Proposed experiments on the
instability of confined wakes and jets
Matthew Juniper
CAMBRIDGE UNIVERSITY ENGINEERING DEPARTMENT
INTRODUCTION
Cambridge - Advanced
linear stability theory
describing the behaviour
of confined jets and wakes
Cambridge - Test
theory with careful
experiments under wellcontrolled conditions
Loughborough –
Perform thorough tests
on realistic injector
geometries
The proposed work completes an important link between theory and application
Rolls Royce Implement in
industrial aeroengine injectors
current work
proposed work
Many injectors used in industry, from fuel injectors in aeroplane engines to centrifugal separators such as the Dyson
vacuum cleaner, can be classed as confined wake or jet flows. Although the behaviour of unconfined wakes and jets has
been studied extensively, very little is known about the effect of confinement. Recently, the PI has implemented an
advanced stability analysis on such a flow and has found that confinement significantly affects behaviour. What is more, it
appears that industrial injectors designs have, by trial and error, evolved to exploit this behaviour.
The work proposed here has both scientific and industrial motivation. The proposal is to build a carefully-controlled
experimental rig to test various hypotheses which are deduced from the theory. In itself, this has significant scientific merit.
However, there is also a clear path for this work to be implemented in industry, through collaborations with Loughborough
University and Rolls Royce PLC.
Experiments on realistic geometries are performed at Loughborough and are used by Rolls Royce to develop their fuel
injectors. However, the complicated geometries and large number of control parameters make it difficult to isolate the root
cause of certain effects, such as the development of precessing vortices. The work proposed here will deliberately limit the
number of control parameters and carefully test their influence. Results will be compared with the theoretical model, which
has the same control parameters, in order to identify the root causes of these effects. Thus the proposed work completes an
important link between theory and application.
DEFINITION OF CONFINED WAKES AND JETS
Overview
Confined wake and jet flows consist of two coaxial fluids within a duct. In a wake flow, the inner fluid has a
lower axial velocity than the outer fluid. In a jet flow, the inner fluid has a higher axial velocity than the outer fluid. There is a
further distinction between co-flow and counter-flow. The co-flow situation, where the fluids move in the same direction, is
more common and is the main part of this proposal. The counter-flow situation, where the fluids move in opposite directions, is
very interesting from a scientific point of view due to its characteristic behaviour when confined. The flows can also be swirled,
which gives them an azimuthal velocity. Both the non-swirling and the swirling cases are considered in this proposal.
Furthermore, at sufficiently high swirl, the vortex which is generated can break down, which is also considered. The various
regimes are set out in the following tree diagram.
without swirl
Inner
flow
co-flow
Outer
flow
Duct
without vortex
breakdown
with swirl
with vortex
breakdown
Confined wakes
and jets
without swirl
counter-flow
A confined wake flow
with swirl
Structure of proposal
After a brief introduction to instability of spatially-developing shear flows, each type of flow is
considered in turn. For each flow the proposal describes:
• the industrial and scientific motivation;
• the theory behind the expected behaviour;
• the experimental apparatus which is proposed to test the behaviour;
• the experiments proposed, both hypothesis-driven and investigative;
• resources and management of the project.
INSTABILITY OF SPATIALLY-DEVELOPING SHEAR FLOWS, SUCH AS WAKES AND JETS
The instability of spatially-developing shear flows is a vibrant area of research in fluid mechanics. Two different, but linked,
points of view have been adopted by considering the development of perturbations either locally at each streamwise location
or globally in the whole physical domain [Ref. Chomaz 2005].
In the local view, each streamwise location of the flow can be designated as stable, convectively unstable or absolutely
unstable. In a convectively unstable region, perturbations grow in time but are convected out of the unstable region. However,
in an absolutely unstable region, perturbations grow in time and install themselves permanently throughout the region. Thus
the global behaviour depends on the competition between local instability and basic advection. An open flow may be globally
linearly stable even though it is locally convectively unstable because perturbations are continually transported away from the
unstable region. When externally forced, such a flow behaves as an amplifier. Conversely, an open flow will be globally
linearly unstable when a sufficiently large region of the flow is absolutely unstable, since self-sustained resonances occur in
the unstable region. Such a flow behaves as an oscillator and is insensitive to external forcing. Thus the behaviours of the
two types of flow exhibit a clear distinction, which can be observed experimentally [Ref Huerre & Monkewitz for a review].
If one assumes that a flow is almost parallel, the local analysis becomes very tractable, frequently allowing an analytic
solution. This proposal concerns the testing of such a model. An analytic solution allows easy examination of each control
parameter of the model flow. Evidently, such local analyses are extremely useful. They also predict quite accurately where
transition to a globally unstable mode occurs, if not the exact frequencies of these modes. However, with the recent increase
of computer capability, the fully global point of view becomes tractable. With Direct Numerical Simulation (DNS), flows can be
non-parallel and stability analyses can be linear or non-linear. Non-linear analyses give more accurate frequency predictions.
