UNSTEADY AERODYNAMICS OF AN AERO-ENGINE · PDF fileUNSTEADY AERODYNAMICS OF AN AERO-ENGINE...

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Proceedings of ASME Turbo Expo 2004Power for Land, Sea, & Land

June14-17, 2004 - Vienna, Austria

DRAFT GT2004-54212

UNSTEADY AERODYNAMICS OF AN AERO-ENGINE DOUBLE SWIRLER LPPBURNER

Edward CanepaDIMSET - Università di Genova

I-16145 Genova, ItalyE-mail: [email protected]

Pasquale Di MartinoAvio S.p. A - R.& D.

I-80038 Pomigliano d'Arco, Napoli, ItalyE-mail: [email protected]

Piergiorgio FormosaDIMSET - Università di Genova


Marina UbaldiDIMSET - Università di Genova


Pietro ZuninoDIMSET- Università di Genova


ABSTRACTLean premixing prevaporizing burners represent a

promising solution for low-emission combustion in aero-engines. Since lean premixed combustion suffers of pressureand heat release fluctuations that can be triggered by unsteadylarge-scale flow structures, a deep knowledge of flow structuresformation mechanisms in complex swirling flows is a necessarystep in trying suppressing combustion instabilities.

The present paper describes a detailed investigation of theunsteady aerodynamics of a large scale model of a doubleswirler aero-engine LPP burner. A 3-D laser Dopplervelocimeter and an ensemble averaging technique have beenemployed to obtain a detailed time-resolved description of theperiodically perturbed flow field at the mixing duct exit andassociated Reynolds stress and vorticity distributions.

Results show a swirling annular jet with an extended regionof reverse flow near to the axis. The flow is dominated by astrong periodic perturbation which interests all the threecomponents of velocity. Radial velocity fluctuations causeimportant periodic displacement of the jet and the innerseparated region in the meridional plane.

The flow, as expected, is highly turbulent. The periodicstress components have the same order of magnitude of theReynolds stress components. As a consequence the flow mixingprocess is highly enhanced. While turbulence acts on a largespectrum of fluctuation frequencies, the large scale motioninfluences the whole flow field in an ordered way that can bedangerous for stability in reactive conditions.

INTRODUCTIONDue to the rapid increase of air traffic that according to

projections will be doubled within 2020, the reduction ofpollutants associated to air traffic has become a primaryobjective in the design of modern aircraft gas turbine engines.

The trend of advanced combustion chamber is to increaseinlet pressure and temperature in order to increase the efficiencyof the engine cycle and reduce the fuel consumption. This is theonly way to reduce CO2 emissions, one of the most importantcauses of the Green House effect. Increasing of maximumtemperature in the combustor has the drawback of high NOx

emissions that are produced at high temperature.In the conventional combustors the fuel is injected in the

primary zone, provoking regions of stoichiometric mixtureburning at very high temperature with high NOx production.One of the most promising ways to reduce emissions is to injectthe fuel in premixing ducts at exit of which the fuel isprevaporized and the mixture is lean. In this case occurrence ofstoichiometric zones is avoided and NOx production is reduced.

Unfortunately lean premixed combustors suffer fromserious problems related to combustion instabilities, flashbackand autoignition in the premixing ducts. Self-sustained largeamplitude pressure oscillations may cause severe mechanicaldamage to the combustion chambers and in case of flashbackinjectors may be even destroyed.

Due to the technical relevance and scientific challenge ofthe problem, numerical and experimental efforts have beenmade in recent years by the industrial and scientific communityin order to identify and understand the physical mechanismswhich govern the instabilities of lean premixed combustors. An


extensive research activity is currently been carrying out oncombustion instabilities in aero-engines in the framework of aE.C. founded project titled ICLEAC (Instability Control of LowEmission Aero-engine Combustors). The research approach ofICLEAC includes studies on aero-thermodynamics of air-fuelmixing process, thermoacustics of the combustion chambers,heat release and flame response to velocity and pressurefluctuations. The present investigation contributes to theresearch project with detailed experiments on the unsteadyaerodynamics of LPP systems in isothermal conditions. Theinvestigation is focused on the detection of large-scale periodicflow structures that may drive low frequency combustioninstabilities in real LPP geometries.

A special feature of the present experiment is the largescale of the LPP model under investigation which results in avery high spatial resolution of the measurements. The injector isa double co-rotating swirler premixing device representative ofadvanced aero-engine LPP technology.

The great details of the experiment and the simultaneousdetection of the three velocity components allow acomprehensive description of the unsteady flow field whichincludes Reynolds stress distributions and time resolvedvorticity vector. The results help to clarify some still unresolvedaspects of the unsteady aerodynamics of premixing swirlerdevices and provide a suitable data base for advanced CFDcodes assessment.

NOMENCLATUREC velocityD mixing tube exit diameterf frequencyp static pressurer radial coordinateR1,R2, autocorrelation of signal 1 or 2R12 crosscorrelation of signals 1 and 2t timeT periodx axial coordinate at the mixing tube exitρ densityΩ vorticity

Subscriptsa in the axial directionr in the radial directiont in the tangential direction

Superscripts and overbars' fluctuating component time averaged~ ensemble averaged

EXPERIMENTAL FACILITY AND INSTRUMENTATION

Experimental set upThe experiments were carried out on a large scale model

(5:1) of an LPP (Lean Premixing Prevaporizing) injector foraero-engine applications.

