Paper 1317 "Experimental ..... method for determ/ning flow quality during the expansion tube run period. Figure ...... time by Pergament (1963) _hieh follows. ...... and equilibrium conditions in shock tunnels. Report. I_pt. Physics,. Australian.
/H -39" NASA
Contractor
Report
191573
fo. /g/
Shock
Tunnel
Studies
Supplement
8
R. J. Stalker,
P. Hollis,
S. Tuttle,
D. Mee,
G. Kelly,
Phenomena
G. T. Roberts,
R. G. Morgan,
D. R. Buttsworth,
J. Simmons,
University St. Lucia,
G. A. Allen,
R. J. Bakos,
C. Brescianini,
of Scramjet
M. V. Pulsonetti,
K. Skinner, N. Ward,
and
L. Porter, A. Neely
of Queensland Queensland
Australia
(NASA-CR-191573)
Grant
NAGW-674
December
STUDIES SUPPLEMENT
1993
131
OF
SHOCK
TUNNEL
N94-23532
SCRAMJET PHENOMENA, 8 (Queensland Univ.)
p
Unclas
G3/34
n SA National Aeronautics Space Administration
and
Langley Research Center _ Hampton, Virginia 23681-0001
0203618
r
SitOCK NASA
TUNNEL GRANT
Following
STUDIES
NAGW
the
format
OF SCRAM
JET
674 - SUPPLEMENT of previous
PHENOMENA
1992
8
reports,
this
consists
of a series
of reports
projects, with a brief general introduction commenting on each report. follow the introduction in the order of the headings in the introduction. The projects are considered under funded jointly by NAGW 674 and Australian
sources
PROGRAM
specific
project
reports
the headings "Program A", corresponding to work Australian sources, and "Program B", funded from
alone.
A
(i)
Expansion
Tube Studies
(a)
Flow
the Diaphragm
near
_R.J. Stalker, This
The
on
P. Hollis,
started
of an Expansion
G.A.
Allen)
out to be a numerical
of determining
Tube
the minimum
study
length
of expansion
of driver
tube
required.
operation,
with
It soon became
the aim clear
that
the delay occasioned in opening the secondary diaphragm was a very important factor, and that this could not be estimated accurately, because of the flow through the opening The
diaphragm.
conclusion
model
reached
accurately,
Influence (G.T.
by the
consisting
that new emphasis
(b)
Therefore
increasing disturbances
pressure
(R.J. What
objective
the
was
that
steady
to techniques
flow
and unsteady
for pre-opening
Dia p_h___gm h on Flow Quali_"
study
of the effect
of diaphragm
diaphragm thickness may at the test section to occur
static pressure disturbances. deformation of the diaphragm
Mass
was
the main
of this project.
extremely
difficult
expansion.
to
It suggests
the diaphragm. in Expansion
Tubes
Roberts)
An experimental
(c)
study
of a mixed
be given
of Seconda_"
this became
and the upstream Loss of Te.st Gas
mass
A somewhat surprising has a beneficial effect
static
on the flow.
be expected earlier, as well
It showed
to cause as causing
pitot larger
that
pressure upstream
result was that allowing on both the downstream
prepitot
pressure.
in the Boundary
Layer
of an Expansion
Tube
Stalker) has
been
here.
This
layer,
thereby
compensate important
described
effect
involves
inducing for
as the
the
for practical
removal an
mass
"fountain of gas
extra
loss.
effect"
mass
from flow
It is found
flow conditions.
in expansion the in
that
test the
the
tubes
region
by the
downstream effect
is analysed
is not
boundary
direction likely
to to be
Thrust
Balance
(Sean
Tuttle)
This )'ear transverse
was spent in perfecting the "twisted sting" configuration bending modes and allowing thrust to be measured.
constructed, (iii)
and
Comparative Effects (R.J.
Development
subjected
Studies
of Oxygen Bakos,
to satisfactory
bench
Dissociation
on Hypen'elocity
appropriately choosing combustor duct pressure:: The diffcrence betxveen expected
to yield
(R.J.
Bakos
Sc_ramjet
in T4 and in ttypulse was in both facilities and, by
temperature
used.
Lower
inlet
temperatures
are
difference. Thrust
Production
scramjet combustor and nozzle thrust agreed v,ith computations.
were
tested
in T4.
It was
which
were
conducted
found
B
Scaling
and Jgnilion
(M.V. This
combustion was tested
R.G. Morgan)
An axisymmetric that the measured
PROGRAM
inlet
a greater
and
Experiments
test conditions, it could be arranged that measured were sensitive to dissociation enhanced heat release alone. the two facilities was small, but this was due to the
combustor
Axisymmetric
Combustion
& J. Tamagno)
A comparative experimental study involving continued. An identical combustor model
high
testing.
in T4 and lt,,_pu!se
R.G. Morgan
relatively
for removing the A nozzle has been
Effects
in Scram'el£_
Pulsonetti) is a more
combustion
considered
report
in a large
duct
on experiments
(48
mm
x 100
qualitative agreement with theory,, although order of magnitude less than predicted. lt_ersonic
Ignition
mm
x 1300
at low
pressure
mm).
in 1991
on
Results
were
in
delays
were
an
ignition
in a Scramjet
(A. Paull) Combustion
of Hydrogen
compared.
Ethane
enthalpies 1).
(_
Ethane
Modelling
yielded
12 Mj kg"),
may
suffer
of
predicting experimental
same
pressure
from mixing
Flow
using
rise
as Hydrogen
it at low stagnation limitations
various
than
at high stagnation
enthalpies
(_ 9 Mj kg
Hydrogen.
Turbulence
Models
and R. G. Morgan)
three the
the
but fell below
more
of a Scramjet
(C. Brescianini Testing
and of Ethane in a 27 mm x 54 mm x 800 mm duct were
turbulence
flow results
models,
in a scramjet accurately
of
increasing
combustor.
over the entire 2
None length
degree of
the
of
sophistication,
models
of the combustion
predicted duct.
by the
Shock
Interactions
,_ith
Hypersonic
and R.G.
Morgan)
Mixing
Layers
- Stead)'
Flow
Analysis
and
wave
vdth the
variable
Mach
number
flow
Experiments (D.R.
Buttsxvorth
A stud)' field
of the
produced
interaction by a mixing
A Time-of-flight (K. Skinner Results
of a shock
Mass
layer.
Spectrometer
for High Speed
Flows
and R.J. Stalker)
with a time-of-flight
is the detection
of driver
concentration.
However,
concentration
during
Measuring
the
_Hyperveloci_"
mass gas
in a shock
the
the test
effect
on
spectrometer
method flow
are presented.
tunnel, can
The
example
and the development
be applied
studied
of driver
to measurement
of
gas
species
period.
Drag
Aaroduced
by Nose
on
Bluntness
a Cone
in
Flow
(L. Porter, D. Mee and J. Simmons) This reports work on the extension of the stress wave effect of nose blunting on the drag of a slender cone. A Studx of Re_.nold's Skin Friction Gaug£ (G. Kelly,
A. Paull
Analog
in
Redistribution
Boundary
to measure
Laver
using
the
a new
and J. Simmons)
A comparison betv,een skin friction using the skin friction gauge ,xhich Ener_"
Hypersonic
balance
of Non
and heat transfer has been reported
Equilibrium
measurements previously.
Hvpervelocity
on a flat plate,
Flow
in a Scramjet
Duc____! (N. Ward and R.J. Stalker) Flow visualisation with calculations. Flow
Measurements
(A. Neely This flow limits
of nitrogen
flow
in a two dimensional
and Calibration
of a Superorbital
and
Expansion
comparison
Tube
and R.G. Morgan)
is a pilot stud)' of an expansion speeds in excess of 10 km.s". the value
produced
intake
of the diagnostics
at speeds
of 13 km.s _.
tube in a configuration aimed at producing Though the response of pressure transducers
used,
it appears
that a usable
test
flow
has
been
FLOW
NEAR
THE
(_ R.J. Stalker,
1.