As this approach becomes the state of the art and capable of predicting features such as the frequencies of globally unstable
modes, comparison with experiment becomes even richer.
INSTABILITY OF CONFINED WAKES AND JETS
Koch (1985), Monkewitz (1988) and other authors have shown convincingly that the vortex street which develops in the wake of
a bluff body is the result of an absolute instability just downstream of the body. Experimentalists and theoreticians have studied
the effects of density ratio, velocity ratio, Reynolds number and swirl on unconfined wakes and jets. However, the effect of
confinement has largely been overlooked. Until recently, it seems to have been assumed that confinement has a stabilising
effect, which is in line with the results of Shair et al (1962), whose experiments were at low Reynolds number (40 < Re < 140).
However, Bearman (1978) discovered that a cylinder placed near a wall has a better-defined vortex shedding frequency than
one in an unconfined flow. This result, at high Reynolds number, is consistent with a stronger absolutely unstable region.
However, this result does not seem to have been commented on by future researchers.
In 2003, Juniper and Candel demonstrated that an inviscid two-dimensional confined wake flow is absolutely unstable over a
much wider range of density and velocity ratios than an equivalent unconfined flow. A series of experiments which examined the
global instability of a water/air coaxial injector backed up this hypothesis [Ref Exp in Fluids, in print]. However, the experiments
were not precise enough to be conclusive.
The PI has since greatly generalised the theory to cover axisymmetric wakes and jets. The following parameters can be varied
in the model: velocity ratio, density ratio, confinement ratio, swirl number and surface tension. A linear instability analysis is
performed, making the parallel flow assumption, and an analytic dispersion relation is produced. By solving this numerically, the
absolutely and convectively unstable regions of the flow can be found in parameter space. Despite their simplicity, linear
analyses which make the parallel flow assumption identify these regions quite successfully. Confinement is found to have a
very strong effect.
The experiments proposed here will test hypotheses about where transition occurs in parameter space, particularly examining
the effect of confinement. Experimentally, one can only observe global modes. A globally stable mode which behaves as an
amplifier is indicative of convective instability. Conversely, a globally unstable mode which behaves as an oscillator and which is
insensitive to extrinsic forcing is indicative of a large region of absolute instability. At transition, the presence of a Hopf
bifurcation can be examined by seeing whether the amplitude develops as the square root of the deviation of a control
parameter from the stability boundary. Further information will also be obtained, for instance on oscillation frequencies of
unstable global modes. This will be compared with predictions from fully global analyses, which will be developed separately
and in parallel. One particular advantage of the experiments proposed here is that, by confining part of a flow, the investigator
can create a pocket of flow which is unambiguously absolutely unstable, surrounded by regions which are unambiguously
convectively unstable. This will permit examination, for instance, of the result of non-linear global analyses that only a very small
region of absolute instability is required to create a global mode.
Confined co-flow wakes and jets without swirl
MOTIVATION
Industrial
Rocket motors, such as those in Europe's Ariane 5, require high combustion efficiency. The reactants are liquid
oxygen and supercritical hydrogen. Good mixing of these reactants is essential for high combustion efficiency. Through trial and
error, engineers have found that confined co-flow wake injectors give good mixing. In this configuration, the oxygen stream is
injected coaxially and at low velocity inside the hydrogen stream. The aim of these experiments is to test a theory that would
explain why this gives good mixing. If successful, this will lead to useful design rules for future generations of injectors. The
theory has also been extended to swirl injectors similar to those used in aero engines.
Scientific
The scientific motivation of this proposal has already been explained.
Confined co-flow wakes and jets without swirl
THEORY
Model
The model consists of two inviscid irrotational flows within a duct.
Initially, each has uniform velocity and density. A normal mode analysis is performed,
which captures all the potentially unstable modes. This reduces to the dispersion
relation, which is an analytical relation between the angular frequency, ω, axial
wavenumber, k and the parameters: azimuthal wavenumber, m; density ratio, S; velocity
difference ratio, Λ and confinement ratio, h.
r
U1
(1     ) 2 I ' (k ){I ' (kh  k ) K (k )  K ' (kh  k ) I (k )}
k  m
m
m
m
m
DS
0
2
I m (k ){I 'm (kh  k ) K 'm (k )  K 'm (kh  k ) I 'm (k )}
(1     )
k
The non-dimensional surface tension, We, has also been included in the model but, for
simplicity, is not shown here.
