles obtained during this stage are denoted by the index C (Uc) (Figure 2). During the second stage of the calculation, the velocity field in the hall (U) is calculated using a correction denoted by a velocity shift (Us) and shown by Equation 18. The velocity, Uc, and temperature difference, T, are determined by adding momentum flux and excess heat as a result of elementary jet interaction (Tarnopolsky and Gelman 1987; Tarnopolsky 1989): M

Bol2

Hol2

J=I E

-dol2 f

-Ho12 J

(1)

and

rUi2dodT]lgBoHo

Cpr UcT M

Bol2

Hol2

E J=l

f -dol2

J -Ho12

(2)

CprUiTidodT]IBoHo,

Moshe Tar;iopolsky is a research scientist in the Department of Civil Engineering, Technion, Haifa, Israel. ASHRAE

"!i

ansactions:

Symposia

1195

(0)

I'

H

X3 X'2

(c)

H

t Figure 1196

1

Schematic description of the air motion induced by (a) isothermal,

(b) heated, and (c) coldjets. ASHRAE Transactions: Symposia

I~

Ar

1-'

r

r

1 H r I

..r----\T---~ I" , ., I

H

r

,

I

...,-~ -----t-T--------j ~

-H H "-H H HtH

H

r

"I

t~

1=

~

J~~=~~-~-J: ].,I

'i-

~

-,-~ L..-.- _

I +

_._Lt :'_) --__-_l ~ -.J

__ (

~

1"+

I-I

I ~i )

•I ~

Br-·-I-~I '" I •."~ -- $-+--~- -+--E~ I t- - r..., ~ + - - -+; --:y h--' __ LJ I

--I

"'1;1

I--I~(~~---~

~B I I,'{Br-B )..-" I... BIB I· .....•...... Br-B I(" Br-B ... :. I'

C·__-C --E8-'-L ~ __ .--L _ L..J _

I.•

Figure 2

where ered:

"f

~_I"i'

.:L:'-1I

.2B+Y~ , ~2{Br-B)-'!:1

Air jet interaction diagram.

is the specific weight of the air at the point consid-

"f

=

"fa

Ta/(Ta

+ T),

where Yj and Zj are coordinates of the point inj:

Yj

(4)

=

BrU-M-(-1)j)/2) - B (1 + ( -

-« Yj + 0)2

+ (Zj + 1/)2))/2 C2 S2]

1)j)

(6)

- Y

and Zj = HrU - (M -

-H(l +(-l)j ASHRAE Transactions: Symposia

(5)

Ti = Trn(UilUrn)u

(3)

where Ui and 1i are the air velocity and temperature difference, respectively, induced by the elementary jet i is given by Ui = Urn exp[

and

(-l)j -Z.

/2) (7)

1197

The values of Um and Tm have to be selected from the

This solution must be corrected to take into consideration

constancy of momentum flux (Ie) and excess heat (Qe):

the counterflow between the jet and the enclosure. assumed that the real velocity field (U) is given by U=Ue-Us

B,-B /(,-/(

J -B and

JH

'Y

Ue2dYdZIg

= Ie

J

(18)

(8) where Us is a velocity "shift, " determined by the equation of continuity: Br-B Hr-H

Br-B Hr-H -B

It is

Cp'YUeTdYdZ=Qe.

J

-H

(9) JH

JB

Taking into consideration Equations further integration, we obtain

1 through 3 and after

Accordingly, 18, and 19:

'Y UdYdZ

=

G.

(19)

we obtain the following from Equations

12,

(10) (20)

Us = Gel'Ya Br Hr - Ue, and (11)

where Ue is the air-removal velocity in the considered cross section of the auditorium,

Equations 1 and 2 and further integration, the velocity and temperature difference can be presented as Ue = (gIel'YaBoHo)O.5

(21)

Ue = GI'Ya Br Hr;

which can be used to find Um and Tm. After substitution of Equations 4, 5, 10, and 11 into

Ge is the quantity of air in the considered cross section,

(12)

Uy Uz

and Ly and Lz are nondimensional

discharge cofactors,

and Br-B

(13) Ly = where Uy and Uz are the nondimensional velocity Uc:

J

-B

Uy dylBo

(23)

UzdzlHo.

(24)

cofactors of the Hr-H

M

Uy = (~

j-I

(Erf[(Yj+BoI2)/CS]

-Erf[(Yj

-BoI2)/CS]/2)o.5

and

Lz= (14)

To determine the trajectory of the jet, we have to calculate the effect of the momentum flux and buoyancy flux. The momentum flux in the cross section of the hall is

M

Uz = (~

j-I

(Erf[(Zj

J -H

+ Ho12)1 CS]

B,-B /(,_}(

(15)

- Erf[ (Zj - Ho12)1 CS]/2)o.5.

Iu =

J

-B

JH

'Y U2

(25)

dy dzlg,

Similarly, Tyand Tz are given by or, taking into consideration Equations 23 and after integration, we obtain

M

Ty = ~

j=I

-Erf[«(1

(Erf[«(1

+ (J)/2)o.5 (Yj+Bo/2)/CS]

+ (J)/2)O.5 (Yj - BoI2)/C

S])/2

Uy

(16)

and M

Tz

=

~

(Erf[«(1

Iu = Ie(l

-Bo

Ho Ly2 Lz21Br

Hr) +Ie

(26)

where Ie is the momentum flux of air removal considered cross section of the auditorium:

in the

+(J)/2)o.5(Zj+HoI2)/CS]

j-I - Erf[ « 1 + (J)/2)o.5

1198

18 and 20 through

Ie = 'Ya Uel Br Hrlg. (Zj - H 012)1 C S]) 12 Uz.

