A STUDY OF THE PROPAGATION OF A PLANE TURBULENT JET IN FLOW-THROUGH CHAMBER WORKINGS K. Yu. Laigna and E. A. Potter

Continued improvement of productivity of mines and quarries is essential for the further development of the mining industry. One side-effect of this intensification is an increased pollution of mine atmosphere and climatic disruptions of underground workings. This applies primarily to chamber mines with multiface systems, placing stringent requirements on ventilation of mines with distributed working zones and multiconnected tunnel networks. In a chamber workings, air, typically, moves in jets. Chamber workings are often ventilated with plain turbulent jets. In spite of this fact, studies of such jets have not been alone on a sufficient scale [i]. These are still no definitive theoretical and experimental explanations of the aerodynamics of the transfer processes in plane jets constrained by tunnel walls; numerical values of the turbulent effusion of impurities in such jets have not been estimated [2, 3]. Abbot and Klein [4] were the first to study the spread of a planar constrained. They showed that the expansion of such a jet is asymmetric if the confinement ratio of the jet B/b0 > 1.5 (where B is the model width and bo initial jet width). They also found that in a broad range of Reynolds numbers Reb0 = 2.2 • i0 ~ to 5 x 104 this parameter does not affect the jet flow structure at all. Experimentally, the turbulence characteristics in confined planar jets were studied in [5, 6]. In [5] it was shown that the expansion of a planar jet is asymmetrical when B/b0 > 1.25. From published experimental data [4-7] it appears that in open-ended chamber workings a planar turbulent jet depending on the confinement ratio B/h0 may lose stability and begin to spread asymmetrically despite the symmetrical position of the input opening of the jet with respect to the chamber and a uniform initial velocity profile. The purpose of the present study was to determine experimentally the parameters of the microstructures of confined planar jets and to investigate the specific features of turbulent diffusion of impurities in such flows. In studying a turbulent airflow in a flow-through chamber working, three stream zones were identified: jet zone, transient zone, and channel zone. In the first zone a planar jet is in contact with two tunnel walls (horizontal and vertical); it is surrounded by circulation currents on the other two sides. After passing through the transient zone, the jet fills the entire transversal cross section and a ducted airflow begins. We will describe the results obtained by us in studying a confined planar jet flowing from a slot with width b0 = 20, 22, 30, and 42 mm and height H = 150 mm coaxially into the model of a chamber working of a rectangular transversal cross section. The study was conducted in the range of H/B = 1-3, B/b0 = 1.2-5. The support systems in the model in some of the experiments were built as incomplete linings of circular metal pipes of a diameter dK = i0 mm. The longitudinal caliber of the support system, Z/d K, was varied from 3 to 9 (where is the span between support props). The coordinate system was chosen as follows: the x axis was directed downstream the je~, and the axes y and z in the horizontal and vertical directions. The origin of the coordinates was placed at the center of the inflow opening. The averaged and pulsating characteristics of the jet were measured hy a DISA-55 AOI thermoanemometer, as described in [8]. Adjustment factors were introduced when measuring the pulsational characteristics of the jet in zones of intensified turbulence [9].

Civil Engineering Research Institute of the State Construction Agency of the Estonian SSR, Tallin. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 89-95, July-August, 1987. Original article submitted January 26, 1987.

0038-5581/87/2304-0357512.50

9 1988 Plenum Publishing Corporation

357

o,.l o,sI i

x!

o,41

!

"J

o.2!

A4

' .~"

i

I r

~

i

~

J

i

-o,;L 0

.

t,,

o,1

-grs

-a~"

. o

a,r

f

zlv~s

Fig. i. Distribution of dimensionless averaged velocity in transverse cross sections of a plane Jet: a--Btbo-i,2;B=l/7~J; b - - B/bo ~

Bet.o~43,5-:Nn;

3,4: B = " Y ~ ;

X/bo:

R e b o ~ 46,1.10:l;

1--0,05;

2--0,5;

3--1;

4--2;

xlbG: I - - 2,5; 2 - - 5 : 3 - - 8; 4 - - ! t;

$ - - 29.

TABLE i. Influence of B/b0 Parameter on the Propagation of a Turbulent Plane Jet

Blbo

t,2

2,5 3.4 5,0

Shift of the Length of reverse maximum velocity away flow zone from the chain. Ljet Ltr ber axis, y/B