Analysis
A spatio-temporal instability analysis of the dispersion
relation is performed, in which ω and k are both complex. At a point
in parameter space, the flow is either stable, convectively unstable or
absolutely unstable. Convectively unstable flows, such as a single
shear layer, behave as amplifiers. On the other hand, absolutely
unstable flows can develop global modes and behave as oscillators.
This distinction can be determined through careful experiments, such
as those by Strykowski & Niccum (1991).
The absolutely unstable regions and the transition lines for the three
most influential azimuthal modes are shown in the figure opposite for
flows with a density ratio of one and with no surface tension. This
corresponds to a water/water or air/air experiment.
U2
D1
D2
x
S
1
2

U1  U 2
D  D1
h 2
U1  U 2
D1
wakes
jets
co-flow
m=1
m=0
m=1
m=2
convectively unstable region
absolutely unstable region
Confined co-flow wakes and jets without swirl
EXPERIMENTAL APPARATUS
Complete Rig
Working section
The apparatus may be placed the other way up. This would
improve access to the working section between tests and
would avoid the diagnostics being placed underneath a large
reservoir of water. However, it has disadvantages. For
example, in the oil/water experiments, the inner injector
would need to be capped between runs to avoid it filling up
with water under gravity.
Confined co-flow wakes and jets without swirl
EXPERIMENTAL APPARATUS
Overview
The flow to be investigated will be as similar as possible to that in the model. A liquid/liquid configuration has
been chosen so that the flow velocity and perturbation frequencies are low. Flat velocity profiles with reduced turbulence will
be achieved in both flows by smoothly reducing the flow area just before injection. The confinement ratio and the confined
length will be changed by having a large selection of perspex shrouds, which will be placed in the outer flow. There will also
be a selection of different diameter nozzles for the inner flow.
Fluids
Two combinations of working fluids are proposed: water/water and water/oil. The water/water experiments will
have no surface tension and a density ratio of unity. Consequently, short wavelength instabilities will grow rapidly at the
shear layer between the inner and outer flows. They will mix turbulently and the plug velocity profile will deteriorate fairly
rapidly, reducing the applicability of the model. On the other hand, the water/oil experiments will have a non-zero surface
tension, which can be used to stabilise short wavelength instabilities. This inhibits turbulent mixing, while having little effect
on long wavelength instabilities. The global modes associated with the absolute/convective m=0, m=1 and m=2 modes
predicted by the model have long wavelength and can thus be isolated. This technique was used successfully by Juniper
(2004) for water/air experiments and has been shown to work for water/oil in a pilot study. Two types of oil will be used:
vegetable oil and silicone oil. Vegetable oil is cheap and easy to handle, but is viscous. Silicone oil is expensive and harder
to handle but can have the same viscosity as water. The water will be softened to reduce limescale, which could interfere
with the diagnostics over long periods.
Noise
The experiment requires that mechanical noise is kept to a minimum in the working section. This will be
achieved by having two sets of scaffolding. The internal scaffolding will sit on a vibration-damped bench and will hold the
working section, with as few moving parts as possible. The external scaffolding will be solidly attached to the floor and will
hold the water header tank, overflow gutters and pumps. Diagnostics can be attached to either scaffolding, as appropriate.
Driving force The outer flow will be driven by a header tank. The velocity will be changed by moving this tank vertically.
There are two options for the inner flow: a servo motor attached to a piston (as shown) or a header tank. The servo-piston
configuration will allow an exact specification of the inner flow's velocity, regardless of the inner fluid's viscosity or the outer
fluid's velocity. It also allows safer handling of the silicone oil. If this configuration vibrates too much, the servo-piston can be
placed on the outer scaffolding and connected to the working section with a pipe. If this is still unsatisfactory, a header tank
can be used, as for the outer flow.
Confined co-flow wakes and jets without swirl
EXPERIMENTAL APPARATUS
Forcing
The experiments will explore the global instability of the m=0 and m=1 azimuthal modes. These mode shapes
are quite distinct. The m=0 mode can be stimulated by applying an overpressure to the inner flow. This can be achieved
either with the servo motor or with a separate device. The m=1 mode can be stimulated by moving the axis of the inner
nozzle in a circular trajectory or by waggling the inner nozzle from side to side (the latter motion excites a combined m=1 and
m=-1 mode). The modes will be stimulated both by an impulse and by periodic forcing. This has been successfully achieved
by Reynolds et al (described in 2003 Ann Rev. F. Mech article). An attempt will be made to force the m=2 mode, probably by
perturbing the outer flow, although this is considerably harder. Frequencies will be of the order of 10 Hz.
Diagnostics The flow will be visualised with Laser-Induced Fluorescence (LIF) of dyes: an Argon/Iron laser with
Fluorescein. Two synchronised cameras will be used, one set axially and one radially.