(27)

(17) The buoyancy force, created by the temperature-density

ASHRAE Transactions:

Symposia

H Y=

difference between the elementary ambient air, is

x

volume of the jet and

dIr =

f

J -H

-B

("fa - "f) dY dZ dX.

(28)

Using Equations 3 and 13, and after approximate integration, Equation 28 becomes dIr = Qe("faBoHolgIe)o.s

QyQzdXITaCp,

Hr-H

(29)

"f U2dZ/(Hr-H)

J

where Qy and Qz are nondimensional excess heat:

cofactors

of the -

Ty dYIBo

J -H

J

-H

TzdzlHo.

x

(31)

The components and the resultant momentum flux in the cross section of the room will be Ix = Iu cosa cos{3,

(32)

Iy = Iu sina cos{3,

(33)

s

Iz = Iu cosa sinb + Jo dIr,

(34)

and (35) The coordinates of the jet trajectory can now be calculated: S

!i

(40)

The plane jet trajectory can be calculated using Equations 36 and 37, taking into consideration Equation 38:

i

.:1H =

X =

"f U2dZIH

(30)

Hr-H Qz=

dYIg Br.

o

Br-B

J -B

(39)

dPBodX,

where dP is the static pressure difference induced by the lower and upper parts of the jet and calculated from the momentum flux equation: dP =

o

Qy =

I

Ip =

Br-B Hr-11

i Ix d S I I ,

(36)

Now, the static pressure in the cross section of the hall for both a series of jets and a plane jet is given (from the momentum flux equation for closed space):

To implement the solutions of the above-mentioned equations, initial values of the total quantity of the air and momentum flux of the jet should be known. The total quantity of air depends on the position of the inlet and the cross section considered. If the distance from the outlet to the cross section is less than the distance to the inlet (X < Xa), the total quantity of air in this cross section equals the initial value (G = Go). The initial momentum flux can be calculated (taking into consideration that when S = 0, Ly = Lz = 1, and Iu = 10) from Equation 26 as follows: Ie = (10 -Ie)/(1

(37)

(42)

P = (1a+PaBrHr-l)IBrHr.

sS

IzdSII. IydS/I,

(41)

(1z+Ip)dXII.

-Bo HolBr

Hr).

(43)

In the case of air supply and removal from the same end of the auditorium (Xa = 0 and G = 0), the initial momentum flux includes the momentum of both the jets and the removal:

(38)

G02

10 + -_ This analysis can also be used to calculate the air distribution for the case of a plane jet. In this case, Bo = Br and Uy = Ly = 1. It should be noted that plane jets are greatly affected by the ceiling as a result of the Coanda effect. The static pressure difference between the lower and upper parts of the current creates a vertical pressure force:

ASH RAE Transactions:

Symposia

Ie

=,

g

"fa(Br

(1 -Bo

Hr -Bo _ HolBr Hr)

Ho) (44)

When the outlets and inlets are placed in the walls perpendicular to one another, additional correction to the velocity field must be made; this is not discussed in this paper.

1199

COMPARISON WITH EXPERIMENTAL

Uc/Uo

DATA

Dmm Uomls

For a comparison of results of the analytical study with experimental data, tests have been conducted in small-scale models, where the forced air passes through a 2-kW electric heater into a static pressure chamber via a collector, gradually reducing the flow from round nozzles with diameters of D = 10, 20, 30, and 40 mm. Preliminary tests were conducted supplying "free" jets into the laboratory hall; these were 7.5 m long and 5.0 m by 4.5 m in cross section. The horizontal and vertical velocity and pressure profiles were measured using a pitotPrandtl tube connected to a micropressure gauge at the jet stream cross sections; it is placed 75 mm from the nozzle outlet. The temperature profiles were measured at the same points by thermocouples connected with potentiometers. The initial velocity (Uo) and temperature (To) profiles were practically uniform. From these two profiles, the initial momentum flux and excess heat were calculated:

II • II •

0.8

0.6

-UclUo

0.4

0.2 IS

0.0

o

20

o

•

Qc = QrCpGoTo,

-0.02

(46) -0.04

X/D

40

X/D

..•------_.- •....._ .....~

II b)

40

..L.

0.02

(45)

and

52.8 52.1 53.2 52.8

a)

0.00"'1 •

10 = Ir Go Uoig

10 20 30 40

EI

II

/tf

•......

•#

••••II

;

• • • •

If

.1: .',

DmmUomis 10 52.8 20 52.1 30 53.2 40 52.8

where Ir and Qr are the kinematic and thermal characteristics of the nozzles; Ir = 1.06 to 1.12 and Qr = 1.1. • •••• PsiPu The trajectories, determined as a locus with maximum •• ...L Ps/Pu velocity in cross sections of the isothermal jets, were horizontal. Satisfactory coincidence was obtained in Figure Figure 3 Isothermal centerline (a) velocity and (b) 3a between measured axial free jet velocity and calculated pressure in free jet. values using Equation 18 by an empirical constant C = 0.082, Prandtl number 11 = 0.5, Y = Z = 0, and Bo = Ho = nO·S D/2. by BolBr = 0 and HolHr = 0 using a geometric length scale, Measured values of the axial static pressure in the jet were compared in Figure 3b, with formulas proposed by (49) Xd = (Br Hr)O.S , Hinze (1959):

