Flow Turbulence Combust (2010) 85:73–93 DOI 10.1007/s10494-010-9257-4

In-Nozzle Measurements of a Turbulent Opposed Jet Using PIV Benjamin Böhm · Oliver Stein · Andreas Kempf · Andreas Dreizler

Received: 28 September 2009 / Accepted: 31 March 2010 / Published online: 21 April 2010 © Springer Science+Business Media B.V. 2010

Abstract Turbulent opposed jet burners are an excellent test case for combustion research and model development due to the burners’ compactness, relative simplicity, and the good optical access they provide. The flow-field in the flame region depends strongly on the turbulence generation inside the nozzles, so that realistic flow simulations can only be achieved if the flow inside the nozzles is represented correctly, which must be verified by comparison to suitable experimental data. This paper presents detailed particle image velocimetry (PIV) measurements of the flow issuing from the turbulence generating plates (TGP) inside a glass nozzle. The resulting data is analyzed in terms of first and second moments, time-series, frequency spectra and phase averages. The measurements show how individual high velocity jets emerging from the TGP interact and recirculation zones are formed behind the solid parts of the TGP. Vortex shedding is observed in the jet’s shear layer were high levels of turbulent kinetic energy are generated. Time series measurements revealed periodic pulsations of the individual jets and implied a coupling between adjacent jets. The peak frequencies were found to be a function of the Reynoldsnumber. Keywords LES inflow data · High-speed particle image velocimetry · Large eddy simulation · Turbulent opposed jet burner · Turbulence generating plate · Wind-tunnel turbulence

Electronic supplementary material The online version of this article (doi:10.1007/s10494-010-9257-4) contains supplementary material, which is available to authorized users. B. Böhm (B) · A. Dreizler Fachgebiet Reaktive Strömungen und Messtechnik, Centre of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany e-mail: [email protected] O. Stein · A. Kempf Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK

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1 Introduction Turbulent flames involve a complex coupling of an unsteady flow and chemical kinetics over wide ranges of spatial and temporal scales. Chemical reactions can only occur if the reactants are mixed on a molecular level. The flow-field determines the convective transport, and turbulent advection will steepen scalar gradients and hence increase molecular mixing (diffusion), leading to greater rates of chemical reaction. This interaction between turbulent motion and chemical reactions is often referred to as turbulence–chemistry interaction. Turbulence-chemistry interaction affects the flame structure, the reaction rate, and hence flame stability and pollutant emissions. For these reasons, the correct prediction of the underlying flow-field is key to the prediction of turbulent flames. The experimental investigation of turbulence-chemistry interaction requires a simple and well-defined test case, and turbulent opposed jet (TOJ) configurations have proven to be very useful for this type of study. These burners are often operated in the non-premixed mode, where a fuel jet impinges on a counter flowing oxidizer stream. This simple and compact configuration can easily be simulated as only a small computational domain is required. Turbulent opposed jet burners have been subject to numerous experimental and numerical investigations [4, 5, 11, 14, 17, 19, 20, 23, 26, 29, 30] as summarized by Geyer et al. [10] and Lindstedt et al. [21]. Experimental investigations of velocity and strain rate characteristics of the isothermal flow-field were performed by Korusoy and Whitelaw [19], Kostiuk et al. [20] and Lindstedt et al. [21] with the focus on the stagnation plane in-between the opposed nozzles whereas no information is available on the flow-field inside the nozzles in the vicinity of the turbulence generating plates (TGP). The opposed jet burner investigated in the present work was developed by Geyer et al. [10] at Darmstadt University. Many detailed investigations of the flow, mixing and reaction in this burner have been performed so far [10]. Additional information on scalar gradients are reported in the form of scalar dissipation rates [11]. Another series of simultaneous measurements of the flow-field and the flame position provides information on flame turbulence interactions [2] with additional time resolved measurements of the extinction process caused by the turbulent flowfield [4]. This burner has also been investigated by numerical simulation [7, 10, 14]. Geyer et al. [10] and Kempf et al. [14] have performed Large Eddy Simulations (LES) of the case, a technique that resolves the large energy-containing scales (eddies) directly, by integrating the underlying conservation equations, while modeling the effect of the small scales. They have found a good agreement with the available experimental results, but they also report uncertainties regarding the very detailed inflow conditions required for LES. To simulate the flame, the set of partial differential equations, the boundary conditions and the initial conditions have to be prescribed. For Reynolds Averaged Navier Stokes (RANS) simulations, only the Reynolds averaged mean quantities, Reynolds stresses and length scales must be known at the inflow and the simulations are relatively insensitive to small errors of the inlet conditions. For LES, even more detailed information is needed because the unsteady, three-dimensional, turbulent velocity field must be imposed at the inflow at each time step [3, 16, 24]. Therefore temporally evolving velocity profiles as well as information on the structure and shape of the turbulent eddies are required. Unfortunately, such comprehensive