The LPP injector was designed by Avio S.p.A with thetargets to have a limited length and a fixed external and exitdiameters in order to be mounted in a pre-existing combustorcasing. The design was divided in 2 phases: in the first onesimple 1D methods were used to obtain a a limited number ofpremix duct geometries with specified swirler angles andnumber of blades that assured the desired swirl number. In thesecond phase the chosen geometries were analyzed by CFD(single phase and two-phase flow) to assess if the performance(including the vaporization rate) were acceptable.

The LPP injector geometry is currently being utilized in theframework of the E.C. project ICLEAC for research purposes:assessment of numerical tools (RANS and URANS codes)versus experimental results, and investigation of unsteady flowphenomena in swirling flow LPP combustion systems.

The device is a co-rotating double swirler centripetalinjector. The injector is depicted in Fig. 1. It has been designedwith the objective to obtain a high degree of prevaporizationand air-fuel mixing within a very short axial length of thepremixing tube. The large initial section of the mixing tubeaccompanied by a large degree of swirling flow determines asuitable residence time for fuel vaporization. The followingstrong contraction with flow acceleration maintains the wallboundary layer thin, helps preventing flame flashback, andkeeps residence time moderate in order to not exceedautoignition limits. The design swirl number is 0.5.

The experiments were carried out within an atmospherictest rig with isothermal flow. Due to the relevance ofaerodynamic phenomena in the subsonic range, real operatingconditions were scaled down to atmospheric conditions usingthe Reynolds similarity.

Different operating conditions have been tested. Extensiveinvestigations have been performed at the maximum poweroperation. The corresponding Reynolds number based on the

Figure 1. LPP injector


mixing tube exit diameter and the mean axial velocity at the exitis 260000. Test conditions are summarized in Table 1.

Air is fed to the LPP injector model through the settlingchamber of a wind tunnel equipped with a honeycomb andscreens to guarantee steady uniform flow at the inlet. The LPPmixing tube terminates in a rectangular single sector combustor.The mixing tube exit diameter is 104 mm. The flame tube has asquare cross section of 250 mm x 250 mm with optical accessfrom three sides. and it is 750 mm long.

The large scale of the test article allows for a high degreeof spatial resolution which is an important prerequisite for acareful investigation of the flow organized structures that mayaffect the flow field and for the generation of data bases ofexperimental results suitable for CFD code assessment.

The experimental domain is shown in Fig. 2. Theexperimental grid is made of 25 radial traverses from x/D=0 tox/D=1.29. Each traverse is defined by 40 measuring pointsranging from r/D=0 to r/D= 1.00. The total number ofmeasuring points is 1000.

The main instrumentation consists of a fiber optic 3D LDVsystem. An hot-wire anemometer was employed for preliminaryinvestigation, for frequency domain unsteady flow analysis andfor the generation of a reference signal for phase locked LDVdata acquisition and data processing. The measurement chain isshown in Fig. 3.

3D LDV system characteristicsTime resolved measurements of the three velocity

components of the flow at the exit of the LPP burner have beenperformed by means of a six-beam three-color fibre optic LDVsystem with back-scatter collection optics (Dantec Fiber Flow).The light source is a 300 mW argon ion laser operating at 514.5nm (green), 488 nm (blue) and 476.5 nm (dark blue).

The LDV set up is obtained combining a 2D and a 1Doptical probe, both with 310 mm focal length. Typical probe

volume dimensions were 90 µm diameter and 1.9 mm length.In order to obtain coincidence of the two probe volumes

one of the optical probe is mounted on a manual micrometric 3axis plus rotation stage. A special view-finder made of a 120µm pinhole and two photodiodes is used to monitor themicrometric movements and verify the volumes coincidence.

The twin-probe assembly is stiffly mounted on a three-axiscomputer-controlled probe traversing mechanism. The motionis transmitted to the carriages by stepping motors through apreloaded ball-screw assembly with a minimum lineartranslation step of 8 µm. A Bragg cell is used to apply afrequency shift (40 MHz) to one of each pair of beams,allowing to solve directional ambiguity and reduce angle bias.

The flow is seeded with a 0.5-2 µm atomized spray ofmineral oil injected in the settling chamber. The signal from thephotomultipliers were processed by three Burst SpectrumAnalysers (Dantec BSA). Measurements of the three velocitycomponents were made in coincidence mode. Typical values ofthe data rate were in the range 1000-5000 Hz. In therecirculating flow regions the data rate failed down to fewhundreds Hz.

LDV data processingIn the present experiment an ensemble averaging technique

suitable for LDV data processing has been applied. A singlesensor hot-wire probe located in the flow field provides areference signal in phase with the relevant periodicphenomenon. To obtain statistically accurate ensembleaverages, a total of 120000 validated data for each velocitycomponent have been sampled at each measuring position.Instantaneous velocities are sorted into 30 phase bins eachrepresenting a particular phase of the cycle.