I

llfi ~0.21

~,9.33 ~0,39

o..51 9

5,S

o.51 7.S

22.5

The direction of the flow in the recirculation zone and the boundaries of this zone were defined using a cylindrical three-duct extension pipe with outer diameter of 4 mm. The study showed at B = 1.2 the length of the zone of the flows opposite to the jet are equal to ~3.51b0. The distribution of averaged velocity U/Uot (where Uot is the initial jet velocity) in transversal jet cross sections is symmetrical; the maximum is observed on the model axis (Fig. la). In Fig. la, F B denotes the transverse cross-sectional area of the chamber model. For B/b > 1.5 the symmetrical distribution of U/Uot was violated in the transverse cross sections (Fig. ib). Two zones of opposite flows of different length appeared; as a result, the maximum velocity point was shifted from the axis toward the wall of the chamber (adherence of the jet to the wall). It is seen from Table I that the displacement of the velocity maximum was increased with increasing B/b0. The length of the opposite flow zones was also increased. Outside the jet flow zone the velocity profiles of U/Uot became symmetrical. The asymmetrical propagation of the jet is explained as follows. Velocity pulsations at the edges of the output jet opening cause regular eddy structures. A downstream drift of these eddies results in their consecutive pairwise influences and an intensification of eddy perturbations in shear layers between the forward and inverse streams. The interactions of these ordered structures with the chaotic turbulent background is associated with pressure pulsations which, in confined conditions, result in pressure gradients between the walls of the chamber. The separation of the inverse flow zones formed by the foward flow prevents an equilization of the pressure on the chamber walls; the resulting transverse excess force causes the jet to adhere to the wall chamber.

358

4-?.lul

I i

0,4[

x :

[

02

0,3i

)J

a

I

o.,

w,-,

O,#i +"

,,4

?

' t.t ?, 'tx t o2 AJ 14

!7" L

c

1

Fig. 2. Distribution of longitudinal component of turbulent intensity in transversal cross sections of a plane jet. Notations as in Fig. I. On the basis of the data given in Table i relations were derived for the length of the inverse flow zones in the range of the parameter B/b0 = 1.2-5: a short zone of inverse flows:

Ljet -- 3,58 In p 0,078; t'o %- - -

(1)

L jet + Ltr = t0,32 {ln B~l,s _ 0,09t, b t bo]

(2)

and a long zone of inverse flows:

where Lie t is the length of the jet flow zone, and Ltr is the length of the transient flow zone. Figure 2 gives the turbulence intensity profiles ] f ~ / U

in transverse cross sections of

the chamber. From Fig. 2a we see that during the symmetrical expansion of the jet (B/b0 = 1.2) the turbulence intensity has a uniform distribution at the center of the flow. The maxima of ~f~Uare

observed in the zone of jet flow near the interface between forward and inverse

flows at the chamber wall in the ducted flow zone.

The distribution profiles of longitudinal

turbulence intensity for asymmetric jet expansion are shown in Fig. 2b.

We see that V ~ - ' ] l "

has a minimum at the side of the chamber model (relative to the longitudinal axis), where the maximum of U/Uot is located. In the inverse flow zone, the turbulence intensity in high: 4050%. Downstream the profiles of in a pressure channel.

~P~U

0 become equalized and resemble the picture observed

Figure 3 shows the distribution of dimensionless velocity U/Uot in the vertical direction of the chamber model at B/b0 = 3.4. The velocity maximum is near the wall due to secondary flows, which arise immediately outside the jet opening and attenuate downstream. The chamber support with circular props reduces the asymmetry of dimensionless average velocity U/Uot toward the wall of unsupported chamber at x/b0 = 5 (see Fig. ib) was y/B = 0.35. With a support system of a longitudinal caliber 6, this value was 0.14 (Fig. 4). As can be seen from Fig. 5 and curve 5 of Fig. 2b, the turbulence intensity on the longitudinal axis with a support system is smaller, and near rough wails is greater, than in an unsupported chamber, i.e., a redistribution of intensity takes place. An increase in the aerodynamic resistance of the chamber model leads to an increased turbulence intensity of the jet in its transverse cross sections and reduces the adherence effect. These experimental data on the turbulent structure of planar jets have been used to study the convectional and diffusional transfer of impurities in chamhers. Numerical values of longitudinal jet diffusion coefficient have been estiraated with the use of local turbulence

359

~ I

~

!

I

aver I 0,4

~"

•

Ix i

ol-o,7

!

&! o2

!

I

~

A4us•

X

""

Of

02

x~

j

~j

I

-o,J o Fi.g. 3

"

X/

o,41~ I

"

o,J zl~l~o

I

o,,s Fig.

I

4

Fig. 3. Distribution of dimensionless averaged velocity in transversal cross sections of a planar jet: H=]/~7,; BI!, o = 3 . ~ ;

Fig.

H % 0 * 4."~.'~.10a; x / b , :

4. D i s t r i b u t i o n

transversal

according

x/b0:

4--~:

of dimensionless

cross sections

R%o = 43.2.10:1;

characteristics

I - - 11.2; 2, - - 2 . 5 ; 3--5; a -- 20.

5

It;

averaged velocity

of a planar jet:

I/d1r

in

BII,o='3.4;

I - - 5. 2 - - 1'2. 3 - - 20.

to the methodology

of [i].