,

Ps

=

-Kp Pu,

(47)

Ud = (g Icl'YJ'.5IXd.

where Pu is the axial dynamic pressure in a jet: (48) Kp is an empirical coefficient that was calculated from experiments as Kp = 0.132 against Kp = 0.15 in Hinze

(1959). Then, using obtained characteristics of the free jets, we can compare results of the calculation of the axial current velocity in the limited space using Equation 18 by Y = 0 and Z = 0 with the corresponding experimental data, where nozzle outlets were placed in the center (BIBr = HIHr = 0.5) of the open end of the model, which measured 1.275 m or 0.375 m long and 0.15 m by 0.15 m in cross section. Figure 4a shows that the axial velocity in the main part of the current can be roughly described with a single curve 1200

and a velocity length scale, (50)

When air supply and removal were provided from the opposite ends of the model (Xa = Ar), velocity "shift" became lower than in the first case and correspondingly increased current velocity and decreased counterflow velocity. In the first case, the model was under higher pressure than in an inlet, while in the second case, this pressure difference was negative. Using Figure 4a and Equation 43 or 44, we can roughly estimate the distance Xl where the jet crosses the upper level of the service area by the required velocity. To fulfill the conditions by which this velocity is the maximum velocity along the upper level of the service area, the distance from the jet axis to the service area must be more than ASHRAE Transactions:

Symposia

•

, -

"

10 40 3051.7 10 591 8.5 532 2052.2 30 34.5 3552.5 0as 2.5 as1b) 11.1 638.5 01.5 3.6 .7 54.5 2.S

U/UdXalXd mm Uo m/s BrlHr

UlUd1I

0

Pd _ 3 Xd, the velocity in the counterflow near the floor can achieve the maximum value of U3 = 0.8 Ud.

(52)

Axial velocity in the cold jet is less than 0.2 Ud if the length of the auditorium exceeds

Xl = 5Xd.

(53)

Axial static pressure in the main part of the current in the model has a satisfactory coincidence with Equation 42, taking into consideration Equation 47 (Figure 4b),

Ps

=

P -Kp Pu,

(54)

and using the geometrical length scale, Xd, and the pressure length scale,

Pd ASHRAE Transactions:

= Ic1Xd2•

Symposia

(55)

Figure 5

2

X/Xd

Isothermal centerline velocity in limited jet by variable (a) H/Hr and (b) Br/Hr.

The influence of the interaction between jet and ceiling is illustrated in Figure 5a, where the relative height of the supplying jet, HIHr, increases from 0.71 to 0.96 and, correspondingly, increases the axial velocity depending on the relative distance from the outlet. We can see that data regarding absolute height (Trox 1991) or relative height (ASHRAE 1991) for determination of ceiling effect are insufficient. Figure 5b shows a comparison of the results of calculations and experiments of Sadovsky (1955) by supplying air through a nozzle of D = 32 rom to the open end of a model measuring 2.0 m long and 1.0 m by 0.15 m in cross section. We can see the increase in axial velocity corresponding to an increase in the dimension ratio in a cross section of the auditorium (HrlBr). If the distance to the cross section considered is more than 8 Hd (where Hd is less than Br and Hr), axial velocity can be calculated using formulas for plane jets. Figure 5b shows a comparison between the results of calculations of the plane jet and experiments supplying air through a slot (Bo X Ho = 150 m X 5 rom) to the open end of the first model using 1201

Xd = Hr

(56)

as a geometric length scale. Figure 5b also shows a comparison between the results of calculations and experiments of Fortmann (1934) by supplying air through a slot measuring 0.65 m by 0.03 m to a model with a length of 2.0 m and 0.65 m by 0.18 m in cross section. Calculation results of the axial current temperature difference in the limited space (Equation 13) by Y = 0 and Z = 0 and corresponding experimental data, where heated air was supplied by vertical discharge angle {3 = 3.5° through a nozzle outlet of D = 40 rom placed in the center of the open end of a model with a length of 2.15 m and 0.35 m by 0.35 m in cross section, are compared in Figure 6a using the geometrical length scale, Xd, and the temperature difference length scale: Td = QclCp

Zd = g Xd2 TdlTa

The analysis of Equations 36 and 37 and the comparison· with experiments (Figure 6b) shows that the trajectory. det1ection from the initial direction of the current, (58)

Zt = (~H - X tg {3) cos3 {3,

Uo mls To oC XdIZd •

21.1

53

321

•

26.8

90

257

127

57

173

15

(59)

Ud2.

Equation 59 becomes the most important principle of auditorium modeling, as proposed by Baturin (1959). Analysis shows that if a cold jet touches the ceiling, its trajectory becomes horizontal and can be roughly determined by {3 = 0 using Figure 6b and Equations 52 and 53. However, in this case, the trajectory is much shorter than in the case of supplying air by inclined jet, when the distance from outlet to ceiling is greater than the maximal trajectory det1ection of the jet: ~Hm

(57)

"'faXd2 Ud.

T/Tdi

can be described with a single curve by BolBr = HolHr = 0, using the geometrical length scale (Xd) and the trajectory length scale:

=

(8 q 19 (1 + q) C rfl·5 Zd)O.5 (Xd sin {3)1.5.

