Jets in Confined Spaces General Description of Confined Flow

Current mixing-type air distribution methods typically consider occupied zone ventilation with jets intercepting its upper boundary. These methods include air supply with vertical jets through ceiling-mounted air diffusers and air supply with inclined jets. They also include air supply with vertical upward-directed jets or horizontal jets along room surfaces. In the latter case, the jet reaches the opposite wall/ceiling and fol­lows room surfaces until it reaches the occupied zone (Fig. 7.35). If the combination of room sizes (height, length, and width) allows such an airflow pattern, this room is considered to be “short.”89 The room in which air jets dissolve before reaching the opposite wall is considered to be “long.” In such rooms, the occupied zone is venti­lated by “reverse” flow. Initially, studies of jets in confined spaces were carried out for mining, chemical, and mechanical engineering applications.3’32’84 In the current chap­ter three methods of air supply in confined spaces are discussed:

• Horizontal jet supply

• Inclined jet supply

• Horizontal jet supply with directing jets

• Vertical jets Experimental Studies of Isothermal Horizontal Jets in Confined Spaces: Airflow Pattern, Throw, Velocities


подпись: (a)

FIGURE 7.35 Jet flow in a room: (a) “short» room; (b) “long” room. Reproduced from Etheridge and Sandberg.90

figure 7.35 jet flow in a room: (a) “short" room; (b) “long” room. reproduced from etheridge and sandberg.90
The first experimental data on confined air jets used for ventilation date back to 1939, when Baturin and Hanzhonkov studied air supply method with

The occupied zone ventilation by “reverse” flow. Later, this method was called concentrated air jet supply. Baturin and Hanzhonkov concluded that the air­flow pattern in the ventilated space depends on the location of air supply out­lets and practically does not depend upon location of air exhausts.110

Studies by Nelson and Stewart,111 Bromley,112 and Gunes11″ provide ex­perimental data on air velocities and temperature distribution for this method of air supply at different room configurations, locations of air supply outlets, and velocities and temperatures of air supply.

The effect of the room length and position and shape of the air supply outlets was studied by Linke.114,115 These studies show that there is a maximum room length that can be effectively ventilated by the supply air jet (Fig. 7.36 a). For the


Hr ISgpr ifiSr

Jets in Confined Spaces


Jets in Confined Spaces
Jets in Confined Spaces
Jets in Confined Spaces
Jets in Confined Spaces

FIGURE 7.36 Flow patterns in rooms of different lengths with various types of air supply and exhaust: (O) reproduced from Linke118, (6) reproduced from Mьller.119 I—(.,/H, = 3; 2—Lr/Hr = 4; 3—L,/Hr = 6; A—schematic of primary, secondary and tertiary vortexes in the room with Lr/H, = 6.

Linear (2-D) air jet attached to the ceiling supplied at the Reynolds number in the range from 1825 through 12 000, the maximum room length does not exceed three times the room width. The rest of the room downstream is poorly ventilated. When the air supply slot is symmetrical (located at 1/2H), the effectively ventilated room length increases to four room widths. Air supply through a round nozzle with a nonattached jet allows the effectively ventilated room length to increase up to five transversal cross-section sizes, (B x of

The room.

The airflow pattern in rooms ventilated by linear attached jets with IJH ratio greater than that for effectively ventilated rooms was studied by Schwenke105 and Mьller.116 The results of their air velocity measurements and visualization studies indicate that there are secondary vortexes formed down­stream in the room and in the room corners. The number of downstream vor­texes and their size depend upon the room length (Fig. 7.36b). Mass transfer between the primary vortex and the secondary vortex depends upon the dif­ference in characteristic air velocities in the corresponding flows 1/, and U2 and can be described using the Stanton number, St:116.

Jets in Confined Spaces





Jets in Confined Spaces

Where x an(i c are empirical coefficients. For the jet spreading along the wall (U2= 0), the Stanton number is equal to 0.01. This approach was used to predict mass transfer between the primary and secondary vortexes and the characteristic air velocities in the secondary vortexes. These pre­dictions were compared with experimental data. Though experimental data deviate from predicted air velocities, the proposed model provides some understanding of the mechanism of mass transfer between different room zones. Average rotation velocity and mass transfer decreases from the primary vortexes to the secondary and the subsequent vortexes.

