Direct Vessel Impingement Flow into Reactor Downcomer" Experiment and Analysis

Sang H. Yoon 1, Yun-Kang Park 1, Kune Y. Suh 1, Chul Hwa Song z, Moon Ki Chung z, Seung O h 3

Department of Nuclear Engineering, Seoul National University San 56-1 Shinrim-dong, Kwanak-gu, Seoul, 151-742, Korea Phone: +82-2-880-8324, Fax: +82-2-889-2688, E-mail: kvsuh@snu.ac.kr

2Korea Atomic Energy Research Institute, Taejon, Korea 3EPCO Electric Power Research Institute, Taejon, Korea

ABSTRACT

The direct vessel injection (DVI) into the downcomer is one of the major design features of the Korean Next Generation Reactor (KNGR) emergency core cooling system (ECCS). For this type of the ECCS, however, the patterns and multidimensionality have not yet been fully investigated for the flow in the downcomer during a loss-of-coolant accident (LOCA). Also, the experimental and analytical studies on the hydraulic phenomena are not complete enough to allow for detailed design of the system. One of the important phenomena is the impingement by the ECC injection flow. To investigate the behavior of flow such as the impingement, it was necessary to first understand the injected flow motion on a vertical fiat wall with well-defined boundary conditions. Experiments were conducted using two acryl plates to measure the flow width. Results of the measurements are easily understandable. The flow width increases downstream. As the injection velocity increases, so does the flow width. The outer boundary of the fluid flow is thick. Also, the greater the injection velocity, the larger the flow width and the smaller the average film thickness. In an effort to understand the impingement flow characteristics observed from the tests, a simplistic numerical code was written to analyze the hydraulic behavior relevant to the fiat plate flow pattern. In reactor applications, flows from the four DVI lines may get in touch with one another, and thicken to interfere with upcoming steam to the extent the flooding characteristics in the downcomer may change. Experimental and numerical results shed light on the width of the DVI film flow, which is pivotal in determining the steam flow passage and subsequently the amount of ECC bypass due to flooding and entrainment.

INTRODUCTION

The LOCA analysis for the DVI system is geared to optimizing the ECCS performance for the KNGR. The KNGR that has a DVI configuration with four nozzles at the upper part of the reactor vessel downcomer is an advanced light water reactor (ALWR), whose design shares similarities with the ABB-CE System 80+. The DVI system which is located approximately 2.1 m above the centerline of the cold legs is planned to be adopted in the KNGR, while the involved thermal- hydraulic phenomena [1] are not yet fully known. It is presently considered that the downcomer ECC flow behavior is strongly governed by the location of the ECC injection nozzles. The impingement in the reactor vessel downcomer is one of the unknown important phenomena during a LOCA. There is thus a strong need to find how the injected flow strikes the inner downcomer surface and how wide the liquid film spreads by the impingement phenomena [2]. The experiment was designed to simply observe the expected flow behavior on a flat plate [3] linearly scaled down to 1/10 of the prototype. The low-velocity injection tests were carried out in the DVI impingement experiment. The DVI impingement tests were conducted to determine the annular passage for up and transverse flow of the superheated steam from the core and the cold legs, and to estimate the amount of penetration of the subcooled ECC water from the DVI system [4]. During reflood, the tests were conducted to observe how wide the injected water from the safety injection (SI) pumps spreads.

In this work numerical and experimental studies are performed on the spreading flow width of the DVI water being horizontally injected on the vertical flat plate varying the water injection velocity, the gap size and the pipe diameter. Results of the numerical analysis are obtained from the potential theory, the continuity and momentum equations for the two- dimensional (2-D) flow. Results of the experiments suggest that the relation amongst the injection velocity, the pipe diameter and the gap size turns out to be rather complex. The experimental results shed light on the width of the DVI film flow, which is pivotal in determining the amount of ECC bypass versus penetration due to flooding and entrainment.

NUMERICAL ANALYSIS

Impingement Region Coleman and Richard [5] investigated the boundary between the impingement region and the wall jet region for the

impingement phenomena as shown in Figure 1. Their results yielded the pressure distribution on the flat plate around the stagnation point in Figure 2. They showed that the radius of the impingement region is about 1.8 times that of the nozzle, viz.

rboundary = 1.8 × rradius (1)

The potential function of the impingement region is well described by a logarithmic function just like a line source in two dimensions. The gravity effect is ignored in the impingement region because the velocity of the impingement region is very high while the cross-sectional area of the flow is small. Thus the square of velocity is proportional to the potential logarithmic function, i.e.