According to the triple decomposition scheme proposed by

Figure 2. Measuring point locations

Table 1. Test conditionsUpstream total pressure pt1 = 103520 PaUpstream temperature Tt1 = 298 KStatic pressure downstream p2 = 101300 PaReynolds number Re = 2.6x105

Figure 3. LDV measurement chain


Reynolds and Hussain [1] for the study of coherent structures inshear flows, a generic velocity component v in a genericposition P can be represented as the sum of the time averagedcontribution v , the fluctuating component due to the periodicmotion )~( vv − and the random fluctuation v’.

')~( vvvvv +−+= (1)

The time-varying mean velocity component v~ can beobtained by ensemble averaging the samples.

∑=

=iK

ki

kivK

iv1

),(1

)(~ (2)

where i = 1 ... I is the index of the phases into which aperturbation period is subdivided and k = 1...Ki is the index ofthe samples for each window associated with a particular phasei.

The time averaged velocity component v can be simplydetermined as

∑=

=I

i

ivI

v1

)(~1(3)

Ensemble averaged rms, which are proportional to theReynolds stress normal components, are obtained as

( ) [ ]∑=

−−

=iK

ki

ivkivK

iv1

22 )(~),(1

1)(

~' (4)

The results are collected in a data base of 3 ensemble

averaged velocity components ( aC~

, tC~

, )~

rC and 6 ensemble

averaged Reynolds stress components (~

2'aC , ~

2' tC , ~

2' rC ,~

'' ta CC , ~

'' ra CC , ~

'' rt CC ). Each component is defined as a

function of the spatial coordinates (x, r) and time t (phase) for atotal of 25x40x30 values.

The ensemble averaged velocity and Reynolds stresscomponents have been further averaged in time to obtain a setof time averaged components defined on the spatial measuring

domain ( aC , tC , rC , ~

2'aC , ~

2' tC , ~

2' rC , ~

'' ta CC , ~

'' ra CC ,

~'' rt CC ).

According to the triple decomposition theory, the timeaveraged momentum equation of a flow with relevant periodicfluctuations contains additional terms, analogue to the Reynoldsstress components, due to the time correlations of the largescale periodic fluctuations. These six additional stresscomponents have also been evaluated:

2)~

( aa CC − , 2)~

( tt CC − , 2)~

( rr CC − , )~

)(~

( ttaa CCCC −− ,

)~

)(~

( rraa CCCC −− , )~

)(~

( rrtt CCCC −− .

LDV measurement accuracyA comprehensive review of errors in laser-Doppler

velocimetry measurements and guidelines to evaluate them are

given by Boutier [2] and Strazisar [3]. A specific evaluation ofthe errors for frequency domain processors is given byModarress et al. [4].

The error on the instantaneous velocity due to randomnoise from the photomultiplier tube depends on the backgroundscattered light and on the processing technique. BSA canmeasure with a signal to noise ratio as low as -5 dB, withoutapparent increase of the standard deviation [4]. The resolutionof the BSA processor depends on the record length of the FFTand on the background noise. For the present experiment, evenin the worst cases, it was below 1 percent of the mean velocity.

A statistical bias can occur because the arrival times of themeasurable particles are not statistically independent on theflow velocity which brings them into the probe volume. If thevelocity is not constant in time, the resulting non-uniform datasampling causes an error when simple arithmetic averages areperformed. To obtain correct time averages instantaneous, dataneed to be weighted with the residence time of the particles inthe measuring volume. However the ensemble averagingprocedure that has been widely adopted in the presentexperiment, where the samples in each bin are statisticallyindependent because collected during different cycles, avoidsstatistical bias, as observed by Lyn et al. [5].

Angle bias occurs when the particle trajectories are notnormal to fringe orientation. Moving the fringe pattern in theprobe volume by means of the Bragg cell allows to minimisethis error. For the present experiment the angle bias was keptlower than 1 per cent of the mean velocity.

Statistical uncertainty in mean and rms velocities dependson the number of sampled data, turbulence intensity andconfidence level [2]. For the present experiment, considering atypical set of 1000 sampled data, a confidence level of 95 percent and a local turbulence intensity of 50 per cent,uncertainties of ± 3 and ± 5 per cent are expected for the meanand rms velocities, respectively.

RESULTS AND DISCUSSION

Spectral characteristics of the flowTo evaluate the time-varying flow characteristics, a single

sensor hot-wire probe (DANTEC P11) was operated with aConstant Temperature Anemometer (DANTEC M10).

For each measuring point the CTA signal was low-passfiltered at 25 kHz and sampled at the frequency of 50 kHz. Thetotal number of data taken for measuring point was 135168.These data were used for evaluating power density spectra with32 FFT of 8196 data, 50% overlapping.

The hot-wire probe was traversed at several locationswithin the experimental domain shown in Fig. 2. An example ofvelocity time-traces (x/D=0.1, r/D=0.4) and associated powerspectral density is shown in Fig. 4. At this point the flow isperturbed by large amplitude oscillations. From the densityspectra a well distinct frequency containing energy at about 220Hz is detectable. The corresponding Strouhal number StD = f


D/U based on mixing tube exit diameter D and averaged exitaxial velocity U is 0.58.