The influence of room transverse cross-section configuration on air flow patterns created by air jets supplied through round nozzles in prox­imity to the ceiling was studied by Baharev and Troyanovsky117 and Nielsen90 (see Fig. 7.37). Based on experimental data, they concluded that when the room width B is less than 3.5H, the jet attaches to the ceiling and spreads, filling the whole width of the room in the manner of a linear jet. The reverse flow develops under the jet. When B > 4H, the reverse flow also develops along the jet sides. Baharev and Troyanovsky117 indi­cated that air temperature and velocity distribution in the occupied zone is more uniform when the jet develops in the upper zone and the occupied zone is ventilated by the reverse flow. Thus, they proposed limiting room width to 3-3.5Hr

Detailed experimental data were obtained by Sadovskaya nM19 on a phys­ical model in isothermal conditions. She has found that the confined air jet has two critical cross-sections (Fig. 7.38). In the first cross-section, where the ratio of jet cross-sectional area to the area of ventilated space equals 0.24, the jet



Influence of room configuration on airflow pattern: (o) 6/H


3.5: (b) B/h


Jets in Confined Spaces

Reproduced from Nielsen.91

Develops as a free jet. Between the first and second critical cross-sections,

Where the jet occupies 40% of the room cross-sectional area, is the zone of

:onfined jet. Beyond the second critical cross-section is the zone of jet degra­

Dation. Sadovskaya has found that the lengths of all three zones depend upon

The coefficient of turbulent structure a of the jet at the air supply and deter­

Mined empirical equations tor the length of each zone and air velocities in the

Air jet and in the reverse flow:


X » =


Jets in Confined Spaces

FIGURE 7.38 Schematic of air jet in confined space proposed by N. N. Sadovskaya. Reproduced from Grimitlyn.5

In these studies, nozzles with a = 0.07 were used. For the values of pa­rameter (BH/A0)1/2 used in the studies, from 2.44 through 71.5, maximum jet throw is in the range

Xmax = (from 4.07 through 5.1 )JBH.

Based on experimental data from Sadovskaya118’119 and Rozenberg120 as well their own experimental results, Baharev and Troyanovsky117 derived empirical equations to design air distribution with horizontally supplied confined jets.

Studies conducted by Grimirlyn56 led to generalized Eqs. (7.117) and (7.118) for air diffusers with different velocity decay characteristics

Xt = 0.22K. JBH

X2 = 0.31 KjJFR

Xmax = 0.62iCj JBH

For compact jets, and

X-, = 0.1 KjHr x2 = 0.15 KHr xmax = o 3Kjm

For linear jets.

To avoid high velocities in the occupied zone due to direct effect from the supply air jet, and to increase the length of the effectively ventilated zone for a single jet in rooms with height Hr from 4 m to 10 m, Baharev and Troyanovsky117 proposed supplying air from the height h0 = 0.6-0.7Hr.

Effect of Jet Proximity to the Celling

Studies by Sawyer,102 Bourque and Newman,100 and Regenscheit121 showed (Fig. 7.39) rhat a two-dimensional jet supplied from a slot with a

Re = 1.3-3.7x K)6


0 Measurements L bv W. Linke r«j ‘

E 1 e


-Z- h


Jets in Confined Spaces
Jets in Confined Spaces
Zlhn Zld


FIGURE 7.39 Reattachment length xa vs, the distance z from the ceiling surface to the supply outlet. Reproduced from Regenscheit.121


Jets in Confined Spaces

Width h0 at the distance z from the ceiling surface will become attached to this surface at the distance xa given by

^ = 0.2 +2.7f7^l°’8 . (7.119)

»o ho)

Research reported by Jackman122 showed that the effect of proximity of air supply to the ceiling is also important when air is supplied with compact jets. The nonuni­form entrainment from either side of the jet resulted in a force deflecting the jet to­ward the ceiling. The attraction of the jet toward the surface is greater the closer the air supply is to the ceiling and the higher its aspect ratio (grill width over grill height).

