Sara Nauri3, Pedro A....

15th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 05-08 July, 2010

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Flow temporal reconstruction from non time-resolved data

Mathieu Legrand1, Shigeru Tachibana2, José Nogueira1, Antonio Lecuona1, Sara Nauri3, Pedro A. Rodríguez1

1: Department of Thermal and Fluids Engineering, Universidad Carlos III, Madrid, Spain, [email protected]

2: Aerospace Research and Development Dir., Japan Aerospace Exploration Agency, Japan; [email protected] 3: Design Systems & Services, QinetiQ, Farnborough, England, [email protected]

Abstract: This paper offers the fundamentals of a space-time reconstruction technique from non time-resolved, statistically independent data. An algorithm has been developed to identify and track traveling coherent structures in periodic flows. Flow field phase average is reconstructed with a correlation-based method, similar to POD. This method provides a tool for shedding light on flow dynamics and allows for global dynamics study, instead of being limited to mean statistics or point-based techniques.

Flow field phase-average is reconstructed with this novel technique. Noteworthy, the involved computational time is relatively small.

Phase-locked average data from time-resolved experiments have been used as a comparison basis. This allows for a direct comparison between real and reconstructed flow fields. Good agreement reveals the method suitability for Particle Image Velocimetry (PIV) measurements. The reconstruction technique is then applied to a set of non time-resolved S-PIV measurements in an atmospheric burner, under combustion conditions.

Finally, the limitation of the technique applicability to any pseudo periodic flow is further discussed on the basis of the relative modes strength of the Proper Orthogonal Decomposition (POD). The discussion offered allows defining a parameter that indicates the suitability of the technique. 1. Introduction

There is an increasing interest in identifying and tracking coherent structures in flows of industrial or scientific interest. They have shown to be key features in the understanding of complex flows and unsteady/transient flow dynamics. Their relevance is especially important to describe flows presenting some periodicity, transition, or unstable phenomena. There are few experimental techniques for coherent structures temporal description of quantitative nature. One of the reasons can be addressed to this simple fact: whereas computational fluid dynamics (CFD) simulations is able to resolve the flow both in time and space, experimental data acquisition is usually limited to either space or time resolution. Two main experimental approaches are available:

i) Single/multi point-wise techniques. They generally give access to high sample rate measurements and allow for temporal evolution comparison at one/several points, e.g. impact probes, thermocouple, hot wire probe velocimetry, Laser Doppler Anemometry (LDA). Their main limitation relies on no global information on the instantaneous flow field; and hence no structure description, excepting when several closely spaced probes can be used to track flow structures during a short time.

ii) Global measurement techniques. They permit extracting coherent structures from the instantaneous field. However, in the context of high spatial resolution and/or flows of industrial interest, measurements generally exhibit a lack of temporal resolution that disables any chance to track structures evolution, e.g. Particle Image Velocimetry (PIV), Planar Laser Induced Fluorescence, etc.


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In the last decade, there is a growing trend in the use of global techniques for the validation of CFD codes and for the experimental verification of prototypes design. In particular, robustness and accuracy of PIV had converted this technique in an appreciated resource for flow measurements and diagnostics. Besides that, extracting coherent structures embedded in turbulence remains a challenge, and literature abounds in this direction: e.g. vortex core detection (Jeong and Hussain, 1995), spatial correlation based techniques, Proper Orthogonal Decomposition (POD, Berkooz et al. 1993), and more recently Dynamic Mode Decomposition (DMD, Schmid and Sesterhenn 2008. However, in spite of many relevant achievements, the temporal resolution still lags far behind those of point-wise techniques. Although many efforts have been made toward time-resolved PIV (e.g. Tachibana, 2009), its application remains bounded to low speed or small spatial resolution as a consequence of the limited electronics throughput. Lasers used for illuminating the flow field show either limitation in pulse energy or repetition rate, excepting those that are very expensive. Consequently, the contemporary global techniques are nowadays considered not optimum for large fields of view and simultaneously high accuracy requirements (e.g. Timmerman et. al., 2009), or are extremely costly. A different approach consists is combining both global and time-resolved techniques to extract more information from the flow field, but again few results are published, although some work seems promising (LDA and PIV in Timmerman et. al., 2009). Recent enhancements in CFD provide some capacity to capture important unsteady flow features (e.g. Bogey et. al. 2009). However, especially for large-scale realistic applications, experimental data are needed to qualify numerical codes performance. Unfortunately, comparisons are sometimes restricted to mean flow statistics, like average and root mean square (rms) values, since they are usually the only quantitative output from experimental data reduction of high Reynolds number turbulent flows. Further qualitative assessment can be obtained by direct comparison of instantaneous data of experiments and simulations, but almost no tool is available for non-biased quantitative results. In this sense, POD analysis seems to provide further evaluation possibilities, as found in Druault, 2005, Meyer et al., 2007 and Perrin et al., 2007. In order to better diagnose accuracy of simulations, coherent flow fluctuations need to be separated from proper stochastic turbulence. For this purpose, coherent structures need to be identified and separated from the rest of the flow in their space-time evolution.

