Flow Turbulence Combust DOI 10.1007/s10494-016-9789-3

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating Joachim Klinner1 · Christian E. Willert1

Received: 6 January 2016 / Accepted: 4 November 2016 © Springer Science+Business Media Dordrecht 2016

Abstract In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90◦ pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (Red = 32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of T=50 K and T=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10◦ . Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward. Keywords Turbulent mixing · Pipe bend · Acetone PLIF · Turbulent flux · Error convergence

The online version of this article (doi:10.1007/s10494-016-9789-3) contains supplementary material, which is available to authorized users.  Joachim Klinner

[email protected] 1

German Aerospace Center (DLR), Institute of Propulsion Technology, Measurement Technology, Linder Hoehe, D-51147 Koeln, Germany

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1 Introduction The present investigation is motivated by the performance assessment of established numerical methods with regard to prediction of turbulent scalar transport and mixing of turbulent jet injection into a confined co-flow. In particular the optimisation of exhaust gas recirculation for NOx-reduction in internal combustion engines requires a detailed knowledge of mixing processes of the engines’ gas, oxygen, fuel and additives. The optimisation of the mixing port geometry by computational fluid dynamics (CFD) requires experimental data to validate the underlying Reynolds stress and mass transport models. In general, the physical understanding of the mixing of turbulent jets is of major theoretical and practical relevance and consequently an objective of intense research over several decades [20, 22]. While early studies focussed on the visualisation of the large-scale organised motion and the topology of jet mixing (e.g. see Brown and Roshko [3], Fric and Roshko [11], Kelso et al. [17]) more recent investigations utilised laser induced fluorescence and particle image velocimetry that allow quantification of mixing fraction and provide higher order correlations to fluid velocities with high spatial resolution. From the CFD point of view, modelling of the Reynolds stresses and turbulent fluxes within the shear layer of the jet still remains a challenging task especially if RANS and LES methods are applied [22, 23, 32]. For example, the determination of scalar mass transport often requires to evaluate the steady-state Reynolds-averaged equation for conservation of the mean concentration of mass [8]: ui 

  ∂ ui c ∂ C 1 ∂ 2 C − =− . ∂xi Re Sc ∂xi ∂xi ∂xi

(1)

Here, Re and Sc are the Reynolds and Schmidt number, c and ui are the instantaneous mass fraction and velocity and ui c describes the turbulent mass flux vector which gives both the direction and the magnitude of the mass transport by turbulence. Several numerical models exist to represent the turbulent mass flux (e.g. gradient diffusion model). Experimental validation of those models involve the steady-state turbulent mass flux vector ui c  which can only be derived from simultaneous measurements of velocity and mass fraction to enable computation of covariances from instantaneous components of both quantities. A few simultaneous velocity and concentration field measurements of turbulent jet mixing in non-reactive flows are reported in the literature: Antoine et al. [1] investigated the mixing of a round turbulent water jet in a low velocity co-flowing water stream inside a square channel by simultaneous laser induced fluorescence of Rhodamine 6G and 2D laser Doppler velocimetry. The authors found models of Reynolds stress transport in good agreement with experimental data in the self-preserving zone of the jet and observed stronger magnitudes of the radial turbulent mass fluxes in comparison to experimental data without co-flow. Aside from a reduction of the jet spreading rate the authors observed enhanced turbulent mixing in the presence of a co-flow, resulting in higher longitudinal and radial turbulent fluxes in comparison to a pure jet. On the basis of the experimental data provided by Antoine et al. various subgrid-scale scalar flux models for LES were assessed later on by Mej´ıa et al. [23]. Feng et al. [9] investigated the mixing of a liquid-phase confined rectangular jet in co-flow using planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The authors noted that the confinement leads to nonzero values of turbulent kinetic energy and Reynolds stress near the walls. Thus the boundary layer developing along sidewalls strongly influence mixing, especially downstream from the potential core. In a later paper about a similar experiment, Feng et al. [8] additionally evaluated spatial