(60)

Calculation results of the axial velocity using Equation 18 by Y = 0 and Z = 0 and corresponding experimental data of Peterson and Bayazitoglu (1992), where heated air was supplied vertically upward through a nozzle outlet of D = 20 rom placed in the center of a model with a height of 1. 8 m and 1.15 m by 1.15 m in cross section, are compared in Figure 7 using a geometrical length scale, Xd, and a velocity length scale, Ud. An increase in the temperature difference and velocity in the main part of the jet by decreasing the ratio XdIZd is noticed (see Figures 6a and 7) .

10

a)

CALCULATION

OF AIR DISTRIBUTION

Results of the above-mentioned

5

calculations

used to examine the velocity and temperature three critical points (see Figure 1): o o

'Z1/Zd;

2

OmlsTo • 21.1 53 • 26.8 90 • 18.8 127 • 12.9 173

5

X/Xd

3

•

b)

3 2

o o

Figure 6

1202

2

3

Heated centerline (a) temperature and (b) trajectory of limitedjet.

•

the position where the jet crosses the upper level of the service area,

•

the the the the

•

-ZVld

XrXd difference

are then

difference at

position service position t100r is

where the velocity along the upper level of area is highest, and where the velocity in the countert1ow near highest.

If the dimensions of the auditorium for jet Ar, Br, and Hr (m); kinematic and thermal characteristics Ir and Qr; dimensions Bo and Ho (m) and position of outlets H (m) and inlets Xa (m); initial discharge angle {3 (Rad); initial velocity Uo (m1s); and temperature difference To (0C) are known, then the adopted solution can be checked by means of direct calculations. The velocity, U (mls), and temperature difference, T (0C), at the critical points of the service area must not exceed the required values Ur and Tr. If these requirements are not fulfilled or, in the case of a new design, a reverse calculation is required, the results of the analysis of the foregoing equations permit us to ASHRAE Transactions:

Symposia

X

- ......•• -----

•.

3.28 0.281 3.15 1.07 0.002 5.35 1.646 0.154 53 1.78 0.024 130 163 85 • 0.007 174 ' ..•.. •• .•..•. 2.6733

I U/Ud

...

x+••

X •.••••.•••••

XI

iii

I

0

I

• Uo mls To oC XdIZd

60

20

o 0.0

Figure 7

0.4

0.2

Z/Xd

0.6

Heated centerline velocity in venical jet.

choose the minimum number and right size of air diffusers and their arrangement at a maximum heat load. From the bulk heat balance calculations, we should determine total heat load, Qt (kW), total quantity of air, Gt (kg/s), and initial temperature difference, To (0C), of the supply air for major operating and climatic conditions of the auditorium. We have to choose the main direction of supply air and a corresponding total length, At, and width, Bt (m), of the auditorium. First, we should calculate air distribution by cold jets (see c in Figure 1). Proceeding from the required velocity in the counterflow (U3 = Ur) from Equations 45, 49, 50, and 52 by Ic = 10 (at the first step) and taking into consideration that Bt = Nd Br

(61)

(m)

and Gt = Nr Nd Go

(62)

(kg/s),

(kW),

Qt = Nr Nd Qcl Qr we obtain a temperature Td = Qr QtlNr

difference

(65)

length scale:

Cp "fa Bt Hr Ud

CC) ..

(66)

Relative distance from the outlet to the position where the jet crosses the upper level of the service area (X1Xd) should be determined proceeding from the required velocity (upper curve in Figure 4a by UIUd = UrIUd) and the required temperature difference (lower curve in Figure 6a by TITd = TrITd) at this point. Then, using a maximum from these relative distances, we can obtain the relative trajectory deflection, ZtIZd, from Equation 58 and Figure 6b and calculate a trajectory length scale proceeding from the position of the outlet H and the discharge angle {3 (in the first step, we can use the highest position of the outlet close to the ceiling by H = Hr and {3 = 0):

(m) (67)

Zd = (Hs-H-X1tg{3)cos3{3I(ZtIZd) we obtain the maximal initial velocity: Uo = Nr"faBtHrUr2/0.64IrGt

(m/s),

(63)

where Nr and Nd are the quantity of rows and diffusers in the row, respectively, in the row in the auditorium (in the first step, we can adopt Nr = 1). If the calculated initial velocity, Uo, is lower than the velocity from the sound level, Ua, we should adopt a calculated initial velocity. In an opposite case, we should choose another type of diffuser with a higher acoustic characteristic or continue calculations by Uo = Ua. Then, from Equations 45, 49, 50, 61, and 62, we obtain a velocity length scale,

where Hs is the height of the service area (m). The geometrical length scale can be obtained Equation 59: Xd = Ud( Ta Zdl g Td)o.s

and from Equations consideration that

(m/s),

Equation 49, Br = Xd21Hr

Symposia

(m),

(69)

and the quantity of diffusers in the row, (70)

(64)

46, 49, 57, and 61 and taking into

ASH RAE Transactions:

(68)

Then we can estimate the distance between diffusers from

Nd = BtlBr. Ud=(lrGtUoINr"faBtHr)O'S

(m).

from

Now we can choose a convenient position of the outlet H (m) and determine a maximum vertical discharge angle 1203

upward, {3, from Equation 60 by ARm

=

level of the service area (U2 = Ur) from Equations 59 and 68 and taking into consideration Equation 51:

Hr - H:

{3 = arcsin t.Hm [ (9(1 +(j)Cno.5~~8(j)1/3

t.Hm2l3]

(Rad).