At this aim, this paper offers the fundamentals of a space-time reconstruction technique from non time-resolved, statistically independent data. The developed algorithm allows identifying and tracking traveling coherent structures in periodic flows. Flow field phase average is reconstructed with a correlation-based method, similar to POD. This method helps shedding light on flow dynamics in a global way, instead of using mean statistics or traditional point-based techniques. 2. Mathematical background

In this section, a novel method is presented. It allows identifying and tracking pseudo-periodical traveling coherent structures with a method based on diagonalizing the cross-correlation matrix. It is aimed at reconstructing a phase average from statistically independent and non-time-resolved snapshots (i.e. time between two successive realizations is much larger than flow time-scale and the acquisition is not performed at a fixed frequency). The reconstruction is based on sorting the measurement snapshots along a time period by fitting the theoretical temporal evolution of the first three POD eigen-vectors


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2.1. Fundamentals: Proper Orthogonal Decomposition has been used in the past in low dimensional modeling in many disciplines (Sirovich, 1987), looking for maximizing flow energy with the first few modes of the decomposition. Usually, POD consists in looking for an ortho-normal basis for the time-space correlation tensor ( , ', , ')x x t tℜ . However, for non time-resolved data, ℜ is not generally available and so called “Snapshot” POD may be used instead (Berkooz et al., 1993). Applied on the ( )iu rr scalar or vector fields from N statistical realizations (each of them

is x yn n⎡ ⎤×⎣ ⎦ ), it traditionally leads to the resolution of the reduced eigen-value problem:

(1)( ) ( ) ( ),

1

Nk k k

i j j ij

C=

χ = λ χ∑

λ(k) are the sorted eigen-value (λ(0) > λ(1) >...> λ(N)), and χi

(k) [ ]1N × are the corresponding eigen-

vectors. Ci,j stands for the [ ]N N× cross-correlation matrix, defined as:

(2)* 2,

1 1 ( ) ( )i j i j i jC u u u r u r drN N Ω

= = ∫∫r r r

Ω is the region of interest and * denotes complex conjugate, if dealing with complex values. Then, the POD eigen-modes ( ) ( )k rΨ

r ( x yn n⎡ ⎤×⎣ ⎦ ) are computed as linear combinations of the ( )iu rr , with

the χi(k) coefficients, as in equation (3). ( ) ( )k rΨ

r is of the same size as ( )iu rr .

(3)( ) ( )

1( ) ( )

Nk k

i ii

r u r=

Ψ = χ∑r r

As ( )kiχ is the contribution of the snapshot number i to the kth POD mode, this is the “temporal

coefficient” of the flow for this mode. 2.2. Application to periodic convective flow: the detailed analytical resolution of eq. (3) for periodical flows is omitted here for shortness (Legrand et. al 2010). The main assumptions made to lead to the general results of eqs. (4) are: i) Taylor hypothesis: i.e. convective and weak dissipative structures are present into the flow field. ii) Integration domain Ω (region of interest) is much larger than the typical structures sizes. iii) The flow is periodic (or pseudo periodic) and it is dominated by its fundamental frequency f. iv) The ensemble average flow field ( )U rr does not vary much along

the convection direction.