DIAPHRAGM
P. tlollis
OF AN
and G.A.
EXPANSION
TUBE
Allen)
In
Introduction the
classical
diaphragm and the
of
expansion
tube
flow,
it
is
assumed
is instantaneously removed from the flow upon supersonic flow behind that shock is subjected
expansion
which
It is known different set
analysis
produces
that
the
in motion
finite
by
the
the shock
the
secondary
arrival of the primary shock, to a simple wave unsteady
the test flow. mass
to this, and a more
stationary,
that
of the secondary
sophisticated
arrival
of
reflects
the
as from
diaphragm
model
treats
primary
wall
cause
the diaphragm
shock.
a rigid
must
Since
and
flow
as a piston,
the
propagates
the
diaphragm
to be
which
is
is initially
upstream.
Then,
as the
diaphragm accelerates, expansion waves are generated These co_ntinually overtake the shock wave and weaken
which also propagate upstream. it until, after a sufficiently long
time,
the reflected
to reach
short
with respect
tube approaches delay' occasioned
wave
disappears.
to the overall
shock
operating
that produced by' the need
If the time
time
of the expansion
by the classical model, with to accelerate the diaphragm,
this state tube.
is sufficiently
then the flow
in the
the differences that there is a that the test gas close to the
diaphragm suffers an increase in entropy due to the reflected shock, and that this gas may also suffer a change in composition due to the same cause. The importance of these effects
depends
minimising The
purpose
consequence
how
much
of
the
present
of bringing
is impacted process
on
the model
by the primary
of acceleration,
shock,
gas
is affected,
the
allows
diaphragm
is to
a step closer it not only
it is also opening.
or the gradual
2.
test
investigation
the diaphragm, situation
of the
and
this can be minimised
separation
flow through
make
a preliminary
to physical moves
This
may
exploration
reality.
When
but also ruptures, take
the
form
of the "petalling"
of shattered
diaphragm.
Either
- it becomes
a "leaky'"
diaphragm,
and
Hueristic
of a free
diaphragm
(or
the of way
it is this
.A.nal,'sis to begin
by considering
the
motion
accelerating into a vacuum under the action of a pressure p. The diaphragm tube of constant area, which is infinitely long in both directions. Therefore, 1.,
there
undisturbed situation
is an
pressure which
i
PAGE BLANK
unsteady
expansion
and speed
of sound
prevails
Stalker, Mech.,
PI_iXIDtf_
the
the diaphragm
so that during
of the pieces
itself
of
that we analyse.
It is convenient
Fig.
by
the mass of the diaphragm.
NOT
of
for a time after shock
R.J.
"An approximate
Vol. 22, pp 657-670,
FILMED
5
gas
,o, and
upstream u,.
reflection
theory 1965.
This
of the is a good
moves in a as shown in
diaphragm
from
approximation
if the diaphragm
of gun tunnel
a piston)
the
to the
is not leaky.
behaviour".
Joum.
FI.
Thus
the pressure
P/PR
at the diaphragm
= (1
where
y - 1 2
u)2Y/(v aR
u is the velocity
of motion
is given
may
and
(y-lu) 1 --
Pr
2 X
wave
relation
be written
of specific
The
heats.
equation
as
- i}
a r :v
2
this can be solved
and 3' the ratio
therefore
/(v
du dt-
simple
- 1)
of the diaphragm,
for the diaphragm
by the unsteady
(eg.
aar
ref. !) to yield
1 -
1
the co-ordinates
y + 1
u
2
ar
of the diaphragm
1 --Y
- 1
trajectory
(1)
u
--
y
* 1
PR
2
a R
j
1) / (y - i) 2 t
a aR
j
y -1 2
_
y+l
To
yield
quite
Pr
a gain in stagnation
high
stagnation
values
of u/as.
enthalpy
(0.001"), and (2) diaphragm, We now
enthalpy Thus
"
across
with
u/as--
(2)
an unsteady
expansion
2.0 and 3' = 1.4 there of two,
u/a R = 3.
it is necessary is only
Since
reason for choosing the expansion tube mode that tt/aR = 3 or greater. With a diaphragm
to use
a 16% gain
the gain
in
in stagnation
of operation, it seems of mylar 25 # thick
a = 6.0 x 10 .2 kg.m "2, and with a s = 2000 ms t and Ps = 10 MPa, equations (!) indicate that u/aR = 3 at distance x = 12.4 m from the initial position of the at time t = 2.4 x 10 .3 sec. consider
the flow
diaphragm
motion,
diaphragm
may
diaphragm the area
u a R )_(,¢
- for a gain by a factor
enthalpy is the prime reasonable to assume
present
as
u/as
through
the diaphragm
_ 1, so that
be taken
as the
the
if it is leaky.
pressure
undisturbed
and
values
speed
PR and
In the early of a s.
sound, The
stages
of the
upstream
of the
"leakiness"
of the
is represented as a single orifice in the diaphragm, of area b(t) A, where A is of the tube, and b(t) is a factor which generally varies with time, but for the purpose
is assumed
3' = 1.4, the mass flow
to be constant.
rate through
The
the diaphragm
6
flow at the orifice will be
will be sonic
and, with
ria
= 0.578
where The
laR a a b(t)
Pa is the density
A,
in the
pt/
pa
=
the time
Ar
-- 1.73
1
y-1 2
of the expansion
/J, a R )2/(y -
to pass
(1
--u ]z`(v-I) aa)
-
1
If f = 2 m, a R = 2000
tube is p,AL,
and p, is the density
where
L is the length
in the test region,
of
given
by
I)
for this mass
y
region.
the test region,
2
0.1)
undisturbed
mass of gas in the test region
the slug of gas constituting
and
(3)
through
the diaphragm
is
e/a a b(t)
ms 1, U/aR = 3, and we take
the diaphragm
as
10% open
(i.e.
b(t)
=
then At = 177 x 10 's see.
These examples are fairly typical, and other parameters which may
involving values of diaphragm thickness, test slug length be used in practice. They suggest that the behaviour of
the diaphragm as it accelerates and ruptures may have an important influence on the state of the test gas. The turbulence induced by the fragments of diaphragm may affect the quality
of flow
quality of heat not the case. The
fact
produced transfer
in a time
diaphragm
(or
necessary being
records
that an amount
diaphragm
of
which
fragments
to think
processed
as the
by
obtained
gas
is an order
the diaphragm, tubes
to constitute
the
of magnitude
to reach
of a different
an unsteady
through
in expansion
sufficient
thereof)
in terms
steady expansion before follows it. This could
test gas passes
the
model
expansion,
the
test
suggest
test
shorter velocity
for producing test gas
may
although that
flow
than
passes that
the
high
is probably
through for
the
it may
be
test flow.
Instead
of
pass
required
the
that
suggests first
this
the
through
a quasi-
it is accelerated to the test velocity by the action of the gas which change the chemical state of the test gas, though it should be
remembered that the quasi-steady is less than that of the test flow, test flow on its chemical state.
expansion takes place from a stagnation enthalpy and this will tend to reduce the effect of the history
7
which of the
To explore this effect in somev,hatmore detail, a numericalmodel hasbeenconstructed. Due to the natureof thephysicalprocessesinvolved in the bursting of the diaphragmand the subsequentcomplexflow pattern, simple models of the bursting processhave been developedwhich ,,,,illprovidesomeestimateof the flow duringthis process. The
model
for
diaphragm fashion.
the
bursting
of
the
diaphragm
to reduce from full)' covering The mass of the diaphragm
itself
is just
to allow
the
area
of
the
the tube to some minimum area in an exponential remains constant and it is assumed that the
diaphragm remains in one plane throughout the process, i.e. the diaphragm fragments all travel at the same velocib. The time for the burst process to occur and also the reduction in area To
that
occurred
calculate
the
due to the diaphragm
the velocity
diaphragm
must
burst
and acceleration
be found.