Effect of Ceiling Beams or Obstructions in the Jet Zone

Ceiling beams will not affect jet attachment to the ceiling if they are located further than 1.6xa from the air supply outlet.123 If a beam is located closer than 1,6xa, the impingement of the jet on this beam will change the jet direction.

The effect of ceiling beams and light fittings on ventilation jets was also studied by Holmes and Sachariewicz.124 Their studies were limited to the two­dimensional case: air supply through linear slot and a two-dimensional barrier (Fig. 7.40). The results of these studies show that the ceiling jet can take one of three courses when it encounters an obstruction:

1. Separate from the surface and take up a flow angle approximately equal to the angle between the upstream face of the obstruction and the surface;

2. Separate from the surface and reattach some distance downstream from the barrier; or

3. Almost ignore the existence of the barrier.

The jet will separate from the surface if the axial distance between the slot and the obstruction, xd, is less than a specified critical distance xc (Fig. 7.41). The

Jets in Confined Spaces

FIGURE 7.40 Beam influence on the airflow pattern along the ceiling. Reproduced from Holmes and Sachariewitz.124

Values of xc given in Fig. 7.41 are only for an obstruction of transverse dimen­sion tv equal to or less than the slot span s.

In the second course, the flow downstream of the barrier can be ade­quately represented by a determination of both the maximum separation of the line of maximum velocity from the surface (Fig. 7.42) and the velocity de­cay after the barrier





подпись: vo— xd

Where xd is the distance from obstruction to the slot, 0.5 < w/s < 1.

Obstruction does not affect the jet if the obstruction is further than about eight critical distances (xc) from the slot. In this case the velocity decay of the jet may be obtained from



подпись: v-m


* ~Xr


подпись: wHere b0 is an effective slot width and x0 is the virtual origin of the jet.

Jets in Confined Spaces


|: FIGURE 7.41 Critical distance xc from the slot to the beam: b — width of two dimensional slot, d = beam height, x0 = jet core zone length. Reproduced from Holmes and Sachariewicz.128

Although the tests were conducted only for two-dimensional cases, the authors suggest that their results can be extended to three-dimensional cases as follows:

• If the obstruction span is less than half the slot span, the effect of obstructions can be ignored provided xd > xc,

• The value of xc for a short barrier will be less than for a long one and it will be safe to use the values obtained in the studies.

• The velocity decay downstream of a short barrier may be represented by

2.211 -0.785-U/2

подпись: 2.211 -0.785-u/2


подпись: 'o1/2

, (7.122)

X — X(j

V° , , where 0.5 < s/w < 1.

• If the barrier is longer than the slot, the flow will be deflected at right angles to the normal jet trajectory, causing a possible thinning of the jet at the barrier and increasing the critical barrier distance. It is not possible to estimate accurately the extent of such an increase from the studies of two­dimensional situations. The authors consider that such an increase will not exceed 100%.

Graphical interpretation of the factors influencing the critical distance xc from air supply to the linear obstacle with a height dc for air supply through a slot diffuser with height h0 and for air supply through a round nozzle with outlet di­ameter d0ns are presented in Fig. 7.43. Nonisothermal flow has an influence on

Jets in Confined Spaces

0 0.01 0.02 0.03 0.04 0.0.5 0.06 0.07 0.08 0.09 0.10 0.U


Jets in Confined Spaces

FIGURE 7.42 Maximum jet separation ym from ceiling: b = width of two-dimensional slot, b = beam height, x0 = jet core zone length. Reproduced from Holmes and Sachariewicz.128

The critical distance, and Archimedes number, Ar, is an important parameter to­gether with the geometrical relations.125 Ventilation with cooled air increases the effect of obstacles, and warm air supply decreases this effect.126’127

Air can be supplied in rooms by one or several jets. Air supply openings can be located along one wall—parallel air jet supply (Fig. 7.44a)-—and/or on opposite walls—contrary-directed jets supply (Fig. 7.446). In special cases air can be supplied in a fan-type manner (Fig. 7.44c).

Air circulation with a parallel jet supply is illustrated in Fig. 7.45. Jets are located at distance t from each other, and each jet forms return flow similar to that induced by a single jet in the room with a width В = t. Thus, in the case of N parallel jets, the room should be considered divided into several zones with a width В = BT/N, separated from each other by airtight walls.