V b . . . . da,-y --" ~ / 1 o g rboundaly / l o g rnozzle X V 0 (2) The impingement region is depicted in Figure 3 as seen from below.

2 r.o~zle

K21

oe,et e ,on / i / { Wall jet region

region . . . . . . . . . . . . -[ . . . . . . . . . . . Imping . . . . t ~ ~ 2 ~ j

S t a g n a t i o

P/Po J

0 .98

0 .96

0 .94

0 .92

0 .9

0 .88

0 .86

0 .84

0.82 0.8

I Po" the pressure at the stagnation point I

0 0.5 1 1.5 , F/Fnozzle 2

Figure 1 Flow Configuration Figure 2 Stagnation Region Pressure Distributions for Flat Surface (Taken from Reference 3)

m rnozzle

l"boundary Vboundary

l !

Figure 3 Impingement Region, Plan View

Wall Jet Region The gravitation and the friction are the important factors in the wall jet region as shown in Figure 4 [6]. Thus the

momentum equation may be written as dV

p ~ = - V p + pg + Ff,.iction (3a) dt

Since the pressure-gradient factor is zero in the wall jet region, Equation (3a) may be simplified as follows dV

p__~_ = pg + Ffriction (3b)

If the fluid is incompressible, the continuity indicates that the volume flow is constant. Thus 1

V c r : - z

Hence,

dV ~ g(dV)2 Ffricti°n -- ~ - ~ Z (4)

Vy+ dy

m _

Ffricfion

dy 4 tion .........""

v/ ..... ,.//""

I.. vy 2. P dx

Figure 4 Infinitesimal Area in the Wall Jet Region

In the rectangular coordinate system, Equations (3b) and (4) yield the following expressions"

. , a~o~0 dL '(dLv)2 - - - - = C O S 0

dt p

dV, ~ (dVov ): a - a s i n O - =-T--- s i n O - g Y dt p

where

d. I/V +Vx+dx/ 2 +/Vy+Vy+dy} The minus sign is for downward flow, while the plus sign is for upward flow, respectively, in Equation (5b).

Computation Equations (5a) and (5b) must be modified for numerical calculation as presented in Table 1.

Table 1. Modifications for Computation

Vx Vx(n) Vy Vy(n)

gx+dx gx(n+ 1) gy+dy gy(n+ 1)

After all, Equation (5a) reduces to

dy 2

or

Vx n+m Vx n : ] dX/dt dt 9 2 2 I(dX~dt ~ + (dY~ddt) 2

If the time interval, dt, is very short, following approximations may be made"

Vy(n+l ) -t- Vy(n ) Vx(n+l) --I-Vx(n) .~ Vx(n) , ~ Vy(n ) 2 2

The above equations may be rewritten as

(5a)

(5b)

V x ( n + l ) - V x ( n ) = ~ IV x 2 2] Vx(n) dt P (n) -b Vy(n ) (6a)

gx(n.+l) -- Vx(n) dt P (n) °r- Vy(n) )

- - I ~ /Vx(n) ' l -Vy2(n)"Vx(n)] d t + v x ( n )

Equation (5b) may be transformed using the modifications in Table 1 as

/ 2 2 Vy(n+l) Vy(n) - g E ~/ Vx(n ) .4_ Vy(n ) . Vy(n ) _ g dt p

Vy(n+l ) __ . . T E / V 2 2 (6b) P 3~/ x(n) nt- Vy(n) "Vy(n)dt- gdt + Vy(n ~

Values for Vx@ and Vy(0)are obtained by analysis in the impingement region. The flow pattern on the fiat plate can be drawn through summation of Vx(n)dt and Vy(n)dt as

X = EVx(n,dt

Y = ZVy(n,dt (7)

EXPERIMENTS

Experimental Method The experimental facility consists of the 2-D acryl flat plates, the water supply pump, and the digital camera for

measurements. Figure 5 shows a schematic diagram of the test rig. The two acryl plates were used for visualization inside the variable gap in-between. The water injection nozzle was located in the upper part of the front flat plate. The injection flow rates were determined by referring to the KNGR design parameter from 10 to 30g /min. To investigate the parametric effects of the injection velocity, the gap size, and the nozzle diameter, sensitivity analyses were conducted to obtain the spreading film width for the controlling variables.

