Laboratory for Turbulence Research in Aerospace and Combustion, Monash University, Melbourne Victoria, 3800, Australia,
Pulsed jets can potentially be integrated into a multitude of aerospace systems, one of which is within a combustion chamber in an aircraft gas turbine engine. A comprehensive understanding of pulsed jets is essential before they can be integrated into aircraft propulsion systems. This paper focuses initially on a flow visualization study of free pulsed jets using Planar Laser Induced Fluorescence (PLIF) followed by instantaneous and mean measurements of the flow field using Multi-grid Cross-correlation Digital Particle Image Velocimetry (MCCDPIV). Experiments were conducted in a quiescent water tank; the jet was generated via a stepper motor actuated piston moving in a 50mm diameter cylinder forcing fluid through a 10mm diameter circular orifice plate. The pulsed jets investigated had Reynolds numbers ranges of 500 – 2500 with frequencies of 1.0-2.0 Hz. The magnitude of the Strouhal number was observed to affect the speed of transition to turbulence. The pulsed jet was observed to have a greater radius of spread compared to a continuous jet.
Nomenclature A = Amplitude of oscillation AR = Contraction ratio Do = Orifice diameter (mm) Dp = Piston diameter (mm) f = Frequency of oscillation (Hz) LD = Slug length Lp = Piston stroke length (mm) Uc = Jet centerline velocity (mm/s) Um = Mean jet velocity (mm/s) UP = Piston velocity (mm/s) Upeak =Maximum jet velocity Rem = Mean Reynolds number of the jet St = Strouhal number T = Period of oscillation (s) ux = Axial component of jet velocity (mm/s) ur = Radial component of jet velocity (mm/s) IW = Interrogation window size (pixel2) δ1/2 = Jet half-width (mm) ρ = Density of water (kg/m3) ν = Kinematic viscosity of water (m2/s) ωθ = Out of plane vorticity (1/s)
I. Introduction ulsed jets can potentially be integrated into a diverse range of applications within aerospace, from stall suppression devices within aerodynamic active flow control systems to mixing aids in propulsion engines.
P * Final Year Undergraduate Student, Department of Mechanical Engineering, Student member #231531
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45th AIAA Aerospace Sciences Meeting and Exhibit8 - 11 January 2007, Reno, Nevada
Pulsed jets differ from continuous jets in that they have an integral periodic oscillatory component, characterized by the velocity amplitude of the imposed forcing. Previous studies conducted revealed higher levels of entrainment in pulsed jets compared to the equivalent continuous jet1. Additionally, other work found that increasing the frequency of oscillation results in an increase in entrainment2. These increasing levels of entrainment after an oscillation is imparted on to the flow carry with them the ability to mechanically enhance mixing within certain fluid streams3. This property makes them particularly useful in vectored thrust applications like VTOL/STOL thrusters for which the length of the mixing zone needs to be minimized.
The focus of this study is to investigate the effect of varying the mean Reynolds number and the frequency of oscillation (Strouhal number) whilst keeping the amplitude of the oscillation constant.
II. Experimental Technique
A. Flow Geometry The experimental measurements of the continuous pulsed jets were carried out in the Laboratory for Turbulence
Research in Aerospace and Combustion at Monash University within an acrylic tank 1000mm long, 500mm wide and 500mm deep, filled with filtered water. To remove the air/water interface within the facility, the tank has a riser tube with an inner diameter of 56.5mm located on the Perspex roof at the far end of the tank from the piston normal to the jet axis, and the facility was filled with water to the Perspex roof. The purpose of the riser tube is to remove the net mass injected during the continuous pulsed jet experiments. A schematic of the experimental facility appears in Fig 1.
In each experiment jets were formed by discharging water from a circular cylinder of inner diameter Dp = 50mm through an orifice plate of diameter Do = 10 mm, positioned in the centre of the end wall of the tank using a stepper motor actutated piston within a cylindrical cavity. The dimensionless groups that characterize the geometry of the apparatus are: a contraction ratio (AR) and a slug length (LD). These are given by AR=Dp
2/D02 and LD=LpAR/D0
respectively where Lp is the stroke length of the piston kept constant in this experiment at 500mm.