This
could
be specified.
of the diaphragm,
was
found
by
the pressure
an iterative
on either
procedure.
The
side
of
average
velocity of the gas on the upstream and downstream sides of the diaphragm were calculated by assuming that sonic flow occurred through the open area of the diaphragm and the remainder of the flow (over the diaphragm itself) moved ,,_ith the velocity of the diaphragm. These two velocities were then averaged taking into account the appropriate areas. From this average velocity, the average pressure on either side of the diaphragm could
be
could
again
The
calculated
flow
solved
using
wave
relations
and
then
the velocity
of the
diaphragm
be estimated. upstream
of the diaphragm
by G. Allen.
velocity
simple
of the
Bursting
was
calculated
of the diaphragm
gas at the diaphragm
using
was
to be the
the wave
included
average
model
in the model
velocity
calculated
developed
and
by forcing by the
the
above
procedure. Two
simple
intermediate through to exist
1. By
models and
acceleration
section
to examine fluids.
the
location
of the interface
Both
assumed
that
the
mass
the diaphragm in any given timestep is known because sonic velocity at the diaphragm. The models then considered two extreme situations,
Model assuming
the expanded be calculated.
between flow
the
passing
is assumed thus:-
1 an isentropic
expansion
back
to the original
area of the tube,
the density
of
mass can be found hence the length which this fluid parcel vdil take up can These lengths were summed sequentially and an estimate of the location of
the fluid interface each mass parcel assumed
were developed
to have
can be found. No correction as it progressed away from
was made for variation of the length the diaphragm, i.e. each mass parcel
constant volume.
8
of is
2.
Model
The
2
isentropic
density
of
expansion
the
diaphragm, mass could
test
was
flow.
Then,
the volume and be calculated.
Test
Conditions
Test
conditions
were
continued
knowing
therefore
chosen
until
the the
the length
to match
a well
density mass
of the
of
the
v,'hich tube
documented
gas
had
which
velocity
Pressure
experimental
(Pa)
Driver
1068.87
33 x 106
1.6667
Intermediate
1019.3
690
1.6667
Acceleration
1019.3
16
1.6667
diaphragm
Pipe
with - Gas
Helium Study
24 metres 0.0762
Secondary
diaphragm
thickness:
Secondary
diaphragm
density:
The
case Perfect lII)
the
up by this
9.93 metres
location:
radius:
PROGRAM
through
taken
2.44 metres
location:
Seconday diaphragm Test section location:
to the
Gamma
(m/s)
Primary
equal
passed was
as the driver and test gases (NASA Tech. Paper 1317 "Experimental of Expansion-Tube Flow Characteristics". J.L. Shinn & C.G. Miller
Sonic
was
metres
38 x 10 .6 metres (Mylar 8.52 x 10 .3 kg/m 3
diaphragm)
OUTPUT
main outputs
of the program
are:
(a) (b) (c)
The path of the shockwave The path of the secondary
reflected diaphragm
The path of the interface for models 1 and 2.
between
(d)
The
from
mach
from
the
line generated primary
from the secondary the intermediate
the intersection
diaphragm
and
the
and
between
reflected
diaphragm acceleration the
section
shockwave
shockwave
from
fluids,
transmitted the
secondary
diaphragm. The simulation and
75%.
One
area
reduction
has been further
nan for burst times of 0.15 ms with simulation
for comparison.
was The
performed
results
for a burst
of these
The final figure is a simulation of the diaphragm not burst but is allowed to move.
9
simulations
acting
area
reductions
time are
as a frictionless
of 10, 25, 50
of 0.30 shown
ms and
25%
in the figures.
piston,
i.e. it does
FigureNotation Burst times Sincethe areareductionis exponential,the burst time usedin the calculations is the time for the areato reach90% of its maximumreduction. Area ratio The areareductionfigure quotedin the atlachedfiguresis the amount by which the area of the diaphragmhas been reducedby the bursting process,(A,,,,u_-AnJ/A,,,,j_. Thus, a 75%reductionindicatesthat the final diaphragmareais 25%of the initial area.
4. The
Results outstanding
acceleration
feature
gas
- test
of the gas
results
interface
is the
as predicted
are apparently unrealistic. Model 1 because expansion to the test conditions, and Model of
gas
which
conditions.
have (This
passed
through
is witnessed
wide
the
by the
disparity
by Model
between 1 and
the
Model
position 2.
of the
Both
models
it does not allow for what is clearly a massive 2 because it does not allow for large anaounts diaphragm
but
velocit2, ." of the
are
not
interface
expanded
predicted
to by
the
this
test
model,
which is far in excess of any reasonable value). It follows that the unsteady expansion after the diaphragm, which has been neglected in both models, is of prime importance. The
motion
of the diaphragm
tends
to slow
down
as the opening
increases.
This
motion
depends on the velocity of the gas at the opening, and is calculated by assuming a simple wave compression from the undisturbed state in the acceleration tube on the downstream side of the diaphragm. Model 2. The overall
picture
It will therefore
which
the results
be unaffected
present
are of a mixed
of the test gas, with the accelerating remains unsteady expansion. It is difficult to analyse required uncertainties diaphragm
for
each
diaphragm
associated before
with
the shock
thickness this, wave
it may
by the choice
steady
be_'een
and
of the diaphragm located such a flow, and a new
and
each
be
arrives.
lO
better
set
of test to think
conditions. of
means
Model
unsteady
1 and
expansion
somewhere in the analysis would be To
avoid
of removing
the the
X
Wave
Diagram
for Diaphram
Acceleration
11
Distance
from
diaphragm
burst
(metres)
0 o ..
I
1
1 0
%
o 0 o o L_ I
%
•
!'_
o
/
_J U
0 0
/ /
_3 0
kO 0
/ / ",_
_
/
"4 ! / t_
o
/
14
! :
"\
!
!
/ 1.4
•
li: I
0
I
i
, :
_._ _ o", u _: _ o-_ _ j: ,-i j:_ .c
_: U
"_. _,
O_ u (_ ,,,,--4 _ O_
_
:
_), % % _ _ I
--_....-'-.
/
! :
/
: ' : , : ,
_, l:
H
/
-,-t
.I I i
0 0 o
l
/ .-
0
." "
0 r-4
I t
•
0
0
12
Distance
from
diaphragm
burst
(metres) 0 0 o
00 0 0 0
I I I I I I
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•
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"O C U
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oo o_ o_
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I / I /
-M
I / /
0 0 0
/ / /
0
/ / / / I I / / 0
J_ u_ 0 I
13
0 ,-4 I
Distance
from
diaphragm
burst
(metres) ,--4 o o I J
•
/°
%
/ I I I
%%%%
l•
I (x) o o o
I %
%
%
_"
%
%
%
%
%
I ! %i
%
I I
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I l
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I 16
I
INFLUENCE
OF
SECONDARY
DIAPHRAGM
ON
FLOW
QUALITY
IN
EXPANSION
G.T.ROBERT$ Lecturer,
Department University
of of
Aeronautics Southampton,
SEPTEMBER
17
1992
and
Astronautics
U.K.
TUBES
ABSTRACT Experiments University which
were
of
the
influence
operated
in
secondary
its with
the
disturbances interface. reducing
momentum and
flow
tube
with
the
of
the
shorter
Pre-deforming reflected
as
only the
is to
gas), the
wave
the
the
flow
the
shock
was
overpressure
disturbances.