The spreading width of the injected water was measured from the images on the digital camera, which had recorded the thin grid of the resolution of 1 mm vertically and horizontally at the outer surfaces of each acryl plate.

,iiiiiiiiiiii'ii!!iiii:iiiii~ ~ . . . . . . . i!!ii!iiiiiiiii!ii~ v,, i neigh~ i ~1~?i~!~i?i!~1!i!~?i!~?i~[i!;~i;~;~;~;~i~}~i~i~;~i~!;~!~i

ptica c a m e r a 0 cm [ tile width

Figure 5 The Experimental Setup

Test Conditions The geometric test conditions were determined from the linear scaling method since the tests were concerned with the

variable effect of the pipe diameter, the gap size, and the injection velocity. The injection flow rate was fixed at 10, 15, 20, 25 and 30~ /rain, respectively. Tests were conducted at the standard atmosphere and the room temperature of about 10 °C.

RESULTS AND DISCUSSION

Computational Results According to the previous numerical method, the flow width was calculated at each flow elevation for the pipe diameters

of 2.2 and 2.54cm. Figure 6 illustrates results of the calculation for the expected flow pattern for the pipe diameter of 2.2cm given the water injection velocities. Typical calculated results are collected in Table 2 for the maximum width, the flow film width at 50cm below the point of water injection and the maximum height of the impingement region measured from the point of the water injection.

Table 2. Corn )utational Results for the Pige Diameter = 2.2cm

10 43.87 74.70 64.04 8.55 7373

15 65.80 106.30 94.54 15.72 11059

20 87.73 135.38 122.10 24.28 14746

25 109.67 162.02 148.58 33.50 18432

30 131.60 186.30 172.50 42.84 22119

×

i i

Figure 6 The Flow Pattern for the Pipe Diameter = 2.2cm

Table 3 and Figure 7 present the results of the flow pattern for the pipe diameter of 2.54cm given the water injection velocities.

Table 3. Computational Results for the Pi ~e Diameter = 2.54cm

32.91 42.70 36.42 4.16 7373

49.36 60.72 52.02 6.41 11059

65.82 78.06 67.50 9.40 14746

82.27 94.72 92.54 12.99 ! 8432

98.73 110.70 98.30 17.06 22119

115.18 126.02 112.28 21.47 22119

x

i ..........................

×

2?°272

Figure 7 The Flow Pattern for the Pipe Diameter = 2.54cm

i ..............................

Experimental Results Figure 8 shows the flow spreading width with the test conditions given in Table 4 for each flow rate. The pipe diameter

is 1.7cm and the gap size is varied as 17, 20 and 25mm. If the injection flow rate increases, the flow spreading width increases accordingly, as expected. The Reynolds (Re) number puts a limit on the width increasing ratio, however. For Re exceeding 22,000, the flow spreading width does not increase appreciably because of the number of droplets formed by breakup of the water jet at high enough Re.

Table 5 and Figure 9 illustrate the relation between the spreading width and the vertical locations for the pipe diameter of 2.2cm. In comparison with Figure 8, the impingement phenomena were affected by the gap size and the pipe diameter. If the gap size increases at the same velocity, the spreading flow width slightly decreases. Also, the spreading width greatly decreases at the bottom of the flow film, if the pipe diameter increases from 1.7cm to 2.2cm.

Table 4. Experimental Conditions for the Pipe Diameter = 1.7cm, Pipe Area = 2.27cm ~

10 73.47 9541

15 110.20 14312

20 146.93 19083

25 183.66 23853

650 -

- r

< 2SO- UJ

c o .

5 o

DIAMETER=17 ram, G A P SIZE=17 m m

~ M A S S FLOW = 15 ~ /rain

^ ~ , MASS FLOW = 2O t /rain

, ~ 7 , : . . 7. , 2 . : . . . . . . . . . . . . . . . . . . .

., .

,.

-55 -50 .45 -40 -35 -30 -25 -20 -15 -10 -5 0 5

H E I G H T ( m m )

6 5 0 .