Figure 1. Schematic of the
The continuous pulsed jet was generated by programming function illustrated in Fig 2 superimposed over a long, constaanalysis at the interface between the piston and orifice and the imean velocity(Um) of the jet based on the piston speed was calcUc due to the development of a boundary layer as it passes throug
1. Solo PIV Nd:YAG laser 2. Riser Tube 3. Image Plane 4. Piston Assembly 5. Lead Screw 6. Stepper Motor
1
2
3
r6
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the nt ncoulah t
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erimental facility.
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scillate with a time-periodic ke. Using a control volume ntinuity equation Eq.(1), the e Um will not be the same as
(1) 0=⋅∇~U
Pulsed Jet Profile
00.20.40.60.8
11.21.4
0 0.25 0.5 0.75 1
t/T
U/U
m
Figure 2. Normalized pulsed jet velocity profile
Previous experiments conducted in the facility on continuous jets by Cater et al4 revealed the generation of a
reverse flow outside the jets due to the bounded nature of the facility and a minor net migration of the jet towards the riser tube.
B. Experimental Parameters The dimensionless groups that have been identified to chracterise the pulsed jet flow field are the jet Reynolds
number, Strouhal number and Amplitude of oscillation. In order to non-dimensionalize the flow field using the aforementioned parameters the appropriate length, velocity and time scales have to be identified. From the flow generation assembly, the diameter of the orifice was chosen as the length scale to classify the global flow pattern and behaviour. This scale is used in the both jet Reynolds number Eq. (2) and the Strouhal number Eq.(3) The characteristic velocity scale was chosen as the mean velocity of the jet calculated from the mass continuity equation.
ν
omm
DU=Re (2)
The Strouhal number based on the frequency of oscillation and the same velocity and length scales is
m
o
UfD
St = (3)
The amplitude of oscillation is determined by the ratio of the peak velocity above the mean to the mean velocity Eq. (4). The amplitude will be kept constant at A=0.25.
A = (Upeak – Um)/(Um) (4)
The out of plane vorticity was calculated from the MCCDPIV velocity field measurements using a local least- squares fit procedure to the velocity field, followed by analytical differentiation6 using Eq. (5)
xu
ru rx
∂∂
−∂∂
=θω (5)
Following this the out of plane vorticity was normalized by the characteristic length scale (Do) divided by the characteristic velocity scale (Um). From this point on out of plane vorticity will be referred to as vorticity.
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C. Flow Visualisation The effect of the Reynolds number and Strouhal number on the structure of the pulsed jet flow field was
visualised using Planar Laser Induced Fluorescence (PLIF). PLIF involves illuminating a plane of interest within a flow with a laser beam expanded onto a thin light sheet after passing through a cylindrical lens. A camera is oriented orthogonal to the illuminated plane of interest in order to capture a cross-sectional image of the flow field. Following this a fluorescent dye is then injected into the flow. The light from the laser is either scattered by the molecules in the dye or absorbed, if the latter occurs the molecules will fluoresce. The flow visualisations were recorded using a PCO Pixelfly CCD camera with a 55mm telecentric Computar lens with a red light filter, mounted on rails giving three degrees of freedom. The fluorescent dye used for these experiments was Kiton Red 620, which fluoresces orange (corresponding to a wavelength of 620nm) when illuminated by light with a wavelength of 532nm, in this case a dual cavity Nd:YAG laser. Dye was supplied for flow visualisations using a device that provides a constant effusion velocity for liquids5 known as a Mariotte bottle. The effusion velocity of the Mariotte bottle is independent of the reservoir level enabling reproducible experiments. The Mariotte bottle was fitted with a micro valve to precisely adjust the flow rate of the dye. the dye was injected through multiple ports in a cavity behind the orifice plate around the periphery of the orifice.
