C.P. No. 912
/+4213
MINISTRY OF TECHNOLOGY
AERONAUTICAL RESEARCHCOUNCIL
CURRENTPAPERS
Studies
of the Flow Fields Created
Single
Downwards
Vertical
upon
Jets Directed
a Horizontal
M. Cox and W. A Abbon
LONDON:
HER MAJESTY’S
STATIONERY
1967
Price
by
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C.P. No. 912 *
October,
I 964
- by -
M. Cox and 3. A. Abbott
sfiy,,; 4;iy
I-
The velocity
single
surface
and temperature
nozzle discharging
hot pas vertically
have been studied.
amount of recirculation
conditions
in the space surrounding
downwards on to a horizontal
Except at very loii exit
to an intake
a
situated
velocities,
the
on the axis of the jet
away .,.>( 0 i 'li'.c.
5.~
from the axis is indepenknl
of the height of the nozzle above the/*gkund.
2 h13:;;::y L j
These limits
are decided by Yie s;~reod of the jet before it reache'$he
13
\'.
Qf
ground, and by the lateral
ex-Lent of t!le je t before it separates and rxses."
small.
Within
limits
, the d;rnamic head at ground level
is
at a point
from the ground.
A parameter
$erature
its
is used to define
lateral
extent
if
mic head in t!le jet
In transic;nt
the jet
including
it
alon
experiments,
the initial
velocity
both the vertical
strikes
its
of the ~jet and its
penetration
the ground.
The rate
of the jet
temand
of decay of dyna-
axi s and ac?xss the ground has been studied.
the rate
of progress
across the ground has been determined.
Replaces!'.C.T.E. X.3% - n.Fc.c. No5
of the initial
sLx-ead of
-,
2-
COl+TTm;PS
1 .o
Introduction
2.0
Apparatus
3.0
Transient
4.0
Initial
5.0
Steady-state
rate
Horizontal
6.1
6.2
.6.3
Vertical
8.0
Discussion
2;
9.0
velocity
around the jet
6
7
field at ground level
along axis of jet
extent
extent
6
measurements
of jet
flow
Choice of correlating
Experimental results
Effect of temperature
7,.0
8.1
in the field
of spread of the jet
Velocity
Velocity
5.1
5.2
6.0
temperatures
a
parameter
:
ratio
TJ/T,
.
9
of the jet
9
of choice, of parameters
9
Velocity
and temperature ratios
extent of flow
The buoyancy parameter, horizontal
The buoyancy parameter, vertical
penetration
of jet
Conclusions
13
References
Detachable
IO
IO
13
15
abstract
cards
7Title
-NO.
I
List
of symbols
II
The buoyancy effect in flow
impinging, heated jet
III
The buoyancy effect'in
vertically
downwards
spreading
a hotjot
from.an
diroctod
-3-
Fig.
Title
MO.
1
Test apparatus
2
Temperature field
3
Initial
4
Relation betneen velocity
at ground level
anii distanca from axis oi' vertical
jet in
transient
and steady-state
conditions
5
Variation
of velocity
at ground level
related to total pressure at point of
progress
of ~jet across ground
impingement
Variation
horizontal
of velocity
extent
along axis of jet
of ho-: jet at ground level
Relation between jet dynamic pressure and
temperature for constant horizontal
extent
of jet
9
Vertical
extent
of hot jet
10
Separation from the ground. of flow spreading
from impinging jet
11
Horizontal
parameter
12
Calcula.ted
13
Comparison between experimental observation
of vertical
extent of hot jet and theory
extent of hot jet.
Correlating
includes tem;?erature ratio term
penetration
of vertical
jet
-4-
1.o
Introduction
The use of' direct jet thrust for
assisting
aircraft
to take off
vertically
raises a number of problems in operation,
one of which is the
possibility
that the temperature of t!~ie air into the engine intake may be
increased
owing
to recirculation
of ho' L gases from the lifting
jets.
In
the region near the jet exits, where the gases still
have an qpreciable
velocity,
the flow of the gases is dependent on geometrical factors,
that
is, on the relative
disposition
of the jets and adjacent surfaces.
Thus
recourse is often made to model tests'
to investigate
heating effects on
surfaces
of the aircraft,
and it is usual to simulate the full-scale
velocity and temperature of the jet gases.
Temperatures at the engine intake of a few degrees above ambient
can seriously
affect engine performance;
for example, a rise of IO'C may
cause a loss of up to 5 per cent in thrust.
Thus we are concerned in
this respect also with gases which may have recirculated
from more distant
parts of the flow field,
where velocities
are low, and where forces on the
gases due to their buoyanoy become an important factor in establishing
the
flow patterns.
In this situation
it is not clear what the relationships
between the various parameters are which have to be observed yihen simulating full-scale
conditions
in model
tests.
The object of the present
experiments was to study the flov from a single jet directed towards the
ground, particularly
in regard to law of scaling appropriate to the outer
regions of the flow field,
and to investigate
whether recirculation
from
this region, bobh under steady-state
and transient
starting
conditions,
xas affected by the presence of an intake situated just above the jet discharging hot gas,
2.0
Apparatus
A
The set up for the experiments is illustrated
in Figure 1.
~&ply of hot gas was provided by an aircraft
combustion chamber burning
kerosine;
a simple air-driven
ejector was used as a source of subBoth these supplies,nero
ducted through concentric
atmospheric pressure.
pipes to a point zell away from surrounding obstructions
xhere the hot gas
i:as led to a jet pointin
vertically
doxwards,
and the suction pipe terminated in a rounded inlet located above the jet.
The height of the jet
above the floor could be altered by interposing
suitable distance pieces
in the pipes.
Both supplies could be turned on or off suddenly by operating slate valves in the supply pipes.
The temperature of the air around the jet ;:as measured by a rake of
thermocouples.
The couples themselves were made of fine wires about
a.005 in. diameter, and a suction of about 5 in. of water gauge was eqplied
to draw air over the couples to onsure rapid response.
The outputs from
the couples and from a thermocouple located in .tha gas just upstream of
the jet exit
vere
recorded on a sensitive
recording galvanomctor
having
twlve separate
channels.