(71)

Then, we can estimate the maximum length of the jet Xl .using Equation 53 and a distance from the outlet to the position where the jet crosses the upper level of the service area: Xl = Xd(X/Xd)

(72)

(m).

Experience shows that in order to avoid large deviations in the uniformity of auditorium conditions, the length of jets in a row, Ar, must not exceed the maximum length of the jet Xl, and the distance from the outlet to the position where· the jet crosses the upper level of the service area (Xl) should be equal to about 0.5 to 0.75 Ar. Now we can estimate the new quantity of rows of diffusers, Nr: (73)

Nr = At/Ar. The quantity of air supplied through the diffuser is Go = Gt/Nr

Nd

(74)

(kg/s).

We should choose dimensions of the outlet Bo and Ho (m) from a catalog and then estimate the new value of the initial velocity: Uo = Gol"( Bo Ho

(m/s).

(75)

Calculations must be repeated from the beginning using new values of parameters until they coincide throughout the calculations. When air distribution by heated jets is calculated (see Figure 1b), the main results of the foregoing calculations of cold jets are used with three changes: 1.

Relative distance from the outlet to the position where the heated jet crosses the upper level of the service area IS Xl = AtlNl

2.

The geometrical

+Hr-Hs

(m).

(76)

length scale can be obtained by

Xd = XII Ku(XI Xd)

(m)

(77)

where Ku is a cofactor of the heated jet interaction with the ceiling, Ku = .z0.5. 3.

The maximum vertical discharge angle downward, {3, should be determined by proceeding from the required velocity at the point where the jet touches the upper

1204

= H - Hs - C Xl .

(78)

Finally, a convenient position for inlet Xa is chosen and an examination of the velocity, temperature difference, and static pressure at critical points of the service area is performed by means of direct calculations for major operating and climatic conditions of the auditori-

um. REVIEW OF FULL-SCALE TESTS Several detailed full-scale tests of the performance of the air-conditioning and air distribution systems in particularly large and complex projects (designed using the above calculation procedures and studied in small-scale models) were performed by a laboratory in Moscow. These tests provide an opportunity to evaluate the quality of the proposed design method and to demonstrate the principles of design discussed here. Three examples will be briefly reviewed: an indoor Olympic stadium seating 45,000 people (Tamopolsky 1983), an Olympic swimming pool complex accommodating 15,000 spectators (Tarnopolsky 1983), and an auditorium for an audience of 6,100 people (Ovchinnikov and Tamopolsky 1987). Indoor Olympic Stadium Calculations made according to the procedure outlined earlier have shown that the optimum distribution of cold air with minimum air exchange in the sports arena of the indoor stadium is reached when most of the air (1,340,000 m3fh) is supplied at an exit velocity of7.6 to 9.2 m/s with a temperature difference of -9°C. Accordingly, highperformance hinged nozzle diffusers (Tamopolsky et al. 1981a) were arranged circumferentially in the stadium at a height of 30 m under the suspended ceiling, as shown schematically by jet 1 in Figure 8. The cold air is supplied to the stadium through 52 hinged nozzle diffusers by compact streams touching the ceiling. Under the influence of the buoyancy flux, the streams bend downward onto the stadium field at a distance of 36.6 m from the outlets. To prevent stall zones, 32 additional diffusers with hinged flanges (Tamopolsky et al. 1981b), located under the lighting gallery (see jet 2 in Figure 8), deliver 192,000 m3fh of air at a velocity of 7.6 m/s and a temperature difference of -9°C to the central part of the hall, and 64 conical diffusers (Tamopolsky et al. 1981c) and 80 anemostats (Trox 1991) installed in the suspended ceiling (see jets 3 and 4 in Figure 8) deliver 493,000 m3fh of air at a velocity of 6 m/s and a temperature difference of -6°C to the upper rows of the large and small stands. Most of the air (1,273,000 m3fh) is removed through the wall grilles located between the principal diffusers (see ASH RAE Transactions: Symposia

I

®

X/a26.6

Figure 8

m

Schematic description of the air distribution system in an indoor Olympic stadium.

inlet 5, Figure 8). The remainder of the air is removed through inlets in the steps (see inlet 6, Figure 8) under the seats of the large stands (511,600 m3/h), through the ceiling inlets (see inlet 7, Figure 8) in the center of the hall (60,000 m3/h), and through the wall grilles (see inlet 8, Figure 8) at floor level (180,000 m3/h). The adopted air distribution solutions have been checked in a 1:43 scale model of one-quarter of the stadium. Air velocity and temperature measurements, as well as pictures of smoke flows in the model, have shown that supply air flows from the hinged nozzle diffusers to the field and the first rows of the mobile part of the large stands. As for the diffusers with hinged flanges, their flows reached the mobile stands near the partitions. Jets from the conical diffusers supply stable streams to the upper 10 to 12 rows of the large stands, and fan-shaped streams from the anemostats reach the small stands and the balcony. All jet trajectories in the model matched the calculated ones. However, an initial assumption that the conical and fan-shaped jets could be flushed off by a counterflow ejected by the hinged nozzle diffusers has not been confirmed. Both the calculations and the measurements in the model of the average and maximum air velocities agreed

well with the values measured during the full-scale tests (see Table 1). Standard deviations of the air velocities and temperatures in the various zones did not exceed 0.07 m/s and O.3°C, respectively. It is interesting to note that the designed air distribution system made it possible to accomplish some difficult tasks during prolonged operation in the post-Olympic period. One of them was to quickly heat the large hall during the cold period. When the hall was heated conventionally by supplying air into the upper zone at a high temperature, it took about 24 hours to increase the temperature in the service zone by 6°C to 8°C. As the calc'llations and the full-scale test have shown, when air is supplied downward at a discharge angle of about 45°, a velocity of 9 m/s, and a temperature difference of + 1.5°C, the service zone was heated in only two hours. Another task was to create temperatures of about 20°C to 22°C in the mobile stands in the winter, when the stadium field was covered with ice. The problem was solved by creating an air curtain on the bypass track between the mobile stands and the field. Olympic Swimming