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variations of the turbulent Schmidt number. Using two point correlations of fluctuations and linear stochastic estimation the authors were able to associate conditional structures with flow events that are responsible for inward and outward mass and momentum transport in the jet’s shear layer. For mixing experiments in gaseous flows acetone vapour is frequently used as a fluorescing medium due to its acceptable quantum yield in the visible range, insensitivity to oxygen quenching, relatively low toxicity, low vapour pressure and well described spectroscopic properties [4, 21, 30]. For instance Smith and Mungal [26] studied the mixing and scaling of the gaseous jet in crossflow over a wide range of velocity ratios and Reynolds numbers using acetone PLIF. Su and Clemens [28] investigated the shape and thickness of scalar dissipation structures in a co-flowing turbulent planar jet and verified the scaling coefficients of sizes of dissipative structures with respect to the Batchelor scale. To achieve this, acetone PLIF and Rayleigh scattering were applied simultaneously in closely spaced parallel planes. The authors specified a high spatial resolution in the order of 0.4λD to resolve the three-dimensional dissipation field, where λD characterizes the finest dissipation length scale. Tsurikov and Clemens [33] also made use of acetone molecular tracer to investigate fine scale structures in a axisymmetric nitrogen jet in co-flowing air by combining high resolution PLIF and PIV measurements. The jet was saturated with acetone vapor to maximise the fluorescence yield and was additionally heated to match the density of the co-flowing air at the jet exit. Due to the high fluorescence signal a non intensified camera could be used for PLIF whereby the Kolmogorov scale was resolved (ην = 0.6 mm ) for both PLIF and PIV measurements. The setup allowed to evaluate scalar and velocity gradient fields visualizing the sheet like structures of scalar and kinetic energy dissipation. The extension of dissipation structures was compared to the structures of kinetic energy dissipation which were found to be thicker and of topologies of higher diversity. Tsurikov and Clemens [33] also found that statistics obtained from velocity fields based on a reduced PIV resolution (2ην and 4ην ) would slightly underestimate kinetic energy dissipation but would have minor influence on vorticity statistics. Su and Mungal [29] characterised the scaling properties of velocity and concentration fields of a turbulent jet in cross-flow in comparison to a pure jet using simultaneous acetone PLIF and PIV at high spatial resolution. Similar to the experiment described by Tsurikov and Clemens [33] a nitrogen jet in air was seeded with acetone vapour to 10 % by volume. Although a large body of experimental data exists for turbulent jet mixing, detailed simultaneous measurements of velocity and concentration fields of the turbulent jet mixing downstream of pipe bends in co-flow are less common in the literature. Recent experimental studies on pipe flows focus on the curvature-induced secondary flow structures downstream ¨ u [15]) or on the effect of pulsaof pipe-bends (e.g. Hellstr¨om et al. [14] , Kalpakli and Orl¨ tions on the turbulent flow at the exit of pipe bend (Kalpakli et al. [16]). The predictability of secondary flow motion in bend pipe flows by LES and RANS was recently assessed by R¨ohrig et al. [24]. In present work, the turbulent mixing downstream of a pipe bend with co-flow is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded injected flow. The generic mixing experiment aimed at providing statistically converged quantities of velocity and concentration, turbulent fluctuations and the degree of correlation of these fluctuations at several downstream locations. Three modes of operation are investigated at constant mass flow rates: (A) isothermal steady jet injection (Red = 32000), (B) pulsed isothermal injection and (C) steady injection at elevated jet temperature. Unlike in other acetone PLIF mixing experiments where a nitrogen jet was seeded with relatively high acetone vapour concentrations of 10 % by volume

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( e.g. [29, 33]) we apply an air-jet which has nearly equal gas composition compared to the co-flow. Substantially smaller acetone tracer concentrations below the flamability limit are applied to the jet (< 3 % by volume). The low tracer gas concentration leaves the thermal capacity of the mixture nearly unaffected and minimizes light-sheet absorption, but on the other hand, requires the use of a intensified camera (MCP based). Hence, measurements of small-scale quantities may have to deal with increased noise due to the lower fluorescence signal and spatial resolution limitations of the intensified PLIF imaging system [19]. Therefore, resolution capabilities and the dynamic range of concentration measurements are estimated by means of the knife-edge technique [7] and through analysis of background noise. Statistical convergence of the random error of measured quantities and their higher order moments is determined by empirical bootstrapping according to an approach published by Stafford et al. [27]. In this way, the statistical error of all measured quantities over the number of samples is assessed in exemplary regions within the shear layers of the mixing zone during steady injection. Finally, exemplary results of measured quantities are discussed.