In many cases, it r:as necessary to warm the pipe leading from the
combustion chamber ta the jet before starting
the experiment proper,
To
do this, an exhaust pipe eras positioned under the jet nozzle, so that the
hot gas was led away from the test area.
Having wrmed the pipe, the
valves were moved to by-pass the hot &as and the exhaust pipe was removed.
-5-
The floor nas smooth cement, but no special preparation
of the surface was made.
Usually, the hot gas nas not allowd
to flow for more
than 30 seconds during a test, and there ;,as no significant
erosion of the
floor.
3.0
Transient
temperatures
in the field
around the jet
The thermocouple rake was erected at various radial distances from
the jet axis and recordings of the temperatures uere made during a
30 second period after
the jet and intake flows vere turned on suddenly.
A thermocouple located just inside the intake nas monitored to determine
the temperature of the air at this point.
So far as could be determined, the temperatures in the region
around the jet and in the vicinity
of the intake ?~ere the same iihether or
not suction uas applied to the intake.
There appeared to be a small
amount of recirculation
of hot gas to the intake region, the temperature
rise being about I to 2 per cent of the temperature above ambient of the
jet at exit.
Observations of temperature close to the nozzle were made
difficult
because there nas always a small leakage of hot gas from the
nozzle when the valve eras closed, and this gas convected upuards and
Yhen the jet was
caused the intake thermocouple readings to fluctuate.
turned on, the readingsat
the intake steadied very considerably,
but all
the thermocouple readings during the test runs showed fluctuations
in
temperature, except when tho couples were directly
in the faster moving
parts of the jet near the floor.
The fact that the temperature fluctuations
in the outer regions
of
the jet field were of a similar magnitude to tiio temperature differences
being measured, meant that it was difficult
to get precise quantitative
measurements.
An indication
of the steady-state
temperature
pattern is
Approximately,
the maximum value of excess temperagiven in Figure 2.
ture close to the ground, 0, varied inversely -;;ith radial distance from
were similar
the axis of the jet and it WE noted that these indications
4
to the measurements of Reeves .
4.0
Initial
rate of spread of the jet
A transient
phenomenon which could clearly be determined from the
temperature records u&s the rate at.nhich the initial
boundary of the' jet
spread across the floor when the jetnas
first
turned on.
The sudden
&fined
on the record, and by placing
change in temperature i;as clearly
the rake in a horizontal
position
just above the floor surface the.time at
Figure 3 show how
which Lhe jot reached a given radius could be found.
these measurements fall on curves in which distance is proportional
to
(time)~n
The curves for the same jetexit
velocity,
but with the height
of the jet above the ground varying in the range
1 to 36 diameters,
are
Results for nozzles with diameters of 2 in. and 1 in. are
the same.
shown.
The curves of Figure 3 give the rate of progress of the jet boundary, u, as the slope of the ourve at any instant,
t.
The curves are of
the form
il
:
ct '
=- ct
=z
(where c is a constant)
-3
2
R
Values of the velocity
u have been obtained from the results in this
nay and are~plottcd
on Figure 40 The velocity
is shown relative
to V
the velocity
of the jet at the nozzle and the distance is related to t ii'e
diameter of the.nozzle.
It is seen that the measurements may be correlated quite well-by this form of non-dimensional plotting.
It was not immediately apparent that the rate of spreading of the
jet should be the same for widely different
heights of the nozzle above
the ground, since it was clear that the ?rcssures in the jet at the region
of impingement nith the ground were vary much reduced as the nozzle height
Therefore, measurements of the steady state velocity
was increased.
field were made.
5.0
Steady-state
velocity
measurements
The dynamic head of the jet.flon
at ground level was measured on a
sensitive
water manometer using a total head probe ;ihich.was held at a
small distance above the ground (usually about 4 to 1 in.) at the height
which nas found to give the maximum pressure reading.
The pitot pressure
at the exit plane from the nozzl c and the pressure close to the ground at
the point of jet impingement were also measured xith the same pitot tube.
Generally, .the jet air was at ambient temperature, and the jet velocities
ranged from 350 ft/s to 1100 ft/sccond.
5;1'
Velocity
field
at ground lcv&
_.
A non-dimensional
plot of the measurements is shown on Figure 4;
the squnre~root of the ratio of the dynamic pressure reading to the dynamic pressure at the jet exit,
(q/43)5, is equivalent to the velocity
ratio
V/VJ for isothermal,
incompressible
conditions.
The readings lie.close
to a characteristic
for all heights in the range Z~DJ = 1 to 36, all jet velocities
and two
That is, within limits
the velocity
at a point near
nozzle diemeters.
the ground awey from the jet axis is a fixed proportion
of the jet exit
-7velocity,
irrespsctivz
of the hoi&t
of the nozzle above the pound,
Fear the axis of the jet, the velocity
does vary nith tho height of the
nozzle above the ground.
If, alternatively,
the dynanic pressure q is relattd
to q9, the
pressu:c at ground level on the axis of the jet, and Dlottod agalnst
radir.1 distance as shoirn on Yii;ure 5, the proportionality
is different
for each nozzle hci Qt so that the str.aight-line
chzractcristics
intercopt the axis (q/q TF = 1 at vnlues of R/DJ ;:hich increase with height.
Those distances mi&t be termed "effective"
diamiturs
of the jot at
impingement; that ins
A fen tests rierc made with the get heated to about 300°C, end these
confirmed that the relationship
(q/q~)" to (R/DJ) was ths eczmees when the
jet 'was at ambient temperature.
Zeferring
again to Figure 4 it is seen that the rete of adv,znce of
the initial
nave, u, is about one qulrtcr
of the final steady velocity
appropriate to each rndiai station.
5.2
Velocity
along axis of jot
The decay of dynamic prc ssuro c.long the axis of the jet t-193
measured irith the jet exit at several heights above ths ground,
Figure 6.
After an initial
distance over which thcrc is little
change,
the velocity
decreases lintzly
with distance.
The vclue of k is between 6 and 6.5 which is similar
to that reported by
Squire2~3 and othcr~ .
It also apTears that the dynamic pi.essure at the
point of impingcmont is the saw RS the vrlue at that axial distance in
absence of ground effect,
On the same graph, tho "eff;ctj.ve"
diameters of the jet D$DJ at
the various nozzle heights determined from Figure 5 have been plotted to
show that Do hes the same but invcrsc rclntionship
with nozzle height as
the velocity
on the jet axis.