The response to forcing will be measured by Particle Image Velocimetry (PIV) or by Laser Doppler Velocimetry (LDV), both
of which have sufficiently high temporal resolution. PIV gives better spatial information, measuring two velocity components
in a plane, but requires the flow to be seeded. This could interfere with the instability. In particular it could affect the surface
tension between water and oil. LDV also measures two velocity components, but only at a point. With LDV, the flows do not
require further seeding, since tapwater contains sufficient impurities.
Confined co-flow wakes and jets without swirl
EXPERIMENTAL CONTROL PARAMETERS
Parameters Denoting the inner fluid by subscript 1 and the outer fluid by subscript 2, the independent physical quantities
are: ρ1, U1, μ1, D1, ρ2, U2, μ2, D2, σ. There are three dimensions: mass, length and time. Therefore six dimensionless numbers
govern the behaviour:
S
1
2

U1  U 2
U1  U 2
h
D2  D1
D1
Re 1 
1U1 D1
1
Re 2 
 2U 2 D2
2
We 

1 D1 (U1  U 2 )
2
Globally unstable modes will oscillate at a particular frequency, which can be expressed in terms of a Strouhal number
St = fD1/U2. The amplitudes can be expressed in terms of a characteristic length D1 and a velocity U2.
In water/water experiments, the density ratio is unity and We is zero. Thus the behaviour is governed by h, Λ, Re1 and Re2.
Experiments on unconfined wakes show that if Re2 is above 300, the Strouhal number is independent of Re2. Initially, we will
assume that this also applies to Re1 and perform experiments with Re1 and Re2 > 300. Thus the effects of h and Λ will be
isolated and investigated.
Water/oil experiments have a density ratio of approximately 0.8 and non-zero Weber number. The inner injector diameter
must be varied if We is to be kept approximately constant while retaining sufficient range of Λ in a fibrous break-up regime, as
defined by Eroglu and Chigier (1991). The Weber number only needs to be approximately constant because its exact
influence on instability is not being tested. It is merely being used as a useful stabilising mechanism for short wavelengths.
With silicone oils, Re1 and Re2 can both held above 300 and the effects of h and Λ can be isolated, as for the water/water
experiments. With vegetable oils, the inner flow will have a low Reynolds number. Consequently the model must be adapted
to include viscosity if these results are to be properly examined. Although challenging, this has been achieved in two
dimensions by Yecko et al (2002). As a final point, buoyancy effects will be small but can also be included in the model.
Confined co-flow wakes and jets without swirl
PILOT STUDY
Objective
A pilot study was performed in order to test the general principle of the experiments. In particular, this study
showed that the water/oil combination permits clearer visualisation of the long wavelength global instabilities, which are the
focus of this study. The water/water combination also works.
Water / water pilot study – co-flow wake at h=1
Two water flows are injected
coaxially. The inner flow is dyed blue
and is injected slowly (Re1 ≈ 300).
The outer fluid, which is faster (Re2 ≈
2000) passes through a convergent
nozzle upstream.
The confinement ratio, h, is equal to
1. According to the model, this gives
rise to maximum absolute instability
of the m=1 helicoidal or sinuous
mode.
Flow visualisation with a digital video
camera seems to show a helicoidal
instability, as expected. However, at
faster velocities, the fluids mix
rapidly and visualisation is less clear.
Water / vegetable oil pilot study – co-flow wake at h=1
Vegetable oil is injected coaxially
inside a faster flow of water (Re2 ≈
2000), which passes through a
convergent nozzle upstream.
The confinement ratio, h, is equal to
1, which gives rise to maximum
absolute instability of the m=1
helicoidal or sinuous mode.
Flow visualisation seems to show a
helicoidal instability, as expected.
This can be seen both on the jet
itself and on the shadow of the jet,
which is on the left of the picture.
The advantage of using vegetable oil
is that surface tension damps small
instabilities at the interface of the two
fluids, slowing mixing. However, this
does not damp the long wavelength
global instabilities, which are the
focus of this study.
Confined co-flow wakes and jets without swirl
HYPOTHESIS-DRIVEN EXPERIMENTS (1)
Hypothesis
Analysis, water/water
Analysis, water/oil
Comments
1. Confinement and velocity ratio
affect the transition from a linearly
stable to a linearly unstable global
mode in accordance with the
diagram below:
The four control parameters are h, Λ,
Re1 and Re2. Keep Re1 and Re2
above 300. Vary h and Λ. Stimulate
the m=0 and m=1 modes and
examine the response. The
amplitude response of a global
linearly stable flow with convectively
unstable regions is in proportion to
the amplitude of excitation. The
response of a global linearly unstable
flow, indicative of absolute instability,
is independent of the amplitude of
excitation.