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datasets on the inflow conditions are generally not available. Simulations must then rely on computing the flow far upstream of the area of interest, or alternatively estimate the inflow conditions based on a synthetic turbulence generation procedure [6, 15, 18]. A general review of methods to provide inflow conditions for LES is given by Keating et al. [13]. With LES, the large energy containing eddies must be prescribed correctly at the inflow, which becomes even more challenging if the turbulence is not isotropic, inhomogeneous, and not fully developed. The overall simulation results are then strongly dependent on the inflow conditions. It is often not possible to measure the transient inflow conditions that are required for LES, and hence a validation of the inflow conditions that are actually used is crucial [16]. With the opposed jet, the inflow conditions must represent the turbulence generated by the perforated plates inside the nozzles. From these holes in the perforated plates, a multitude of jets emerge that interact with each other and eventually coalesce to form a homogenous turbulent flow near the nozzle exit. Immediately downstream of the perforated plates, regions of high shear are found where the turbulence is generated. In these regions the jets are coupled with the wakes formed behind the solid parts of the plates. Further downstream the flow is homogenized by the jet-wake interactions until eventually no jet or wake can be distinguished [22]. This return to isotropic, homogenous turbulence cannot be expected in the opposed jet burner because the perforated plates are located less than two diameters upstream of the nozzle exit. Therefore the turbulence at the nozzle outlet cannot be expected to be fully developed, isotropic and homogenous [10]. With this “young turbulence”, the structure and shape of eddies may have a significant influence on the flow at the stagnation plane and hence the flame. In the LES of the opposed jet, Kempf et al. [14] observed a large sensitivity of the results to the inflow conditions. The original computational domain only included the region between the nozzle exits, but it was quickly found that the domain had to be extended upstream to the turbulence generating plates (TGP). The flow velocities from the perforated plates were described as inflow conditions, superimposed with synthetic turbulence to break symmetry and to trigger jet break-up. However, the level of the synthetic inflow turbulence had to be adjusted to achieve a realistic jet break-up point, and hence the correct turbulence levels between the nozzles. It was even observed that high turbulence levels at the perforated plates led to early jet breakup and hence lower fluctuations at the stagnation plane, while lower turbulence levels at the perforated plates led to later jet breakup, and hence higher fluctuations at the stagnation plane. The observed (somewhat counter-intuitive) sensitivity of the flow demonstrates that detailed flow measurements inside the nozzle are required to validate the LES inflow conditions before one can aim to predict results at the stagnation plane. The present work investigates the flow immediately downstream of the TGP inside the opposed jets nozzles. The characteristics of the isothermal flow-field are first demonstrated qualitatively by instantaneous images from planar particle Mie scattering. Quantitative results were obtained by in-nozzle particle image velocimetry (PIV) at 10 Hz and are presented as profiles of mean and fluctuating velocities. Highspeed PIV measurements were also performed, showing the temporal evolution of the flow, providing time-series and phase-averaged velocities granting insight to the jet-jet interaction.

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2 Experimental Setup 2.1 Turbulent opposed jet burner The measurements were performed in the turbulent opposed jet burner developed by Geyer et al. [10]. A sketch of the burner is shown in Fig. 1. The burner consists of two vertically opposed contoured nozzles with a contraction area ratio of 9:1. The opposed flows impinge on each other with equal momentum in the horizontally aligned stagnation plane. The nozzles, each 30 mm in diameter (D), were separated by a distance H = 30 mm (H/D = 1). To generate turbulence, perforated plates were located downstream of the contraction, 50 mm upstream of the nozzle exits. The plates have a blockage of 45% and feature hexagonally arranged holes with a diameter of 4 mm. To provide optical access to the flow inside the nozzle, the co-flow nozzles were removed and the original steel nozzle was replaced with an equivalent glass nozzle. This allowed to measure the flow-field as close as 2.5 mm downstream of the TGP, as the laser sheet was blocked by the Morel-nozzle parts designed to hold the inlet-nozzle and the co-flow.

Fig. 1 Sketch of the opposed jet burner and the turbulence generating plate (TGP). The origin of the coordinate system is centered at the stagnation point (halfway between the nozzles) with z denoting the axial and r the radial coordinate. All quantities are given in mm