That is
which establishes
the compatability
of the two equations relating
velocity
of the spreading jot v,ith radial distance given above.
the
6.0
Horizontal
extent
of jet
flow
As the jet spreads across the ground, the maximum dynamic pressure
of the flow decreases in inverse proportion
to the square of the radial
distance;
.homever, the temperature.of
the gases near the ground decreases
at a much slower rate, the excess temperature varying in inverse proportion to apprcximately
the first
poner of the distance.
Whi1st.e.t small
radial distances the dynamic presswe of the flog is vary great compared
with the forces;due to buoyancy of the gase.s, in the outer regions the
magnitudes of these quantities
become~opmperable, and the jet flow will
tend to lift
from the ground.
6.1
Choice
ozi^ correlating
parameter
The non-dimensional
parame'ter usually aszociated aith natural oonIt is formed from the
vective processzs is the Grashof number, F.
the first
term is Reynolds.number, the second is
product !k@?x 9;
I-I
the non-dimensional
parameter :Jhich appears in the generalised analysis of
velocity
and temperature fields in a fluid.
'This latter
parameter,
a
rewritten
as .8@3Cp + e is seen to be the ratio between the buoyancy
forces on an element and the viscous shearingforces.
In the present
instance nc are primarily
concerned with the relative
effects of buoyanoy
and the kinetic
forces in the flow SO that a more suitable parameter aould
be
Since velocity
and temperature are related to the initial
values VJ and SJ,
and DJ is a oharaoteristic
dimension of the system, a suitable correlating
parameter for a first
attempt at analysing the experimental results is
6.2
Experimental
results
"The point at which the jet flak leaves the ground was determined by
advancing a sensitive
suction thermocouple hold close to the floor inwards
toaards the jets axis until a point was reached xhere fluctuations
in the
Although
galvanometer indication
shoved the presence of some hotter gas.
the point at which fluctuations
commenced was VC11 defined, its radial distanco from the jet axis v.aried consiierably
in a random way with time, so
that the radial extent. of the jet, R', is an estimate based on a series of
observations made over the space of a minute or so.
The observesions are plotted on Figure 7, vrith the extent of the
jet as the'ratio
R'"/DJ,~~ terms
of the parameter ,derived in the previous
Results are shomn for two sizes of nozzle 1 in. and 2 in.-,
paragraph.
diameter, for jet velocities
from 50 to 500 ft/s and temperature at the
the height of the nozzle
nozzle exit from 63OC to 265Oc above ambient;
exit above the ground ranged from 6 diameters to 23 DJ:
-y-
From the upper graph of Figure 7, where log/log scales are zsed it
is seen that a good epproxim~tion to the course of the points is R /DJ
proportional
to (VJp/fig3 JDJ)"; therefore,
the horizontal
scale has been
chosen accordingly
in the lower graph.
6.3
Effect
of temperature
ratio
Although Figure 7 shows a fair
chosen, the range of temperature used
the flow too unsteady for the results
involving
the temperature ratio (TJ&)
account.
As will be indicated latter,
cal analysis and accordingly
a further
ate the temperature (or density) ratio
TJ/T~
correlation
between the parameters
was too small, and the boundary of
to show whether there W.S a factor
which should be taken into
this term appears in the theoretites t was made to attempt to evalueffect.
The apparatus was re-arranged to bring the combustion chamber
nearer to the jet exit, and three suction thermocouples at distances &O,
51 and 59 DJ were supported just above ground level.
Records of the temperature at these points were taken over periods of about 30 seconds while
the gas conditions at the nozzle were held constant.
Several tests of
this sort were made at different
combinations of jet pressure and temperature.
Later, the temperature records Here examined to see whether the
trace was steady or fluctuating
denoting that the boundary of the exhaust
gases fell short of or extended beyond the fixed point.
The results are
ressure
has
been
corrected
in each
shown on Figure 8; the jet dynamic $
case t0 apply t0 a radial distance R = 50 1)~.
If for
a given horizontal
extent
of the jet
the parameter
constant
then rie can draw characteristics
on Figure 8 corresponding to various
constant values of n.
Those for n = 0 and n = 4 are shown; it seems
unlikely
that n should lie much outside these limits.
7.0
Vertical
extent
of the jet
Having determined the horizontal
extent of spread of the jet after
it touched the ground, it seemed worthwhile to find how high above the
ground the nozzle had to be before the vertical
part of the jet just
failed to reach the ground.
Similar experiments ;iere, therefore,
made by
searching beneath the nozzle, chich was raised ~11 from the floor,
with
the suction thermocouple so that the lcrrest point reached by the hot gases
might be determined.
Again the results correlate
VJe/&e JDJ, as shonn on Figure 9.
8.0
Discussion
quite well
using the parameter
of choice of parameters
From the data presented ire can gain an assessment of the factors
on which the velocity
and temperature patterns in the field around a single jet depend.
The dynamic pressure of the spreading flow is
- IO -
to the exiti‘dynamic
pressure at the nozzle and varies
inversely.;?ith
the Bquiire of the raditis;
similar
dynamic pressure'ratios
occur at p,cints having the same ratio.of
radial distance,$o nozzle diameter.
Near the'axis
of t'e jct,~'-the dynamic pres&r&s depend on the
height of the jet nozzle above the ground;
the pressures in this region
and their extent can be decided.from considerations
of the decay of dynamic pressure and the growth of a jet discharging
axially
from a nozzle.
pr$o&icnal
The rate at'vjnich the bbunda$
is given approximately
.&c&e quarter
radial position.
.,
off the jet spreads along the ground
of the steady-state
velocity
at each
The,,extent of the r&i+
s&oad of the jet acboss the ‘&xxx-&is
found'to correlate with a non-dimensional
parameter VJ"/~~&JDJ, i7hich
relates the jet dynamic pressure to the initial
buoyancy forces on the
jet.
cissed,
results
Thc.several parameters used in these relationships
will ndw be diswith reference particularly
,to extending the application
of the
to higher.velocities
and temperatures
than those 'used.in the tests.