(4)

(0) (0)0

(1) (1)1,1

(2) (2)1,1

12

2 cos(2 )4

2 sin(2 )4

i

i

i

ECN NE iN NE iN N

λ = + → χ ≈

πλ = α + → χ = ± π −

πλ = α + → χ = ± π −

where 2 iπ is the phase-angle. A correction may be applied to eqs. (4), if condition iv is not fulfilled (see Legrand et al. 201X for more details). In that case, the results for eigen-values and non-normalized eigen-vectors are:


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(5)

( )( )

(0)(0) (0)* 2 2

0 1,1 1 1 01

(1)(1) (1)* 2 2

0 1,1 1 1 01

(2)(2) (2)* 2 2

1,1 1 1 01

1 cos(2 )2

1 cos(2 )2

sin(2 )

i

i

i

EC Q A B iN B

EC A B i QN B

E A B iN B

+

−

λλ = + α + ∆ + → χ = + + π −φ

λλ = + α − ∆ + → χ = + π −φ +

λ′λ = α + → χ = + π −φ

1,1α , 1A , 1B , ∆ , 0φ , Q+ , and Q− are constants. Note that ( )*k

iχ are the non-normalized eigen-

functions (for simplicity). Also note that: 2 21 1Q A B Q+ −> + > . Legrand et al. 201X gives a

detailed demonstration of the expressions of eqs. 5, as well as the expression of the constants. 2.3. Relation with POD: Other authors (Ben Chiekh et al. 2004, Van Oudheusden et al. 2005), already observed the ( )k

iχ temporal evolution of the first 3 modes (as in eqs. 4) of POD analysis on

Large Eddy Simulation (LES) data (Meyer et al. 2007) or phase locked/time-resolved PIV data (Perrin et al. 2007) for different flows. They suspected that POD modes 1 and 2 were somehow linked to coherent structures convection. The contributions of ( )k

iχ to the first three POD modes have the same periodicity as the flow field. Even if snapshots are not ordered in time, as it may occur in non time-resolved measurements, the diagonalization of the correlation matrix yields the same result. This is because permutations in the kernel ,i jC have no effect on its eigen-modes. As a result, experimental eigen-vectors ( )k

iχ% are

identical to the ( )kiχ , but in a different order. Taking advantage of this, unsorted PIV snapshots (or

any 2-D data) can be sorted along a period by fitting the experimental ( )kiχ% to the ( )k

iχ functions given in eqs. (4) and (5). Then, bin-to-bin phase-average can be performed easily from the reconstructed time series. Each reconstructed phase sθ is obtained by minimizing over s the following expression:

(6)( )

2 2( ) ( ) ( )

02

( )

0

2 if minimum

k k ks i

ks s

k

k

iN

=

=

ω χ −χπ

θ = ξ = =ω

∑

∑

%

( )kω are the inverse of the peak to peak amplitude of the normalized ( )kiχ . One of the advantage of

this kind of reconstruction is that reconstructed flow field time evolution does not show phase jitter, as it usually occurs in quasi-periodic phase-locked measurements (Perrin et al. 2007).

3. Application to time-resolved PIV data The purpose here is not the study of the flow itself but rather testing the capability of the described procedure. The flow under study is the one reported in Tachibana et al., 2009, whose experimental setup is briefly described in Figure 1. Main flow is a mixture of air and methane, while secondary air is injected through four tangential orifices, which confer angular momentum. The resulting diverging outflow allows for anchoring a lifted premixed flame above the nozzle (Cheng et al.


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1995), so that a good optical access to the flow is possible. A high speed Direct Drive Valve (DDV) produces the swirl flow oscillations at a fixed frequency of 50 Hz, which results in the flow stretching rate oscillate after the nozzle exit. Corresponding to the flow oscillations, the flame front position and the flame brush thickness vary at the same frequency. Real phase-angle ϕ can be extracted from the valve controller signal. The PIV measurements are conducted at 5 kHz during 1 second approximately. Phase averaging is then performed for 32 phases (each 11.25 deg.) from

5,099N = PIV snapshots. Thus, the number of snapshots per phase is about / 32 160pN N= ≈ , providing a good reliability for average calculation.

a b

Oscillating Low Swirl Flame

Recorded phase φ

Figure 1: a) Configuration of the jet-type Low Swirl Burner. b) Experimental setup.

Reproduced from Tachibana et al., 2009. In this particular case, as the flow periodicity follows on tangential active forcing, there is not an a priori evidence that the flow is not varying much along convective direction. This is the reason why the more general expressions of eqs. (5) are used to perform the fitting for POD modes contributions, reported in Figure 2a. Actually, the first mode coefficient exhibits the fluctuating behavior reported in eqs. (5) and not found in eqs. (4). Although some dispersion persist in the fitting in Figure 2a, a good general agreement can be observed. Thanks to the time-resolved acquisition, the real phase ϕ can be obtained. This allows constructing the plot of θ as a function of ϕ , as shown in Figure 2b. Reconstructed phase standard deviation around the real phase θσ has been calculated from this plot, yielding a reasonably small value:

22.4degθσ = .

a b

ϕθ

θ

Figure 2: a) Phase fitting using eqs. (4) and (5). b) Reconstructed phase θ as a function of real phase φ.