Pool Area

Separate air delivery systems were used to condition the sports area and the spectator area of the Olympic

TABLE 1

-

Comparison

of Predicted

and Measured

Velocities

at an Olympic

Indoor Stadium

Zone 0.32/0.64 0.6 0.3 0.25/0.3 0.35 0.32 0.25Number 0.33/1.15 0.310.55 0.65 0.35/0.8 0.27/0.3 0.28 15 0.38/0.9 0.33/0.8 0.33/0.74 0.28/0.56 0.29/0.64 0.45/0.9 Full-Scale Model 13 12 9 11 10 14 16 Zone Average/MaximumAir Velocities (m/s) Calculated

ASHRAE Transactions: Symposia

1205

delivered to the pool in isothermal horizontal compact streams at a velocity of 1.9 mis. About 65 % of the air delivered was removed from the upper zone through grilles in the partitions between the halls, and 35 % was removed from the lower zone at the bypass track level (see inlets 6 and 7, Figure 9). During the Olympic Games in 1980, an additional volume of air was removed through windows at the level of the upper circle of the temporary stands (see inlet 8, Figure 9). In the cold period, the air intake for recirculation was carried out on the level of the air distributors. A similar air distribution was used for the diving-pool hall. The average and maximum air velocities measured during the full-scale tests were in good agreement with the calculated estimates, as shown in Table 2.

Figure 9

Schematic description of the air distribution system in an Olympic swimming pool arena.

swimming pool, thus providing an air curtain between them (Figure 9). Ninety-six diffusers with hinged flanges, installed in a suspended ceiling at a height of 8 to 12 m, delivered 90,000 m3fh of air to the permanent stands at a velocity of 8.3 mis and a temperature difference of up to -9°C in vertical compact streams (see jet 1, Figure 9). A discharge of 110,000 m3fh of air was delivered to the temporary stands at a velocity of 6.0 mis and a temperature difference of up to -9°C from eight conical diffusers and five anemostats (see jets 2 and 3, Figure 9) installed in the suspended ceiling at a height of 5 to 6 m and 3.5 to 4 m, respectively. The curtain between the permanent stands for the spectators and the pool was supplied by two systems (with a total capacity of 41,500 m3fh) delivering air from 20 slotlike nozzles (4.9 m by 0.02 m) located in the upper barrier surfaces of the permanent stands at a height of 3 m upward in flat ,streams at a velocity of 5.9 mis and a temperature difference of +4°C (see jet 4, Figure 9). Two systems delivered 37,840 m3fh of air through 11 grilles in the front wall of the barrier in the gaps between the slot-like nozzles at a height of 2.5 m (see jet 5, Figure 9). This prevented the colder air from the stands from entering through the gaps between the nozzles. The air was

Standard deviations of air velocities and temperatures in the separate zones of the swimming-pool hall did not exceed 0.04 mis and 0.23°C; in the diving-pool hall, they were less than 0.051 mis and 0.22°C, respectively.

Auditorium In the original distribution system of the auditorium being studied, ventilation air was supplied through nonadjustable decorative grilles. On the one hand, air conditions were controlled by varying the volume flow and temperature of the supply air with four air conditioners with a total air capacity of 330,000 m3fh, and, on the other hand, by the redistribution of air between zonal supply ducts. Tests of the air-conditioning system showed a high velocity of air in the service zone and a considerable temperature rise during session activities, indicative of nonuniform air distribution and ineffective use of the supply air. To improve the climatic conditions, a comprehensive study of the air distribution in the auditorium was conducted. The selection and analysis of various schemes for air distribution in the auditorium in view of the existing air supply facilities resulted in the adoption of a zoned air distribution system, which is shown schematically in Figure 10. Most of the air was supplied by long-distance jets through 60 side-wall registers (see jets 1 through 5, Figure 10) into the parterre; the rest was delivered through end-

TABLE 2 Comparison

Zone

1206

-

of Predicted and Measured Velocities

-

at an Olympic

Swimming

Pool

0.22/0.8 0.31/0.72 0.3/0.8 0.28/0.8 0.33/0.7 0.33/0.76 Full-Scale 9 0.31/0.72 10 Zone Number 11 Averagel1\taximum Air Velocities (m/s) Calculated

ASHRAE Transactions:

Symposia

facility's activities and with heat load variations. In addition, annual energy consumption decreased by 25 %. CONCLUSIONS

Figure 10

Schematic description of the air distribution system in an auditorium.