8.1
Velocity
and temperature
ratios
j
Iqmost
of the tests, the Mach number of the jet flow was too low
there to be a grea;t difference
batween the quantities
dynamic.pressure
(total pressure - static pressure) and kinetic
pressure (&prr") pr between,'
total and static temperature.
In any case, in regions of flow mere than'
a few jet diameters azey from the point of impingement, these +fferences
will a.lws,ys be negligible.
However, in maw practical
cases, vfhere hot
gases at choking pressure ratios are involved, the choice VJhether the
operative
yrameter
is (Pt - P,)/(Pt
- Ps) J or +~+/(-~$V")J
can alter
estimates of velocity
in the spreading jet by an Qnportant fraction.
In
cases where the velocity
decw durves for the SZIIC system have been ccmpared ever a range of jet pressure ratios, we have noted that the correlation between tests at Cfferent
pressures ?< s better when dynamic presAn examination of.Kuhn's ff data sho?s B similar
tendency
sures were used.
for the correlation
to be wcrse if kinetic
pressure ratios ai% used instead
Anderson and Johns4 studied jets at Mach
of ratios of dynamic prcs+re.
numbers up to 3.5, and concluded that linearity
of the &al
decay parameters when plotted to logarithmic
scales 'iias obtained when the pressure
ratio was formed from pitot tube readings,' related to a pitot pressure
Therefore,
measuyement made immediately doimstream of the nozzle exit.
in the present tests, the quantity q is taken to be.the difference
between
the pressure measured on a pitot tube aligned with the flow, a& the surrounding ambient static pressure, and it is proposed that this relationship
should be used when extending present data to.pressure
levels beyond those.
actually'tested.
for
The s8me author&
the axis of high, velocity
peratures sh&ld'beus&d
ture differences
in order
8.2
V'/$&lD
report measurements of the temperature decay along
jets from iihich it,is
concluded that total temin f&ming.non-dimensional
ratios between temperato correlate
measurements.
The buoyancy parameter,
horizotital
extent
bf flow
In an initial
correiation
of the e,xperim6ntel data'the parameter
was used1t.o express th& interaction
betqeen buoyancy and kinetic
-
II
-
forces in the flow field.
mile
it is clearly possible that the interaction of these forces can decide the path of a freely-moving
buoyant element of fluid,
it is not so clear that they are relevant when the flow is
bounded on one side by a surface.
Dr. B. S. Stratford
suggested that the
separation of the buoyant flow from the ground might be analogous to the
separation of isothermal
flows which occurred in many cases when the rise
in static pressure at the surface exceeded a fraction
(usually between
0.3 and 0.55) of the dynamic head of the main stream.
In the present
instance the pressure rise at separation may be equated to a defect in
pressure of the jet flow at the surface due to the buoyancy of the heated
gas above (Figure IOa).
It might be anticipated
that separation will
oocur when the pressure rise exceeds a certain fraction
of the local maximum dynamic head in the spreading jet, &V'.
A theoretical
analysis of the buoyancy effect has been made in
Appendix II.
It has been assuncd that the distributions
of velocity
and
temperature transverse to the direction
of flo1-i follon a normal error law,
and that the ratio between the rates at -cthich tomperaturc and velocity
effects sproad across the flow is characterised
by a factor 'b', the value
of which is not much different
from 1.
It is shonn that thu pressure
defect at the surface due to buoyancy is
Since, approximately,
V/VJ and R/DJ are in inverse relationship,
Ap is
constant within the region of the spreading flow and, for a given jet
temperature, is proportional
tc nosele diameter.
It is further
shol-m
that the ratio of this pressure dofeot to t:he local maximum dynamic pressure of the flow is
Where compressibility
effects in the jet
this relationship
msy bs written
at the nozzle exit
are small,
Since this expression contains a temperature ratio term, a* the results
shown on Figure 8 are compatible also \iith a factor (TJ/T,)~,
the results
of horizontal
extent have bcsn replottcd
to include this on Figure Il.
The straight
line which best fits the observations is given by
So that when separation
occurs
=
0.14
(b = I)
=
0.17
(b =
1.4)
The value of b is probably within the limits
indicated;
if b = 1,
then temparature effects are spreading across the flow at the same rate as
Usually in mixing systems, tomperaturc effects spread slightly
momentum.
It may be
the faster,
so that b is probably rather greater than unity.
said that qualitatively
the extent of the jet to the point of separation
Ap/$pVa is
follows the oresent analysis, but that the pressure coefficient
about-6 to +Aof,the value found in o.ther types of separating flow.
Another situation
where separation of,the spreading flow occurs is
U opposes the jet flon along
shown in Figure lob, where a wind of velocity
The pressure rise which the jot flov is seeking to overcome
the ground.
Therefore, the pressure coefficient
is
will be near to &-pu".
For the values 0.14
to 0.17
found previously,
U
7 = 0.37
w have
to 0.41
In the present tests we have the velocity
of advance of the initial
is
0.25V.
Honever,
the
two
cases
are
not
strictly
comparable as
iiave, u,
If we assume that the presthe initial
navt is's transient
phenomenon.
sure rise to be accomplished in the transient
case is about twice that in
the equivalent
steady-state
whore .&cross-nind
of velocity
u is opposing
the flow, then
- 13 -
$j =
0.26
which is not far from the experimental
8.3
The buoyancy parameter,
to 0.29
value.
vertical
penetration
of jet
A theoretical
approach to the interaction
of kinetic
and buoyancy
This
forces in a downwardly-directed
hot jet is given in Appendix III.
leads to a buoyancy parameter of the form used initially
to correlate
the
experimental results,
but a temperature retie
term is new included.
Thus
ka
VJ~
= i;;x~~~D,x~
*a
Again there is reasonable qualitative
agrcomont between theory and
exporimont, although the theoretical
line ahox-mon Figure 13 overestimates
the penetration by a factor of about 1.4, indicating
some shortcomings in
the theoretical
analysis.
There are certain similarities
bctwsen this
problem and that of the Ixnetration
of a column of heated air upwards into
the atmosphere which has been studied by Taylor and other35, but in their
case
the buoyancy forces at the startin, - condition were of the 3aaaemagnitude a3 the dynamic forces in the plume.