Similar frequencies were identified in swirling flows byChao et al [6] and Li and Gutmark [7]. They associated thesevelocity oscillations to the precessing vortex related to thevortex breakdown phenomenon. Similar features are reportedalso by other authors investigating swirling flow burners [8, 9].

In the present investigation the same frequencies have beendetected for all the axial traverses investigated and for mostradial locations. However the energy peak attenuated toward theaxis and was completely suppressed in the region outside theexhaust swirling jet.

To find typical perturbation propagation speeds, two hot-wire probes were displaced in space: in axial direction (sameradial and circumferential positions) and in circumferentialdirection (same radial and axial positions). Signals from the twoprobes were sampled simultaneously and cross-correlated intime.

At r/D=0.4 the propagation speed in axial direction wasapproximately 20 m/s, which is about one half the mean axialvelocity at the mixing tube exit. This value is fairly close to theaxial phase speed evaluated in the experiments of Panda andMcLaughlin [10] on the instabilities of excited swirling jets.

At x/D=0.1 the two probes were circumferentiallydisplaced of 90 deg as shown in Fig. 5. Auto and cross-correlations of the signals according to the following definitionswere evaluated at different locations:

∫ τ+=∞→

T

Tuu dttutu

TR

0

)(')('1

lim

∫ τ+=∞→

T

Tuv dttvtu

TR

0

)(')('1

lim

where u' and v' are the fluctuating signals from the two hot-wireprobes.

Autocorrelation functions show that signal periodicity isconserved for a large radial extension. Periodicity is attenuatednear to the axis (r/D=0.04) and it is completely lost outside thejet (r/D=0.6).

At r/D=0.4 the autocorrelation peak for t=0 is only slightlylarger than the amplitude of the periodic oscillation, indicating avery relevant periodic content compared to the stochastic partof the signal.

It is interesting to observe that from r/D=0.4 to r/D=0.15the time lag between the signals of the two probes evaluated bythe cross-correlation function peak positions was nearlyconstant and equal to one quarter of the fluctuation periodτ=0.0045 s. That means the periodic phenomenon observed is aperturbation which propagates in circumferential direction atconstant rotational speed, covering one revolution during oneperiod of the velocity fluctuation for all the radial positions.The rotational speed of the perturbation resultedω=2π/0.0045=1382 rad/s.

This analysis confirms the precessing nature of thefluctuations. It establishes also the rationale for the spatialreconstruction of the periodic flow field from phase-lockedvelocity distributions detected with a common phase referencesignal at different spatial positions.

0.000 0.020 0.040 0.060t (s)

0

20

40

60

80

100

c (m

/s)

x/D=0.1 r/D=0.4

10 100 1000 10000f (Hz)

1E-005

1E-004

1E-003

1E-002

1E-001

1E+000

1E+001

1E+002

pow

er d

ensi

ty

(m2 /

s2)

Figure 4. Velocity time trace and power spectrum

0 0.004 0.008 0.012 0.016 0.02

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

R1

R2

R1

2

R1

R2

R12

r/D=0.6

0 0.004 0.008 0.012 0.016 0.02

-0.10

-0.05

0.00

0.05

0.10

R1

R2

R1

2

r/D=0.4

0 0.004 0.008 0.012 0.016 0.02

-0.10

-0.05

0.00

0.05

0.10

R1

R2

R1

2

r/D=0.15

0 0.004 0.008 0.012 0.016 0.02t (s)

-0.10

-0.05

0.00

0.05

0.10

R1

R2

R1

2

r/D=0.04

1

2

T/4

Figure 5. Auto and cross-correlations of signals ofprobes 1 and 2 at the premixer duct outlet (x/D=0.1).


Time averaged velocity distributionsA survey of the time averaged distributions precedes the

analysis of the time-varying periodic flow to provide an overallunderstanding of the flow field. The time averaged flow fieldrepresent the base upon which the motion of organized flowstructures is superimposed.

Figure 6 on the left shows the time averaged axial velocitydistribution in the meridional plane downstream of the mixingtube exit. Vector plot of the meridional velocities issuperimposed.

The distribution of the axial velocity reveals that the flow isconcentrated in an annular jet confined by two recirculationzones. Close to the mixing tube exit the jet has large positivevalues of axial velocity which gradually decrease with axialcoordinate increase. Moving downstream, the jet diverges andthe cross section becomes larger. At the same time, due toturbulent mixing, the distribution tends to attenuate non-uniformities.

A moderate corner recirculation zone is present betweenthe external edge of the jet and the flame tube wall, but the mostimportant feature is the existence of an extended recirculationzone near the centerline associated to the large tangentialmomentum and the sudden jet expansion in the combustionchamber.

The superimposed vector plot provides an immediaterepresentation of the meridional mean flow field. The suddenjet section enlargement and the two inner and outer separatedflow regions are highlighted. Two couples of vortices can bewell identified: the first one located in the outer region of the jetin the initial part of the flame duct, which is typical of abruptsection enlargement; the second couple is situated at the

interface between the jet and the inner recirculation bubble at x= 70 mm. This second couple seems to separate the ring likeflow into two regions: an upstream one characterised by thereverse flow leaving the bubble, and a downstream area wherethe flow enters the bubble moving from outer diameter towardsthe duct axis.