The five control parameters are h,
Λ, Re1, Re2 and We. Keep We
roughly constant and use surface
tension to dampen small
wavelength instabilities in order to
inhibit turbulent mixing. Thus isolate
long wavelength instabilities. Avoid
the Rayleigh and superpulsating
break-up regimes. Keep Re1
(silicone oil) and Re2 above 300.
Examine the response of the m=0
and m=1 modes, as for the
water/water experiments.
If done carefully, this
series of experiments
is an excellent test of
the theory and has a
good chance of
success.
As for the co-flow wake, vary h and Λ
with Re > 300. Stimulate the m=0 and
m=1 modes and examine their rates
of growth.
Keep We roughly constant as for the
co-flow wake. Avoid the Rayleigh
and superpulsating break-up
regimes. Examine the response of
the m=0 and m=1 modes, as for the
water/water experiments.
This series of
experiments is also
an excellent test of
the theory and has a
good chance of
success.
Convectively Unstable
(linearly stable global mode)
m=1
Absolutely
Unstable
2. Co-flow jets do not have
absolutely unstable regions and their
global modes are therefore always
linearly stable. However, they
contain convectively unstable
regions and the amplification rate
varies with confinement. Between a
confinement ratio of 0.6 and 0.8 the
m=1 mode will be more unstable
than the m=0 mode. Outside this
range, the m=0 mode is the most
unstable.
Confined co-flow wakes and jets without swirl
HYPOTHESIS-DRIVEN EXPERIMENTS (2)
Hypothesis
Analysis, water/water
Analysis, water/oil
Comments
3. Between a confinement ratio of
0.3 < h < 0.34, the m=2 global mode
of a co-flow wake is linearly unstable
and more unstable than the m=1
mode, in accordance with the figure
below.
Look for natural development of the
m=2 mode. Then stimulate this mode
with a specially-designed central
nozzle or a perturbation in the outer
flow. Measure the response, as for
the previous experiments. In the
water/water experiments the inner
flow will rapidly penetrate to the outer
boundary, which may compromise
these experiments.
The analysis is the same as that of
the water/water experiments.
However, the water/oil configuration
has a higher chance of success.
It will be fascinating
to see whether a m=2
'fluting' mode
appears naturally in a
wake flow, in place of
the standard m=1
'helicoidal' mode.
4. Confinement effects are
independent of Reynolds number at
high Reynolds number. (This
hypothesis is dependent on
development of the viscous theory)
Vary Re1 and Re2 at given h and Λ
near to the absolute instability
boundary. Measure the response to
excitation, as for previous
experiments.
As for water/water experiments
This would be
expected from
experiments in
unconfined flows.
5. Confinement has a stabilising
effect at low Reynolds number.
(This hypothesis is dependent on
development of the viscous theory)
Dope the water with glycerol. Vary
Re1 and Re2 at given h and Λ near to
the absolute instability boundary of
the high Reynolds number flow.
Measure the response to excitation,
as for previous experiments.
As for water/water experiments
This would be
expected from the
results of Shair et al
(1962).
Both modes
Absolutely
Unstable
m=2
AU
m=1
AU
All modes
Convectively
Unstable
Confined co-flow wakes and jets without swirl
HYPOTHESIS-DRIVEN EXPERIMENTS (3)
Hypothesis
Analysis, water/water and water/oil
Comments
6. Conditions at the upstream station
of the absolutely unstable region
determine the properties of the
global mode which it produces.
The configuration proposed here has a confined pocket which is
unambiguously absolutely unstable, surrounded by an unconfined region
which is unambiguously convectively unstable. The velocity profile at the
upstream point can be measured or calculated precisely. From this one can
deduce the properties of the absolutely unstable flow at that point. These
can be compared with the measured properties of the global mode.
This is a particularly
valuable feature of
the proposed
experiments
Confined co-flow wakes and jets without swirl
INVESTIGATIVE EXPERIMENTS
Question
Rationale
Analysis
Comments
1. What streamwise length is
required in order for an absolute
instability to establish a global
mode?
Current linear models of shear flows
cannot predict how far the absolutely
unstable region must extend
downstream for a global mode to set
in. Current non-linear models
suggest that this region needs only
to be quite small.
Choose values of h and Λ which are
known to produce a global mode
when confined but only convective
instability when unconfined.
Determine whether the global mode
is linearly stable or linearly unstable
as the confined length varies.
This information is
very useful to injector
designers, who may
want to provoke
global instability in
order to enhance
mixing.
This information can be obtained
from the experiments simply by
varying the confined length.