It may bc that the analysis
could be improved by considering the momentum of the sys-tom, starting
from
a point on the axis of the jot !?here mixing has reduced the dynamic pressures to the same order of magnitude as the buoyancy forces.
However, a
satisfactory
result along these line3 has not been found.
9.0
Conclusions
single
The velocity
and temperature condition3 in the space surrounding a
nozslo discharging
hot gas vertically
downwards hnvc been studied.
?l'hen the jet strikes
the amount of recirculation
to be small.
the ground it spreads radially
outrrords~and
of hot gas to the region of the nozzle appears
The dynamic head of the flow at ground level decreases inversely
as
the square of the distance from the jet ‘axis and is proportional
to the
dynamic head at the nozzle exit.
To a c1030 approximation,
the dynamic
head at ground. level at any point outside the region of direct impingement
of the jet is independent of the height of the nozzle above the ground.
The lateral
extent of the flow at
in terms of a parsactor relating
the jot
to excess tcmporaturo above ambient.
A
to correlate
the vertical
oxtunt of a jot
level.
ground love1 has been correlated
dynamic head to its buoyancy due
similar parameter has been used
discharging no11 above ground
The evidence of the tests supports tho view that in model experiments vthere the flow field around jets diroctod towards the ground is of
importance,
the value of the paramctcr
should be tho same
-.1.!+
-
in model
and full-scale
C~SCS~
The value of the index n should be 0.5
rihore the jet strikes the ground, and 1.0 if the jet does not reach the
ground.
Thosc values for n are based on a theoretical
approach, and
while the experiments do not establish absolutely
that they are correct,
the experimental
results and theoretical
values are nevertheless
compatible.
A slightly
altored form of the parameter is recommended for cases
rihere cqmpressibility
effects in the jet flow at the nozzle exit must be
taken into accotint.
In tests where the jot was suddenly switched on, the rate,at
which
the initial
boundary'of
the jet advances across the ground has been found
to be about dne quarter of the final stoati velocity
of the gases
at each
radius.
-
15 -
REFEREZCES
No.
Title,
Author(s)
etc.
1
D. Reeves
Conderning the heating effects
jet exhaust gases from vertical
take-off
aircraft
A.R.C. 16057, &n-i1 1953
of the
2
H. B. Squire
Jet flow and its effects on aircraft
Aircraft
Engineering,
701. 22,
P? 62-67,
1950
3
R. 2. Kuhn
in investigation
to determine conditions under which downwash from VTOL
aircraft
will start surface erosion
from various types of terrain
N&L Technical Note u-56,
September 1959
4
?.. R. Anderson
F. R. Johns
Characteristics
of free supersonic
jets exhausting into quiescent air
Jet Propulsion Vol. 25, pp 13-15
1955
5
B. R. Morton
G. I. Taylor
J. S. Turner
Turbulent gravitational
convection
from mnintained and instantaneous
souroes
proc. Roy. soo. 2. Vol. 234,
PP I-23,
1956
-- 16 .WPEiKDIX
I
List
of symbols.
b
+acto+, ha/h>," defkng
relative rates at which temperature
&I motientumeffects penetrate transversely to the flow
0
constant
CP
speo@'ic heat
D
diameter
De
of
.'&uivalent
.;
jet
diameter of. jet at ground k&l
due. to, gravity
is
.aoceleration
h
height above'&ound in &eld away from jet axis
hl:, ha
height, ,tioving away from surface, at which v and (T - Ta) ',
have decreased to l/e of the maximumlocal values, V and B
L
Z
BJ
LO~
L
e
8 ,c~raoteris~tio
AP
defect in pressure at&face
9
dynamic head in jet flow
R
radial distance from jet
I-P
limit
T
absolute temperature,
t
time
u
velocity
of advance of initial
U
velocity
of cross-wind
V
velocity
of flow above ground level
V
maxLmum
velocity
X
(1
+ ba)' * $
Y
S-
along
z
vertical
at
XT
limit
y =0
length
of radial
axis
axis
extent of jet across ground
TJ
= jet total
temperature
jet wave
in jet flow at given radial
of jet
distance downwards from nozzle etit
distance
APFzENDIX
I (cont'd)
limit
of vertical
penetration
expansion coefficiefit.
of hot jet
of gas $a
P
density
0
temperature difference (T - Ta), maximumvalue in jet flow
at given radial distance
Suffices
a
ambient conditions
J
conditions at exit plane of nozzle
0
conditions at ground on axis of jet
- 18 APF'EJDIX II
The buoyancy effect in flow spr@ading
from an impinging,
heated jet
The flow outwards from the point of impingement is assumed to
be symmetric about the vertical
axis of the jet.
Let us consider the conditions where the flow crosses a surface defined by a vertical
cylinder
radius R, and suppose that the variations
of temperature and horizontal
velocity
with height h follovv normal error distributions;
that is that
v
T-T,
= Ve
= Be
V and 0 are the values of velocity
and temperature difference
at ground
level,
that is they are maximum values, and t3 is small compared with Ta.
The buoyancy force acting on an element of the floaing
dh and unit cross-section
due to its density p being different
ambient is
gas height
from
-p)-g*dh
=p
(P*
=
Therefore, the defect
ancy of the gas above is
pP
in pressure
(T - Ta)
g a
at ground level
due to the buoy-
m
Ap
=
p?
0
- Ta)
g a
0
a
Because the change in absolute
constant in this integration.
value of p is small,
it
is regarded as
- 19 The total
quantity
heat passing the cylindrical
surface
time is
E 2?rRpv (T - Ta) Cp . db
=
2xRpCp
/
v (T - Ta) dh
dh
++ba)
(3,"
dh
where
Put
(I + ha>(2)’
= xa
ha
dh =
/(I
:.
Total
quantity
of heat
=
+V8Cpha
i(1
This must equal the total
+ ba) ' dx
+ba)
heat discharged
-2
Io e
dx
from the nozzle
in unit
20 -
-
Pep0
’ hz
/
e
42
dx
z
DJaVJPSJ
pg.