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Regarding the reconstructed flow fields, the upper row of Figure 3 shows the phase averaging for 4 equally separated anglesϕ . Similarly, the lower row represents the same result for the reconstruction procedure, with the corresponding θ angles. A very good overall conformity can be appreciated. Nevertheless, some discrepancies persist due to phase dispersion.

+

Figure 3: Axial velocity map and pseudo-streamlines.

Top row: real phase-locked average flow. Lower row: reconstructed flow. (Black cross mark the location of the reference point in Figure 4)

A black cross, shown in Figure 3, allows for a comparison of time evolution between real flow and the reconstructed one at this reference point. It is located 10 mm above the burner exit along the centerline. Figure 4 shows both the real phase-locked average and the reconstructed average at this point for the axial velocity. In addition, the same graph shows in-phase rms values. Again, the procedure performs a good reconstruction, as flow average does not exhibit discrepancies higher than 10 % for any phase-angle. Furthermore, rms trend is well conserved and differences are relatively small, less than 20 % of the real in-phase rms values for the greatest difference. Figure 4 also shows the reconstruction using only the first 3 POD modes and their corresponding theoretical coefficients, ( )k

iχ (as in eqs. 5). It underestimates axial velocity, and it shows the disadvantage of reproducing locally a pure cosine function. These discrepancies illustrate the loss of POD spatial contents already discussed in paragraph 2.4.iii. Nevertheless, for that case, the general tendency is conserved.


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Figure 4: Axial velocity at 10 mm downstream the burner exit in the center line.

Filled squares: phase-locked statistics (average and rms) ; Open squares: Reconstructed statistics (phase average and phase rms)

4. Application to real 3-D flow S-PIV data and applicability of the procedure

In the previous sections, the procedure for a space-time reconstruction of a periodic flow has been described and applied to a flow whose time evolution was known (i.e. time-resolved PIV results in section 3). That allowed for comparisons between real flow evolution and its reconstruction in order to support the capability and reliability of the technique. However, the real interest of the technique is to reconstruct the unknown flow temporal evolution from statistically independent planar measurements. At this aim, the following subsection presents an example of application to a set of non time-resolved stereo PIV measurements.

4.1. Application to real 3-D flow: non time-resolved S-PIV data: The flow under study corresponds to the one issuing from a Low Swirl Burner (LSB) distinct from the one of section 4. Here, the main body of the burner consists in a cylindrical plenum. It is fed with a propane/air premixed mixture at ambient temperature, issuing through two symmetric opposite pipes with tangential outlets that provide angular momentum. The swirling flow exits the plenum through the outer coaxial annulus passage of the central straight pipes. This passage is connected to the plenum at its lower end by three symmetrical slot-like ports at 120º azimuthal positions, leaving approximately 90% open area. The inner axial pipe passes through the back-plate and does not interact with the plenum neither carry any swirl. Both flows merge inside the nozzle, of diameter D = 26 mm, before reaching the exit plane, and come out to the open atmosphere. Bulk velocity Ub at the exit plane is about 7.5 m/s. The flame is anchored in a diverging flow, ensuring its stability above the nozzle exit plane. Figure 5 briefly describes the experimental setup and the flame topology obtained (for a Reynolds number 14,000D bRe U D= ν ≈ , and swirl number 0.51S ≈ , as defined in Legrand et al., 2010). Detailed information on the facility and experimental S-PIV setup is available in Legrand et al., 2010.


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a b

c

Figure 5: Stereo PIV setup.

a) Sketch of the burner and typical flame shape in LSB configuration, dimensions are in mm; b) S-PIV setup for vertical measurement plane; c) For horizontal measurement planes. Coordinate system is also indicated.