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The flow-field measurements were performed on the isothermal flow only, since no meaningful flame-measurements can be taken without the co-flow. A range of Reynolds-numbers was investigated that matched the cases studied on the same burner by Geyer et al. [10]: Reynolds-number 5,000 (TOJC), 6,650 (TOJD) and 7,200 (TOJE). The configurations were named in consistency with previous work on this burner, although the Reynolds-number is the only difference between these configurations. The present paper focuses on the isothermal flow TOJD with Re = 6,650, but additional cases are presented to demonstrate the Reynolds-number dependency. 2.2 Particle image velocimetry (PIV) A conventional 10 Hz and a high-speed PIV system were used to capture the isothermal flow-field. The 10 Hz system was chosen to provide statistically independent data at high spatial resolutions, as the system uses a camera with high resolution, high dynamic range, and very little noise, based on an interline-transfer CCD (PCO, 1376 × 1040 pixels) equipped with a Nikkor lens (105 mm, f# 2.8). The light was provided from a double pulsed, frequency-doubled Nd:YAG laser (New Wave) with relatively high pulse energy. The beam was formed into a light-sheet of ∼600 μm thickness to illuminate planar regions of the flow-field intersecting with the vertical centerline of the burner. The pulse separation was set between 25 and 50 μs, depending on the Reynolds-number and the flow region of interest. The flow was seeded with oil droplets (DEHS) with a mean diameter of ∼1 μm. The resulting PIV images were processed on a regular grid with interrogation areas of 32 × 32 pixels, leading to a spatial resolution of 0.6 × 0.6 mm2 . The 10 Hz system is unable to capture time correlated data, which was obtained from an additional high-speed PIV system. It features a frequency-doubled, dualcavity Nd:YVO4 slab laser (IS4II-DE, Edge Wave) at 532 nm with a repetition rate of 5 kHz and a pulse to pulse separation that was set depending on the local flow conditions to values from 30–100 μs. The Mie scattering was recorded with a CMOS camera (HSS5, LaVision) equipped with a Zeiss lens (100 mm, f# 2). A light-sheet illuminated a plane intersecting with the centerline of the burner and its thickness was set to ∼800 μm. Due to the lower pixel resolution of the high-speed camera (the usable area was 512 × 512 pixels at 10 kHz), the high-speed PIV data was processed on a grid with interrogation areas of only 16 × 16 pixels, resulting in a slightly coarser spatial resolution of 0.7 × 0.7 mm2 . For calibration purposes, a grid was placed in the measurement plane to determine image distortion by the curved glass, so that distortion effects could be eliminated in a post-processing step. The PIV data was processed based on an algorithm presented by Böhm et al. [2] using a multipass interrogation scheme with window shifting.

3 Results 3.1 Mie scattering visualizations Figure 2 shows instantaneous snapshots of the isothermal flow visualized by means of planar particle Mie scattering. The structure of the single jets emerging from the

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Fig. 2 Instantaneous snapshots of the isothermal flow imaged by laser Mie scattering for Re = 5,000 TOJC (a) and Re = 7,200 TOJE (b) with the central jet of the TGP seeded only. The cross section of the nozzle (white box) and TGP is overlaid. The temporal image sequence of the mixing layer (c) is obtained from the grey box at the top in image (b) for TOJD. For these realizations, only the lower nozzle was seeded

TGPs is characterized qualitatively in Fig. 2a, b. The flow from the central hole of the TGP was visualized by individually seeding a tube with an inner diameter equivalent to the hole diameter. Figure 1 demonstrates the seeding tube which was inserted for the flow visualizations given in Fig. 2a, b only. Because no seeder was available to seed the very low mass flow of the central hole, a bypass with a needle valve was installed behind the seeder to adjust the flow rate. Two criteria were used for adjustment: The central jet was not allowed to distort the averaged mixing layer (which is a very sensitive measure) and PIV processing was performed on the jet outlet to match the outlet flow with previously obtained PIV results (presented in the sections below). However, the visualizations are only of qualitative nature because the tube used to feed the central hole leads to a fully developed pipe flow profile, while the surrounding flow is almost laminar and largely determined by the restriction formed by the turbulence generating plate. The Reynolds-number of the flow inside the tube was estimated to be 1,800 for TOJC (Fig. 2a) and 2,500 for TOJE (Fig. 2b) based on the tube diameter of 4 mm. These differences can lead to considerable variations in turbulence intensities and integral length scales, as observed by Liu and King [22] for flows passing perforated plates with varying thickness. Instantaneous images from movies recorded at 2.5 kHz are shown in Fig. 2a for the lowest Reynolds-number (5,000, TOJC) and in Fig. 2b for the highest