RV
0
But we have from Equation
it
follows,
It
by substitution
. &T-zFJ
6
. ...(2)
(1) that
in Equation
(2),
AP =Pe'
DJavJf'JBJ . m
RV
has been observed (Figure
that
l *..(3)
8
4) that
a
. ...(4)
If we consider
absent then
first
flow
conditions
=
where compressibility
v
‘“;’
epJ 4
( >
effects
ars
- 21 -
Substituting
thi3
in Equation
(3)
we have
AP = @g eJ DJ t'J 'J '
Thus the pressure defect due to buoyancy varies very little
with radius
and is independent of jet velocity.
At the radius of separation,
R*, the
maximum dynamic head of the flow, is
and the ratio
of the buoyancy pressure
defect
to this
is
. ...(6)
In the present
results
experiments,
(p/pJ)
can be replaced
The proportionality
shown by the straight
on Figure II is that
So that,
R”=
062
DJ
*
-
at separation
AP
1p pva -
(0.62)=
line
g-$
-
v
=
0.14
(b = 1)
=
0.17
(b = 1.4)
by (TJ/Ta)
so that
drawn through the
- 22 This analysis would seem to indicate,
therefore,
that separation
occurs when the difference
between ambient pressure and local surface
static pressure has a value of about 15 per cent of the local maximum
dynamic pressure of the flow.
This critical
condition for separation
might be compared with the critical
pressure rise coefficient
found in
other types of separating flow.
For examule, when detachment of a semiinfinite
flow from a surface occurs, Ap/$p? is often found to be between
0.3 and 0.55, V in this case being the flow velocity
of the main stream
outside the boundary layer.
Clearly,
however, it is invalid
to expect a
direct quantitative
comparison between a semi-infinite
flow on the one
hand and a wall-jet
flow on the other, and it might be expected that the
latter
is incapable of overcoming a static pressure rise of as large a
proportion
of the maximum local dynamic pressure as the former.
If the approximation
4~ s & pJ VeJ is not valid,
(3) can be combined to give
Equations
(4) and
Thus me see that if we wish to preserve similarity
in those parts
of the flow field where buoyancy effects are significant,
then we have to
ensure similarity
between values of the parameter represented by the
expressions in the square brackets.
ratios
In most practical
cases where the gas is air
up to choking value, the substitution
and for nozzle pressure
may be made, where TJ is the total temperature of the jet at the nozzle
Furthermore, temperatures in
exit;
the error is less than 4 per cent.
the spreading flow at points where buoyancy is becoming relatively
important are not far from ambient, so the buoyancy parameterbecomes
qJ
pgeJDj
.-. 2
Pa
For oases where compressibility
effects at the nozzle
parameter has the form discussed in Section 6.3 viz:-
exit
are small,
this
- 23 -
The buoyancy effect
directed vertically
in a hot jit
donnwards
One line of approach to the problem of calculating
the point of
arrest of a jet of heated air directed dowxsrds into quiescent aurroundings is to consider the rate at which the initial
energy of the jet is
dissipated
by mixing and by the buoyancy
forces on the heated gases.
If we consider the conditions
on the axis of the jet,
measurements in the absence of buoytixy effects that
we have from
(where k is a constant)
ZksDJa
qJ '
ss
This term is taken to represent the rate of decrease of snergy per unit
volume of the flori at the axis of the jet.
From Squire ne have the
temperature decay along the axis as
(where k' is a constant)
'Ae may non relate
jet by
the temperature
de
-=
dz
I k'
5--i;
and dynamic pressure
in the core of the
-aFor temperature,
the initial
condition
is that 8 : BJ at z = k'DJ
so that
or buoyancy per unit volurtie bf gas
Ye have seen that the upthrist,
is 8pgp so that over a distance dz, the loss of energy of the jet is
epgpaz. :
Therefore,
the total
decrease in energy of the jet
over a distance
dz is
For energy at the axis,
z = kDJ so that
the initial
condition
is that
q = qJ when
Put
A way has not been found. of integrating
this expression to obtain
the value of L ;?hen y = 0, but it can be done in a step-by-step
fashion.
A fez hand calculations
were made and it is clear that in the region of
greatest interest,
0 is small whcn,buoyancy begins to have an effect,
so
-
that we may take the density
parameter is then
25
-
p to be the ambient value.
The buoyancy
@f’aOJDJ . k,
9r
A computer programm$ was usea to find values of L when y = 0 for
several values of the buoyancy parameter.
These values are shown on
Figure 12, and the relationship
indicated between the variables is
The distance L*, the point where no kinetic
energv remains in the gases at
the jet axis is taken to be the point of arrest of the jet, so
sef
ir;l
in the present
tests
ka
qJ
2’o F * @SJDJpa
=
where the jet
velocity
iias low.
On Fi,we 13 the experimental
observations have been plotted
against the parameter given above, and the calculated line has bee added,
taking k = 6.5 and k’ = 4.8, yihich are the values quoted by Squire 8 for
velocity
and temperature decay along the axis of a jet.
f P. W. “. “me
pmrrmmed
this
aperatlo”
md Wteined
ths Tp8ultS
quoted.
To
buction
b
pump
-
nermocouple
wires
copper
constantan
40 SWG (D005”dia
Hot gas supply
from
combustion
chamber
.)
Thermocouple
rake
8ft
FIG.
I
Test
apparatus
high\
6
5
Nozzle
Nozzle
7
Jet
velocity
VJ
=
in
in.
1350
5
ft/sec
eJ ~240’
C
‘C
6
7
5
5
7
6
5
7
3
7
6
0
5
7
7
7
6
6
55
37
28
23
9
6
IO
23
II
21
5
7
//---,Y
DJ -2
i!,=Z
Jet temperature
above ambient.
Temperatures
are
above ambient
5
7
diameter
height
6
5
13
I4
IO
II
0
7
-/.7
Scale
of
feet
I7
v-
//
-
\\
4
FIG.2
Temperature
field
I2
IO
-/.7-
II
II
I3
II
I2
IO
\\
IO
I2
9
IO
0
-//
-
200
R
.
.
‘riches
too
0.
,//
DJ’ 2 ” OJ -225’C
Z,/DJ
=I
VJ~535”lSec
ft lsec
0’
;
200
R
R
DJ= 2*
DJ =I”
-240’
8~
0J = 215’ C
Zo/ DJ -23
VJ
-mono
ft
Time -seconds
FIG. 3
Initial
progress
of
jet
across
C
ground
/
set
I.0
Steady
Nozzle
l
z,
r
height%
I'
3,
+0
II,.