2 Test Facility and Boundary Conditions The measurements are performed in a small scale wind tunnel as outlined in Figs. 1 and 2. The wind tunnel is operated in suction mode and has a 830 mm long test section with a square cross-section of internal width of 76 mm. Quartz windows with 45◦ edge bevels provide optical access to the entire cross-section. Flow conditioning is provided by a settling chamber containing screens and straightening tubes. Reproducible turbulent flow conditions are provided by a turbulence grid made of perforated steel that is placed immediately upstream of the test section at the exit of contraction nozzle. The mixing port is placed at a third of the test section length and consists of a 90◦ bend (industrial norm DIN EN 1254, Type 5001a), shown in Fig. 3. The bend exit is aligned coaxially with the channel’s center line. The wind tunnel is mounted on a two-axis translation stage to enable measurements in different regions while the PLIF-PIV setup remains stationary. Successive measurements in x − z or x − y planes are made possible by rotation of the measuring section around the tunnel’s centerline by 90◦ . In Table 1, operational parameters of the tunnel are provided. Under steady isothermal operation the Reynolds number of the incoming main flow of the tunnel is 16000 based on bulk velocity and hydraulic diameter. The homogeneity of inlet velocity and the turbulent

Fig. 1 Schematic diagram of wind tunnel facility with approximate location of acetone PLIF and PIV measurement area

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Fig. 2 Schematic of the combined PLIF-PIV experimental setup (left) for measurements in the x-z plane of the nozzle coordinate system (right)

fluctuations of the main flow upstream of the mixing port are verified by stereoscopic PIV measurements in the x − y and x − z center planes as described in [18]. Figure 4 shows the mean inlet velocity profile and the variances of all three velocity components upstream of the bend exit at x = −8d. The following definition has been used to calculate the turbulence intensity:  1 1   Tu = (2) (u u  + v  v   + w  w  ), u0 3 where u0 is the bulk velocity of the tunnel inlet (see Table 1) and u u , v  v  , w w   the variances of the velocity components in x, y, z. Equal variances near the center line indicate isotropic turbulence. At the same time the grid-induced turbulence intensity along center line has decayed to Tu = 4 % at x = −8d and to Tu = 2.8 % at x = −5d. The friction velocities uτ at both inlets given in Table 1 are obtained by a near-wall PIV measurement technique as reported in [35]. The friction velocity at the tunnel outlet is based

concave inner wall

0.73d

Flow

z

Rc=1.34d

convex inner wall

0.26d

d

x

Flow

0.06d

30d

Fig. 3 Schematic diagram of bend and channel geometry

D=3.04d

Flow Turbulence Combust Table 1 Flow paramter during steady isothermal injection Tunnel inlet

Bend exit

Tunnel Outlet

Units mm

Position

-110

0

200

Mass flow m ˙

22.5

11.5

34

g/s

Hydraulic dia. D (tunnel), d (nozzle)

76

25

76

mm

Bulk velocity u0

3.25

19.5

4.9

m/s

Re0 based on d, D and u0

16250

32000

24500

Friction velocity at upper wall uτ

0.199

0.181

0.265

m/s

on the flat plate model and the pressure difference from pressure tabs at tunnel inlet and outlet. The curvature parameter of the 90◦ bend is κ = 0.5d/Rc = 0.37. During steady isothermal operation the exhaust gas flow is injected into the tunnel flow at approximately half of the inlet mass flow rate. The Reynolds number Re0 at the bend exit is 32000 based on bulk injection velocity and the inner pipe diameter. An important parameter to characterise the secondary √ motion downstream of curved pipes is the dimensionless Dean number, given by De = Re0 κ. During steady isothermal injection the Dean number is 20000. For pulsed isothermal injection a rotating valve is connected to the partially flexible metal hose about 80d upstream of the injection port. The pulser consists of a rotating hollow shaft with two radial outlet bores. While the relative area change of the rotating valve over a single pulsation cycle (see Fig. 5) clearly is not sinusoidal, it is sufficiently representative for the specific exhaust gas recirculation system. The rotating valve is driven by a belt and a frequency-stabilised AC motor allowing the pulsation frequency to be set at f = 66Hz. A parameter describing the balance between pulsatile inertial √ forces and viscous forces in pipe flows is the Womersley number, defined as α = d/2 2πf/ν. The Womersley number of the present configuration is 65, indicating inertia dominated flow at the bend exit (c.f. [16]).

1.5 1 /u²0 /u²0 /u²0

y/d

0.5 0

-0.5 -1 -1.5 0

0.5

1

/u0

1.5

20

0.005

0.01

0.015

0.02

0.025

/u²0, /u²0, /u²0

Fig. 4 Mean streamwise velocity and Reynolds shear stress components upstream of the bend normalized by the inlet’s bulk velocity at x = −8d in the x − y center plane measured with stereoscopic PIV (Average over 3600 samples)

Flow Turbulence Combust Fig. 5 Relative open area of the rotating valve as function of revolution angle

1.2

Avalve / Atube [−]

1.0 0.8 0.6 0.4 0.2 0.0

0

100

200 φ[ °]

300

For measurements at increased jet temperature a 3.7 kW electric heater is connected to the thermally shielded supply line about 80d upstream of the injection port. The jet temperature is measured by a thermocouple placed in the pipe center 4d upstream of bend exit using a thin capillary tube. The exit velocity profiles was verified through measurements by PIV and showed no evidence of flow disturbance through installation of the temperature sensor.