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Reynolds-number (7,200, TOJE). The images give an impression of the development and break-up of the central jet. For Re = 5,000, the jet has a waveless border for the first ∼5 mm (up to z ≈ −60 mm) before vortex shedding is observed. Large scale structures (of the order of millimeters) appear periodically in the shear layer of the jet and can be observed as bulges at the jet boundaries. The location of the jets is indicated by the cross section of the TGP, at the bottom of the respective figure, which gives an estimate of the axial distance where the individual jets begin to merge. The interaction of these evolving structures can be observed from z ≈ −57 mm onwards. Mixing of the fluid from the jets is driven by large-scale eddies, which can be seen by the fluid pockets that begin to separate and penetrate into the neighboring flow from z ≈ −50 mm onwards. The jet spreads over two-thirds of the opposed jets’ nozzle diameter at its outlet. The flow downstream of the developing region of the turbulence grids, beyond the strong jet-jet interactions, is generally found to be nearly isotropic [28]. For this reason, grids and perforated plates are commonly used to generate turbulence in wind-tunnels. Interesting to note are the here observed horizontally elongated structures observed close to the stagnation plane which are caused by the compressive strain in axial direction. This anisotropic behavior indicates that length scales may differ significantly with respect to the spatial location in the vicinity of the stagnation plane. For the higher Reynoldsnumber of 7,200 (Fig. 2b) the jet is already unstable at the perforated plate and breaks up earlier. This may be explained by the transition from a laminar pipe flow inside the 4 mm tube used for seeding (Re = 1,800, Fig. 2a) to a turbulent flow (Re = 2,500, Fig. 2b). These visualizations are therefore only of qualitative nature to give an impression of the jets inside the nozzle. Figure 2c shows a temporal sequence for TOJD of the stagnation plane region as indicated by the grey box in Fig. 2b. The mixing layer is apparent as the interface between the seeded flow from the bottom and the unseeded flow from the top nozzle. The mixing layer is distorted by large-scale eddies forming bulges of 4–8 mm in size. Stirring takes place on these large scales, as can be seen by the small fraction of seeded flow which rolls into a vortex and generates an island of seeded flow. 3.2 Individual flow-field sequence obtained by high-speed PIV Figure 3 shows a sequence of the isothermal flow-field obtained by high-speed PIV at 5 kHz for the base case TOJD (movies for case TOJC and TOJD are accessible as supplementary material: Online Resource 1 and 2). The flow-field is observed in a plane intersecting with the centerline of the burner. Every second image of the selected sequence is shown, resulting in a time separation of 0.4 ms between the images. The central jet (−2 < r < 2 mm) and parts of two adjacent jets issuing from the holes in the TGP can clearly be distinguished. Between the jets and downstream of the solid parts of the TGP, regions of low velocity are observed where vortices are generated and advected downstream. The vortices are distorted by the neighboring jets and vice versa. The jets begin to interact directly with each other starting from z ≈ −57 mm. Up to z ≈ −50 mm strong fluctuations are observed in the area of the shear layer between the jets caused by the direct interaction (region II). Further downstream, the amplitude of the shear layer fluctuations decays rapidly. The flow homogenizes and individual jets can no longer be distinguished while the influence of the shear layer remains observable as slight local deviations of the vectors in the

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Fig. 3 Temporal sequence of the instantaneous flow-field in the nozzle above the TGP taken from high-speed PIV at 5 kHz (every second flow-field is shown only) for TOJD. The location of the three distinct flow regions is demonstrated: initial jet (I), strong jet–jet interactions (II) and decaying turbulence (III). Magnification of the region above the solid part of the TGP is obtained from the box in the second image. The axial jet velocity at the TGP is ∼9 m/s

instantaneous flow-field, even at the nozzle exit (not shown here). Figure 3b shows a magnification of the region just above the solid part of the TGP, obtained by increasing the magnification for PIV recording to achieve higher spatial resolution and resolve the small vortices. For visualization purposes an overlap of 50% was used for PIV processing. In the measuring plane a pair of counter-rotating vortices approximately 1 mm in size is found at the base of the jets (region I). Large scale distortions, seen as contractions and bulges of the jets, are clearly visible in region II. Geers et al. [9] found similar large-scale distortions of jets, arranged in an array, from statistically independent PIV measurements. The time correlated measurements obtained by high-speed PIV, as shown in Fig. 3a, reveal a quasi-periodic behavior of these distortions. The wavelength of these structures can be estimated to be approximately 4–6 mm, which is of the order of the holeseparation of 5 mm. With a velocity of approximately 8 m/s, the vortex shedding frequency can be expected to be of the order of 1–2 kHz, which will be discussed in greater detail in the section on autocorrelations. 3.3 Flow-field statistics The mean and fluctuations w of the axial velocity component in a plane intersecting with the centerline of the burner are shown in Fig. 4. The velocities were measured with the 10 Hz PIV system, providing accurate statistically independent data. Approximately 1,000 images were recorded for each measuring plane. The velocities in the field of view were in the range of 0–10 m/s, and the PIV setup was optimized to capture the high velocities so that the accuracy of the velocities