18
flow
and
test
the
the
before
shown
side
of
the to
delaying
was
the
exerts but
diaphragm
arrival
a
also
on
shock of gas
beneficial the
a
(compared
driver-test have
and
gases.
reflected the
in
location
conditions
of
TQ
facility
diaphragm
is
with
the
and
inertia
greater
interactions
diaphragm
driver
gas
duration
facility mass,
either
secondary
test the
tube
experiments,
the
the
Engineering,
diaphragm
pressures
both
greater
test
expansion
these
that on
Mechanical
secondary
equal
indicate
general,
attributed
the
argon
not
of In
(i.e.
of
driven
quality
mode
obtained
In
Department
investigated.
influence
duration.
interface
shock
results
strength
by
was
the
free-piston
on
diaphragm)
considerable
in
Queensland
pre-deformation
The
performed
arrival
effect of
the
CONTENTS
PAGE
Title
1
Abstract
2
Contents
3
Nomenclature
4
I.
INTRODUCTION
5
2.
THE
3.
TEST
4.
EXPERIMENTAL
EXPANSION FLOW
4.1TQ
TUBE
QUALITY
- PRINCIPLES IN
EXPANSION
TUBES
tube
facility
4.2
Operating
conditions
4.3
Secondary
diaphragm
Without
RESULTS
7
9 9
variables
I0 11
5. RESULTS 5.1
- TYPICAL
9
DETAILS
expansion
5
OF OPERATION
secondary
diaphragm
11
5.2 Effect
of diaphragm
thickness
13
5.3 Effect
of diaphragm
pre-deformation
15
5.4
of diaphragm
location
16
Effect
6. CONCLUSIONS
16
ACKNOWLEDGEMENTS
17
REFERENCES
18
FIGURES
20
I - 14
19
-
42
NOMENCLATURE
-i a
-
sound
speed,
ms
f
-
frequency,
M
-
Math
p
-
pressure,
kPa
U
-
incident
shock
speed,
-
distance
from
priraary
-
ratio
-
period
between
z
-
steady
run
t
-
total
Hz
number
-i ms
s x
of
specific
diaphragm,
heats shock
period,
and
m
(1.67
for
argon)
test
gas
arrival
(expansion
tube
_s
Subcripts:
Shock
tube
region
(Pitot)
nomenclature:
1
-
initial
test
gas
2
-
post
incident
3
-
post
primary
4
-
initial
5
-
post
reflected
shock
-
post
secondary
unsteady
6
-
post
steady
I0
-
initial
20
-
post
shock unsteady
driver
gas (reflected expansion
expansion
acceleration
incident
expansion
shock
(reflected
shock
tunnel
(expansion shock
tunnel
only) tube
only)
only)
gas in
2O
(expansion tube only) n acc tube (expansion tube
only)
only)
1.
INTRODUCTION
This 1992
report
whilst
describes
the
University
of
Aeronautics
secondary
d/aphragm of
the
head
2.
THE
EXPANSION
TUBE:
An
expansion
tube
of
a
gas
the
reflected shock
low
expansion
reservoir in
the
initially
separates
Figure
I
in
shock
velocity flow
test
is and
use the
obtained
gas of
a
use
sound
typical
whereas,
speed or
a
the
pressure
light
of
in
and
test
gas
free-plston of
tolerated
the
driver under
the
a
from
In
shock
a
gas
above
steady
is
to
that,
a
in
capable
perform/ng
operating shock after
tube,
the
in
rupture
pressure
driver
shock,
tube, primary
of
shock
unsteady which gas.
although
raise
transiently could
Note
region 5
is
Mach
behind
itself number
employing
latter
by
section,
facility.
stagnant
helium)
that
an
acceleration
by
The
test
diaphragm
region
the
followed
the
undergoes
the
a
stagnant in
types
is
between former,
essentially
maximised
levels
the
reflected
both 5
conditions.
21
is
for
high
pressure
ratio.
or
gas
secondary
for
speed
also
d/fference
gas
lower
the
tube
[2]
the
aerothermodynamic
conditions
(thin)
both,
driver
was
that
a modified
from
expansion
(hydrogen
suggested
test
is by
region
sound
topic
initially
shock-heated
the
The
simulated
essential
tube
diagrams
in
region.
the
nozzle
tunnel,
of
gas.
hypervelocity
wave
influence
and
well
quiescent
test
of
driven
the
for
basically
processed
gas
shock
gas
a
expansion
location test
is
If|,
the
work
free-piston
facility
spaceplanes
reasonabl}
contoured
tube
the
enthalpy)
driver-test
an
The
of
R.J.Stalker.
tunnel
suitable
separating
attain
the
reflected
reflected
hence
to
at
shows
the
a
wind
into
further
expansion
centred
high
is
through
expansion
the
gas
conditions,
whereas
that,
and
UNIQ
Prof.
Department
OPERATION.
it
al
the
Engineering,
U.K.
flow.
UNIQ,
or
under
et
gas
flows
pressure
Stalker
tunnel
test
gas
propogated diaphragm
heated
steady
is
at
OF
the
July-September
Mechanical
from
investigate
test
group
of
Southampton, in
to
of
tunnel,
primary
shock
order
vehicles
shock
by
in
test
relatively
described
experiments
period
leave
of
impulse-type
studies
wave
(thick)
an
reentry
the
sabbatical
quality
the
Department
of
Tunnel
is
the
on
PRINCIPLES
of
Like shock
and As
Shock
combustion
a
the
enthalpy
models
conditions. which
the
high
supersonic
(TQ)
on
during
University
number
facility
by
of
visiting (UNI0)
a
tube
testing
undertaken
Astronautics,
perform/ng
producing
was
Queensland
expansion
of
the
author
and
involved
work
a
normally
normally
(and
high d/ctates
increasingly both
the
the
common pressure
In
the
pressure same
expansion ratio
test
for
producing shock
dissociation
in
in
the
reservoir,
stagnant thus
reentry
vehicle
combustion
main
exceedingly magnitude The
reason
for
illustrated flow
is
in
that
this
can
Figure
driver-test
by
gas
operated
in
reflected
the
by
expansion
arrival
at
the
test
Stalker
these
of
the
occur
viscous of
the
test
In
a
even
reason
for
effects:
foot
the
of
this
is by
not
the
the
run
duration
flow,
of
a
typical
supersonic
case)
an
order
wave
period
of from
the
is
through is
to
gas
the
the
limited
unsteady
driver-test
steady
transparent
gas
the
of
diagrams
tunnel
is
is
facilities.
the
the
duration
is
facilities
reflected
interface
off
levels
temperatures
tunnel
tunnel
of
the
the
tube
about
to
tail
over
that
such
is
reservoir
The
acceleration
of
the
unsteady
expansion
the
by
the
expansion
or
interface.
Paull
when
of
optimised
both
the
between
period
of
and
the
driver
shock
and
test
constant
much
causes
with
22
run
than duration
growing
speed
gas
further
interface
earlier the
test
to
but gas)
expansion
also to
due
flow
behind
the
increase
in
the
reflection
be
truncated
_
accelerate. would
been
the
causes
speeds
have
to
from
gas
causes would
in
shocks
layer
shock
often
tests
incident
boundary
uniform
gas
the
in
the it
the
theoretically
observed of
attenuates
length
occur
predicted
times
[5],
driver-test
therefore
run
Mirels
remain
to
times
attenuation
only
the
then
run
the
interface
and
would
and
of
reference
run
showed
expansion
high
a
shock
the
the
the
actual
sufficient
equalize
flow
the
short
the
noted
the
shock
inviscid
the
wave
(and tube
eventually
as
shock
gas
shock
incident
reflected that
often
the
either
of
expansion)
stagnant
however,
of
shown
is
or
where
the
tube,
overestimate
One
(as
the
large.
simultaneously.