3 Combined Acetone PLIF/PIV Setup The flow chart in Fig. 6 shows the instrumentation of the wind tunnel air supply and suction system as well as the PIV seeding and acetone supply. Orifice plates and a thermal mass flow meter (Yokogawa Rotakalor RK22C) are used to monitor the suction and injection mass flow rates. During long PLIF-PIV acquisition runs (12 minutes, 3600 images at 5 Hz frame rate) the suction mass flow is stable to within ±0.4 % and the injected mass flow is stable to within ±0.2 % related to the mean mass flow rates. The nitrogen mass flow through the bubbler is enriched with acetone tracer gas to initial volume concentration levels of approximately 40 vol%. The estimation of the initial concentration is based on the saturation vapour pressure of acetone taken from [21] at a acetone bath temperature of 35◦ . Inside the mixing tube the initial acetone concentration is further diluted to levels of 0.5-1.0 vol% tracer gas concentration before it is fed into the injection pipe. The acetone bubbler, the mixing tube and the acetone supply lines upstream of the mixing tube are temperature stabilised at 35◦ to avoid acetone condensation and to keep the acetone tracer concentration stable during the long runs. The optical setup for the combined PLIF-PIV measurements is depicted in Fig. 2. Measurements of instantaneous concentration are achieved using planar laser induced fluorescence (PLIF) of the acetone seeded injection flow. Acetone has a wide absorption spectrum between 200 and 325 nm [21] and is excited with a quadrupled Nd:YAG pulse laser at 266 nm resulting in fluorescence in a spectral range of 320...600 nm with a peak emission at a wavelength of 410 nm [4]. The utilised pulsed UV-laser has a pulse energy of 80 mJ at 266 nm and a pulse width of 12 ns (Quanta Ray, Spectra Physics). The laser beam is converted into a divergent light sheet which has a width of 120 mm at the wind tunnel’s centerline. The sheet thickness was estimated by evaluation of fluorescence images of the beam waist from a strongly inclined UV detector card (Thorlabs VRC1). The UV sheet thickness is 80 μm at the tunnel’s centerline and 440 μm at the tunnel window.

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g

h

h

g

compressed air

A

N2

a

C

B

e

a e

d e

f

b c

a. b. c. d. e. f. g. h.

Laskin seeder Aceton bubbler Water bath, temperature stabilized Mixing tube, temperature stabilized Mass flow meter Centrifugal pump Temperature probe Pressure tab

Configuraons A. Straight B. Pulser C. Electric heater Fig. 6 Flow chart and instrumentation of the wind tunnel

Images of the acetone fluorescence are acquired with an intensified camera (DicamPro, PCO AG) equipped with a S20Q photocathode which has a quantum efficiency of 20 % at λ = 410 nm. The camera’s photocathode is gated at 40 ns coinciding with the UV-laser pulse. The intensifier’s gain is set to 20-30 % which corresponds to 3 − 6 counts/photoelectron. Pixel binning by a factor of 2 × 2 increases the signal yield but does not compromise the spatial resolution which is limited by the micro-channel plate. The camera is equipped with a Nikkor 50/f# 1.2 lens and a 5 mm close-up extension ring leading to a total magnification of M=0.082 or 6 pixel/mm at a image size of 640 × 512 pixel and a field of view of 110 × 85 mm. A short pass edge filter with a 65 % cut-off wavelength of 500 nm is placed in front of the lens to protect the highly sensitive camera from PIV laser light in the event of incorrect triggering. Simultaneous recording of the PLIF laser sheet intensity profile allows a calibration of temporal and spatial fluctuations of the excitation energy distribution as described in [13]. Using a beam splitter plate, roughly 4 % of the PLIF laser sheet energy is guided to a reference cell filled with a rhodamine 6G ethanol mixture. Permanent recycling of the fluid using a circulation pump and a reservoir prevents degradation of the dye due to photo bleaching. The green fluorescence of the dye is imaged by a CCD camera (PCO.1600, PCO AG) and is used to correct the simultaneously acquired acetone fluorescence images thereby enabling shot-to-shot intensity normalization. Simultaneous planar 2-C velocity measurements are obtained using particle image velocimetry (PIV) in a conventional orthogonal viewing arrangement. The dual frame

