Callaghan, E. E.

Ruggeri, R. S.

English

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NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
TECHNICAL NOTE 
TN No. 1615

INVESTIGATION OF THE PENETRATION OF AN AIR JET

DIRECTED PERPENDICULARLY TO AN AIR STREAM

By Edmund E. Callaghan and Robert S. Ruggeri 
Flight Propulsion Research Laboratory

Cleveland, Ohio 
Washington
June 1948
U
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
TECHNICAL NOTE No. 1615 
INVESTIGATION OF THE PENETRATION OF AN AIR JET 
DIRECI'ED PERPENDICULARLY TO AN AIR STREAM
By Edmund E. Callaghan and Robert S. Ruggeri 
SUMMARY 
An experimental investigation was conducted to determine the 
penetration of a circular air jet directed perpendicularly to an 
air strewn as a function of jet density, jet velocity, air-stream 
density, air-stream velocity, jet diameter, and distance downstream 
from the jet. The penetration was determined for nearly constant 
values of air-stream density at two tunnel velocities, four jet 
diameters, four positions downstream of the jet, and for a large 
range of jet velocities and densities. An equation for the pene-
tration was obtained in terms of the jet diameter, the distance 
downstream from the jet, and the ratios of jet and. air-stream 
velocities and densities.
INTRODUCTION 
The introduction of a gas or vapor into an air atream.f or the 
purpose of heating the air stream by mixing or burning often neces-
sitates rapid mixing of the gas or the vapor with the air stream. 
The high degree of turbulence created by a jet directed perpen-
dicularly to an air stream offers a means of obtaining satisfactory 
mixing. The jet must rapidly penetrate the air stream in order 
that this mixing be accomplished in a short distance. One method 
of obtaining adequate penetration is the utilization of the kinetic 
energy of a high-velocity jet. 
An investigation to determine the penetration of a high-
velocity circular air jet directed perpendicularly to an air stream 
was undertaken in a 2- by 20-inch-duct tunnel at the NACA Cleveland 
laboratory. The penetration at several positions downstream of the 
jet was determined at tunnel velocities of 260 and 360 feet per 
second for four jet (orifice) diameters and a range of orifice 
pressure drops from 5 to 50 inches of mercury.
NACA TN No. 1615 
APPARATUS AND PROCEDURE 
The experimental investigation consisted of two parts: 
(1) calibration--of the orifices, and (2) measurements of the depth 
at penetration of the jets. 
Calibration of orifices. - Four thin-plate orifices, 1/16 inch 
thick and 0.250, 0.375, 0.500, and 0.625 inch in diameter, were 
calibrated in still air and the total-pressure distribution at the 
orifice plane for each jet was determined for a range of static-
pressure drops across the orifice. 
Measurement of depth of penetration. - The penetration of the 
jet Into the air stream was measured at four positions downstream 
at the orifice center line. At the rearmost position, 20.25 inches 
downstream
', a permanent rake was used that consisted of 22 total-
pressure tubes and 22 thermocouples alternately spaced. 1/2 inch 
apart. An adjustable rake consisting at 24 thermocouples spaced.. 
on 1/4-Inch centers was used to measure the penetration 4.63, 7.94, 
and 14.19 inches downstream of the orifide center line. At each 
position of the adjustable rake, the jet penetrations were inves-
tigated for a range of static-pressure drops from 5 to 50 inches 
of mercury at tunnel velocities of approximately 260 and 360 feet 
per second for nearly constant values of air-stream density. 
In order to facilitate the determination of the penetration, 
heated air for the jet was supplied at approximately 4000
 F by 
passing the air through an electric heater. From the heater, the 
air was passed. Into, a plenum chamber, the upper wall of which con-
tained-the jet orifice, as shown in figure 1. 
The temperature data were recorded on a flight recorder and 
the pressure data were photographed from a multiple manometer. 
SYMBOLS 
The following symbols are used In the calculations: 
a 
	 local speed of sound at vena contracta,, feet per second. 
Dj
 diameter of orifice, feet 
g	 acceleration, due to gravity, 32.2 feet per second per second 
1	 depth of jet penetration Into, air stream at distance a down-
stream, from orifice center line, feet
NA.CA TN No. 1615 
P 	
jet total pressure, inches of mercury absolute 
B	 gas constant, 53.3 foot-pounds per pound per 
a	 mixing distance or distance downstream from orifice center 
line, feet 
total temperature of jet, % 
Vj velocity of jet at vena contracta, feet per second 
V0 velocity of free stream, feet per second 
w	 duct width, feet 
Y	 ratio of specific heats of air, 1.400 
viscosity of jet, slugs per foot-second 
viscosity of free stream, slugs per foot-second 
P	 mass density of jet air at vena contracta, slugs per cubic 
foot 
PO mass density of free-stream air, slugs per cubic foot 
METHODS OF CALCULATION 
The total-pressure distribution across the orifices4ndicated 
a uniform total pressure for a large part of the diameter, as 
shown in figure 2. Because of this uniform distribution, the jet 
velocity Vi was based on the maximum total pressure. The 
velocity Vj and the density' Pj at the vena contracta, or mini-
mum section,were determined with the compressible-flow relations 
for the subsonic or unchoked condition. 
When the static-pressure ratio across the orifice exceeded 
that necessary for choking, the jet velocity at the vena contracta 
equalled the local' speed of sound In the heated air. The jet 
velocity at the vena contracta for this case was determined from 
the following equation: 
Vj = aj =
	