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Fig. 4 Planar distribution of axial velocity, mean (left) and RMS (right), with the overlaid PIV grid. Areas where less than 70% of the PIV data were validated are black. The vertical dashed lines (right) mark the locations where line profiles of velocity were extracted from the 2D datasets (see Figs. 5 and 6)

close to zero was poor. In post-processing, a set of signal-to-noise as well as peakheight filters were applied to reject spurious vectors, especially those in the near zero velocity regime above the solid parts of the TGP and in regions of large scattered light interferences. Because interpolation is based on neighboring vectors this would have resulted mainly in high velocity vectors in the low velocity regimes. To avoid this bias rejected vectors were not interpolated. To limit the resulting error, the mean and the RMS were calculated only for interrogation areas where more than 70% of the vectors were validated so that each value is an average of at least 700 single values. This procedure causes the blank (black) regions in the velocity maps, especially in the low-speed regions between the jets. As previously mentioned, one can distinguish three regions of distinct flow characteristics (see Figs. 3 and 4) inside the nozzle: An initial jet region I for z < −60 mm where the jet interaction happens indirectly via the vortices formed behind the solid parts of the TGP. Significant turbulence is already generated in these regions of high shear, as shown in the instantaneous images in Fig. 3. Region II (−60 < z < −50 mm) is characterized by strong jet-jet interactions. A conically shaped decay of the axial velocity is observed that is typically caused by the radial expansion of jets. The jets coalesce and the influence of the shear layer moves towards the jets’ centerline. Turbulence is enhanced strongly in region II. Further downstream in region III (50 < z < 15 mm), the flow is homogenized resulting in a decaying turbulence. Beyond z = −40 mm individual jets can no longer be distinguished based on the averaged velocity field information. Figure 5 shows axial profiles for TOJD of the mean axial and radial velocity components and respectively and their fluctuations w and v extracted along three parallel lines at different radial positions, as indicated by the dashed

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vertical lines in Fig. 4: the first line characterizes the central jet on the burner’s centerline at r = 0 mm. A second line was extracted at the centre of a neighboring jet (at r = −5 mm), and the final line is located between the jets at r = −2.5 mm. The axial velocity on the centerline is nearly constant = 8.8 m/s in the potential core of the jet throughout region I, and the fluctuation levels are low (<0.25 m/s). The expected contraction, which is characteristic for jets emerging from sharp edged, constant diameter orifices, as observed by Geers et al. [9] in a multihole plate configuration, could not be verified due to the lack of data directly at the TGP. The axial mean velocity profiles for the centerlines of the central and neighboring jet are very similar, but differences are observed for the radial velocity component . Values with only slight deviations around zero are observed for the central jet, indicating its rotational symmetry. The neighboring jet, in contrast, is pushed outwards in radial direction away from the central jet with a maximum radial velocity of = −0.3 m/s reached at the end of the initial jet region (z =

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−60 mm). The axial as well as the radial fluctuations are twice as large as for the central jet. The initial jet length for single turbulent round jets is approximately 4 to 5 nozzle diameter in length [12]. This is reduced significantly by the interaction with the surrounding jets down to 1.25 nozzle diameter. Vortices generated in the shear layers of neighbored jets enhances local velocity gradients amplifying the instabilities in the shear layer. The region of strong jet–jet interactions (II) is characterized by a decay of the axial mean velocity along the centerline of the jets, and by a simultaneous increase of the fluctuations. The kinetic energy of the jets is redistributed into turbulent kinetic energy. As shear causes instabilities and high turbulence production, profiles of w and v along the shear layer between the jets at r = 2.5 mm show very high velocity fluctuations of up to 1.5 m/s. The fluctuations decrease rapidly in the shear layer as they increase towards the jets’ centerlines. Thus, the fluctuations at the centerlines increase until they reach a maximum of w = 1.0 m/s and v = 0.9 m/s respectively at z = −50 mm. The radial velocity of the neighboring jet, which is initially pushed away by the central jet, decays, overshoots slightly to positive values, and becomes zero at z = −48 mm. Region III is characterized by the decay of turbulence. The fluctuations decrease towards an asymptotic value of 0.3 m/s, with axial fluctuation values approximately 20% higher than the radial fluctuations at the nozzle outlet z = −50 mm. The flow is homogenous, reaching constant mean values of zero for the radial velocity and 3.7 m/s for the axial velocity. The approximately 10% increase of the peak centerline velocity compared to the bulk velocity (3.4 m/s) results from the lower velocities near the walls and overall mass conservation. Already 5 mm upstream of the nozzle exit, at z = −20 mm, the influence of the outlet and stagnation plane can be observed by the decay of the axial and an increase of the radial velocity away from the centerline. The axial velocity decreases almost linearly towards zero at the stagnation plane, independent of the radial position. The mean radial velocity along the centerline remains approximately zero. Slight deviations from zero are observed indicating small imperfections of the flow symmetry or possible alignment errors of the PIV setup. Consistently higher radial velocities are found for the off-axis profiles with peak velocities of = 1.0 m/s at the stagnation plane (z = 0 mm) for r = −5 mm. The fluctuation levels of axial w and radial velocity component v increase towards the stagnation plane with peak values at z = 0 mm, independently of the radial position. The axial velocity fluctuations at the stagnation plane are 0.55 m/s and about twice as high as the respective radial fluctuations. Apparently the flow is already non-isotropic inside the nozzle, while the anisotropy increases outside the nozzle approaching the stagnation plane due to the strong compressive strain encountered between the nozzles. Figure 6 shows the influence of the Reynolds-number on the flow development. The lower Reynolds-number case TOJC (Re = 5,000) is compared to the already presented base case TOJD (Re = 6,650). At lower Reynolds-number, the development of the above-described three regions is delayed due to the reduced mass flow rate. The axial velocity is lower at the jet outlet = 6.6 m/s and the initial jet length is increased by ∼1 mm. Thus the initial influence on the neighboring jet is reduced resulting in a lower radial velocity peak of the neighboring jet. The slope of the axial velocity decay is lower for TOJC. The area of homogenized flow (III) is moved further downstream towards z = −45 mm. The axial fluctuations w are