The distribution of the time averaged tangential velocitycomponent is shown in Fig. 6 on the right. The tangentialvelocity component behaves like a Rankine vortex with freevortex distribution in the external region and solid body rotationnear the jet centerline.

Moving downstream the tangential velocities undergo arapid decay that can be explained by the divergence of the jetand the dissipation of the angular momentum due to theturbulent diffusion action against flow non-uniformities. Thedecay of the centrifugal force associated to the tangentialvelocity represents in swirling flows the main mechanism offlow separation at the centerline, as explained by Merkle et al.[11]. In the meridional plane the flow is in equilibrium in radialdirection under the centrifugal acceleration associated to theswirl (Ct

2/r) and the centripetal radial pressure gradient

∂∂

ρ−

r

p1. The radial equilibrium generates a minimum of

pressure on the axis. If the centrifugal force decays indownstream direction also the radial pressure gradientdecreases and consequently the minimum of pressure on theaxis attenuates generating a positive gradient along the axis. Ifthe axial gradient of angular momentum is large (large swirlnumber and rapid tangential velocity decay) the flow near theaxis separates and a flow recirculation bubble forms.

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100

60

54

48

42

36

30

24

18

12

6

0

-6

-12

Ca (m/s)

___~

x (mm)r

(mm

)

0 50 100 150

-100

-50

0

50

100

40

36

32

28

24

20

16

12

8

4

0

Ct (m/s)

___~

Figure 6. Time averaged velocity components distributions


It is a well-know fact that a recirculation core, obtained bya swirling ring like jet, is a flow structure suitable forcombustion chambers applications, acting as a fluid-dynamicflame-holder. By the way the recirculation zone has not toextend upstream of the premixing duct exit section to avoidflashback phenomena. The profile of mean axial velocity showsthat the reverse flow zone interests, at the end of the convergingnozzle, a round section with a radius of about 20 mm. Thatindicates that the recirculating bubble begins within thepremixing duct. Besides, once the bubble reaches the flameduct, it expands quickly up to a diameter of about 40 mm thatremains quite constant through the channel until the end of theinvestigated zone, where no trend of closure appears.

Time averaged rms of turbulent and periodicfluctuations

Figure 7 shows the distributions in the meridional plane ofthe time averaged rms of turbulent and periodic fluctuations.

The )'(~aCsmr distribution indicates that large turbulent

fluctuations are placed at the border between the reverse flowzone and the swirling jet and maximum values are located inlater axial positions (from x=40 to x=130 mm). On the other

hand the )~~

( aa CCrms − distribution shows that the intensity of

periodic fluctuations in the flow is strong in a region very closeto the inlet section and decreases quickly in axial direction..Downstream x=100 mm the periodic feature is no longersignificant. In this zone the turbulent fluctuations increase andreach the maximum. On the axis, within the reverse flow

internal core, both )'(~aCsmr and )

~~( aa CCrms − values are low.

The )'(~rCsmr has the same order of magnitude of the mean

radial velocity component. Two symmetrical maxima for x = 70mm and r = 30 mm are present. In the same region also

)~~

( rr CCrms − is large. The general behaviour of

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 20

18.2

16.4

14.6

12.8

11

9.2

7.4

5.6

3.8

2

rms(C'a)

_______~

(m/s)

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 20

18.2

16.4

14.6

12.8

11

9.2

7.4

5.6

3.8

2

rms(C'r)

_______~

(m/s)

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 20

18.2

16.4

14.6

12.8

11

9.2

7.4

5.6

3.8

2

rms(C't)

_______~

(m/s)

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 20

18.2

16.4

14.6

12.8

11

9.2

7.4

5.6

3.8

2

rms(Ca - Ca)~ ~

__

(m/s)

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 20

18.2

16.4

14.6

12.8

11

9.2

7.4

5.6

3.8

2

rms(Cr - Cr)~ ~

__

(m/s)

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 20

18.2

16.4

14.6

12.8

11

9.2

7.4

5.6

3.8

2

rms(Ct - Ct)~ ~

__

(m/s)

Figure 7. Time averaged rms of turbulent and periodic fluctuations


)~~

( rr CCrms − indicates that the strongest periodic fluctuations

are localised near to the axis at the premix duct exit. Movingdownstream this periodic unsteadiness remains high on aconical region extending up to x=100 mm and r = 70 mm.

Both periodic and random fluctuations of Ct show highintensity near to the axis especially in the sections near to themixing duct exit. Here is located the zone of solid body rotationdistribution, where the mean tangential velocity undergoes themaximum radial gradient decreasing to zero on the centreline.

Concerning intensity of turbulent and periodic fluctuations,the axial components are by far the largest, while the tangentialones are the lowest.

Time averaged turbulent and periodic shear stressesTime averaged turbulent and periodic shear stresses have

been evaluated according to the definitions reported in the dataprocessing paragraph. A qualitative analysis of the distributionscan be attempted making reference to the eddy viscosity

concept. In the present paper only the ~

'' ra CC component is

considered (Fig. 8)

∂∂+

∂∂

µ−=ρ=τ=τx

C

r

CCC ra

Traraar

~''

Assuming that streamwise variations ( x∂∂ ) are smaller

than radial variations ( r∂∂ ), a simplified relationship for arτ

can be obtained

∂

∂µ−≅τ

r

CaTar

Looking at the radial variation of the axial velocitycomponents (Fig. 6), one can observe an initial positive radialgradient of the velocity near to the axis which is followed in theexternal part of the annular jet by a negative velocity gradient.This distribution explains the alternating of negative andpositive variations of this shear stress component in radialdirection.