In each experiment, the piston was moved to its fully forward position and dye was injected into the cavity behind the orifice plate until a visible stream of dye could be seen emerging from the orifice plate, the piston was then slowly retracted sucking the dye into the piston cylinder. The micro-valve was then closed, and time was allowed for any transients in the flow to settle, before an experiment took place. The small injection of mass flux from the dye was assumed to be negligible compared to the mass flux from the continuous pulsed jet.
When conducting any experiment it is necessary to know the limitations of the method. Lim6 advises caution in interpreting vorticity when introducing a scalar quantity (in this case dye) as the dye and momentum may not diffuse at the same rate due to differences in their respective transport equations, Lim notes this is especially important in flows where strong vortex stretching is present.
D. Multigrid cross correlation particle image velocimetry Particle image velocimetry (PIV) is a non-intrusive, optical velocity measurement technique in which the
measurement of velocity is calculated indirectly via the introduction of light reflecting tracer particles within a flow. A plane of interest within the flow is illuminated by 2 successive pulses of a coherent two dimensional light sheet (usually from a laser) spaced a short time apart. The light scattered from the particles by each laser pulse is then recorded using a single exposure photographic method. The two single exposure recordings are then divided into discrete regions known as interrogation windows (IWs) and a cross correlation is performed on the successive exposures within this window. With the knowledge of the time between light pulses both the particle’s displacement and velocity can be determined.
Multigird cross-correlation digital particle image velocimetry (MCCDPIV) has its origins in an adaptive and iterative algorithm which successively refines the size of the IW by instituting a hierarchy of grid levels. Each successive level having a smaller fixed IW size, down to the finest grid level IWn further information regarding the algorithm can be found in Soria7,8.
For the PIV experiments the flow was seeded with Potter’s Sphericel hollow glass spheres, which have a nominal diameter of 11µm and are approximately neutrally buoyant with a particle relaxation time of 7µs. The tracer particles were illuminated by pulsed laser sheets generated by a dual cavity 532nm wavelength Solo PIV Nd:YAG laser. The laser is fitted with an articulated arm and mounted such that it has three degrees of freedom. This laser has an intensity variation that is approximately Gaussian and pulse width of 3-5ns. The time interval between laser pulses was set at 750µs, based on the maximum displacement of the particle being less than 25% of the interrogation window (IW).
The PIV image acquisition was performed using a PCO Pixelfly digital camera with a 1024 x 1280 pixel2 CCD array using a 85mm Micro-Nikkor lens. Pairs of singles exposed images were analysed using an in house developed multigrid cross-correlation digital particle image velocimetry (MCCDPIV) algorithm that is described in detail within Soria6. Details of the performance, accuracy and uncertainty of the MCCDPIV algorithm with applications to the analysis of single exposed PIV images has been reported in7,8. A square isotropic IW was used; the smallest correlation window used in the analysis was 24 pixel2. 161 individual realisations of the MCCDPIV measurements were used to calculate mean velocity and mean vorticity of the flow field.
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III. Results and Discussion Figure 3 represents a sample of the PLIF images taken in this study, with a Rem of 500. At St=0.2, the jet
appears initially laminar with 3 clearly visible vortex pairs, before a breakdown into a transitional jet. At ≈4D0 downstream of the orifice plate structures with considerable larger length scales compared to the orifice are present. As the jet propagates downstream some asymmetry is produced. The St=0.4 condition has only 2 clear vortex pairs are visible before the turbulent breakdown is observed and a more pronounced separation is visible between vortex pairs. Additionally, the aforementioned asymmetry is further pronounced after what resembles vortex breakdown in a swirling jet. It is suggested that the asymmetry of the vortex pairs is due to the development of an azimuthal instability, ultimately resulting in helical motion.
a) b)
9Do
12Do
Figure 3. Dye flow visualizations at Rem=500 up to 12Do downstream.
a) St= 0.2 b) St = 0.4. Figure 4 depicts 2 instantaneous flow visualizations at a Rem=1000, at St=0.1 and St=0.2 respectively. As with
the Rem=500 case the jet is initially laminar before a breakdown into turbulence. At the higher St there appears to be a more rapid transition to turbulence. At St=0.1 flow appears symmetrical as opposed to St=0.2 where asymmetry can be seen downstream. The radius of spread of the jet appears larger for the lower St. The separation between vortex is reduced compared to Rem=500 case.