Jets in Confined Spaces

0 20 40 60 80 100 120

Jets in Confined Spaces
FIGURE 7.43 Critical height of an obstacle dc vs. distance from supply slot with a height h0 (a) and supply nozzle with diameter dc (b) Reproduced from Nielsen.12’ Analytical Studies

Abramovich3 was the first to study axisymmetric confined jets analyti­cally. He suggested the method based on utilizing the equations of continuity and momentum conservation. He also assumed that the width of the layer of a jet mixing with a counterflow equals the width of a free jet with a velocity dis­tribution according to Schlichting’s formula:


подпись: (7.123)V ~ Vtev V*~

Where b = 0.22* — half of the free jet width.

Analytical methods suggested by Shepelev and Tarnopolsky,128 Grimitlyn and Pozin,129 and Sychev and Volov130 differ from the one described above only in the way the authors described velocity distribution in the mixing layer:

• Shepelev and Tarnopolsky:

-IU — f

‘ ^rev _ Ј ^{CXJ


подпись: 3ih



Jets in Confined Spaces Jets in Confined Spaces(b)

—— ^
———————- -/.< i*m——————- —
Jets in Confined Spaces
Jets in Confined Spaces
! /
^ ! / ^
» / !
/ 1

Jets in Confined Spaces

Jets in Confined Spaces

FIGURE 7*44 Schemes of room ventilation with parallel jet supplied from the same wall (o), from opposite walls (b), and in a fan-type manner (c). Reproduced from Baharev and Troyanovsky.117

«t ‘-H — -‘ ‘ —

S S — « _ 1- i — O-vN X

I 1 1 C • _ ‘ 11 v



-> » l V V — / / . I s

— ” i — — “
— — •
‘ /


‘■ :■
I Fc—.


— — ^ ‘cvc /
N » > u-L
. AVvlr——————- VJ)) ‘
Jets in Confined Spaces
Jets in Confined Spaces

Jets in Confined Spaces

FIGURE 7.45 Room ventilation by parallel jets. Reproduced from Regenscheit. ( 1975)

Grimitlyn and Pozin:



Jets in Confined Spaces




Sychev and Volov:

Y 2
V — vr,
= 1-6
Jets in Confined Spaces




It is assumed in the above-mentioned methods that the influence of confined space on the supplied jet can be described by the reduction of the axial component and the value vKV, as for jet development in the counterflow. The value of v[ev is as­sumed to be the same throughout each cross-section but variable along the jet length. The value of vKV can be found from the continuity equation, which in the case of jet distribution in a space of cylindrical shape can be presented as


подпись: (7.127)Vr dr + vrev(R2 — rl) = 0

For air supply and air exhaust located in the same wall and for air supply and air exhaust located in opposite walls.

According to Shepelev and Tarnopolsky128 air velocity on the axis of the jet at the distance x from the outlet for air supply and exhaust located on the same wall can be calculated from

1 R

21 cx

1 — exp


Jets in Confined Spaces

And the maximum (in the cross-section) velocity in the reverse flow can be cal ­culated from

1 — exp


R 0
VKV = v0 V 7rr^





Jets in Confined Spaces


Velocity in. the reverse flow reaches its maximum value at x* = 4.88R equal to


The equations presented above can be applied to spaces of rectangular shape by replacing ttR2 by BH.

A similar approach was used by Zhivov131’132 in his studies of sys­tems of coaxial jets in confined space. The distance x from the air dif­fuser to the cross-section with a maximum velocity in the reverse flow for the case without coaxial jets was found to be 1.9(BH)0-5 at K, = 6.2, and 1.4(BH)°-S at Kl = 4.5. For a nonisothermal jet, it was also found132 that the reverse flow and confining surfaces increase the upper limit of the cold or heated supply air temperature A?0, which ensures a horizontal jet projection.

The results of different analytical and experimental studies of the con­fined horizontal jet described above are presented in Table 7.17. The main reason for the differences in the analytical results is different approxima­tions of reverse flow velocity profiles.