Unfortunately, considerably
of
section
have
(shock
so
the flow
who
steady
the
2).
reflected
shock
also
conditions
which
by
poor
expansion
Figure
O(10-4)s,
reflected
if
the
duration
observed
a
by
combustor
run
to
advantage
flight
see
most
mode
expansion
[4]
events
tubes.
or,
drainage
the
and
the
tailored-interface
In
head
be
disturbance
nozzle.
the
In
interface
shock,
of by
easily
the
the
being
in
employ
[3],
stagnated
caused
the
(e.g.
that
offered
i.
of
inside
is
never are
to
on
to
is
Trimpi
primary
experienced
engine
typically
than
limited
which
conditions
by
the
due ratio
superior
is
dependent usual
pressure
However,
not
being
proposed
simulation
disadvantage
less
this
flow
also
restrictions
theoretically
are
is it
to
first
flows,
(scramjet)
small,
if
the
air
the
ramjet
Their
was
a better
or
best
that
(say)
provides
diaphragm,
flows.
is
velocity
Subject
is
is
enthalpy
of
which
it
concept
tunnel
flow
secondary
expansion
high
test
gases.
tube
unsteady
reflected
the
later)
expansion
the
the
acceleration
(described
The that
across
and
quality
tube,
length.
the
of case
early.
in
Nevertheless it is possible and
currently
facilities
establishments
[e.g.
advantages wide
over
rather have
been
viscous
observed effects
Early steady
test
operating [10].
at
condition However,
more
there
depending
on
have
indicated
also
pressure) acoustic
TEST
FLOW
In
work
performed have
increase
as by
of
head
the
case
the
the
Figure various
4
best,
of
inhibit
the is
test
the
conditions
predicted
taking
there
there
was
acceptable
the
that,
In
either a
for
low
any
given
conditions,
addition,
recent
(particularly
transmission
no
single
acceptably
operating
observed
to
was
only
was
indicated
employed.
an
the
arrival
of
the
of
studies
in
pitot
transverse
gas;
steady of
indicated; large
this
is
tail
of
the
from
the
the
the
flow
indicates each
gas
pitot (of
a
the
instead,
the to
23
rise
75
is
is
is
In and
40
@s,
has
operating
pitot
the
arrival
further terndnated
the
reflection In
pitot
either
pressure.
in in
smeared
figures
pitot
signal
or
probably
However,
the
run
in
disturbance.
render
a
increase
arrival
probe).
tO
by
obtained
small
(this
approximately
due
flow
ideal
interface.
signals
arrival
pressure
the
gas
gas
is
an
expansion
further
the case,
terminating
magnitude
above,
unsteady
acceleration
test
the
by
determ/ning
followed
driver-test
indicated
In
rise
soon
pressure
3 shows
initial
the
[13])
the
The
pitot
for
Figure
described
to
of
period.
tube'
conditions.
arrival
run
here,
method
As
from
rate
reported
arrives.
is
RESULTS
diagnostic
tube
expansion
to
TYPICAL
that
main
expansion
gas
(taken
of
TUBES:
including
expansion
response
sufficiently
to
steady
concluded
have
gases
EXPANSION
date,
finite
of
test
related
due
period
number
co,unity
unsteadiness
of
are
increase
steady
number
run
corresponding
the
[4,11]
disturbances
term/nation
before
a
and
test
of
periods
tended
which
offered
theoretical
durations
at
flow
the
larger
are
run
or,
the
acceleration
operating
pressure
a
aerodynamic
tubes
that
for
the
run
be
provided
density
either
to
IN
the
signal low
8,9]
tests
to
during
the
[e.g.
recent
QUALITY
measurements
pressure
has
times
[12,13].
3.
quality
at
their
for
short
test
tested
What the
expansion
which
the
waves
short
realising
within
the
during
driver
during
and
conditions
with
all
ought
the
of
the
account.
conducted
facility,
of
during
of
tunnel.
tubes
even
period
hope
shock
operating
use
developed
the
of
into
tests
in
expansion
range
make
being
reflected
of
narrow
6,7]
the
acceptance
are
to
practice
for
pitot out
by
the
caused
by
the
4a
4b
there
and
respectively) in
a periodic condition
4c
there
is
fluctuation unusable.
no
Paull
and
transverse rupture
gas,
greater filter
whether
that
with
the
The
number,
as
as
in
is
subsequently
the
expansion
of
limitation can
be
on
regular
the
has
rupturing
process)
diaphragm
should
i,,nediately
as
been on
an
instead
initially)
of
t_e
test
as
not (but
of
is
example,
noise
present
as
is
frequency
in
the
converse
interface effect
is
shown
in
show an
to
be
be
flows
has
under
the
focussed
to
a
of
has
caused
if
4
expansion,
appearance
tube
Figure
that,
unsteady
will
The
and
of
were
incident
been
the
observed
major
which
the
to
shock
loss.
In
the and
wave
or
leading
facilities
supporting any valve
the
rupture the
test
increased ideal
gas
will
levels
of
behaviour
diaphragm
necessary
its
case,
else
a
reflected
tube
(and
should
the
commonly
the
expansion
ideal
to
Clearly, but
minimise
in
diaphragm
massless
practice,
of
[14].
shock,
pressure
concern
secondary
quality
the
in
for
the
fast-acting
of
that
pressure
is
difference
disturbance.
arrangement
may
be
employed
a diaphragm. with
the
the
it
reasonable
to
question
Despite
had
cause
it
used
of
quality
a
gas
capable
truncation
this
acts
Stalker
conditions
though
occur
early
of
speed
illustrated
for
expansion
reflected
a mechanical
Additionally,
production.
been
influence
unwanted
will
Alternatively,
flow
and
facilities
the
stagnation
possible it
has
impact
and
diaphragm
is
in
sound
the
runs
effect.
satifactory
which
behave
by
dissociation
across
of
the
Paull
shift
different
range
after
processed
thin
Doppler
gas
dependent.
for
residual
test
low
the
(prior
speeds
filtering
ratio,
gas
sound
whereas
through the
test
a
to
in
the
disturbances,
(by,
frequency
in
feature
developments
the
a
the
present
the
of
due
diaphragm
always
into
interface
for
primary
are
ratio
are
operated.
Another
be
the
the
transmitted
Furthermore,
by
experiments
the the
processed
the
propogated
on
properties
tube)
frequency
disturbances many
flow
hypothesis.
particular
in
the
are
gas,
speed
fluctuations
from
whenever
frequency sound
these
disturbances
depends
are
as
this gas
they
attenuate
cut-off
of
not)
driver
to
well
Inspection
these
interface:
disturbances
unattenuated.
test
the
a tendency
situation
support
gas
that
originating
that
rupture)
in
shown
probably
(or
driver-test
than
have
argue
diaphragm
the
Mach
waves, They
but
secondary
across
[12,13]
acoustic process.
driver to
Stalker
in not
the
expansion been
evidence
run
period the
possible tube
carried
that are role
many caused
of
the
importance flows,
out
prior
24
a
of
the
by
transverse
secondary of
the
systematic to
disturbances
the
work
causing
acoustic
diaphragm
secondary experimental described
in
diaphragm
waves, their on
investigation here.
as
4.
EXPERIMENTAL
4.1
TO
DETAILS
expansion
Figure study.