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sCMOS camera (ILA.sCMOS.PIV, ILA GmbH) is equipped with a Zeiss 85/f# 5.6 lens and observes the field of view at a magnification of approximately 22 pixel/mm. Paraffin tracer droplets, injected upstream of the wind tunnel’s flow straighteners, are illuminated using a frequency doubled Nd:YAG laser with a rated pulse energy of 50 mJ at 532 nm (Brilliant Twins, Quantel/BigSky Laser). Bandpass filters with a spectral width of 10 nm and a center wavelength of 532 nm reject stray broadband light from the laboratory. Both, the inlet flow and the injected flow are seeded at matching tracer concentrations. Under isothermal conditions the seeding consists of paraffine aerosol created by two Laskin atomizers. Impactors in the seeding device reduce the size fraction below 1μm prior to introducing the seeded air respectively to the settling chamber and mixing tube. For the experiments at elevated jet temperatures, the injection port is seeded using a Laskin atomizer filled with a highly refined hydrocarbon mineral oil (Vicount Smoke Oil 135/180) which has a higher boiling temperature than paraffine which tended to evaporate prior to injection into the co-flow. In comparison to isothermal measurements the scattering diameter of the oil droplets at the mixing port outlet at T=393 K (T=100 K) is still sufficient to provide an acceptable PIV signal. The fluorescence of smoke oil and paraffin droplets at excitation of 266 nm was found to be of little significance in comparison of the acetone fluorescence. The droplet fluorescence increased averaged background levels of PLIF measurements of 100 counts by 10 % while the maximum acetone fluorescence is in the order of 2000 counts and more. A planar calibration target with equidistant markers is placed in the light-sheet to determine magnifications of both imaging systems. Due to the use of high-quality lenses, geometrical distortions are negligible. PLIF and PIV images are mapped onto each other by reference-points on the inner and outer rim of the bend exit. Measurements at the large field-of-view of 110 × 76 mm2 (500 samples) are conducted to obtain an global overview of the average velocity and concentration field (named ’global measurements’). In order to evaluate statistical fluctuations of velocity and concentration up to 3600 single shot measurements are acquired in regions corresponding to small, wall normal stripes of about 20 × 76 mm2 (named ’profile measurements’). The axial width of both light-sheets is clipped accordingly to reduce stray light and reflections as much as possible. Trigger pulses for all lasers and cameras are generated by a programmable timing generator (PIVseqPCI, PIVTEC GmbH). The acquisition rate of combined measurements is 5 Hz which is a compromise of having all lasers operating at optimum flash lamp repetition rates (10 and 15 Hz) while all Q-switches are triggered at a common frequency. The pulse separation t was set in a range of 25...35μs according to PIV displacement PDFs to have a maximum particle image displacement of at least 10 pixel and validation rates of at least 80 % in the shear layers. The timing of a single PLIF-PIV measurement was chosen in such a way that the PLIF laser pulse is placed in-between both PIV laser pulses at t/2. During pulsed operation, phase angles are simultaneously monitored with each single shot to enable a posteriori phase sorting and phase averaging. The valve’s phase angle at each combined PLIF-PIV single shot is recorded using two counter channels of a ADWIN16 card running at a 20 khz sampling rate. Phase sorting is preferred to phase locked measurements because periodic triggering of both laser systems at the required rotational speed would not allow to fire both lasers at their optimum flash lamp repetition rate. Phase locked measurements would also require a priori knowledge of specific valve angles, such as peak flow rates at the nozzle exit, which is hard to predict when the pulser is placed 80d upstream of the nozzle. However, a posteriori phase sorting allows averaging at arbitrary cycle positions using arbitrary bin sizes and provides insight into the flow evolvement during the entire pulsation cycle.