gRTj 44.8
4	 NACA TN No. 1615 
The jet dercity for the choked condition was determined from 
the total temperature and the total pressure by using the following 
equation:
1 
P =
	
0.041218 P j = 0.0261 
RESULTS AND DISCUSSION 
A simple dimensional analysis involving the known variables 
was made and the following result obtained: 
fp j
 Vj Dj\ fVj\ \/js \ /w f
(PJ_j	 ) ) ) ) ) )
This development applies to a circular orifice located in a plane 
parallel to an air stream, as indicated in figure 1. 
In order to evaluate the penetration from the temperature 
profiles, it was necessary to define the penetration as the point 
at which the temperature is 1 0
 F above the free-stream total tem-
perature. This arbitrary assumption was made because of the dif
-
ficulty encountered in determining the exact point at which the 
temperature returned to free-stream total temperature owing to the 
rapid change in curvature of the profiles near this point, as 
shown in figure 3. The variation in the maximum temperature rise 
of the various curves is caused by the change in jet-air tempera-
ture and the change in jet mass flow. 
In order to simplify the analysis of the data, it was neces- 
sary to consider the data in terms of a single jet diameter and a 
single rake position. Thus the mixing distance - diameter ratio 
s 	 and the width coefficient w/D j
 became constant. In addi-
tion, because the jet temperatures were nearly constant, the 
variation of the viscosity ratio p jAio was very small and its 
effect was not considered. In this way, all the parameters except 
the density ratio p j1' the velocity ratio V , /V0, and the jet 
pVD 
Reynolds number ' '	 were eliminated.. The penetration coef-
ficient Z/Dj was plotted as a function of the product of the 
NACA TN No. 1615 	 5 
density and velocity ratios and a single curve was obtained. 
Because no consistent trend In these data could be observed, the 
effect of jet Reynolds number was considered to be small. Similar 
plots for other values of the jet diameter at the same rake posi-
tion yielded a family of curves. The family of curves obtained 
at the 7.94-inch rake station for the four values of jet diameter 
are shown in figure 4. Further analysis of this figure indIcated 
that the member curves were separated. by a factor that was equal 
to JE17i. It was therefore possible to plotpenetration coef- 
ficient against the product of the density _ratio, velocityratio, 
and the previously
 determined factor .J1/Dj
 and to obtain a 
single curve. 
A similar procedure was followad for the ri emaining , rake'sta-
tions and a single curve was obtained for each rake position by 
using the same parameters and factor. It was not obvious, how-
ever, whether the width coefficient or the mixing distance - 
diameter ratio was theprimary variable separating the curves 
because both the width and the distance downstream were constant. 
When these plots were combined, the .family of curves shown In 
figure 5 was obtained. Because the width was invariable, the 
mixing distance was assumed to be the primary variable separating 
the curves • A plot of the penetration coefficient against the. 
product of the velocity ratio, density ratio, and the square root 
of the mixing distance - diameter ratio was constructed and a 
single curve was obtained (fig. 6). Because no consistent 
scatter could be observed in the data, the effect of viscosity 
ratio and jet Reynolds number for-all-the jets is indicated 
to be small for a range of viscosity ratios .Iom 1.5 to 1.9 
and jet Reynolds numbers from 60,000 to 500,000.
	 . 
A factor that probably increased depth of penetration in 
these experiments is the confining effect of the tunnel walls. 
For a range of width coefficients from 3.2  to 8.0, however, no 
effect could be found.. 
An equation that fitted the experimental curve of :fiUTO 4 
has been obtained:
1.65	 p V 
( .)	
=2.91
PO V0 
Curves of the mixing distance - diameter ratio as a function 
of the penetration coefficient for constant' values of the product
6	 NACA TN No. 1615 
of the density and velocity ratios as obtained from this equation 
are shown in figure 7. These curves indicate the actual shape of 
the penetration boundary. 
SUMMARY OF RESULTS 
From an investigation to determine the penetration of an air 
jet directed perpendicularly to an air stream, the following 
results were obtained: 
1. The following empirical equation was determined for the 
penetration coefficient-in terms of the density ratio, the velocity 
ratio, and the mixing distance - diameter ratio: 
()	
=2.911 i4/: 
where 1-is depth of jet penetration into air stream at distance s 
downstream from orifice center line; D j , orifice diameter; P, mass 
density of jet air at véna contracta; p0, mass density of. free-
stream air; V j , velocity of jet at vena contracta; and V 0, veloc-
ity of free stream. 
2. The variation of penetration coefficient with jet Reynolds 
nuniber, width coefficient, and viscosity ratio was found to be 
negligible for a range. of jet Reynolds nubers from 60,000 to 
500,000, a range. of width coefficients from 3.2 to 3.0, and a 
range of viscosity ratios from 1.5 to 1.9. 
Flight Propulsion Research Laboratory, 
National Advisory Ccnrnitteé for Aeronautics, 
Cleveland'' 	 March 9, 1948.
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NACA TN No. 1615
8	 NACA TN No. 1615 
10 
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01	 I	 I	 I	 I	 I	 I	 I	 I	 I 
	