The influence of the reverse flow on the centerline velocities vxc was proposed1 to be expressed by the coefficient Kn

VXc = »xKc,

Which, as was shown above, can be derived analytically. The value of Kc de­pends on the ratio of the cross-section area of the free jet and the correspond­ing cross-section of the room. The graphs for evaluating Kc for compact, radial, and linear air jets are presented in Fig. 7.46.

7.4.S.4 Experimental Studies of Horizontal Heated and Cooled Air Supply in Confined Spaces

Gobza134’135 studied air supply with concentrated jets on physical models and in the field and concluded that temperature stratification along the room height may occur if improper supply air temperature difference and air exchange rate are selected. Among the field cases reported by Gobza are industrial halls as long as 150 m (at width equal to 50 m and height 12-15 m).

The effect of supply air temperature on jet behavior in confined spaces was studied by Miillejans.48 Studies of cooled air jets were conducted in rooms with a size from 1.0 m x 1.0 m x 1.6 m to 2.27 m x 3.33 m x 5.31 m with an air supply through the slot (b = BT) or rectangular opening (b«Br). Numerous smoke photographs were taken reflecting supply situa-

Jets in Confined Spaces

Jets in Confined Spaces
X/tKj-fА,) Kj-‘Vx/Ho

(c) ‘

Jets in Confined Spaces


Jets in Confined SpacesM FIGURE 7.46 Coefficient of confinement: (a) compact jet, Ar — B x H; (b) linear jet; (c) radial jet, Ar — B x L Reproduced from Grimitlyn and Pozin.137

Tions with different Re and Ar numbers. Archimedes number was defined by Miillejans as

Ar = (7.131)

V~(Tir + T0)/2

Where v = Q0/(BrHr) [m/s], 0W (Tw), 60(^o) ~ wa^ an<^ supply air temper­atures [°C, K], g = acceleration due to gravity, and Dh is the hydraulic diameter,

P> — 4 BrHr man

Db~ 2 (b;+hx {/A^‘

Miillejans has reported that with air supply through rectangular openings the jet behaves more or less as an isothermal flow when Ar < 104.

To establish a criterion for any size room and outlet, the Ar number was

Bobo 2 ‘ h

подпись: bobo 2 ' hAdjusted using a geometrical factor. The modified Ar* was defined as

Ar* = Ar-—-5^ . (7.133)

With a common value of b0h0/D| = 1/250, the airflow pattern will be similar to isothermal with a modified Ar* number limited to 40.

In the case of a room ventilated by a linear jet, this jet deflects toward the ceiling immediately after entering the room. Maximum Ar values depend upon the L/H ratio and are shown in Table 7.18.

Experimental studies conducted by Grimitlyn56 on heated and chilled con­fined jets showed that the airflow pattern remains the same as for isothermal










2.0 10 000


1.0 11 000


Air supply when Arx < 0.2 at x = 0.22K{(BH)°-S, in rooms with H/B ratio from 0.3 to 1.0, where

‘ Kf «iT,„ (,/M ‘ ‘

The above limitation on the local Archimedes number results in the fol­lowing equation for maximum temperature difference of supplied air:

Vn [An

Д0О = 122^|. (7.13.5)

Similar studies were conducted by Troyanovsky,136 who concluded that to maintain the airflow pattern in rooms with heated or cooled air supply as in isothermal conditions, it is necessary that the rise of horizontally supplied jet does not exceed Ay = 0.1 BH at the distance from the outlet x = OASK^BH)0-5. From this assumption the following equation for the max­imum air temperature difference was derived:

Ле0 = 1300^-^. (7.136)

Comparing Eq. (7.135) to Eq. (7.136), one can see that the value of the maximum temperature difference computed using Eq. (7.136) is higher than that determined using Eq. (7.135). Results of experimental studies on physical models1 indicate that when Н/ В > 1, the limitation on supply air tempera­ture difference should be even more restrictive. The Effect of Confinement on Inclined Air Jets

The investigations of horizontal and inclined air jet trajectory, velocity, and temperature decay under buoyancy discussed in the previous section were conducted with free (nonconfined) jets. Only limited research data is available describing the behavior of inclined jets in confined spaces. Studies by Regenscheit70 of horizontal cooled air supply from linear and rectangular openings can be related to this topic. Graphs in Fig. 7.47 show how the rela­tive distance x0/ L from the supply opening to the point of jet impingement with the floor surface is influenced by the modified Archimedes number Ar:

Ar = .iL4Jo4(^>3 , (7 137)

TmQi2(B + H) ( ‘

Other experimental and analytical studies of nonisothermal inclined jets in con­fined spaces were carried out by Zhivov.88 Experimental studies were conducted on the physical models. The ratio of the model dimensions L x В x H was changed so that the value Н/ В was from 0.3 to 3.0 and L/(B xH) = 2.4-4.9.