Confined co-flow wakes and jets with swirl,
without vortex breakdown
THEORY
Model
The model consists of two inviscid flows within a duct. The inner
flow has solid body rotation and the outer flow has an irrotational line vortex
profile. Initially, each has uniform axial velocity and density. A normal mode
analysis is performed, which captures all the potentially unstable modes. This
reduces to the dispersion relation, which is an analytical relation between the
angular frequency, ω, axial wavenumber, k and the parameters: azimuthal
wavenumber, m; density ratio, S; velocity difference ratio, Λ; confinement ratio, h;
Weber number, We and swirl number R.
This azimuthal velocity profile has the advantage that there is no azimuthal shear,
which means that there are no azimuthal Kelvin-Helmholtz modes. This is one of
many velocity profiles which can be achieved experimentally. The theory can be
readily adapted to fit other velocity profiles and new sets of hypotheses
developed.
Analysis
A spatio-temporal instability analysis of the dispersion
relation is performed, in which ω and k are both complex. At a point
in parameter space, the flow is either stable, convectively unstable or
absolutely unstable. The absolutely unstable regions and the
transition lines for each azimuthal mode are shown in the figure
opposite for a wake flow with a density ratio of one and with no
surface tension. This corresponds to a water/water or air/air
experiment.
W
S
1
2

U1  U 2
U1  U 2
h
D2  D1
D1
R
D1
2(U1  U 2 )
convectively unstable region
absolutely unstable region
m=1
m=2
m=3
m=4
Confined co-flow wakes and jets with swirl,
without vortex breakdown
EXPERIMENTAL APPARATUS
Overview
The apparatus will be similar to that used for the non-swirling
experiments, so that the same rig can be used. The inner stream will be given a solidbody rotation either by rotating the entire nozzle or by rotating a honeycomb inside the
nozzle, as performed by Billant (1998). The former method is more complicated to
achieve but ensures that there is no azimuthal velocity deficit where the flows join, in
line with the model. Swirl vanes will be used to give the outer flow a line vortex velocity
profile. These could be axial swirl vanes (as shown) or radial swirl vanes at entry.
Adjustment of the swirl vanes allows other velocity profiles to be tested in the future.
Rotating the outer nozzle has been discounted for now. Although this would achieve the
desired line vortex velocity profile, through turbulent or viscous momentum transfer, the
entire quantity of working fluid would have to be rotated before the experiment started.
This is difficult to achieve while also keeping a constant head in the rotating container.
Diagnostics The same diagnostics will be used
Fluids
The same working fluids will be used.
Parameters The azimuthal velocity profile in the model has a single independent
variable, Ω, which characterises the swirl. Therefore there is a single new control
parameter: the swirl number R. Since there is no azimuthal shear in this configuration,
the definition of the Weber number is unchanged, remaining in terms of axial shear only.
Other velocity profiles will be tested in the future. These would typically require two
independent variables, Ω1 and Ω2 in order to be defined completely.
Confined co-flow wakes and jets with swirl,
without vortex breakdown
HYPOTHESIS-DRIVEN EXPERIMENTS
Hypothesis
Analysis, water/water
Analysis, water/oil
Comments
1. Confinement and swirl number
affect the stability of global modes in
co-flow wakes in accordance with
the figure below (for the m=1 mode).
Increasing swirl at h~1 will cause
transition from a sinuous mode to a
helicoidal mode. The m=2 mode has
similar behaviour. The m=0 mode
should always be convectively
unstable, hence be globally linearly
stable.
The five control parameters are h, Λ,
R, Re1 and Re2. Keep Re1 and Re2
above 300. For a given value of Λ,
vary h and R. Stimulate the m=0,
m=1 and (if possible) m=2 modes
and examine the response. Thus
determine when the flow exhibits a
linearly stable or unstable global
mode.
The six control parameters are h, Λ,
R, Re1, Re2 and We. Keep We
roughly constant and hence use
surface tension to dampen small
wavelength instabilities in order to
inhibit turbulent mixing. Thus isolate
long wavelength instabilities. Avoid
the Rayleigh and superpulsating
break-up regimes. Keep Re1 and
Re2 above 300. Examine the
response of the m=0, m=1and m=2
modes, as R, h and Λ are varied.
If done carefully, this
series of experiments
is an excellent test of
the theory and has a
good chance of
success.
As above
As above
Absolutely Unstable
helicoidal mode (m=1)
Note: it may be more practical to fix
R and to vary h and Λ. This will not
affect the analysis.