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similar for region I. Because of the weaker shear layer, the radial fluctuations v are lower. The shear layer requires more time to grow towards the centerline. Therefore, the peaks of the velocity fluctuations on the centerlines of the jets are not only lower but moved further downstream, from z = −50 mm (TOJD) to z = −46 mm (TOJC). Region III differs by the lower axial velocity ( = 2.8 m/s) for TOJC while the radial velocity is identical. The velocity fluctuations for TOJC are slightly lower (∼0.05 m/s) in Region III as well. Figure 7 shows radial profiles of the axial and radial velocity means and fluctuations at different heights z = −62, −50, −55, −45, −35 mm above the TGP. Any gaps in the curves result from the already described validation criteria for excluding spurious PIV data. In the axial velocity profile at the outlet (z = −62 mm), three distinct jets with profiles resembling a top hat and strong velocity gradients at their edges can be seen. Further downstream they grow together and form nearly flat constant velocity profiles along the nozzle’s diameter. The radial velocity profiles

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reveal the mutual influence of the jets. The spreading of the central jet is observable by radial velocities around zero, while the neighboring jets have radial velocity components outwards, away from the central jet. This influence decreases until nearly uniform profiles are achieved, at approximately z = −35 mm for the means, as well as the fluctuations. Assuming a symmetric spread of the individual jets, the radial velocity profiles are expected to be point-symmetric to their respective centerlines. Reasons for the observed deviation from symmetry for the radial velocity profiles are not clear. A quantity of a turbulence field is by definition isotropic, if it is statistically invariant under rotations and reflections of the coordinate system, and homogenous if it is invariant under translation [25]. The fluctuation levels directly above the TGP (z = −62 mm) are low and similar for w and v . Further downstream, the axial fluctuation levels w increase more rapidly than the radial ones v , especially in the region between the jets, largely as a result of intermittency. The unequal fluctuation levels reveal anisotropic turbulence above the TGP. Further downstream, beyond region II, the fluctuation levels are redistributed, reaching nearly isotropic conditions of the in-nozzle flow beyond z = −35 mm. The invariance of the fluctuations with respect to a rotation of the coordinate system was investigated using an additional measurement plane. This was set up perpendicular to the basic measurement plane

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intersecting with the burner’s centerline as well. These additional profiles are shown in Fig. 8 for z = −50, −45, −35 mm, revealing similar fluctuation levels compared to the basic plane at z = −35 mm. Similar behavior is observed for the Reynolds shear stresses, which are approximately zero at z = −35 mm. As the gradients of the fluctuations are approximately zero in radial as well as in axial direction (see Fig. 5), nearly homogenous isotropic turbulence can be assumed, inside the nozzle, beyond z = −35 mm. This applies from a statistical point of view locally for the main flow inside the nozzle and not for regions close to the boundary layer and the stagnation plane. In contrast the influence of the emerging jets from the TGP can still be observed from instantaneous flow fields once in a while resulting in remaining local deviations of the flow vectors at the nozzle exit similar to the winding paths of the jets as shown in Fig. 3. This is in good agreement with observations of extinction events by Böhm et al [4] where approximately half of the observed extinction events revealed an unorganized vortex structure as expected for real turbulence while the other half were more organized resulting in counter rotating vortex pairs impinging on the flame at the stagnation plane. 3.4 Temporal autocorrelation In addition to a visual characterization of the flow-field and its temporal development, the time dependency of time correlated PIV measurements can be used to derive temporal autocorrelation functions Ruu [25] from: u (x, t) u (x, t + τ )  Ruu (x, t, τ ) =  u2 (x, t) u2 (x, t + τ )

(1)

The autocorrelation function is used to quantify the temporal behavior of the flow at a specific location. This can be derived for each interrogation area from the PIV measurements. According to the Shannon–Nyquist theorem a sampling rate of at least twice the maximum resolvable frequency is required. As the repetition rate of PIV was limited to 5 kHz in this experiment the maximum resolvable frequency