Whereas the flow was tangentially excited in section 3, here the LSB flame is free of any

artificial forcing. Besides that, the flow naturally tends to present a pseudo periodical behavior that allows for applying the procedure for temporal reconstruction. Fundamental frequency is found to be around 500 Hz, while S-PIV image pairs are acquired every 1.5 seconds approx., ensuring non time–resolved conditions for these measurements. For the vertical S-PIV measurement plane, Figure 6a shows the contribution of each of the 1,000 snapshots to the first 3 POD modes, while Figure 6b shows the fitting used (eqs. 5 and 12) in order to sort the PIV snapshots along a time-phase. Here, the fitting is not as clean as in Figure 2b because of the effect of a strong turbulence (turbulent kinetic energy is about 15 m2/s2 in the shear layers). For the horizontal measurements planes, snapshots contributions and fitting are very similar and for this reason, they are omitted.

a b

Figure 6: Snapshots´ contributions to POD modes (vertical plane measurement). a) Unsorted; b) Sorted along phase-angle θ by fitting as in eq. (12)

To offer a better view of the mean flow field topology, the left-hand side of Figure 7 shows a 3-D rendering of 3 measurement planes: r2/D = 0, z/D = 1.0 and z/D = 3.0. The null axial velocity contour is depicted with dashed white lines to bound the recirculation zone. The phase averaging method for the time history reconstruction has been used to analyze this LSB flame dynamics. Now, the correlation matrix ,i jC has been computed from 3 velocity components (3C) fields, as


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stereoscopic PIV measurements offer this possibility. Results are presented in the right part of Figure 7. Four different θ time-phases are presented. The axial velocity is depicted in the top row of images for a vertical measurement plane and in the bottom row for the horizontal plane at z/D = 1. Flame front location, depicted as a continuous white line, has been estimated from seeding density spatial gradient as in Legrand et al., 2010.

a b c d

e f g h Figure 7: LSB reacting flow.

Left: 3-D representation of average axial velocity. Right: Reconstructed phase average axial velocity from 1,000 PIV snapshots. (top) r2/D = 0; (bottom); z/D = 1. Dashed lines indicate correspondence for the 2 planes.

a-e) θ = 0º; b-f) θ = 90º; c-g) θ = 180º; d-h) θ = 270º. Operating conditions: 0φ = 1.5, S ~ 0.51, ReD ~ 14,000.

Results in the top row are very consistent with the ones in the bottom row, even if the fitting

has been performed from 2D-3C velocity data from two different planes (r2/D = 0, z/D = 1.0). The agreement between the reconstructed time evolutions in different measurement planes is a further indication of coherence and verisimilitude of the results in real flow conditions. Central jet bulk describes a circular path around the burner axis, close to the nozzle exit. This perturbs the recirculation zone and the low velocity region comes down towards the nozzle lip (left hand side of Figure 7b). This low velocity region is rotating, as can be observed in the horizontal planes, shown in the bottom row of this figure. The asymmetry exhibited by this motion confirms the one observable in the left side of Figure 7, showing stronger recirculation on the down left position than on the upper right one for this figure.

4.2. Validation of the methodology: It is worth to notice that the flow fields of sections 3 present some characteristics that are not common in flows of industrial interest. The oscillating low swirl flame is strongly excited tangentially, so that the flow exhibits a clear frequency peak that widely dominates the flow spectrum. These issues do not fully support the applicability and suitability of the technique to real flows, where frequency peaks are generally not so pronounced and where stochastic turbulence and experimental noise use to be important. As it can be seen in Figure 6b, the strength of turbulence seems to play an important role in the dispersion of the phase fitting; and thus in the efficiency and accuracy of the reconstruction. In order to study this effect and subsequently to determine a range of applicability of the methodology, a set of different flows has been analyzed varying their turbulence intensity.

First, an artificial periodic flow field has been generated. It corresponds to the straight convection of a vortex in a rectangular box. When the vortex reaches the end of the box, it appears again at the beginning, ensuring periodical conditions for this artificial flow. In order to test the efficiency of the time reconstruction technique under more realistic conditions, artificial stochastic


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turbulence has been overlaid to the vortex flow. To achieve that, the digital filter proposed by Klein et al., 2003 has been used with different turbulence intensities (ranging from 0 to 150% of maximum velocity maxV ).

Finally, the time-resolved data from the forced LSB flame of section 3 was also used, for 7 distinct forcing cases (Tachibana et al., 2009). For high forcing cases, turbulence intensity is relatively low compared to the energy contribution of the large-scale oscillations of the flow. On the contrary, for low forcing cases, turbulence dominates the flow, while large-scale fluctuations are almost absent. Those differences are used in order to study the effect of the turbulence intensity on the accuracy of the time reconstruction procedure.

For each of the above described test cases (19 in total), the time reconstruction procedure has been applied. The reconstruction computational time with a standard personal computer ranges from several minutes for the smaller sets of data, up to a couple of hours for 5,099N = . This relatively short computational time, even for large sets of acquisition series, makes the technique quite attractive in term of machine time consumption.