The distribution curves of longitudinal turbulent diffusion coefficient for various transverse cross sections of a chamber model (Fig. 6) show that in the jet flow zone D x are not constant. The maxima of Dx are found in the part of the chamber where the m a x i m u m of averaged velocity is located. The maximum D x is greater by two or three orders of magnitude than outside the jet flow zone. In the zone of inverse flows, D x is smaller by 15 to 25 times than its maximum values in transversal jet cross sections. When the aerodynamic resistance of the chamber is increased, the asymmetry in the distribution of D x is reduced, as the adherence of the jet to the wall chamber is lessened (Fig. 7). A support system does not change the longitudinal turbulence diffusion with respect to the transverse jet cross section significantly in the jet flow zone. As seen from Figs. 6 and 7, outside the jet flow zone for a longitudinal support of ~ 6 the coefficient D x is lower by about 10% than in the chamber without support.

caliber

Practical applications of local coefficients D x for calculations of ventilation systems for tunnels are difficult. Based on the experimental data on the distribution of D x, the average D x for various jet cross sections have therefore been obtained by the method of graphic integration:

Dx = ? i e t

D~dF,

(3)

t

where Fje t is the jet

cross

sectional

By a m a t h e m a t i c a l p r o c e s s i n g coefficient Dx i n t h e j e t - a f f e c t e d

~. =

area.

of these data, the following zone ( x ~ L j e t + L t r l :

(.4~ -

A,) exp

[(

"In - ~~ -

--

,

-

-

):]

A2

+

has been obtained

A4.m'/sec

where

( B "~"!/" .,.n.~ \ 4 - ~ o ] ]j' "lle,;o ,

"41 = 4 , S : ~ ' l O - ' ~ A., = In ~.., J t, --

/

l~,b~ 0

"13 - - 2. t 1: -

-

b0

--

0.$3

A4 _-= o 99.10 - I : [ B Re,0)2.03 360

I

for

the

(4)

b o,s,<,~

Y 1,5

0,3

o,z

'I

94

7,0

?

o,5

1

x3 \

x. -o, Js

~7

-o,]s

Fig. 5

o

g cg

~J5

Fig. 6

Fig. 5. Distribution of longitudinal component of turbulence intensity in transversal cross sections of a planar jet. Notations as in Fig. 4. Fig. 6. Variation of the longitudinal turbulent diffusion ratio in transversal cross sections of a plane jet:

B,bo-3,4:x/bo:I

Ret,o=~6.~.~o~;

- -

5:2

- -

12:3

l

- -

,

20;

4

- -

11; 5

--

20.

I

D~, m /se~ I e7

o,5

-o, as

-o,~s

a

o,~s yl4"~a

Fig. 7. Variation of the logitudinal turbulent diffusion ratio in transversal cross sections of a planar jet. Notations as in Fig. 4. Formula

(4) is applicable in the Reynolds number range.

2~.10~
361

The following conclusions were drawn from these results: -- a planar turbulent jet in flow-through chamber workings propagates asymmetrically the confinement ratio of the jet B/b0 > 1.5;

if

the propagation of a planar jet is accompanied by secondary flows arising immediately after the jet opening and increasing the turbulent mixing in the jet; - -

-- an increase of aerodynamic resistance of a chamber working reduces the adherence of the jet to tunnel walls and increases the turbulence intensity averaged over the jet transverse cross section; and the turbulent diffusion coefficient in the jet-affected zone is greater by two or three orders of magnitude than in the remainder of the flow. Contrary to the accepted practice, it is therefore incorrect to use turbulent diffusion coefficients of confined flows for evaluations of the jet diffusion of impurities. - -

LITERATURE CITED i.

2.

o

4. 5. 6. 7. 8. 9.

362

K. Yu. Laigna, Calculations of Convection and Diffusion Transport of Gas Impurities in Shale Mines of the Estonian SSR [in Russian], Valgus, Tallin (1982). Yu. M. Pervov, "Calculation of turbulent-free jets spreading in confined spaces," in: Problems of Mine Aerology and Sudden Bursts of Coal and Gas [in Russian], Izd. Akad. Nauk SSSR, Moscow (1958). I. I. Medvedev and M. A. Patrushev, Ventilation of Potassium and Rock Salt Mines [in Russian], Gosgortekhizdat, Moscow (1963). Abbot and Klein, "Experimental study of subsonic turbulent flows past single and double ledges," Tekh. Mekh., No. 3, (1962). P. R. Nehta, "Flow characteristics in two-dimensional expansions," J. Hydraulics Division ASCE, 105, No. HY5 (1979). R. Smith, "Ducted flow measurements in plane geometrically symmetric sudden expansions," NEL Fluid Mechanics Silver Jubilee. V. A. Arutyunov and Yu. M. Perepelkin, "A study of the propagation of a plane jet in a chamber," Izv. Vyssh. Uchebn. Zaved., SSSR, Chern. Metall. No. ii (1969). J. O. Hinze, Turbulence, 2d ed., McGraw-Hill, New York (1975). C. Gaultier, "Measurement of air velocity by means of a triple hot-wire probe," DISA Information, No. 21 (1977).