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Distance across orifice, in. 	 - 
	
Figure 2.	 Typical total-pressure profile or jet.
NACA TN No. 1615 
10 . 5 
a. 
S 
5' 
0 
o U. 
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Figure 3. -. Temperature profiles .20 • 25 . inches downstream of 0.625-
inch-diameter jet. 
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• _____// 
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Jet  
diameter 
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NACA TN No. 1615 
- pV 
Product of density and velocity ratios,
p00 
Figure 4. - Variation of penetration coefficient with product of 
velocity and density ratios for various jet diameters. Distance 
downstream from .let s, 7.94 inches.
NACA TN No. 1615 
if
 
1 
/___ 
If)/ 
/ Jet	 Distance 
diameter downstream 
Di	 from jet, s 
(In.)	 (in.) 
 0
	 0.250	 20.25 
0.	 14.19 
7.49 
0	 4.63 
	 0.375	 20.25 - 
R	 14.19 
.7.49 
4.63 
0.500	 20.25 
14.19 
7..49 
4.63 
•	 0.625	 20.25 
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4.63 
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p0v0  
Figure 5. - Variation of penetration coefficient with 
for various values of s.
ic 
E 
4 
PjVj 
POVO
 Dj 
10 
12	 NACA TN No. 1615 
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10	 20	 30	 40 
V 
Penetration parameter, p .i'
	 - 
P0V0
 Dj 
Figure 6. - Variation of penetration coefficient with penetration
parameter. 
p74
Jet	 Distance 
diameter downstream 
Di	 from jet, a 
(in.)	 (in,) 
o	 0.250	 20.25 
0.	 14.19 
A ____
p	 7.49  
'0	 4.63 
0	 0.375	 20.25 
U..	 14.19 
7.49 
4.63 I O	 0.500	 20.25 14.19 7.49 4.63 
0.625	 20.25 
4.	 14.19 
7.49 
4.63
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NACA TN No. 1615	 13 
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Investigation of the penetration of an air jet directed perpendicularly to an air stream

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