In order to study the reliability of the reconstruction, the standard deviation θσ of the reconstructed phase-angle θ around the real phase ϕ has been calculated since the real time evolution is known for each test case. θσ has been normalized by the standard deviation of the data if it were completely random 3maxσ = π . Figure 8 depicts maxθσ σ versus the relative strength of the

second POD mode (1) ( )

1

Nk

k=λ λ∑ .

Increasing turbulence intensity

Section 3

Figure 8: Evolution of the normalized phase standard deviation versus the relative strength of the second POD

mode. As it is noticeable in Figure 8, every point seems to fit the same exponential tendency, independently of the kind of periodic flow considered. As turbulence intensity increases, the relative strength of the second POD mode decreases and maxθσ σ gets larger, reaching almost unity when intense turbulence dominate the flow energy. This graph allows for establishing a limit of validity of the application of the time reconstruction procedure for any periodic flow. When

(1) ( ) 2

1

5 10N

k

k

−

=

λ λ < ×∑ (i.e. when mode 1 and 2 cumulate contribution to fluctuating flow is less than


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10%), the phase standard deviation is too large ( max 0.7θσ σ > ) to guarantee a reliable reconstruction. Without any a priori knowledge on the flow behavior, this criterion allows to determine if the reconstruction will be accurate or not. 5. Conclusions

This paper offers the fundamentals of a space-time reconstruction technique from non time-resolved, statistically independent data. An algorithm has been developed to identify and track traveling coherent structures in periodic flows. Flow field phase average is reconstructed with a correlation-based method, similar to POD. The mathematical model, aimed at discriminating space-time coherent structures from proper stochastic turbulence, helps shedding light on flow dynamics. This could offer an interesting tool for further experiment-simulation comparisons, allowing for dynamical contents comparison, instead of using mean statistics or traditional point-based techniques.

The application on time-resolved PIV measurements from a Low Swirl Burner excited tangentially offers promising results. In addition, the knowledge of the flow temporal evolution allows for comparing real flow with the reconstructed one, leading to discrepancies in velocity less than 10% of the real phase average. The application to statistically independent measurements on a low swirl flame, and for different measurements planes shows the consistency of the reconstruction. The reconstructed phase average coincides for the two measurements planes and this for any of the considered phase-angles. Moreover, it allows for a better understanding of the flow dynamics, even under difficult experimental conditions (e.g. combustion facility).

Some considerations about the applicability of the reconstruction procedure are also taken into account, especially the influence of non time-correlated turbulence intensity on the reliability of the reconstruction. Through the study of the reconstructed phase dispersion, the accuracy of the procedure has shown to be sensitive to the relative strength of the POD modes 1 and 2. This allows for establishing a limit of validity of the application of the time reconstruction procedure for any periodical flow when its temporal evolution is unknown. Acknowledgements This work has been partially funded by the CoJeN European project, Specific Targeted RESEARCH Project EU Contract No. AST3-CT-2003-502790; the Spanish Research Agency grant DPI2002-02453 “Técnicas avanzadas de Velocimetría por Imagen de Partículas (PIV) Aplicadas a Flujos de Interés Industrial” and the Spanish Research Agency grant ENE2006-13617 “TERMOPIV: Combustión y transferencia de calor analizadas con PIV avanzado”. We are also grateful to the Japan Aerospace and Exploration Agency (JAXA) for its collaboration, its time resolved PIV data from their swirl-stabilized burner, and for kindly receiving UC3M personal during 2 months. We would like also to express a special acknowledgement to the laboratory technicians Manuel Santos and Carlos Cobos, for their help in the burner design and fabrication. References Ben Chiekh M., Michard M., Grosjean N., Bera J.C.; (2004) “Reconstruction temporelle d’un

champ aérodynamique instationnaire à partir de measures PIV non résolues dans le temps”, In: 9 Congrès Francophone de Vélocimétrie Laser.


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Tachibana S, Yamashita J, Zimmer L,, Suzuki K, Hayashi A. K. (2009), “Dynamic behavior of a freely-propagating turbulent premixed flame under global stretch-rate oscillations”, Proceedings of the Combustion Institute, 32, 2: 1795-1802.

Timmerman B.H., Skeen A.J., Bryanston-Cross P.J., Graves M.J. (2009),”Large-scale time resolved digital particle image Velocimetry (TR-DPIV) for measurement of high subsonic hot coaxial jet exhaust of a gas turbine engine”, Measuremens Science and Technology, 20, 7.

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