9,
99
v
”
x
I-0
state
=
I
12 DJ
10
6 I 2’
'J
.I
23,D
= I #?
O-I
!( 9J
0.0
-’ ( l-01
Transient
DJ ~2”
.
FIG.4
VJ=550
ft/sec
Zo/DJ
=36
Relation
distance
between
from
and
axis
steady
velocity
of
state
at
vertical
ground
jet
conditions
level
in
and
transient
- 25 -
that we may take the density
parameter is then
p to be the ambient value.
The buoyancy
@P,OJ~J . k,
9r
A computer programmd was used to find values of L when y = 0 for
These values are shown on
several values of the buoyancy parameter.
Figure 12, and the relationship
indicated betseen the variables is
The distance L*, the point where no kinetic
energy remains in the gases at
the jet axis is taken to be the point of arrest of the jet, 80
a
se \
ij;i
in the present
tests
=
2.0
where the jet
ka
T;I- Q
velocity
qJ
@‘JDJoa
‘x&s low.
On Fi,we
13 the experimental
observations have been plotted
against the parameter given above, and the calculated
line has bee added,
taking k = 6.5 and k’ = 4.8, which are the values quoted by Squire 8 for
velocity
and temperature decay along the aria of a jet.
f P.
W. “.
How
p~rcmmed
th,s
aperatIo”
and
obtained
ths
IpBultS
qlloted.
To
buction
pump
-
Hot gas supply
from
combustion
chamber
Tnermocouple
wires
copper
constantan
40 SWG (0.005”dia
/
Ceramic
.)
CJUZ
bush
‘-\
Detail
E
E
-tz
of
thermocouple
-
Thermocouple
rake
8ft
high\
Distance
pieces
1
12‘
: Intake
Suction
line
;
FIG.
I
Test
apparatus
Nozzle
6
5
Nozzle
Nozzle
7
Jet
velocity
VJ
=
in
in.
1350
5
ft/sec
eJ ~240’
C
‘C
6
7
5
5
7
6
5
7
3
7
6
0
5
7
7
7
6
6
55
37
28
23
9
6
IO
23
II
21
5
7
//---,Y
DJ -2
i!,=Z
Jet temperature
above ambient.
Temperatures
are
above ambient
5
7
diameter
height
6
5
13
I4
IO
II
0
7
-/.7
Scale
of
feet
I7
v-
//
-
\\
4
FIG.2
Temperature
field
I2
IO
-/.7-
II
II
I3
II
I2
IO
\\
IO
I2
9
IO
0
-//
-
200
R
.
.
‘riches
too
0.
,//
DJ’ 2 ” OJ -225’C
Z,/DJ
=I
VJ~535”lSec
ft lsec
0’
;
200
R
R
DJ= 2*
DJ =I”
-240’
8~
0J = 215’ C
Zo/ DJ -23
VJ
-mono
ft
Time -seconds
FIG. 3
Initial
progress
of
jet
across
C
ground
/
set
I.0
Steady
Nozzle
l
z,
r
height%
I'
3,
+0
II,.
9,
99
v
”
x
I-0
state
=
I
12 DJ
10
6 I 2’
'J
.I
23,D
= I #?
O-I
!( 9J
0.0
-’ ( l-01
Transient
DJ ~2”
.
FIG.4
VJ=550
ft/sec
Zo/DJ
=36
Relation
distance
between
from
and
axis
steady
velocity
of
state
at
vertical
ground
jet
conditions
level
in
and
transient
6.3 Intercept = De / DJ
Points are mean
of three
readings
tor qJ = 3, IO+ 20” Hg
FIG.5. Variation
of velocity at ground level related
total
pressure
at point of
impingement
l-0
x nozzle
o nozzle
t nozzle
to
height I2 DJ
height I8 DJ
height 56 DJ
0.5.
I.0
o-5
I+
0 QJ
2
De
o-2
O-2
0-I
I
2
FIG.6. Variation
5
of
velocity
IO
Z/D,
20
along
axis
50
of
jet.
04
100
101
IO’
I
I
2
5
I
I
I
I
IO’
2
5
IO’
v,2/#9 eJ DJ
15o-
--
IO O-
R"
0
DJ
-x+-
;
x
5'o-
++
0
+o 4
. t
/
b I’
7
t
Dia. nozzle,
Z, = II
B I” Dia. nozzlr,Z,,
= 23 DJ
. 2” Dia. nozzle, 2,
= 6
; 2” Dia. nozzle,
0'
200
extent
of
hot
jet
at
ground
DJ
Z, = I2 DJ
/
FIG.7. Horizontal
DJ
Iuvel
Conditions
when
hot gas always
reached
R = 50 D
\
0
1
0
7
.Condit ions
when
hot qas did not
reach
R =5OD
\
\
\
\
1
lO(
I
temperature
300
above
A
No
hot
gas
detected
v
Hot
gas
always
o
Hot
gas
detected
Jet
FIG .8. Relation
for
I
200
between
constant
jet
horizontal
I
I
rnrnrn(
400
500
800
ambient -‘C
(iog scale)
over
present
perlod
over
of 30 seconds
perlod
of 30 reconds
intermittently
dynamic
extent
pressure
of
jet.
and
temperature
00
150
cl*
0
0
FIG.II.Horirontal
o
f Dia. nozzk
203 23 DJ
+
f Dia. nozzle,
20~6
x
Z”Dia. norxk.
Lo
temperature
of
300
200
100
cxtrnt
=I2
DJ
DJ
hot
ratio
jet
correlating
tet n
parameter
includes
/A
+’
0
FlG.lZ.
calculated
penetration
Hand calculation
+
Computer
of
vertical
jet
-
l-
/
2oc
IOC
2"
z
5c
o 1”Dia. nozzle
+ i’Dia.
20
50
IO0
200
vJ2
heJo,
600
$
+J
IC
nozzla
_ - ,- ~. _ _ - _ _ . .__----~~--~.----
A.R.C.
October
COI, “.
C.P.
1ga
and
No.
Abbott,
--...__.._-
--.~-_------_----_---_________
_____,
A.R.C.
912
W.
October
COI. Il.