Absolutely Unstable
sinuous mode
(combined m=1 & m=-1)
All modes
Convectively Unstable
2. Confinement affects the swirl
number at which global modes of coflow jets become linearly unstable, in
the way deduced from the model
As above
Confined co-flow wakes and jets with swirl,
with vortex breakdown
MOTIVATION
Industrial
Fuel injectors in aeroplane engines use confined swirling flows to mix liquid and gaseous reactants as
rapidly as possible. The swirl is powerful enough to induce vortex break-down, where a recirculating slug of air sits just
downstream of the injector. This stabilises the flame. Experiments (Loughborough) and numerical simulations (Cerfacs)
show that these vortices also tend to precess. Occasionally a precessing double-helix forms. These precessing vortices
mix reactants thoroughly and therefore improve combustion efficiency. By investigating the dependence of the precession
on confinement ratio and on the confined length, useful design rules for injectors can be developed.
The configuration examined here is, nevertheless, quite different to actual aero engine injectors. For this reason, the PI is
in regular contact with Loughborough University, who perform thorough diagnostics on more realistic geometries.
Inevitably, it is harder to isolate individual control parameters on realistic geometries and, with so many to change, the
number of data points for each control parameter is limited. The work proposed here will deliberately limit the number of
control parameters and carefully test their influence. Results will be compared with the theoretical model, which has the
same control parameters. Thus this work will bridge the gap between the theory of a simple geometry and the results of a
realistic geometry.
There is little in-depth understanding of how confined swirl injectors work. Current designs have been achieved through
informed 'trial and error' experiments. However, an analysis of aero-engine fuel injectors shows that confinement ratios
have converged to regimes which, according to the model, will produce strong absolute instability. This has caused
considerable industrial interest. [letter from RR?]
Scientific
In certain conditions, m=1 and m=2 azimuthal modes have been shown to form behind unconfined burst
vortices [Ref Ruith et al (2003)]. The hypothesis to be tested here is that confining the upstream end of a burst vortex
enhances the m=1 and m=2 absolute instability and hence enhances transition to a global mode. The non-linear development
of these instabilities are, respectively, a precessing vortex and a precessing double-helix. The model developed so far, which
only permits parallel flows, does not represent the actual velocity profiles in a burst vortex. Although this is a useful guide in
the upstream region, only a qualitative match can be expected and other experiments are investigative. Nevertheless, if it is
found that the simple model gives qualitative agreement, the results will be very useful for injector designers.
Confined co-flow wakes and jets with swirl,
with vortex breakdown
EXPERIMENTAL APPARATUS
The apparatus, diagnostics, working fluids and parameters will be the same as the case without vortex breakdown.
However, the swirl number, R, will be higher.
HYPOTHESIS-DRIVEN EXPERIMENTS
Hypothesis
Analysis, water/water
Analysis, water/oil
Comments
1. Confining a burst vortex leads to it
precessing or forming a precessing
double helix.
Vary h, Λ and R. Perform a
qualitative examination of flow using
PLIF flow visualisation and high
frequency PIV.
As for water/water
This has a good
chance of success
and is readily
compared with
results from
Loughborough
INVESTIGATIVE EXPERIMENTS
Question
Analysis, water/water
Analysis, water/oil
Comments
1. What confinement ratios give rise
to precessing vortices?
At values of Λ and R which just give
a precessing vortex, vary h until
precessing stops. Repeat at different
Λ and R.
As for water/water
Compare this with
the case with no
vortex breakdown
2. What confined length gives rise to
precessing vortices?
As above, but vary the confined
length
As for water/water
As above
3. How does confinement affect
downstream mixing?
At fixed L and R, examine two values As for water/water, but use images
of h: one which gives precession and to evaluate droplet distribution
one which doesn't. Use PLIF to
quantify downstream mixing. Note
that comparison with a gas/gas
situation is limited due to the high
Schmidt number
Very useful
experiments, tying in
with work on primary
atomization both in the
group and outside
Confined counter-flow wakes and jets without swirl
MOTIVATION
Scientific
The motivation for this work is scientific. Although the theory is based on velocity profiles which will not exist in
an actual flow, similar theories have been used extensively as useful models for actual flows (Yu + Monkewitz 1988 etc.) .
The theory predicts that confinement will have a very peculiar effect on jets and wakes with slight counter-flow. The absolute
instability of a jet is usually dominated by the m=0 mode. However, at confinement ratios of 0.6 < h < 0.7, the m=1 mode
should dominate. In a wake, where the m=1 usually dominates, the m=2 mode should take over at a confinement of h = 0.3.
This work will examine the axisymmetric equivalent of the two-dimensional counter-flow wake studied by Leu and Ho (2000).
Interestingly, this study showed that stability returned at higher values of counter-flow, a feature which will be examined here.
Confined counter-flow wakes without swirl
EXPERIMENTAL APPARATUS - WAKES
Overview
The rig and diagnostics will be identical to that used for the co-flow experiments. However, the servo-piston
will move in the opposite direction and suck fluid up the inner injector. Only water/water experiments will be performed.