wall registers into the balcony, amphitheater, and pit (see jets 6 through 8, Figure 10). Separate groups of side-wall registers delivered the air into the proscenium, stage, and projector gallery (see jets 9 through 11, Figure 10). The vitiated air was removed through the false ceiling and grilles in the projector gallery and underneath the amphitheater (see inlets 12 through 14, Figure 10). The elaborate scheme for air distribution was investigated on a half-size auditorium model built on a scale of 1/25. The measured values agreed with those obtained by calculation. The results of analytical and model studies were used as the basis for a reconstruction plan. Air supply registers of a new design (Ovchinnikov et al. 1987) were incorporated into the air distribution system adopted for the project. Field tests of the reconstructed air distribution system revealed an improvement of the climatic conditions in the auditorium (see Table 3). Basically, the air velocity in the service zone of the auditorium did not exceed 0.3 mis, compared to 0.6 to 0.7 mls before the reconstruction. The temperature rise during facility activities decreased by 50%, while the volume of air supplied into the auditorium decreased by 30 %. The new air distribution system offered flexibility, enabling a change in the operating mode in accordance with the nature of the

The quality and energy consumption of air-conditioned spaces depend largely on the turbulent motion of the air in these spaces, which is determined by the performance of their air distribution systems. Prediction of this motion for different boundary conditions and heating loads is usually beyond the capacity of most designers, and they are therefore satisfied with an intuitive system design. Consequently, large nonuniformities in comfort conditions are found in many air-conditioned spaces, air quality standards are not always met, and energy consumption is not minimized. This work presents basic calculation concepts based on the author's experience in designing air distribution systems. As shown in extensive full-scale tests, this methodology yields efficient, flexible designs that produce a high level of uniform comfort, together with considerable energy and capital savings. Small-scale modeling of the air distribution system is relatively expensive. Experience indicates, however, that in most cases it is possible to arrive at almost optimum solutions on the basis of analytical calculations. The use of air distribution systems that supply air through diffusers at a high velocity and temperature difference (thus changing their geometric and aerodynamic properties) allows us to create more flexible and economically efficient air-conditioning systems. These air distribution systems enable us to change the operating mode in accordance with the nature of activities in the auditorium and with the heat load variations and, as a result, to reduce the annual cold and heat consumption by up to 25 % . ACKNOWLEDGMENTS

This work was supported by the Center for Absorption of Scientists of the Ministry of Absorption, State of Israel.

TABLE 3

--

Comparison

of Predicted

and Measured

0.21/0.25 0.18/0.4 0.23/0.45 -7.3 0.21/0.4 0.24/0.5 0.25/0.4 21.6/21.8 -4.9 -6.3 0.22/0.44 0.19/0.38 22.3/22.4 21.9/22.0 21.0/21.2 19 21.3/21.5 -4.10.19 -4.1 17 1620 15(m/s) (OC) 3.855 -4.3 Difference Air Velocities Full-Scale 18 Volume 37,820 of 0.21/9.28 Air 105,815 25,290 8,840 55,820 Calculated Average/Maximum Temperature in Figure 10 Temperature (OC) VerticalRegisters

ASH RAE Transactions: Symposia

Velocities

and Temperatures

in the Auditorium

Initial

1207

The help of Professor Michael Poreh of the Department of Civil Engineering, Technion, Haifa, Israel, in preparing this work is gratefully acknowledged.

lu

lx, ly, lz

=

NOMENCLATURE

j Ar

=

for jet along axis X,

Kp

total length of auditorium, m distance from current axis to wall along axis Y, m width of initial jet cross section along axis

Ku

Y,m

Ly, Lz

length of auditorium

m At B

=

Bo

=

Br

=

= width of auditorium for jet along axis Y, m

Bt C Cp D

dlt

dP

=

= = = =

=

g G

= =

Ge

=

Go

=

Gt

= =

H

total width of auditorium, m empirical constant (a value of C = 0.082 is used here) specific heat of air (at constant pressure) round nozzle diameter, mm buoyancy force, created by the temperature-density difference between the elementary volume of the jet and ambient air, given by Equation 29 static pressure difference induced between lower and upper parts of the jet, given by Equation 40 acceleration due to gravity, m2/s total quantity of air moving through cross section of auditorium considered, kg/s quantity of air in considered cross section (given by Equation 22), kg/s quantity of air supplied through diffuser, kg/s total quantity of supply air, kg/s distance from jet axis to floor along axis

M Nd Nr P

=

Pa

=

= height of initial jet cross section along

Hr Hs 1

axis Z, m height of auditorium along axis Z, m height of service area, m momentum flux in cross section of audito-

i

= =

= =

rium, given by Equation 35 ordinal number of elementary jet momentum flux in cross section of auditorium where the inlet is installed

la

=

Ie

= initial momentum flux, given by Equa-

Ie

=

10

=

Ip

=

lr

=

1208

tions 43 and 44 momentum flux of air removal in considered cross section of auditorium, given by Equation 27 initial momentum flux, given by Equation 45 vertical pressure force, given by Equation 39 kinematic characteristic of outlet

ordinal number of jet empirical coefficient calculated from experiments as Kp = 0.132 cofactor of heated jet interaction with ceiling (values of Ku = 1 for the cold jet and Ku = 2°·5 for the heated jet are used in this work) nondimensional discharge cofactors, given by Equations 23 and 24 total number of jets number of diffusers in row in auditorium number of rows in auditorium static pressure um, given by static pressure um where the

in cross section of auditoriEquation 42 in cross section of auditoriinlet is installed

Pd

pressure length scale, given by Equation 55

Ps

axial static pressure injet, given by Equations 47 and 54

Pu

axial dynamic pressure in jet, given by Equation 48 excess heat in jet initial excess heat, given by Equation 46 thermal characteristic of outlet