5
It
is
by air
resides
at
heavy
the
steel
tank the
secondary
location
primary
diaphragm);
secondary The
of
latter
recorder
on
at
40
Operating
operate
to
simplify
of
PCB
on
to
(at the (x
x
-
the
gas) is
A
at
the
full
-
a
Figure
2.111
m
channels
and
34.5
or
25
_Pa. _m
5
is
the of
conducted
the
the with
sidewall
acceleration
in
Data at
to
m).
shock
transducers,
Physical
air
or
downstream
were
and
variation
and
reasonable
in
(P2,t)
shock
gas
aluminium
19.5
offer
3.736
piezo-electric
some
test
driver
the
experiments
along
a
the
range
Shown
pressure
on
the
polyethylene
thought
the
initially
section
of
the _n
pitot
determine
recorded
operating
13
location
locations
were
in
diaphragm
aft
is
high
gas
attached.
as
pressure is
of
gas
the
as
pump
argon
condition.
most
by
acceleration
or
were
driver
test
same
this
_e.g.[6|).
either
both
its
using
Inc.
sample
tubes;
speed
(U). s
All
which
were
pre-
multichannel
rates
of
2MHz,
whilst
kHz.
primary
aim
dlapragm
pre-deforming
to
bursting
the
in
conditions.
secondary
whether
The
study
to
the
the
containing
diffusion
helium
usually
were
used
data
transient
the
various
measured
The
others
in
the
elsewhere
secondary this
necessarily,
use
which
which
section
of
used
accelerated
a
and
massless
taken
also
were
calibrated.
the
the
and
employed
study
ideal
in
at
were
pressures
As
this
diaphragm
(p2)
to
gases.
measurements
pressure
4.2
is
are
forward
in
appears
diaphragms
the
section
rotary
normaly
to
tube
kPa
facility
in
itself
Downstream
diaphragms
to
section,
piston,
not
a
facility
prior
approximation
the
with
tube
kg)
1-10
but
test/acceleration
cellophane;
shock
arrangement
primary
3
Pa.
expansion
driver
order
1-100
section/dump
usual
a
(usually,
order
TO
the
(approx.
of
of
of
free-piston
pressures
of
The
the
a
it,
description
The
schematic
gas
pressures
as
a
facilty.
behind
acceleration
test
a
comprises
compressed pressure
tube
the
a
deformed
state,
these
on
the
the
facility
the
required
of
flow
finite
pressure it
was
flow
quality
diaphragm
in and
experiments
shock
its
has
difference
necessary
to
25
to
explore
and,
in
particular,
any
(rather
analysis.
was
adverse
than Also, (
a 3)
air
to
of
the
if
to
Stalker
[13],
it
speed
was
gas
sound
the
driver-test
disturbances
was greater
gas
originating
in
as
gas
rupture. of
argon
avoid run
driving
argon
causing
vibration
conditions
employed
the
and
test
dissociation
is
given
in
I.
Table
I:
Typical
Run
Conditions
U Pl
reservoir
Primary
2.0
4
2.25
3.7
1
2.75
7.3
pressure:
diaphragm:
Driver
Secondary
the
experiments
mm.
MPa mild
pressure:
diaphragm
Besides
1.85
0.6
reservoir
3
1.65
20
Air
a2/a
s_ 1 (kms )
(kPa)
4.3
unsteady
and
test
filter
choice
to
Paull the
diaphragm
the
preferred
effects).
(i.e.
effective
primary
led
of
where
speed
as
to
analysis
conditions
sound
act
criteria
(the
to at
gas
gas
These
Table
operate
driver
interface
order
according to
the
in
weak.
Finally, necessary
(pl)
75
steel, KPa
burst
pressure
P4
" 19.5
MPa
(argon)
variables
shock
tube
concerned
the
operating
conditions,
secondary
diaphragm.
the
main
Parameters
variables
in
that
varied
were
the
included:
- thickness
(or
- deformation -
The thick
diaphragms
within
102
state,
diaphragms
(prior
tested
cellophane,
undeformed the
location
were
mass)
care
the
were
_uu and was
equalised
to
shock
13 191
taken
the
run) tube
_uu thick
polyethylene,
_m
thick
to
ensure
that
the
pump-down
during
26
mylar.
When the
25 tested pressures
process.
gm
and
in
50
_u
their
either
side
of
5. RESULTS 5.1 Without
Figure
secondary
6
operating
shows
are
of
gas
gas
interface,
can
be
speeds
As also
as
in
Table
both
in
see
is
terminated
any
itself
in
at
without
to
run
rise
obtained
i
obtained
manifests
the
behind time
the Figure
to
any
rise
by
pressure
the
gas
velocity
and
run
period
(T)
the
predicted
mode,
due
to
the
of
rise
in
density
The
except
that
arrival
the
of
pressure.
larger
ratio
one
driver-test
pitot
comparatively
the
nominal diaphragm.
arrival
abrupt
becomes
three
tube
initial
an
the
secondary
expansion
as
the
slightly
unrealistically
of
less
at
wave
is
incident
greater
shock
6
theory
the
is
becondng
gas
the
this
expected,
according
run
those
signals
at
across
It
higher
the
increases.
shown
growth
and
that
in
expect
which
seen
interface
to
course,
acceleration
pitot
listed
similar
not,
shock
typical
conditions
signals would
diaphragm.
the
decreases time
Mirels
[5],
shock.
It
than
that
higher
high
post-shock
theory,
which
with of
be
speeds.
cause
that
shock the
This
the
is
(>
the
viscous
the
pitot
interface
K)
layer
theoretical the
attributed
7000
speed;
boundary
experimentally,
temperatures will
of
turbulent
seen
observed
shock
arrival
assum/ng
can
increasing
discrepancy to
the
predicted
effects
by
to
ideal
be
overestimated. After
the
periodic also
arrival
fluctuations
observed
by
disturbances periodicity
the
steady the
with
occuring
expansion
in 6(b)
in
pressure The the
being pitot
signal
systematic "
4 kPa)
6{a)
or
occuring
at
test-gas
interface
a manifestation
of
(Pl
constant during
the
Figure
higher
has
arrived
the
weaker
during
but
this
disturbance
I
kPa,
for
run
remains
filtering
period exhibits than vs.
some those
28
effect
kHz,
which them
rupture
the
ratio
does
area
not
to seem
the the
these
change
to
be in
runs driver
tests).
fairly
[small) observed
steady,
after
at
although
fluctuations
respectively}.
occurring
by
change
illustrated of
were
process. caused
frequency
scale
to
focusing
respectively, of
large
kHz) by
either
all
kHz
45
frequency
throughout
frequency
27
gas
ratios,
6(a)
{34
frequency
focus
20,
f
a)
discrepancy
in Figure
8 between
the skin
friction and heat transfer trends at position two is a direct result of the lag between skin friction and heat transfer.
(KPQ)
it is evident though that the traces other although only at the first
0.600
generally follow each point does Reynolds
analogy hold. This once again is in agreement with the fact that Reynolds analogy is only purported to be held 0.400_
_hen conditions are laminar. It is interesting that during transition the genera] trend is still followed, although the factor bet_,een the two traces is no longer consistent.
0
0.200
_
•
•
|
I
CONCLUSIONS
0.000 0
lO0
2O0
30O
mm from the Learn|
400
500
gdle
It is concluded that where the flow is laminar, measurement of skin friction and h_t tras_sfer ate consistent with
Figure ? Measured plate for condition 3
output. transition,
and predicted
skin
friction
When change occurs, as in this effect becomes noticeable.
the
along
onset
With
shock tunnel applications and approaching needed for expansion tube applications.
the
on_
of
the rise times
ACICNO XVLEDG EM ENTS This
results previously reported by He and Morgan (1989). it C,all be seen thai for these v_ues one would expect transition to occur somewhere between 200 a,'KI 260 mm the leading edge.
analogy.
effective means of measuring shear stress. The gauge has a rise time of about 20 _s, sufficiently short for most
of
Figure 8 shows resuhs for condition 4. It appears that transition is occumng by the second gauge. The Reynolds number at gauge 2 is approximately 1.02x10' amd the unit Reynolds number is 4.gxl0' m':. From
from
Reynolds
transition Reynolds analogy, as expected, breaks do_,n. Also the skin fricuon gauge is shown to be an
work
was supported
by
the Australian
Research
Council under Grant A5852080 and by NASA under Grant NAGW-674. The authors wish to acknowledge the invaluable technical contribution of John Brennan and the
Gauge 2 is positioned at 210 mm
scholarship
from the leading edge.
supporl from Zonta International
Foundation.
R EFERL'_CES
o Heet Trenster (i/ll'/m_ • Skin l_cUon (KP-) 4,
DUNN, M G, (1981) Current Studies at CaJspan Utilizing Short-Duration Flow Techniques. Proceedings of lhe 13th International Sym__lium on Shock Tubes and
3
0
0
Waves. edited by C E Treanor and J G Hall, of New York, Albany, NY, 3240.