Visualization of airflow in the room with smoke and silk threads was used to describe airflow patterns in rooms with inclined jet supply. Airflow created

103 2 3 4 5 104 2 3 4 5 105 2 3 4 5

Ar ——— —


FIGURE 7.47 Nonisothermal jet trajectory in a room. Reproduced from Regescheit. 70


Jets in Confined Spaces

By inclined jets impinging on the floor surface can be divided conditionally into three zones (Fig. 7.48): (1) free or confined jet, (2) impingement zone, and (3) flow along the floor. The width of the jet depends upon the supply charac­teristics, which can be primarily described by the velocity decay characteristic Kt. Some air diffusers (e. g., ventilation grills) can create jets with coerced an­gle of deflection only in one direction.

The first zone of the jet can be described using equations for velocity and temperature decay as well as jet trajectory with a coefficient Kc accounting for jet confinement. The impingement zone can be characterized by a significant change in the static pressure and great curvature of the air current lines. After the impingement, the radial flow is formed as if it is supplied from the side surface of the truncated cylinder with a uniform initial velocity of LT*. in the basement of the cylinder, there is a particular line that crosses the quasi source of the radial flow. Equations provided in the paper can be used to evaluate ve­locities along the branches with maximum airflow, minimum airflow, and along the particular line.

When the width of the jet (calculated for free conditions) is less than the width of the room, airflow after jet impingement on a floor is similar to that in noncon­fined conditions. When the horizontally directed flow (along the particular line) reaches the wall, it is divided into two branches: one following the direction of the branch with a maximum airflow and another flowing in the opposite direction.

When the air directed backward reaches the back wall of the room, it flows upward to be induced by the jet within its first zone (Fig. 7.49).

The circulation zone is created above the branch with maximum airflow spreading along the floor. The reverse flow is also induced by the inclined jet within its first zone.

If the width of the jet (calculated for free conditions) at the point of its in­tercept with the occupied zone exceeds the room width, side walls transform the jet as if it was formed by the linear jet impingement on a floor.

In design of air distribution with inclined cooled air jets, the following pa­rameters should be considered: air velocity and temperature at the point of jet

Jets in Confined Spaces
Jets in Confined Spaces




FIGURE 7.49 Airflow in a room with an inclined jet supply. Reproduced from Zhivov.88


Jets in Confined Spaces Jets in Confined Spaces

Intercept with the occupied zone—for practical purposes this cross-section can be considered the border between the first and the second zone of the impinging jet; and velocities along jet branches—maximum airflow branch, minimum air­flow branch, and the branch along the particular line.

The latter information is important in evaluating the size of the occupied zone that can be effectively ventilated by inclined jets. It was proposed88 that the occupied zone of rooms is well ventilated by inclined jets (particularly in industrial rooms with contaminant release) if air velocity in the occupied zone exceeds 0.1 m/s.

The influence of confinement on air velocity um in the flow along the floor can be accounted for with the coefficient Kc

C. m ■

подпись: c.m ■(7.138)

The value of this coefficient depends on the relative height of the flow along the floor hf/Hr (calculated in the free conditions), where

Kc = 1 when hf& 1.1, Kc = 1.79-0.72 hf/Hr when bf- > 1.1. (7.139) Air Supply with Vertical Jets

Air supplied in confined space by downward vertical jets creates a similar flow pattern as in the case of air supply by horizontal nonattached jets. With vertical air supply, the occupied zone is ventilated directly by air jets. Grimitlyn137 suggests that the area of occupied zone ventilated by one jet be sized based on the jet’s cross-sectional area at the point it enters the occupied zone. The jet cross-sectional area and configuration depend upon the height of the air supply, the type of air jet, and diffuser characteristics (Kt and K2).