The ~

'' ra CC term represents the axial momentum transfer

in radial direction. Its effect on the axial velocity distributioncan be understood making reference to the turbulent diffusionterm in the axial momentum equation, the most significant

contribution should in fact come from the term )(1

rarrr

τ∂∂− .

The term can be evaluated taking the radial gradient of the~

'' ra CC distribution (Fig. 8). Beginning from the axis outward,

initially negative gradients result in positive axial momentumtransfer to the flow near the axis, then positive radial gradientsresult in negative axial momentum transfer in the region of thelargest jet axial velocity. Finally negative radial gradientscorrespond to a positive axial momentum transfer to the

peripheral region of the jet. Therefore ~

'' ra CC acts to make

uniform the axial flow distribution. The periodic stresscomponent has the same order of magnitude of the Reynoldsstress component and the distributions are very similar.Therefore both terms act in a similar way and the jet mixing ishighly enhanced. However, while turbulence acts with a largespectrum of fluctuation frequencies, the large scale motioninfluences the whole flow field in an ordered way that can bedangerous for stability in reactive conditions.

Time Evolution of Ensemble Averaged QuantitiesFigure 9 shows the axial velocity component distribution in

the meridional plane during six sequential phases within theperiod of the perturbation. Superimposed is the vector plot ofmeridional velocity.

Considering the axial velocity component at the non-dimensional time t/T =0, an intense velocity spot (about 60 m/s)is placed at the beginning of the investigated area in the upperpart of the flow field, near the outer radius of the convergingnozzle of the premixing duct. Increasing the t/T parameter, thespot moves towards larger diameters, and proceedingdownstream progressively reduces its intensity. For t/T =0.51 anew spot arises in the same initial section, but in the oppositepart of the flow field, behaving in the same way of the first one,and therefore defining an evident periodic pattern with a spotrelease every half period.

This velocity distribution is consistent with a rotating spiralflow structure, whose intersection with the meridional plane is ahigh axial velocity spot, that appears alternatively in the upperand in the lower part of the duct and, proceeding downstream,moves to increasing diameters.

x (mm)

r(m

m)

0 50 100 1

-100

-50

0

50

100

C'a C'r~

____

x (mm)

r(m

m)

0 50 100 150

-100

-50

0

50

100 80

64

48

32

16

0

-16

-32

-48

-64

-80

(Ca-Ca)(Cr-Cr)~

____________

(m2/s2)~ ~~

__ __

Figure 8. Time averaged turbulent and periodic shearstresses


Another relevant feature is that the recirculation bubblelooses the axisymmetric time averaged configuration and itsdeformation is strongly connected with high velocity spots inthe outer flow. The region nearby the axis is affected by largeoscillations in velocity: during the period, for a radius betweenr=20 mm and r=30 mm, the axial velocity fluctuates from amaximum of around 30 m/s to a minimum of 12 m/s in thereverse direction.

The vector plots point out the presence of large eddieslocated at the border between the jet and the inner reverse flowzone. For instance, at the non-dimensional time t/T = 0, threemajor structures are clearly recognisable, they are located atabout x = 30 mm and r = 25 mm, x = 65 mm and r = -30 mm, x= 105 mm and r = 40 mm. The two eddies in the upper regionof the channel are rotating clockwise, the one in the lower half-

plane is rotating counter-clockwise. This peculiar configurationcan be explained by the presence of a spiral vortex core, whosewinding cut by the meridional plane appears as a sequence ofvortex cores.

When t/T increases, the eddies move downstream. Fort/T=0.34 one of the two upper eddies has already left theinvestigated area, at t/T =0.51 the general flow structure issimilar to the one showed in the distribution at t/T=0, but simply180° turned around the centreline and the same occurs for nextphases.

Another important feature pointed out by the time sequenceof vector plots of Fig. 9 is the close connection between theasymmetry of the inner separation bubble and the location ofthe spiral vortex cores. The presence of the vortex coredetermines a local outward radial displacement of the separated

0 50 100 150-100

-50

0

50

100

r(m

m)

t/T = 0

0 50 100-100

-50

0

50

100 t/T = 0.17

0 50 100 150x (mm)

-100

-50

0

50

100

r(m

m)

t/T = 0.51

0 50 100 150x(mm)

-100

-50

0

50

100t/T = 0.69

0 50 100 150x (mm)

-100

-50

0

50

100t/T = 0.85

0 50 100-100

-50

0

50

100

60

54

48

42

36

30

24

18

12

6

0

-6

-12

Ca

(m/s)t/T = 0.34

~

Figure 9. Vector plots superimposed to ensemble averaged axial velocity in the meridional plane


bubble contour that gives rise to radial oscillations of theseparated region and consequently also of the surrounding jet.