O
Z
HE,
Y and MORGAN,
R G, (1989)
State Univ. Transition of
compressible high enthalpy boundary layer flow o_vrer• fiat plale..LQ_h Australasian Fluid Mechanics Conferenfe_ Univ Meib. lIB-2, !1-15.
1
=
0
too
2OO
:
,
3O0
I
4OO
'
KELLY,
'
50O
m.m from Iktd_,, I gdl. F_gure 8 Heat transfer corKlition 4
G M,
SIMMONS,
J M,
and PAULL,
A
(1991) Skin-friction gauge for use in hypervelocily impulse facilities. AIAA Journal, ,;_, 844-845. VAN DRIEST, E R, (1952) Investigation of Laminar Boundary Layer in Compressible Fluids Using the Crocco Method. NACA TN 2597.
and skin friction along plate for
124
I I I_ ,'(Ai llrtJh.451tln
I"luld
Um_rsIQ, oJ Taonw,a, 14-18 December 1992
(. OIHerd/k'd
._f¢CPg2/IlCS
Hobart
4B-4
Ausoaha
ENERGY REDISTRIBUTION
OF NONEQUILIBRIUM IN A SCRAM JET DUCT
N.R. WARD
HYPERVELOCITY
FLOW
and R.J. STALKER
Department of Mechanical Engineering University of Queensland QLD 4072,
AUSTRALIA
ABSTRACT
INTRODUCTION
C%emical]y and vibrationally
frozen shock tunnel test flow
As a means of investigating the gas dynamic effects
is passed through a model scramjet duct with the aim of examining heat release and its effects on the flow in analogy to the heat release resulting from combustion. Experimental investigations arc Ca;Tied OUt using a differential interfcromcter optics system for a range of shock tunnel test conditions. The rtsuhing images arc then compared to a numerical simulation using chemical and vibrational nonequilibrium flow theory fined to the duct shape imposed boundary conditions. NOTATION P T p O
= pressure = temperature = density = flow direction
the energy release instead stored in the dissociation
and in vibrational
rn_es
of of
can be con_crted to
heat energy. This evades the problems of imperfect mixing and flow disruption caused by an injecto¢, and isolates the heat release process from the ignition-process present in combustion.
the scramjet, in much the sarnc way as combustion occur in a prcmixed scrarnjct. See figure 1.
Experimentally it is difficuh to =K:curately measure now conditions using electronic gauges without disturbing the flow. Also, such rncthods involving gauges only provide data at disczete locations, allowing fine detail in the flow to be misse.d. To avoid such problems the
time
rate constants temperature for dissociation temperature for vibration density for dissociation
experirr_mal investigations _st carried study the flow through the scrlmjet.
out using optics to
The optical system used is the Di_crenrial Inzerfcromczcr, or $chlierenInterferomezer.A variationon
¢, = equilibrium vibrational energy t = vibrational relaxation time
the basic system is used making it • double pass system, largely because of space consuaints but also because this
R = gas constant h = cnthalpy
configuration
hq = partial derivative of h with respect to q u = velocity u, = component of velocity normal to shock = frozen speed of sound n ffi refractive index ! = interferogram intensity £ = divergence angle of wollaston
would
In this paper it is aimed to investigate this heat release in a scram jet model over • range of T4 test conditions. For this study a nitrogen test gas is chosen.
Cl.C-a,q=,_= = chemical rale constants = vibrational characteristic characteristic characteristic
molecules
provide Energy
the fn:e stream flow and energy redistribution only recommences _tcr the flow crosses the intake shocks of
e, = vitx-ational energy ¥ = ratio of specific heats 15 = intake wedge angle p = shock angle
C,K= O,_= O. = p= =
test flow to combustion.
The T4 shock tunnel is capable of producing high emhalpy test flow which oontains significant levels of dissociation and vibratiomd excitation. These art frozen in
M = roach number ct = dissociation fraction
t =
of the heat release produced by combustion of h)drogcn in a scrarnjct duct it is intended to simulate such heat release by using chemically and vibrarionally excited shock tunnel
doubles the sensidvity.
This system provides shifts are related to gradient Now field. These experimental
results
shock tunnel arc then compared Chemical
prism
and vibrational
See figure 2.
interferograms in which fringe of refractive index within the obtained
from the T4
=o a numerical simulation.
non-equilibrium
th¢o O, is used to
computationally predict the flow pattern through the scramjet duct for the free stream conditions con'esponding to the experirnents.
= wavelength of laser light w = displacement of wollaston prism from kns focus fz = focal length of main lens x = distance along centreline of model W = width of model
EXPERIMENTAL The
P, = stagnation pressure 1", = stagnation temperature h, = stagnation enthalpy
experimentally non-equilibrium
125
METIIOD
differential
interfcromet¢r
used
to
investigate the chemically and vibrationally flow in the scramjet model as produced by
the T4 shock tunnel is sho_,n schematically in figure :2. A pulse..A ruby laser is used as the light source and all mirrors lure &,round to an accuracy of one tenth of" a wavelength or better. A spatial filter with t 5 pm pinhole is used to clean up the light source and a precision qua,-lz wollaston
C e (r'/° w
p As it does so the tempera'aa-c
prism is used _ith a 4 minute prism angle. The image reu-ieval system consists of CCD camera v.ith 210 mm lens
d'r •
plate
steel is used on all leading
edges
of the model.
precision
cro_n glass _indows,
flat to within
one tenth of
• u,avelength. A pitot probe is fitted above the model check the timing of the laser against [he test flow period. NUM
ERICAL The
computer
program
predicts
flow
shown in figure 3. The flow is symmetrical centre line, so only the bottom half is calculated.
-=_-
-
"" p A, (u 2/a/
('7)
(,_,_'= - _, ae,)
(s)
- !)
v, herc h_ is hen: the The pressure
from conservation
about
the
angle p for the shock of the intake v, edge.
emanating of angle
, y._/I (
/P,_(8-v)
2
I. y- I M_s_(8.p) 2
um p
)
of
- p_
(9)
of momentum.
diffenrntial
equations
are
integrated
using
be parallel
to
the y, all.
This
boundary
condition
requires the superposition of • weak Prandtl-Meyer expansion/compn:ssion on the chemically and vibrafionally adjusting flow. For a deflection of -d_ at the ball for the
f.rorn 8. is
adjusting flow the PrandtI-Meyer penurbafion provides equal and opposite deflection, and gives a penurbation the oqher flow variables according Io:
the in
(!) (10)
The flow valuables are then found behind the shock using the Rankinc Hugoniol equations for pressure, temperature and Mach number ratios across a shock.
aM
As the flo_ passes gong the surface of the wedge it adjusts chemically and vibrationally, as described by Vinccnti and Kruger (1965). according to the following e'qu;tliOns:
_=[C,T"a.CzT'_(]-_)Ip[(I
,)c
'dr-
P-Ea '] Pa
M
(t'_
u_)
"
d_
(Z)
(II)
(12)
and d_`, d_
¢`," -c`, z
(3)
These
perturbations
are communicated
along
Mach |inca
throughout zone 2. They arc added to the adjusting now base values which are calculated for each streamline leading off from abe leading shock. In this way the flow is
_rhere
,Re,, e, - _
a
second order Runge-Kuta n'cthed to obtain the chemically and vibrauonal]y adjusting flow along the surface of the intake wedge.
must
calculated by solving the following equation derived by continuity considerations and the Rankine-Hugoniol equation for density ratio across a shock:
un(8._)
derivative
to q
As u, changes the flow direx6on changes due to the component of u tangential to the shock remaining constant. At the surface of the v, edge however the flow direction
first zone is assumed to be chemically and frozen, and the now to be steady and parallel.