-

_ 3 5 0 -

300-

250 .

c o -

5 o

! METER= 17 turn GAP SI = 2O m m

~MASS FLOW = 15 t /m in

- , MASS FLOW = 20 ~ /m in

. . . . . I - - - - M A S S FLOW = 25 t /m in " ' * ' - ~ .

-55 -50 .45 .40 -35 -30 -25 -20 -15 .10 -5 0 5

H E I G H T ( m m )

e 5 o .

55o .

~ , 50o .

4 5 0 .

i 4 0 0 .

35o .

a o o .

250- UJ r r a . 200• co

150.

1oo.

so

D IAMETER=17 ram. GAP SIZE=2S m m

~MASS FLOW = 1 0 t /m in

~ M A S S FLOW = 15 t /rain

-. ~ , MASS FLOW = 20 ! /rnin

. ~ - - M A S S FLOW = 25 t /m in "':".':"'.-': ::. ._

:. :: . . . . . . .

• 55 -50 -45 -40 -35 -30 -25 -20 .15 -10 .S 0 5

H E I G H T ( m m )

Figure 8 Spreading Width vs. Flow Elevation According to the Flow Rate and Gap Size (Pipe Diameter = 1.7cm)

Table 5. Experimental Conditions for the Pipe Diameter = 2.2cm, Pipe Area - 3.80cm z

i~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~::~.~:?:::~:~:~:~:~:~:::~:::::::::~ ............. ~ ......................... :::::::::::::::::::::::::::: ................................................................ ::::::::::::::::::::::::::: .................................................. ~ .............. :::::::::::::::::~:::::::::::::::::::::::::::~:::::::::::~:~:~:::~:::;:~:::~:;:::~:U~:;:::::~..~:~:~:::~:~:::~::.:.~.;:~:i:~:::::~:~:::~:::::~:i:::~:::h.::~:i:~:~:i:~:~:~:i:;:::~:~:~:::~::~:~:::~:::::::::::::::::~:::::~ ............................. u,::l:.:: ................................................................................................... : ................ ~ ................................................................................................................. ~ ................................................................

10 43.87 7373

15 65.80 11059

20 87.73 14746

25 109.67 18432

30 131.60 22119

6 5 0 -

6 0 0 -

s s o .

~ . 500 -

E 4 5 o .

- r 4oo - t--

Q aso -

3 0 0 -

2so-

r t n 200- cn

l s o .

I 0 0 -

50

DIAMETER=22 m m GAP S I Z E = t 7 m m

~ M A S S FLOW'= 10 t /rain

- ~ MASS FLOW = 20 t /rain

- - M A S S FLOW = 25 t /rnin

6S0 -

. . . . . . . . ~ " ~ " " ~ ~ 300 .

~ . " . ' ~ , uJ 2 5 0 .

*-. . r r " . ~ ^ . n

D I A M E T E R = 22 m m GAP SIZE = 20 m m /

~ M A S S FLOW = 10 t /rain

~ M A S S FLOW = 15 I /rain

- • MASS FLOW = 20 l /rain

. -MASS FLOW = 2 5 t /rain

-55 -SO -45 -40 4 5 4 0 -25 -20 - lS -10 -S 0 S

H E I G H T ( r n m ) H E I G H T ( m m )

. . . . . . . . . . . . . . ~ 5 . . . . . . . . . .

DIAMETER=22 rnm. GAP SIZE=25 mm

~ M A S S FLOW - t0 ! /rain

. . . . . . MASS FLOW = 15 t /rnin 6 S 0 - . . . . . MASS FLOW = 20 t /rain

5 5 0 - i m , .

~ - s o o

E 4 5 o

4O0 ' - . . .

350 . . . . . . ~ . .

tu 2so ~ " " ~ . ~ . ' " - " ~ ,

2oo " -

15o

~ o o "~

s o . , . , . , . , . , . ~ . , . , . ~ . ~

H E I G H T ( r a m )

Figure 9 Spreading Width vs. Flow Elevation According to the Flow Rate and Gap Size (Pipe Diameter - 2.2cm)

Just like Tables 4 and 5, Table 6 shows the test conditions for the pipe diameter of 2.54cm. Figure 10 demonstrates that the flow width at the top of the flow film may be neglected at low Re. In contrast, at the bottom of the flow film, the effect of the gap and pipe sizes is significant. The effect of the gap and pipe sizes clearly manifests itself from low Re to high Re.