Ensemble Averaged Axial Velocity Distributions inCross Sectional Planes

Figure 10 shows the ensemble averaged axial velocitydistributions at a fixed time instant for six different crosssections located in the first part of the investigated region, i.e. innon dimensional coordinates between x/D = 0 and x/D = 0.63.Moving downstream the inner recirculation bubble enlarges,while the annular jet moves towards increasing diameters andthe external recirculation zone observable in the initial sectionsdisappears.

Furthermore the circumferential distribution of the axialcomponent in the annular jet shows a high velocity spot which,moving through the six sections, spreads up and reduces itsintensity. The spot’s axial evolution allows to determine what isthe spiral winding enveloping sense. By following the

circumferential displacement of the high velocity core in the sixsections, it is possible to find that the helix is formed bywindings whose direction is clockwise, and therefore oppositeto the main flow rotation. Also the central recirculating bubbleis not fixed with respect to the centreline of the exhaust ductshowing an oscillation strictly connected with the azimuthalmotion of the helix.

VorticityThanks to the fine spatial resolution of measurements, the

time-varying vorticity can be evaluated directly from the curl ofthe ensemble averaged velocity components.

r

aC

x

Crt ∂

∂−∂∂

=Ω~~

~

ϑ∂∂

−∂∂=Ω r

taC

rCr

rr

~1

)~

(1~

x/D=0.10

x/D=0.46 x/D=0.63x/D=0.33

x/D=0.00t/T=0

60

54

48

42

36

30

24

18

12

6

0

-6

-12

Cax/D=0.21

~(m/s)

Figure 10. Instantaneous distribution of ensemble averaged axial velocity in cross sectional planes


x

CC

rta

r ∂∂

−ϑ∂

∂=Ω

~~1~

Tangential vorticity. The time evolution of the tangentialcomponent of the vorticity of the time-varying flow field,depicted on the meridional plane, is shown in Fig.11. Themeridional plane is approximately divided in two concentricregions of positive and negative vorticity. The dividing surfaceis not axisymmetric and changes time. The negative vorticity inthe inner region is associated to the shear layer existing betweenjet and separated flow zone. The positive vorticity in theexternal region is associated to the shear layer between jet andquiescent external flow.

Vorticity associated to the spiral vortex is organised innuclei of large negative values. They are shed at the mixingtube exit, since the forward stagnation point of the innerrecirculation zone is internal to the duct and the spiral vortex is

expected to originate (breakdown point) from the centrelinenear to the stagnation point, as demonstrated in the experimentof Brücker [12].

In practice the positive vorticity annulus seems to be morestable in time, while the negative vorticity starts near to the axis(see for instance t/T=0.69), moves progressively outwards(t/T=0.85, t/T=0.0, t/T=0.17), at a certain position (t/T=0.34,t/T=0.51) it interacts and "cuts" the positive vorticity intoorganised loops.

The vorticity peak values are of the order of 4000 s-1, valuewhich is one order of magnitude larger than the referencevorticity based on the maximum tangential velocity and themixing tube radius.

The vorticity nuclei move downstream with a velocity thatcan be calculated from the axial distance (90 mm) travelled inone period (T = 1/f = 1/220 s). This propagation velocity results

x (mm)

r(m

m)

0 50 100 150-100

-50

0

50

100

t/T = 0.510 50 100

-100

-50

0

50

100t/T = 0.17

x(mm)0 50 100 150

-100

-50

0

50

100t/T = 0.69

x (mm)0 50 100 150

-100

-50

0

50

100t/T = 0.85

r(m

m)

0 50 100 150-100

-50

0

50

100t/T = 0

0 50 100-100

-50

0

50

100

4

3.2

2.4

1.6

0.8

0

-0.8

-1.6

-2.4

-3.2

-4

x1000

(1/s)t/T = 0.34~Ω t

Figure 11. Time evolution of ensemble averaged tangential vorticity in the meridional plane


20 m/s, which is approximately half of the mean axial velocityof the jet and it is equal to the axial propagation speedpreviously evaluated from the cross correlation of the hot-wiresignals.

Axial vorticity The distributions of the axial vorticity inthe cross sectional planes, all represented at t/T=0, are shown inFig. 12. The axial vorticity is structured in a positive nucleusnear to the center and an external annulus of negative values.The pattern is not axisymmetric, but displays a cleareccentricity, and rotates in clockwise direction when the axialdistance of the plane from the mixing tube exit is increased.

Basically the axial vorticity distribution results from theswirling flow rotating counter-clockwise with positivetangential velocity Ct. The inner positive vorticity is associatedto the forced vortex distribution (Ct increasing with radius),while the external negative annulus is due to the external freevortex distribution (Ct decreasing with radius). The asymmetryis due to the periodic perturbation of the radial distribution of Ct

that modifies the free vortex - forced vortex repartition. Theradial displacement of zero tangential velocity determines theoccurrence of sporadic conditions of negative swirling flownear to the axis.

The clockwise rotation of eccentricity confirms that thesense of winding of the spiral is opposite to the mean swirling

flow. Some experimental results for spiral breakdown reportedby Lucca-Negro and O'Doherty [13] indicate that the sense ofwinding of spiral is the same as that of the mean flow, whileother experiments indicate the sense of windings opposite to themean flow. Different explanations for this discrepancy arediscussed in [13] but the problem is still not understood.