Qe Qo Qr Qt Qy, Qz

= =

s

=

T

= temperature difference at point considered

Ta Td

= =

Ti

=

Tm

=

To Tr

=

Ty, Tz

=

U

=

total heat load of supply air, kW nondimensional cofactors of excess heat, given by Equations 30 and 31 distance from outlet to cross section of current along jet axis, m

Z,m Ho

=

momentum flux of jet in cross section of auditorium, given by Equation 26 components of momentum flux along axes X, Y, and Z, given by Equations 32, 33, and 34

=

= Ua

=

(given by Equation 13), °C absolute temperature of ambient air, K temperature difference length scale (given by Equation 57), °C temperature difference induced by elementary jet i (given by Equation 5), °C temperature difference on axis of elementary jet i (selected from Equation 11), °C initial temperature difference, °C required value of temperature difference at critical points of service area, °C nondimensional cofactors of the temperature difference, given by Equations 16 and 17 velocity at point considered (given by Equation 18), m/s velocity at critical points (see Figure 1), m/s initial velocity level, m/s

proceeding

from sound

ASH RAE Transactions: Symposia

= =

velocity (given by Equation 12), rn/s Ud velocity length scale (given by Equation 50), rn/s Ue = air-removal velocity in considered cross section of auditorium (given by Equation 21), rn/s = air velocity induced by elementary jet i, Ui given by Equation 4 Um = air velocity on axis of elementary jet i (selected from Equation 10), rn/s Uo = initial velocity, rn/s Ur = required value of velocity at critical points of service area, rn/s Us = velocity "shift" (given by Equation 20), rn/s Uy, Uz = nondimensional cofactors of current velocity, given by Equations 14 and 15 X = distance from jet outlet to cross section considered, m Xl' X2, X3 = distances from jet outlet to critical points (see Figure 1), m Xa = distance from outlet to inlet position, m Xd = geometric length scale (given by Equation 49), m Xl = maximum length of auditorium (given by Equation 53), m Y = ordinate of point considered, m = abscissa of point considered, m Z Zd = trajectory length scale, given by Equation

Uc

59

=

Zt

a {3 -y

-ya

0,

11

!::..Hm

!::..Y, t::..H

!::..Zz

(J

1-20

trajectory deflection, given by Equation 58 = horizontal discharge angle, Rad = vertical discharge angle, Rad = specific weight of air at point considered, given by Equation 3 = specific weight of ambient air = coordinates of elementary jet i in outlet along axes Y and Z = maximum trajectory deflection of jet (given by Equation 60), m = coordinates of current trajectory (given by Equations 37 and 38), m = distance from jet axis to service area (given by Equation 51), m = turbulent Prandtl number (a value of (J = 0.5 is used in this work) = zone numbers in Figures 8, 9, and 10

REFERENCES

ASHRAE. 1991. ASHRAE Standard 70-1991, MethOd of testing for rating the peifonnance of air outlets and inlets. Atlanta: American Society of Heating, Refrig-

erating and Air-Conditioning Engineers, Inc. Baturin, W.W. 1959. Luftungsanlagenfur Industriebauten. Berlin: Veb Verlag Technic. Fortmann, E. 1934. Uber turbulente strahlausbreitung. Ingenieur-Archiv, No. 11, Bd. 5, H. 1, pp. 342-354. Hinze, J.O. 1959. Turbulence. An introduction to its mechanism and theory. New York: McGraw-Hill. Ovchinnikov, P.A., and M. Tarnopolsky. 1987. Air distribution in the Plenary Session Hall of the Kremlin Congress Palace. ?roc. XVIIth International Congress of Refrigeration, Vienna, pp. 41-47. Ovchinnikov, P.A., M. Tarnopolsky et al. 1987. Air distributor (register). Author Certificate, Central Research and Design Institute for Utilities in Moscow, No. 1315751, July 8. Peterson, J., and Y. Bayazitoglu. 1992. Measurements of velocity and turbulence in vertical and buoyant jets. ASME Journal of Heat Transfer 114: 135-142. Sadovsky, N.N. 1955. Moving of air flow by concentrated air supply, pp. 71-85. Leningrad: Research Institute for Labor Protection. Tamopolsky, M. 1989. Air distribution of public buildings. Questions of Equipment, pp. 22-36. Moscow: Central Research and Design Institute for Utilities. Tamopolsky, M. 1992. Design of air distribution systems in air conditioned spaces. Haifa, Israel: Technion. Tamopolsky, M., and N.A. Gelman. 1987. Air diffuser with controlled flow dissector. Air Distribution in Ventilated Spaces, Stockholm, June, pp. 1-12. Tamopolsky, M., S.L. Gomberg, et al. 1981a. Luftverteiler (hinged nozzle diffusers). Deutsches Patentamt . "Babcock-BSH Ag." No. DE 3000514, July 16. Tamopolsky, M., S.L. Gomberg, et al. 1981b. Luftverteiler (diffusers with hinged flanges). Deutsches Patentamt "Babcock-BS Ag." No. DE 3000534, July 16. Tamopolsky, M., S.L. Gomberg, et al. 1981c. Luftverteiler (conical diffusers). Deutsches Patentamt "Babcock-BSH Ag." No. DE 3000554, July 16. Tamopolsky, M., A.Y. Jashkul, and L.L. Leschinskaya. 1983. Efficient and economical systems of air distribution in public buildings. Proc. of the Joint USSR-USA Technical Seminar Internal Utility Systems and Energy Conservation in Residential and Public Buildings,

Moscow, May, pp. 5-32. Trox. 1991. Klima catalog. Vienna.