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was 2.5 kHz. The autocorrelation functions were derived from 4096 consecutively recorded PIV vector fields at 5 kHz. Although this is generally a large database for PIV measurements, Schneider et al. [27] reported up to 1 million data points, measured by LDV, to achieve good statistics. Therefore, only very pronounced, high frequency structures (0.1–2.5 kHz) are discussed here, because the number of samples decreases with increasing time separation for low frequencies. The autocorrelation function of axial and radial velocity components for TOJD is shown in Fig. 9 for different locations within the central jet. A distinct periodic behavior with decaying amplitude over time is observed. The amplitude of the periodic fluctuations on the centerline of the jet (r = 0 mm) is most pronounced for the axial component Rww at z = −62.5 mm and decays further downstream. At z = −55 mm the high frequency modulations are not detectable anymore. Towards the shear layer (z = −62.5 mm and r = 1.2 mm) Rww decreases while the amplitude of the radial component Rvv increases. The highest fluctuations of the radial component are found in the area of the shear layer where vortices move towards the jets’ centerlines. This behavior confirms the findings of visual inspection from time correlated PIV measurements (see Fig. 3 and Online Resource 2), where vortex shedding was observed, leading to contractions of the jet. The PIV movies indicate that these periodic contractions may lead to the observed pulsation of the axial jet velocity. The frequencies of the observed fluctuations can be identified from the energy– density spectra obtained by a Fourier transformation of the autocorrelation function. The spectra reveal a distinct peak at approximately 1.25 kHz. Figure 10 shows the autocorrelation functions of the axial velocity component and their corresponding energy–density spectra for the central and the neighboring left jet, on their respective

Fig. 9 Autocorrelation function Rww (left column) and Rvv (right column) for three different axial positions on the centerline (z = 62.5, 60, 55 mm) and one off-axis position (r = 1.2 mm, z = 62.5 mm) for TOJD

1.0

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88

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Fig. 10 Autocorrelation function Rww (left column) presented with the corresponding energy-density spectra (right column) on the centerline of the central and the neighboring left jet for TOJD

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r=-5 mm z=-60 mm

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8

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centerlines at z = −62.5 mm. For both jets, the frequency and the amplitude are the same. An additional study of the influence of the Reynolds-number was performed. The energy-density spectra are shown in Fig. 11 for Re = 5,000 (TOJC), Re = 5,800 and Re = 6,650 (TOJD). For an even higher Reynolds-number of 7,200 (TOJE), the peak frequency would have been much closer to the maximum detectable frequency of 2.5 kHz, which may lead to inaccurate results, so that an intermediate Reynoldsnumber of 5,800 was selected. Figure 11 presents the observed distinct frequencies as a function of the Reynolds-number. The experimental measurements can be fitted by a linear function, indicating that the observed frequency scales linearly with Reynolds-number. 3.5 Phase averaged velocities Phase averaging is often used to visualize periodic structures. By knowing the frequency of a periodic structure, data can be selected in relation to its cycle. Averaging of these data can be used to reveal structures related to these frequencies in a statistical manner. This approach was used for example by Froud et al. [8],

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Re 5800 r=0 mm z=-62.5 mm

1E-7 1E-5 1E-6

Re 6650 (TOJD) r=0 mm z=-62.5 mm

1E-7 100

f [1/s]

Eww [s]

Fig. 11 Energy-density spectra (left column) for different Reynolds-number at r = 0 mm and z = 62.5 mm; and the distinct peak frequency given as a function of Re (right column)

1250 1000 750

1000

f [1/s]

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to reveal the structure of a precessing vortex core in a swirl burner. Figure 12 shows phase-averaged profiles of the axial velocity. Here, the local mean velocity was subtracted from each instantaneous velocity field. Phase averaging was then performed for the distinct frequency at 1.25 kHz, as determined from the energydensity spectra for TOJD and 900 Hz for TOJC. This was done for four phase delays: 0◦ , 90◦ , 180◦ and 270◦ . From the equidistant PIV data, only those that were within ±0.625◦ were selected. This reduced the data to approximately 400 samples per phase-locked average. The phase averaged axial velocity profiles for TOJD (Fig. 12, left) along the centerline of the central (squares) and neighboring left jet (circles) reveal a periodic structure related to the frequency of 1.25 kHz with an axial extension of approximately 3.6 mm, which is observable as waves moving downstream. It is interesting to note that the magnitude of velocity for all phases is close to zero for the first 4–5 mm. This agrees with profiles of the axial velocity fluctuations (Fig. 5), which are close to zero for the first 5 mm, before they increase rapidly. The distinct periodic structure is observed up to z = −50 mm. This corresponds to the region where the shear layer