shock edge
Thes_
pas_ia]
h(p.P,ct.e,) _/zh resl_ct changes according to: d.P -
energy e, are all constant,
The leading
by
and for sorr_ q I_ is the partial derivative of hCT.0c,e,) with respect to q and the component of velocity normal to the shock changes accordir,g to:
variables
Consequently pressure P, tem_ratu_ T. density p, flow direction 0, math number M. dissociation fraction cz and
the
(6)
CALCULATIONS
enu 3, to the expansion from the end of the _,edge. allo,_,s the definition o4"three 'zones' of flow, as
vibralional
h'-2_-_'-3=)RT'=_"(!2"
da
experiments has a gap at the cad of the angled intake wedges to allow the shocks to escape ,,_ithout reflection. and the pa.rallel duct ,,,,as designed to be narrow enough to
The vibrationally
to:
to
throughout the scramjet duel from the free stream before the leading edge shocks to the parallel duct behind the shocks after crossing. The test model for the T4
ckny This
according
h is given
when: the cnthalpy
camera to then trigger the laser before clearing the CCD rtgistfrs and storing the image in rnen'or 7 of an IBM 286 compacter. This is then viewed and printed. The model used is 150 mm wide with open sides and is rear mounted in the T4 test secdon. Hardened The intake wedges are 204 mm long and 10 degrees. The shock, tunnel test section is fitted with 200 mrn diameter
changes
- T-i (A,da • k, de ," udu) "r
close mounted connected to a triggered frarncgrabber. Pressure gauges at the end of the shock tube trigger the
gauge
(5)
calculated in zone 2, and the shape of the leading shock is altertd in accordance with the ptnufl)e,d conditions behind it caused by the Prandd-Meyer Fenurbations,
(4)
ee,'T ! 126
The flow using
in zone 3 is calcuhted
the symmea'y
in a similar way,
imposed b_zndary condition of flow
along the duct c¢n1_¢ line heing parallel to t.h¢ duct centre line. Foe each streamline f'mal conditions ahead of the second shock are used to calculate conditions behind the shock which ate then s[a.,'dn i conditionsforthe integration of the chemically and vibratioaally adjusting base flow in zone 3. To these base conditionsthe Prandd-Meyer pcrlurbation$Ire added. From the flow variables thmughom the duct the: refractive index of the flow n and iu gradicn! dn/dx can be calculated using the Gladestone-Dale equation, applied to niuogen molecules and gas with Gladestone-Dale constants as given Merzki_h
in Alpher (1974):
and White
n- ! -
(1958),
as described
pC.g_Ct-a).g_)
by
range of test condiuons chosen there was not recombination in any of them. In order to complete nurncrical simulations for the lest con_Lion$ the free stre_t/n conditions at the entrance to the scram_t were needed 'These were obtained by using l non-equilibrium nozzle flow (NEWZ,F') program to integralc from the shock tube fill pressure, the stagnation pre._sure during the shot and the shock speed in the shock tut_ Numerical simulations obtained using flee svzeam conditions found in this way predicted recombination in zone 2 at least, and an effect which was almost too small to detect when chemical rate constants ts given by Vinccnti
(1990). The
(t3)
interferogram
can be calculated
using the
ecluatJon:
Z The is
imported
_"
numerically into
the
pre_cted sang
experimental interferogram, can be produced, ar,,d this experimental
RESULTS
Iz
differential
which th_se contamination
intcrfcmgram
_,h_ch
holds
the
in this way a pictorial image can then be compared to the
AND DISCUSSION
consequence
and the laser high voltage output trace. The images accorded shov, ed a curvature
of
fringes was observed
produce selection
free stream
vibrational
energy,
the
and
further knowledge
non.equilibrium chemistry and
of T4 conditions
helium contamination will be important of shock tunrgl test condilions for
which in the future
experiments. It is expected that conditions wig attainable in which the nonequilibrium flow through scramjet
the
model
duct
produces heat
release
be the
rather
than
absorption, allowing combustion simulation, although was not the case in the experiments covered here.
this
SUMMARY
AND CONCLUSIONS
Experimental difl'ertntial interfemgrams'of shock tunnel test now througha model scramjet duct have been oblained over a range of high enthalpy test conditions. In
to
vary for different enthalpy and pressun_ conditions, but in all cases the deflection of the fringes was upstream after
all of these cases heat absorption after the intake shocks has been observed. Helium contamination is postulated. Numerical simulations of the flow. when incorporating chemical and vibrational non-equilibrium, have been found
both the fu'_t and SeCOnd shocks. Fringe curvature upon entry to ihe heated outskirts of the boundary layer can also be clearly seen. At the conclusion
a lower
vibration,
edge shock and the second quickly in zones 2 and 3
4. of these
used was as
experiments were carried out helium of the test gas from the driver gas was
See figure 6. h appears that t mort thorough nozzle flow calculation, incorporating
pressures. A differential interferometer image was recorded for each shot together with o'acesof shock speed within the shock tube, stagnation pressure at the entrance to the converging-diverging nozzle, pito_ pressure at the
See figure displacement
energy
fringe shiftis clearlyseen and matches experiment well. As there is an accepted high level of uncertainty in these rate constants comparison against this result is justifiable.
whilst varying the flow pressures and then to choose some other conditions with much lower a to compare. A roach five nozzle was used over this range of enthalpies and
respectively. The
vibrational
Although the fringe displacement at the stm of zone 2 is not suffg'ient to be clearly observed for this calculation. when the calculation is cuffed out using a lower value of the vibrational relaxation time constant C and _ I
image.
fringes after both the leading shock, decaying away quite
fr_ steam
non.equilibrium ctlculafon involving both vibration and chemistry, the computational results were found to be in quite good a_e,,ement with experiment. .See figure 5 for the nmnerical simulation corresponding tO figure 4.
A set of experiments was carried out using the T4 shock tunnel, the results of which are presented here. Chemical pr_esses were initially assumed to dominate the non-equilibrium flow so the test conditions were chosen to maintain a high dissociation fraction a
model
Itwas at this stage
resulting in observations of zero dissociation of nitrogen test gas. in cont;,adic_ion to the pun: test gas case calculated by the NENZF pmgra.m. When this was used in the numerical simulation, coupled with the more complete
=
electronics
were used
predictedby the method of Phinney (1964). Vibrational non.equilibriumeffects_¢re found to bc highly significant to the flow. Skinner (1992) found that at the high cnthalpies at
From the gradient dn./dx, a knowledge of the T4 test section and model gcomc_ies and specifications of the &ffemnfial interfcrometer opticssTstem the fringe intensity | of ihe resulting
and Kruger (1965)
that the previously describ_ ueatment of vibrational nonequilibrium was included, using more re.cent values of the vibrational rate constants as given in Sharma and Park
of the experiments the images
were analysed and the deflection of the wollaston prism calibrated. Consequently it was confirmed that a d¢flectioe upstream signifies a raising of refractive index
to be in good agn:ement with experimenL Future experiments will involve a complete non-equilibrium nozzle flow calculation to select test condilmns which
gradient from zero and thus increasing density. This is verified by examination of the fringe shift entering the boundary layer. This ¢ormslx:mds to energy obwrp6on rather than heat release. The implicatioe of this is that despiz the wide
produce
127
heat
release.
ORIGINAL
PAGE
!$
OFPOOR9UAU
REFERENCES ALPHER,
R A and WHITE,
D R (1958)
Optical
Refractivity of High Temperature Gases. L Effects Resulting from Dissociation of Diatomi¢ Ga._s. The Physics of Ruids, Volume 2 Number.2., 153-16t. MERZKIRCH, W (19"14) Flow Academic Press, New York u_d London. PHINNEY. R (1964) Nondimensional Flows V lu
with
Vibrational
2 Number SHARMA,
simulation
and
Relaxation.
2, 240-244. S P and PARK, diagnostic
noncquilibriurn flows. _Hcat Volume 4 Numtx:r 2, 129.142. SKINNER, K (1992) Department
of
Mechanical
Visualisador_. Solutions
ATAA
C (19