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4 Data Evaluation and Accuracy Estimation 4.1 PIV image processing PIV image data is processed using PIVview 3.6.0 (PIVTEC GmbH) for which the PIV evaluation parameters are summarized in Table 2. Particle displacements are recovered using a coarse-to-fine multi-grid processing scheme with image deformation at each step to take into account the strong shear in the flow. The sub-pixel correlation peak position measurement was performed by a truncated sinc signal reconstruction algorithm. Due to this processing and a sufficient particle image density an accuracy of correlation peak detection below 0.1 pixel can be obtained for regions without strong laser background and without strong velocity gradients. Given the magnification of 22 pixel/mm and a pulse delay of t = 25 − 35 μs , a peak detection accuracy of 0.1 pixel would lead to a absolute velocity uncertainty of 0.13−0.18 m/s for each single shot. Peak locking effects are partially observed in the displacement PDFs and could be reduced by slightly blurring the particle images by defocussing the lens. The final vector spacing is 1.09 × 0.73 mm at a interrogation window size of 2.18 × 1.45 mm . The calculation of statistics involve only validated PIV data excluding all outliers as well as velocity estimates from lower order correlation peaks. The smallest validation rates for the validation parameters provided in Table 2 are 85 % and are found in the outer shear layer near the bend exit.

4.2 PLIF image processing and dynamic range The planar fluorescence signal at an arbitrary point p in the light sheet is given by Sf (p) = Ie (p) C(p)  L(p) A(p) G

(3)

where Sf is the measured fluorescence signal at p, Ie is the intensity of the excitation light beam at p, A is the fraction of fluorescence light collected by the lens, G is the camera gain, is the quantum efficiency, L is the length of the sampling volume along the path of the excitation beam,  is the molar absorptivity, and C is the molar concentration of the fluorophore at p. The linear dependency of the fluorescence signal and the acetone tracer

Table 2 PIV evaluation parameters Field of view

116 × 80 (overview) 19 × 80 (statistics)

mm

2560 × 1760 (overview) 420 × 1760 (statistics)

pixel

Magnification

22.0

pixel/mm

Pulse delay

300 (inlet) 25 − 35 (mixed outlet)

μ

Window size

2.18 × 1.45

mm

Sampling

48 × 32

pixel

1.09 × 0.73

mm

24 × 16

pixel

Interrogation method

Multi-grid + Image deformation

Peak detection

Whittaker reconstruction

Vector validation test

max. displacement diff. (10 pixel) normalized median (6)

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concentration is only given if the energy flux in the light sheet is below the saturation level and absorption is neglected. Bryant et al. [4] reported a linear response of acetone vapour at an energy flux of 353 mJ/cm3 when excited at 266 nm (10 ns pulse width) under ambient conditions. The maximum laser energy flux in the experiment is 500mJ/cm3 at 12 ns pulse duration. The linearity of the signal was verified prior measurements and no evidence of saturation was found. Concentration fields are obtained by the PLIF image processing provided in Fig. 7. After background subtraction, PLIF images are first flat-field corrected. For this purpose, images are divided by a sensitivity image, which is recorded while the channel is flooded with a homogeneous acetone tracer concentration (average over 200 images). This procedure accounts for the angular lens collection efficiency, variations of sensitivity of the camera, the quantum efficiency of fluorescence and spatial variations of laser intensity. In order to correct for additional temporal and spatial deviations of excitation energy, each single image is normalised by simultaneous laser intensity deviations. To achieve this, the intensity profile across the light-sheet is extracted from reference images of the rhodamine cell and averaged. The further proceeding of one-dimensional laser intensity profiles is as follows: 1. 2. 3.

division by the intensity profile obtained by flooding the channel with an acetone-air mixture at rest, replication of 1D profile along image height, mapping according to sheet propagation in the test section, taking the the divergence of the light sheet into account.

The mapping consists of a projective transformation using four point correspondences between reference and signal image. Point correspondences are found by calibration images of a striped light sheet.

Processing of 1D reference profiles

Processing of PLIF images PLIF image me=ti

Reference profile flooded channel

1D profile me=ti

PLIF image flooded channel Background acetone off

Normalized PLIF image

Fluorescence signal unmixed (near nozzle exit)

Sf0

Correcon of temporal and spaal laser intensity fluctuaons

Sf(x,y)

Background laser off

Instantaneous intensity deviaon

Replicaon and projecve 2D mapping

C (x,y)i [-]

Fig. 7 Processing of acetone PLIF images and of 1D laser intensity profiles to obtain local mass fraction

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The dynamic range of profile measurements of mass fraction is estimated from the root-mean-square (rms) of the background in a region where the acetone concentration is zero (x = 0.4d and z > 0.8d). At the highest gain applied to the intensifier (30 % or 6 counts/photoelectron), the rms value of the background is σbkg = 1.4e − 3. Assuming normally distributed background noise, the smallest mass fraction detectable by the setup should be cmin = 2σbkg . The corresponding dynamic range is 340 : 1. The actual dynamic range is smaller due to stray light which stems from acetone fluorescence itself. The blue acetone fluorescence is partially back-reflected by the tunnel windows which are not anti-reflection coated. This inherent background is not homogeneous, depends on the local acetone concentration and therefore can not be quantified. In the aforementioned region above the nozzle exit (zero acetone concentration) the stray fluorescence light leads to biased concentrations slightly above zero which decreases the dynamic range to 220 : 1.