Figures 11 and 12 show the relation between the injection velocity and the pipe size at the top and bottom of the flow film. At the top of the flow film, the spreading width linearly increases, if the injection velocity increases. On the other hand, at the bottom of the flow film, the spreading width increases logarithmically rather than linearly, because the effect of breakup is amplified. Thus, the spreading flow width converges to an asymptotic value rather than increasing monotonically. The numerical and experimental results are compared in Figure 13.

Table 6 Ex erimental Results for the Pi e Diameter = 2 54cm, Pipe Area - 5 06cm 2

10 32.91 6386

15 49.36 9579

20 65.82 12772

25 82.27 15965

30 98.73 19158.31

35 115.18 22351.36

650 -

~-- soo

E 45o

~3,0! 3oo "T

. ~o

DIAMETER=25 ram, GAP SIZE=t7 mm

~ MASS FLOW = 15 1 /rain - - MASS FLOW = 20 -" Imin - -MASS FLOW = 25 l /rain

" * " • . . , ,6. - . . MASS FLOW = 30 l /rain " - - . . .

. . . . ..

~-. . . • , . , . , . , . , . , . , . , . , . , . ~ . ,

6so-

g g 4so:

350-

3OO-

250-

DIAMETER= 25 ram, GAP SIZE = 20 mm ~MASS FLOW = 10 1 /rain

~MAS8 FLOW = 15 1 /rain - ~ MASS FLOW = 2O l /rain • -MASS FLOW = 25 t /min

- - - - MASS FLOW = 30 ! /rain 7":2:L::-::::.:-..:, . . . .

-55 -50 -45 -40 -35 -30 -25 -20 -15 -lO -5 o 5

HEIGHT (mm) HEIGHT (ram)

A

200- ~.. - . , ,, .

15o-

so- ' ~ -55 -50 -45 -4O -35 -30 -25 -20 -15 5

e 5 o -

g

250 t r 2oo a. cn lSO -

01AMETER=25 ram. GAP SIZE=25 mm ~MASS FLOW = 1o Imin

= 15 /rain . . . . . MASS FLOW = 20 /rain

• -MASS FLOW • 25 /rain . . . . . . . = . . MASS FLOW = 30 Imin

. . . . MASS FLOW = 35 /rain

--..<. , . , . , . , . , . , . , . , . , . , . ~ N . ,

-55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5

HEIGHT (mm)

Figure 10 Spreading Width vs. Flow Elevation According to the Flow Rate and Gap Size (Pipe Diameter = 2.54cm)

35o -

E o 25o ,o =

200

15o

._

e

,2 so

I ~p i pe size=17mm, gap size=17mm I 350-

300-

°E 250 . " / 0

• / "~ 200 I" f

/ ~ 15o

-~ mo . 2 " .~

.w " o~ 5o

20 40 60 80 1oo 120 140 160 18o 200

I n j e c t i o n V e l o c i t y (cm/sec)

~p ipe size=t7mm, gap size=20mm size=22mm, gap size=20mm

350 - • ~ . pipe size=25mm, gap size=20mm

°E 2so,

"~ 200.

, ° [ • , 2

50"

20 40 60 ao 1oo 120 140 160 ISO zoo

I n j e c t i o n V e l o c i t y (cm/sec)

~p ipe size=17mm, gap size=25mm ~p ipe size=22mm, gap size=25mm

• " - pipe size=25mm, gap size=25mm

/

. /

.. > J

. . 2 ..~,

• , . , . , . , . , . , . , . . . . 20 40 60 80 100 120 140 160 180 200

I n j ec t i on Ve loc i t y ( cm /sec )

Figure 11 Spreading Width vs. Injection Velocities According to the Pipe Size and Gap Size (1)

700

.~. 650

600

E 550 o

N 300

c 250

200

(~ 15o

I ~p i pe size=17mm, gap size=l 7ram I I

I 700

" / / ~ soo

• ~ N 450

• 400

• J ~ 3so . ' / /

r~ ~ 300

• ~ ~ - 250

200

o~ 15o

. . . . . . . . . . . . 40 " , : o ' 4 o ' ' ' 2 ; o

I n j ec t ion Ve loc i t y ( cm /sec )

