Proposed experiments on the instability of confined wakes and jets

1. Proposed experiments on the instability of confined wakes and jets Matthew JuniperCAMBRIDGE UNIVERSITY ENGINEERING DEPARTMENT

2. INTRODUCTION Cambridge - Advanced linear stability theory describing the behaviour of confined jets and wakes Cambridge - Test theory with careful experiments under well-controlled conditions Loughborough – Perform thorough tests on realistic injector geometries Rolls Royce - Implement in industrial aero-engine injectors current work The proposed work completes an important link between theory and application 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.

3. Inner flow Outer flow Duct without swirl co-flow without vortex breakdown with swirl with vortex breakdown Confined wakesand jets without swirl counter-flow with swirl 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. A confined wake flow • 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.

4. 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.

5. 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.

6. 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.

7. convectively unstable region absolutely unstable region 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. The non-dimensional surface tension, We, has also been included in the model but, for simplicity, is not shown here. wakes jets 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. co-flow m = 1 m = 0 m = 1 m = 2

8. 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.

9. 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.

10. 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.

11. 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: 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.

12. 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 Water / vegetable oil 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. 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.

13. Convectively Unstable (linearly stable global mode) m = 1 Absolutely Unstable 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. 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. 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.

14. m=1 AU Both modes Absolutely Unstable m=2 AU All modes Convectively 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).

15. 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

16. 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. This information can be obtained from the experiments simply by varying the confined length. 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.

17. convectively unstable region absolutely unstable region 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. W 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. m = 1 m = 2 m = 3 m = 4

18. 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 solid-body 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.

19. Absolutely Unstable helicoidal mode (m=1) Absolutely Unstable sinuous mode (combined m=1 & m=-1) All modes Convectively Unstable 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. Note: it may be more practical to fix R and to vary h and Λ. This will not affect the analysis. 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. 2. Confinement affects the swirl number at which global modes of co-flow jets become linearly unstable, in the way deduced from the model As above As above As above

20. 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.

21. 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 of h: one which gives precession and 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 As for water/water, but use images to evaluate droplet distribution Very useful experiments, tying in with work on primary atomization both in the group and outside

22. 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.

23. 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 mode become linearly stable again? Increase counter-flow until self-sustained oscillations cease.

24. 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.

25. 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

26. 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 Comments 1. The absolute instability region in (h,Λ,R) space is in qualitative agreement with that predicted by the theory Vary h, Λand 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. 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.

27. 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.

28. List of tasks