4.3 Stability of acetone tracer supply Accurate concentration measurements require a temporally stable and homogeneous initial acetone tracer density at the injection port. Figure 8 shows the stability of the PLIF signal at maximum (unmixed) acetone concentration within a rectangular region immediately downstream of the injection inlet during a run of 12 minutes with 5 Hz acquisition rate and steady isothermal injection. The acetone fluorescence signal slightly overshots the mean within the first 800 measurements and remains stable throughout the remainder of the sequence with a 4.8 % standard deviation from the average. The slightly higher initial acetone concentration within the first 800 samples occurs while the acetone bath temperature is not in equilibrium with the water bath temperature. The acetone bath tends to cool down with the beginning of nitrogen injection which reduces the acetone rate until the equilibrium is reached. The signal Sf 0 is used to scale PLIF images to maximum concentration respectively mass fraction. The reference is directly obtained from single-shot images if the injection inlet is in the field. If the injection inlet is outside the field of view the fluorescence signal of unmixed fluid is acquired prior to and after each measurement and then interpolated linearly. Thereby, long-time deviations of the initial acetone concentration are compensated. For reference measurements acquired prior and after a run of 12 minutes the mean absolute deviation of both values is 4 %.

Fig. 8 Stability of the unmixed fluorescence signal immediately downstream of the nozzle in the highlighted rectangular region (3600 frames correspond to 12 min acquisition time)

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4.4 Compensation of temperature dependency of acetone fluorescence As described by Thurber et al. [31], the fluorescence of acetone exhibits a temperature dependency which can bias mass fraction measurements at elevated jet temperature. According to the authors, the fluorescence signal per unit mole fraction Sf+ depends on several quantities, i.e., p Sf+ (λ, T ) ∝ σ (λ, T ) (λ, T ) , (4) T where T and p are the temperature and the total pressure of the fluid, σ (λ, T ) is the absorption cross section and (λ, T ) the fluorescence quantum yield. At constant pressure and elevated jet temperature, the influence of local density and quantum efficiency on mass fraction measurements is compensated by c=

∗ Sf m Tm Sf (T0 ) , Sf 0 T0 Sf∗ (Tm )

(5)

where Sf m /Sf 0 is the normalised local fluorescence obtained from PLIF image processing (see Fig. 7), T0 is the temperature of the heated jet, Tm is the local mixing temperature and Sf∗ (T0 ) respectively Sf∗ (Tm ) are the corresponding fluorescence signals per tracer molecule per unit laser fluence. Thurber et al. [31] have shown, that at atmospheric pressure the acetone fluorescence per tracer molecule per unit laser fluence decreases only slightly by 3 % in the required temperature range 295 − 395 K for a excitation wavelength of λ = 266 nm. However, the calibration curve from Thurber et al. is used to calculate Sf∗ (T0 )/Sf∗ (Tm ) on the basis of the local mixing temperature Tm . Under assumption that the injected fluid and the air stream from the tunnel inlet have equal specific heat capacities the mixing temperature can be approximated using Richmann’s calorimetric mixing formula: Tm = c T0 + (1 − c) T0in ,

(6)

where T0in is the temperature of the unmixed air coming from the tunnel inlet. The mass fraction is calculated iteratively. In a first step we set c = Sf m /Sf 0 to calculate the mixing temperature using Eq. (6). The mass fraction obtained with Eq. (5) is than used to refine the estimate of mixing temperature in a second step. After two iterations the mass fraction does not change significantly.

4.5 Procedure of stochastic error estimation The uncertainty of time-averaged velocity, mass fraction, Reynolds shear stress and turbulent mass flux components over the number of samples is assessed by empirical bootstrapping [27]. Bootstrapping relies on random sampling with replacement and can be used to evaluate the random error (e.g. confidence interval) of quantities with unknown distributions [2]. Each bootstrap Xb∗ = {x1 , x2 , ..., xN } is a subset of N samples of the entire data set. Each sample is selected using a random generator. The statistical error of each measured quantity x is estimated on the basis of the relative deviation from a reference value ∗

Er (Xb ) =

∗

Xb − XB XB

,

(7)

where X B is the bootstrap which contains the entire data set. The accuracy of PIV velocity components in x, y and z direction (u, v, w) are not independent due to a unique pulse separation t which is set according to the maximum displacement without loss of pairs.