HYPOTHESIS-DRIVEN EXPERIMENTS
Hypothesis
Analysis, water/water
Comments
1. The unstable region of global
modes in (h,Λ) space is in qualitative
agreement with that predicted by the
theory, shown in the figure below:
Vary h and Λ. Stimulate the m=0, m=1 and m=2
modes. Examine the response to determine the
boundary between stability and instability of
global modes, as for co-flow experiments.
The model predicts rich behaviour of counter-flow
wakes. However, agreement can only be
qualitative because the experiment does not match
the velocity profiles of the model.
2. Around a confinement ratio of 0.3
and over a small range of velocity
ratios, the m=2 mode of a
counterflow wake is more unstable
than the m=1 mode.
At this confinement ratio, look for natural
development of the m=2 mode. Then stimulate
this mode with a specially-designed central
nozzle or a perturbation in the outer flow.
Measure the response at different Λ.
m=1
INVESTIGATIVE EXPERIMENTS
m=0
Question
Analysis
m=2
1. At what level of counter-flow does the global Increase counter-flow until self-sustained
mode become linearly stable again?
oscillations cease.
Confined counter-flow jets without swirl
EXPERIMENTAL APPARATUS - JETS
Overview
The rig will be similar to that used for the co-flow
experiments but the outer flow will be reversed. The diagnostics
will be identical.
Experiments will be performed in bursts, rather than steady state,
in order to prevent interference as the jet is convected back onto
itself.
Water/water and water/oil tests will be performed.
Confined counter-flow jets without swirl
HYPOTHESIS-DRIVEN EXPERIMENTS
Hypothesis
Analysis, water/water
Analysis, water/oil
Comments
1. The unstable region of global
modes in (h,Λ) space agrees with
that predicted by the theory, shown
in the figure below:
Vary h and Λ. Stimulate the m=0,
m=1 and m=2 modes. Examine the
response to determine the boundary
between stability and instability of
global modes, as for co-flow
experiments.
As for water/water
For a short period,
the velocity profile
will be reasonably
good counter-flow.
m=0
m=0
m=1
m=0
m=2
Confined counter-flow wakes and jets with swirl
MOTIVATION
Industrial
Centrifugal separators, such as the Dyson vacuum cleaner, consist of two coaxial flows. The outer flow
contains a particle-laden fluid, which swirls into the separating chamber. The particles gravitate to the outside and the clean
fluid is then sucked through the inner nozzle. This is a counter-flow wake flow exactly like the one being studied here. Control
of the vortex core is a problem in centrifugal separators. Often the vortex becomes unstable and attaches itself to the walls of
the separating chamber, where it entrains the particles that it is trying to avoid (Hoffman et al 1995). The aim of this research is
to understand the dynamics of this situation to see how such instability may be avoided.
Scientific
The model predicts that counterflow wakes and jets will exhibit very rich behaviour. Higher azimuthal modes,
such as m=3, m=4 and m=5 should become absolutely unstable at certain values of h, Λ and R. If velocity profiles are close
enough to those in the model, the experiments will provide a thorough test of the theory.
EXPERIMENTAL APPARATUS
The same apparatus and diagnostics will be used as that in the counter-flow experiments without swirl. For the wake
experiments, swirl vanes will be placed in the outer flow. For the jet experiments, the inner injector will also be rotated.
HYPOTHESIS-DRIVEN EXPERIMENTS
Hypothesis
Analysis
1. The absolute instability region in
(h,Λ,R) space is in qualitative
agreement with that predicted by the
theory
Vary h, Λ and R. Stimulate the m=0 and m=1
modes. Examine the response to determine the
boundary between convective and absolute
instability, as for co-flow experiments. Look for
spontaneous development of higher order
azimuthal modes.
Comments
The behaviour of wakes and jets with counter-flow
and swirl has not yet been completely mapped out
on the model. However, this is a relatively simple
(although time consuming) procedure and will be
completed before these experiments.
Further work
The design of the rig is deliberately versatile. It is anticipated that the basic rig will be used for many years, being adapted as
necessary. Some examples are listed here:
Different density ratios
The density ratio strongly affects whether a flow will be absolutely or convectively unstable,
particularly for density ratios between 0.5 and 2. Fortunately, this range of density ratios is readily achieved in a liquid/liquid
situation.
Water/air experiments
Primary atomisation of liquid jets, with and without swirl, is not well understood. However, it is
very important industrially, particularly for the design of aero-engine injectors. The rig can be adapted so that the outer fluid is
air and the inner fluid is water. Co-flow and counter-flow configurations with or without swirl are possible. The PI's research
group has just started work on Direct Numerical Simulation of primary atomisation. The proposed rig will enable careful
experiments to compare with the simulations.
List of tasks