A.
SITJDIESOF
BY SINW?
WRJWARDS
THE FIKM FIEUX
CREA’ZD
“ERTICAI,
JETS PIRECTFD
UPON A HORIZONMLSLRFACE
C.P.
No. 912
1964
aml Abbott.
W.
- _.___
-_--_-----..~__~
532.?25:533.691.18
A.
SRJDIES
OF THE FIKA4 FIELDS
CREA!IEC
BY SINOIX
VSRTICAL
.,EYS DIRECTEX,
LOUPON A BORIZONPAL
SURFACE
The velocity
and temperature
condltlons
In the space
surmundlng
a
single
nozzle
discharSl”S
hot
gas vertically
darmHardS
on to a hcrizontal
surface
have
been studied.
Except
a very
low exit
velocities.
the
aa!nt
of reclrculatio”
M an I”t&e
situated
on the axis
of the
jet
Is
mall.
Wlthh
limits.
the dynanlc
head at ground
level
at a pofnt
amy
lmm the axis
IS independent
of th3 height
of the nozzle
sbwe
the
!?J’“““d.
Tlx?Se limits
We decided
by the
spread
Of the jet
before
it reaches
the
ground,
ard
by the
lateral
extent
of the jet
teeiore
it separates
and rises
im
the
Sro”nd.
tempemtw
condltlO”s
in th? space
surmmding
a
hot
gas vertically
domwards on t” a ha-lzontal
mmce have been studied. Except
a very
low exit
vel”cltl2s.
the
arount
or recirculation
M a” Intake
situated
on the axis
of the
jet
IS
Snail.
Within
llmlts,
the dynanlc
head at gm”“d
level
at a p”I”t
away
fmm
the axis
IS independent
“I the hel&t
“I the nozzle
ab”ve
the
ground.
These
limits
are
decided
k6’ the
sw-ad
of the
.iet tefom
it reaches
the
ground.
and by the
l&em-extent-of
the jet
before
it separat&
&d
rises
rm t.rE m”,,d.
single
The VelOClty
and
nozzle
dIschsrSi”S
P.T.O.
A.R.C.
C.P.
October
Co&
M.
1964
and
NO.
Abbott,
October
Cm,
tl.
A.
sPODIE.¶
CFTfIE
FLCHFIEUS
CFZATED
BY SINGIS
VERTICAL
JETS DIRECTED
tXX?MARDS
UPON A AORIZONTAL
RJP.FACE
The Velocity
and tenperatwe
nozzle
discl!ar’Sing
hot
e3s
have
been studied.
Except
C.P.
NO. 912
1964
and Abtott.
W.
532.525:533.691.18
A.
STUDIES
OFTHE
FL‘MFIELDSCPEATSD
BY S1NDI.E VERTICAL
JETS DIRECP,Z
IX,lthWm
UPON A HWIZONPAL
SURFACE
in the
space
sulo”“d,nS
a
downwards
on t” a horizontal
low exit
~elocitfes,
the
amol”t Of rec1xulat10n to an intalre situated on the axis 0r the jet is
mall.
Wlthin
limits,
the
dynmlc
&ad
at gro""d
level
at a point
anay
rP33 the aXlS
is independent
Of the hei@,t
Of the nozzle
above
the
md.
These
limits
are
decided
by the
spmad
of the jet
beiore
it reaches
the
ground.
and by the lateral
extent “r the jet ber0m it separates
and rises
im
the
ground.
single
s”l-face
P.T.O.
A.R.C.
912
W.
.--.--.....-..---..
condltlons
vertically
at WY,
P.T.O.
The velOC1t.y
and tempWat”R
CondltlO”S
1” th
Space
SU-m”“d,“F,
a
single
nozzle
discharging hot gas vertically
downwards
on to a h”rIz”“tal
SJI-faCe
baw
bee”
stucied.
Except
at very
low exit
Velo”itleS,
the
amwnt
or recimu1ation
to a” intake
sltuated
on the axlS
or the jet IS
-11.
Wlthin
limits,
the
dynamic
head at Smund
level
at a point
away
from
the axis
Is independent
of th? height
Of the nozzle
ab.xe
the
gM”“d.
These
limits
are
decided
W the
spread
“t the
jet
before
It reaches
the
w,,r,d,
and by the
lateral
extent
or the jet
beR”-e It separates
and Pises
rmm the wd.
P.T.O.
----
A parameter
Including
the lnltlal
velocity
of the
jet and Its Cmperature
is .lsed to define both the vertical
penetratlcm
of the jet and its lateral
extent
If It strikes
the g-and.
The rate of decay of dynmlc head I" the jeC
along
Its
axis
and across
the
grO""d has bee" studied.
I"
cmsient
experiments,
the rate or pmgress
or the initial
spread of the jet acrOSS the ground has bee" detemlned.
A meter
including
the 1nltIalvetilty
of the
jet and Its temperature
is used M define both the vertical
penetratlo"
of Cb jeC and its lateral
erte"t
lf it strikes
The rate oi decay of dynamic head in the Jet
the mund.
along it8 axis and BcI‘OSs the EmU,d ha.9 tee" studied.
I"
transient
experhEnts.
the Iate Of pmgrss
or the in1tm1
qread
of the Jet acmss the md
has been.detemined.
A parameter
lncludlng
the Inltlal
velocity
of the
jet and Its tpnperattm
is used to define
both the vertical
penetrat*on
or the jet and its lateral
extent ii it strikes
tb grolmd.
The rate Of decay Of @"amiC head I" the Jet
along Its axis and acrw.S the gTo""d has Me" studled.
I"
tmS,e"t
experiments,
the rate or pmtipss
or the inithl
spread oi the jet acms~the
zqamdhas
bee" determIned.
'
A parameter
ineludlng
the lnltial
velocity
of the
jet end Its tm.pemuTe
1s used M dellne
both the vertical
penetrac*ml
or the jet and its latelal
extent if It strikes
The ,-ate of decay of ~J,BD,~C head in,th!Z Jet
the ground.
along its axis and acrosti the ground has hem studled.
In
transient
expe-nts.
the rate or progress
or the initial
spread of the jetacmssthe
gmmdhas
been determined.
C.P. No. 912
fP
Nn
917