12Do
a) b)
9Do
Figure 4. Dye flow visualizations at Rem=1000 up to 12D0 downstream. a) St= 0.1 b) St = 0.2.
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Figure 5 depicts 2 instantaneous flow visualizations at a Rem=2000, at St=0.05 and St=0.1 respectively. As with
the Rem=500 case the jet is initially laminar before a breakdown into turbulence, and there appears to be link with the Strouhal number and speed of transition to turbulence and the separation between vortex pairs. Both of the jets appear to be symmetrical along the centerline.
a) b)
9Do
12Do
Figure 5. Dye flow visualizations at Rem=2000 up to 12D0 downstream. a) St= 0.05 b) St = 0.1.
In order to quantify if the St has an influence of the symmetry and radius of spread of the jet MCCDPIV
measurements were taken of the near flow field ( up to 9Do) for the St=0.05 case at a Rem=2000.
From the MCCDPIV measurements of the instantaneous vector plots shown in Fig. 6a) and b) it can be observed the pulsed jet is spreading faster than the continuous jet, additionally the constant jet appears to have constant radius, whereas the radius of the pulsed jet is more variable. It is suggested that this radial variation is relating to the presence of the vortex pairs expanding and contracting the radius of the jet. The pulse jet appears symmetrical up to 1.5D0 as opposed to the constant jet which retains its symmetrical form up to 2D0. The vorticity was observed to decrease more rapidly in the pulsed jet compared to the constant jet. Taking into account the flow visualizations it seems that the vortex appearing in the pulsed jet has an important role in the reduction of vorticity downstream. It is suggested that the vorticity within the constant jet is primarily due to the local vorticity within the shear layer, whereas the pulsed jet has this vorticity within the shear layer in addition to the large vortical structures observed in the flow visualisations.
From analyzing the mean vector flow field (Fig. 7), it is evident that the pulse jet has a greater radius of spread compared to the continuous jet and both jets appear symmetrical along the centerline of the jet. The rate of spread in the continuous jet appears uniform. The mean flow field of the pulse jet seems to have two regions; the first with a uniform rate of spread (similar to the constant jet up to x/Do
of approximately 6) and the second region downstream of x/Do=6 with a sudden increase in the radius of the jet. In order to quantify this, the growth of the jet half-width (normalized by the jet half width at the exit from the orifice) was plotted against axial station normalized by the orifice diameter (Fig 8.). The jet half width is defined as the radius at which the axial velocity is half that of the centerline velocity, and is a property regularly used in the comparison of turbulent jets9. At x=0 the pulsed jet is observed to have a larger half-width (0.35Do) than the continuous jet (0.31Do). This plot illustrates what is initially a similar growth rate of the both the pulsed jet and continuous jet, until x/Do=6 where a divergence in the growth rate of the two jets is observed. However it is interesting to note that this divergence is not present when inspecting the rate of decay of centerline velocity (Fig. 9.) normalized by the center velocity at the orifice. It is suggested that a link may exist between the sudden increase in radius and the faster transition to turbulence by the pulsed jet observed in the flow visualizations.
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During processing the mean out of plane vorticity contour for the pulsed jet, a problem with our experimental procedure was found in that the pulsing frequency of the jet was an integral frequency of the sampling frequency. This resulted in the vortex cores not being fully resolved affecting the computed mean as the samples were not statistically independent. This will be overcome in subsequent experiments by sampling at 3.5Hz instead of 4Hz. Analysis of the mean out of plane vorticity again shows pulsed jet dispersing faster than the equivalent continuous jet. This agrees with the findings of Cater et al (2002)4 who studied a zero-net-mass-flux jet, which is a pulsed jet with zero mean velocity, that the radius of spread is greater for no-zero St.