0.08

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Fig. 12 Phase averaged axial velocity profiles along the centerline of the central jet (squares) and the left adjacent jet at r = −5 mm (circles) for TOJD (left) and TOJC (right) for four different phase delays. The mean velocity was subtracted from each instantaneous flow-field first

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reaches the centerline of the jet, resulting in the peak velocity fluctuations. Further downstream, the periodicity and the energy-density spectra are smeared out more and more as shown by the decreasing amplitudes for the high frequency fluctuation at 1.25 kHz. Figure 12 (right) shows profiles of the phase averaged axial velocity, along the centerlines of the central and the neighboring left jet, for TOJC, where the required frequency for phase averaging was 900 Hz. Compared to TOJD the wavelength did not change and was again approximately 3.6 mm. The Strouhal number is often used as a dimensionless frequency to describe oscillating flow mechanisms. It is defined by the frequency of vortex shedding f (the respective peak frequencies of cases TOJC and D) the fluid velocity u and a characteristic length L (the TGP hole diameter is used here) as: St =

fL . u

(2)

A constant St = 0.55 was determined for the point on the centerline closest to the jet exit for TOJD and TOJC. This supports the finding that the frequency scales linearly with the Reynolds-number (see Fig. 11) and hence the bulk-velocity. The phase averaged profiles of TOJC are very similar to the case TOJD, with slightly higher fluctuation magnitudes. For TOJC, a distinct phase delay between the central and the neighboring left jet is resolved, which is in the range of 90–100◦ while they are in phase for TOJD. Figure 13 shows phase averaged profiles of the axial velocity at a phase delay of 90◦ for three different Reynolds-numbers. The phase shift between

Fig. 13 Phase averaged axial velocity profiles along the centerline of the central jet (squares) and the neighboring left (circles) for three different Reynolds-numbers at a phase delay of 90◦

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the adjacent jets was found to change with Reynolds-number. It was 0◦ for Re = 6,650 (TOJD), ∼180◦ for the intermediate Re = 5,800 and ∼90◦ for Re = 5,000 (TOJC). The observed distinct peak frequency stems from a periodic pulsation of the individual jets. This seems to be related to vortex shedding from the holes in the perforated plates. To correlate vortex shedding with the observed peak frequency the vortex centers and their convection velocity need to be identified. Barbosa et al. [1] determined vortex frequencies in a swirling jet by identifying the vortex centre from high-speed PIV vector fields using a scheme based on the λ2 criterion. Due to general restrictions of PIV regarding the dynamic range the vortex identification is not applicable to this data as the vector quality in the near zero velocity region is insufficient. However, the Reynolds-number dependency of the phase-shift between adjacent jets is striking. One may speculate that this could be a weak acoustic effect, as the eigenfrequency of waves traveling between both perforated plates (separation 130 mm) would be 1.3 kHz, which is very close to the observed vortex shedding frequency of 1.25 kHz for Re = 6,650. Such a standing acoustic wave ‘bouncing’ between the perforated plates might be sufficient to trigger phased vortex-shedding. Further investigation of the flow-field with an improved dynamic range as well as acoustic measurements would be of interest to study the origin of the pulsations and the coupling mechanisms between adjacent jets leading to constant phase delays between each other.

4 Conclusions An extensive experimental characterization of the in-nozzle flow-field of a turbulent opposed jet burner was performed in order to provide a database for the validation of inflow conditions for Large Eddy simulations. Conventional statistically independent 10 Hz PIV measurements were performed, providing accurate data with high spatial resolution. Additional high-speed PIV measurements at 5 kHz sampling rate were recorded to characterize the temporal behavior of the flow. The flow-field measurements revealed high velocity jets emerging from the TGP with recirculation zones located behind the solid parts of the TGP, in-between the jets. Immediately downstream of the perforated plates, the jets were observed to contract, caused by vortex shedding. High levels of turbulent kinetic energy were generated in the region of the jets’ break-up and during mutual interaction. Further downstream, a strong decay of turbulent kinetic energy was observed. Individual jets merged inside the nozzle, leading to smooth averaged velocity profiles at the nozzle outlet while the influence of the single jets was still observable in the instantaneous velocity fields. Almost homogeneous isotropic turbulence was observed in the vicinity of the nozzle exit while the velocity fluctuations revealed an increasing anisotropy of the flow approaching the stagnation plane. Time-series revealed a distinct periodic behavior of the fluctuations at the TGP. The amplitude is highest at the TGP and decays further downstream. These periodic fluctuations are caused by vortex-shedding from the holes of the TGP, at a frequency that scales linearly with Reynolds-number. Phase averaged velocity fields revealed different phase delays between the pulsations of adjacent jets depending on the Reynolds-number.

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Acknowledgements The authors gratefully acknowledge the financial support by Deutsche Forschungsgemeinschaft (EXC 259, Graduiertenkolleg 1344/1) and by the UK Engineering and Physical Sciences Research Council (EPSRC, PhD+ scheme).

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