I pipe slze=17mm, gap size=20mm ~ pipe size=22mm, gap slze=20mm

. v . pipe size=25mm, gap size=20mm

/ f

'oo2o ' ;o " go " 8'0 " ,~o ' , ; o " ,;.o " ,ao ' , ; o " 200

I n j ec t ion Ve loc i t y ( c rn / sec )

l ~p i pe size=17mm, gap size=25mm size=25mm

• * ~ pipe size=25mm, gap size=25mm 7OO- ~o,o! 600 -

E 55o. , ;~

m o 5oo. , . ' /

~ 35o ~ 3oo-. , , /

, /

-~ zoo " /

~) 150 '

loo 20 ' 4'o ' ' ' ' ' ' " ' ' ' ' ' ' ' " '

I n j e c t i o n V e l o c i t y (cm/sec)

Figure 12 Spreading Width vs. Injection Velocities According to the Pipe Size and Gap Size (2)

E 400

~ 300

u _

C C~ 2 0 0 . _

I:::1. 100 O9

Pipe diameter = 2.2 cm - - Numerical result ~ - ~ Result (gap size=17 mm) at the bottom ot llow film -, - ~ Result (gap size=20 mm) at the bottom ol flow film

- • Result (gap size=25 ram) at the bottom o! llow film .~" ,,o,,

• ° . ,~

f " .

5 0 0

E v

4 0 0

17" 300

. _

200

O. O9

Pipe diameter = 2 . 5 4 cm - - Numerical result

~ Result (gap size=t 7 mm) at the bottom of flow film ~ ~ Result (gap size=20 mm) at the bottom ol flow film

- - - ,Result (gap size=25 mm) at the bottom of flow film

~,S '~'~'- ~ ~

..% ~..~"

,,4, o t

°

I I 1 0 0 1 1 0

i

. . . . . . . . . . 4'o ~'0 go 7o s0 9o 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

Injection Velocity (cm/sec) Injection Velocity (cm/sec)

(a) Pipe Diameter- 2.2cm (b) Pipe Diameter- 2.54cm Figure 13 Comparison between the Numerical and Experimental Results

CONCLUSION

Numerical and experimental investigations on the spreading flow width of the DVI water being injected horizontally onto the vertical flat plate were performed varying the water injection velocity, the gap size and the pipe diameter. Results of the numerical analysis turned out to be rather limited in its applicability because of the restrictions relative to the potential flow theory, the continuity equation and momentum equations for the 2-D fluid flow. Results of the experiments suggested that the relation among the injection velocity, the pipe diameter and the gap size is rather involved. Pursuant to results of this study, the following conclusions may be drawn. (1) The numerical analysis based entirely on the basic governing equations cannot fully describe the experimentally observed

flow parameters. (2) The flow width increases with increasing injection velocity given the pipe diameter. (3) The flow width decreases with increasing pipe diameter or gap size given the gap size. (4) Accurate measurement of the flow width gets extremely difficult if Re exceeds 22,000, which empirically appears to be a

criterion for transition to turbulent flow regime in the injection pipe.

REFERENCES

1. Yun, B. J. et al., "Experimental Observation on the Hydraulic Phenomena in the KNGR Downcomer during LBLOCA Reflood Phase," Proc. of the Korean Nuclear Society Spring Meeting, Kori, Korea, May 2000

2. Kwon, T. S. and Park, K. K., "ECC Water Spreading Width for Flat Plate," Proc. of the Korean Nuclear Society Autumn Meeting, Taejon, Korea, October 2000

3. Mohan, D. D. and Ramesh, H. V., "Submerged Laminar Jet Impingement on a Plane," J. Fluid Mechanics, Vol. 114, 1982, pp. 213-235

4. Hwang, D. H., Air-water mixing experiments for direct vessel injection of KNGR, Master Thesis, Korea Advanced Institute of Science & Technology, Taejon, Korea, 1999

5. Coleman, D. D. and Richard, S. S. "A study of Free Jet Impingement. Part 1. Mean Properties of Free and Impinging Jets," J. Fluid Mechanics, Vol. 45, 1971, pp. 281-319

6. White, F. M. Fluid Mechanics, Fourth Edition, McGraw-Hill Book Co., Singapore, 1999