Figure 7. Mean vector field and vorticity plots for a) Continuous jet Rem=2000 b) Pulsed Jet Rem=2000
St=0.05.
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00.5
1
1.52
2.53
3.54
4.5
0 1 2 3 4 5 6 7 8
x / Do
δ 1/2
/ δ 1
/2 (x
=0)
Continuous JetPulsed Jet
Figure 8.Growth of jet half-width with axial distance.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8
x / Do
Uc /
Uc (
x=0)
Continuous JetPulsed Jet
Figure 9. Decay of Centerline Velocity.
IV. Conclusion The result of an investigation of the flow field of free pulsed jets has been presented. Following flow
visualization using PLIF it was postulated that increasing the St for Rem=500 resulted in the generation of an azimuthal instability affecting a helical motion. A quantitative comparison between a continuous jet at Rem=2000 and a pulsed jet of St=0.05 Rem=2000 was made using MCCDPIV. After analyzing the mean flow field of the pulsed jet two regions of flow were identified, the first with a uniform rate of spread as with the constant jet and the second having a sudden radial increase.
Acknowledgements
First and foremost I would like to thank my supervisors Dr. Damon Honnery and Professor Julio Soria for their patience, support and confidence shown within me. Secondly the support of visiting Masters Student Ms. Carolina Marugan-Cruz from Universidad Carlos III de Madrid is gratefully acknowledged whilst learning the experimental and analytical procedure in taking MCCDPIV measurements from Professor Julio Soria (LTRAC) who was extremely patient with both our questions and our mistakes. I would also like to thank Mr. Kamal Parker (LTRAC) and visiting PHD student Ms. Melissa Green, Princeton University, New Jersey for their technical support regarding experimental set up and post processing of PIV data. Finally I would like to thank Mr. Eric Wirth and Mr. Ivor Little for their skilled workmanship in the manufacture and modification of the experimental facility.
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References
1Crow, S.C., and Champagne, F.H. “Orderly Structure in Jet Turbulence,” J. Fluid Mechanics, vol. 48, Part 3, 1971, pp. 547-591 2Binder G., Favre-Marinet, M., Kueny, J. L., Craya, A., and Laty, R., “Jets Instationnaires,” Labor de Mecanique des Fluides, Universite de Grenoble, Oct 1971 3Wu, J.M., Vakili, A.D., and Yu W.K., 1988 “Mixing of an Acoustically Pulsed Air Jet with a Confined Crossflow”, AIAA Journal, 26, pp.940-947
4Cater, J.E., Soria,J.,2002, “The evolution of round zero-net-mass-flux jets”, J. Fluid Mech. vol. 472, pp. 167-200 5Maroto, J., de Dois, J. and de las Nieves, F., 2002, “Use of a Mariotte bottle for the experimental study of the transition from laminar to turbulent flow”, American Journal of Physics, Vol. 70, No. 7, pp. 698-701 6Lim, T. T, 2000, “Flow-Visualisation: Techniques and Examples”, edited by T.T. Lim and A.J. Smits, published by Imperial College Press 7Soria, J., 1996 An Adaptive Cross Correlation Digital PIV Technique for Unsteady Flow Investigations. In Proc. 1st Australian conference on Laser Diagnostics in Fluid Mechanics and Combustion (ed. Masri, A., Honnery, D.), Univeristy of Sydney, NSW, pp. 29-45. 8Soria, J. 1998 Multigrid approach to cross-correlation digital PIV and HPIV analysis. In Proc. 13th Australasian Fluid Mechanics Conf. (ed. M. C. Thomson & K. Hourigan). Monash University,Melbourne, Australia. 9Abromovich, G.N., 1963, The Theory of Turbulent Jets, M.I.T. Press, Cambridge, Massachusetts
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