CONCLUSIONSThe unsteady aerodynamics of the large scale model of a

LPP injector has been investigated by means of constanttemperature anemometry and 3D laser Doppler velocimetry.

Hot-wire probes provided the spectral characteristics of theunsteady flow. A well defined high energy periodic velocityperturbation was found to affect the swirling flow issuing by theinjector. Cross-correlation of the signals demonstrated that theperturbation rotates with constant angular speed and propagatesin downstream direction at half the flow mean axial velocity.

Phase-locked simultaneous 3D LDV velocitymeasurements provided the time evolution of the 3D flow fieldand time dependent Reynolds stress distributions. Highresolution in space of the measurements allowed directevaluation of the time dependent vorticity field.

Complementary analysis of ensemble averaged velocity,turbulence and vorticity fields provided the bases for the

x/D=0.33

x/D=0.10

x/D=0.46 x/D=0.63

x/D=0.00t/T=0

4

3.5

3

2.5

2

1.5

1

0.5

0

-0.5

-1

x1000

x/D=0.21~Ω a (1/s)

Figure 12. Instantaneous distribution of ensemble averaged axial vorticity in cross sectional planes


physical explanation of the time dependent aerodynamics of theinjector. The flow is dominated by a vortex breakdownphenomenon which results in a complex flow configuration. Anexternal annular jet and an extended reverse flow inner regionoscillate because of the interaction with a precessing spiralvortex developing at the interface between jet and separatedbubble.

The time resolved vorticity field demonstrated that thespiral vortex originates at the centreline within the mixing tubeand propagates downstream in axial and radial directions with aspiral winding in a sense opposite to the mean swirling flow.

Turbulence is extremely large and the periodic stresseshave the same magnitude of the turbulent stresses. As aconsequence the flow mixing process is strongly enhanced andflow non-uniformities decay rapidly. Unfortunately, whileturbulence acts through a large spectrum of fluctuationfrequencies, the large scale organised motion influences thewhole flow in an ordered way, that may be dangerous forstability in reacting conditions.

Future work will focus on the mutual interaction betweenthe fuel spray and the unsteady air flow.

ACKNOWLEDGMENTSThe authors gratefully acknowledge the financial support of

the European Commission as part of the GROWTHprogramme, research project ICLEAC "Instability Control ofLow Emission Aero-engine Combustors", contract no. G4RD-CT2000-0215.

REFERENCES[1] Reynolds, W. C., and Hussain, A. K., 1972, "The Mechanicsof an Organized Wave in Turbulent Shear Flow. Part 3.Theoretical Models and Comparisons with Experiments," J.Fluid Mechanics, 54 (2), pp. 263-288.[2] Boutier, A., 1991, "Accuracy of Laser Velocimetry," LectureSeries 1991-05, VKI, Brussels.[3] Strazisar, T., 1986, "Laser Anemometry in Compressorsand Turbines," ASME Lecture on Fluid Dynamics ofTurbomachinery,.[4] Modarress, D., Tan, H., and Nakayama, A., 1988,"Evaluation of Signal Processing Techniques in LaserAnemometry," Proc., Fourth International Symposium onApplication of Laser Anemometry to Fluid Dynamics", Lisbon.[5] Lyn, D. A., Einav, S., Rodi, W., and Park, J.-H., 1995, "ALaser Doppler Velocimetry Study of Ensemble-AveragedCharacteristics of the Turbulent Near Wake of a SquareCylinder," J. Fluid Mechanics, 304, pp. 285-319.[6] Chao Y., Leu, J., and Hung Y., 1991, "DownstreamBoundary Effects on the Spectral Characteristics of a SwirlingFlow Field," Experiments in Fluids, 10, pp.341-348.[7] Li, G., and Gutmark, E., 2003, "Geometry Effects on theFlow Field and the Spectral Characteristics of a Triple AnnularSwirler," ASME paper No. GT2003-38799.[8] Schildmacher, K., Kock, R., Witting, S., Krebs, W., andHoffman, S., 2000, "Experimental Investigation of the

Temporal Air-Fuel Mixing Fluctuations and Cold FlowInstabilities of a Premixing Gas Turbine Burner," ASME paperNo. 2000-GT-0084.[9] Carrotte, J., and Batchelor-Wylam, C., 2003,"Characterization of the Instantaneous Velocity and MixtureField Issuing from a Lean-Premixed Module (LPM)," ASMEpaper No. GT2003-38663.[10] Panda, J., and McLaughlin, 1994, "Experiments on theInstabilities of a Swirling Jet," Physics of Fluids, 6 (1), pp. 263-276.[11] Merkle, K., Büchner, H., Zarzalis, N., and Sara, O. N.,2003, "Influence of Co and Counter Swirl on Lean StabilityLimits of an Airblast Nozzle," ASME paper No. GT-2003-38004.[12] Brücker, C., 1993, "Study of Vortex Breakdown by ParticleTracking Velocimetry (PTV). Part 2: Spiral-Type VortexBreakdown," Experiments in Fluids, 14, pp. 133-139.[13] Lucca-Negro, O., and O'Doherty, T., 2001, "VortexBreakdown:a Review," Progress in Energy and CombustionScience, 27, pp. 431-481.

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