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Thus, uB is used in the denominator of (7) as reference for the stochastic error estimation of u, v, w.

4.6 Sampling error assessment The convergence of the previously defined error estimator versus number of samples is evaluated for regions in the turbulent shear layer during isothermal and steady injection. Data from downstream regions A, B, C (see Fig. 9) with the size matching a single PIV interrogation window are evaluated. These regions have been chosen because they are most susceptible to PIV signal loss due to the presence of high shear stress. For example, in region A the validation rate deceases to 80 % for the outlier detection scheme provided in Table 2. A pronounced turbulent mass flux is expected in these regions due to the presence of fluctuations of both velocity and mass fraction. Figure 10 shows the decreasing random error of u and u u  against the 3000 sample statistic in region A. Each distribution contains 500 bootstraps. Estimates of statistical error base on the size of the 95 % confidence interval of normally distributed data (±2σ ). The error of u is below 1 % from 1500 samples. Second order moments require significantly more samples to converge. From 2000 samples the error of u u  against the 3000 sample statistic is in the order of 4 %. In Fig. 11, the convergence of the 95 % confidence interval towards the 3000 sample statistic of all measured quantities in regions A,B and C is presented. Each confidence interval relies on PDFs of 1000 bootstraps. The error found by bootstrapping is√ fitted against the standard error of normally distributed data using the function Er = a/ N . For first order statistics of normally distributed √ data the fit parameter can be expressed as a = σ and for second order statistics a = 2σ 2 applies. Both, empirical and theoretical error are

Fig. 9 RMS of 500 samples with regions A (x = 0.4d), B (x = 3.0d) and C (x = 5.6d) within which convergence tests are conducted

Flow Turbulence Combust

0.02

0.1

N

2500

500

2500

N

2000

-0.2

1500

-0.04 1000

-0.1

500

-0.02

2000

0

1500

0

1000

Er( ) [-]

0.2

Er( ) [-]

0.04

Fig. 10 Random error of velocity (left) and Reynolds shear stress (right) components over a 3000 sample data set in region A (Fig. 9); the error bar represents the 95 % confidence interval

in good agreement for N < 1000. As sample size increases, the error found by bootstrapping strongly converges towards 0 % with respect to the reference statistic (3000 samples). Therefore, above 1000 samples the relative error is estimated by extrapolation of the standard error fit (dashed lines). From 3600 samples (steady injection statistics) the statistical 10

-1

a √N

5

10

N

104

3

10

2

10

5

10

N

10

3

0

C C C C C C C

-1

Er [-]

10

10

10 10

4

-2

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10

B B B B B B B

A A A A A A A

Er [-]

10

0

5

10

N

10

3

10

10

4

-2

2

10

Fig. 11 Relative error indicating 95 % confidence in velocity, mass fraction, Reynolds shear stress and turbulent mass flux in convergence towards the 3000 sample statistics in √regions A (x = 0.4d) B (x = 3.0d) and C (x = 5.6d); the dashed line represents extrapolation of Er = a/ N

Flow Turbulence Combust

error of u, w and c is below 1 % in all regions while the error of u u  and w w   is below 5 %. Components of the turbulent mass flux u w   and u c  have an error below 6 % from 3000 samples. During pulsed operation and a posteriori phase sorting at least 100 samples are averaged per bin (binsize=10◦ ). Due to this low number of samples only first order statistics are provided for the pulsed operating condition. From 100 samples the statistical error of u is below 6 % and below 3 % for w. The mean mass fraction reaches statistical uncertainties below 3 % (region A) and below 7 % in regions B and C. It should be noted that the statistical error of the mean mass fraction increases almost by a factor of two in regions B and C. The reason for that lies in the fact that in downstream regions the unmixed fluorescence signal present at the nozzle exit is outside of the camera’s field of view. Thus, fluctuations of the initial acetone tracer density does not cancel out and lead to a higher uncertainty. Extrapolation of the standard error (dashed lines in Fig. 11) indicates that convergence of second order statistics (e.g. components of Reynolds stress and turbulent mass flux) to uncertainties below 1 % would require in the order of 30.000-70.000 samples or acquisition times of 100-230 min at a frame rate of 5 Hz which are found to be unfeasible from practical point of view.

4.7 Spatial resolution estimates In this section we determine to what extend small flow structures can be resolved with the previously described experimental setup. The spatial resolution of the intensified PLIF imaging system is evaluated using the knife-edge technique (c.f. Clemens [7]). This is achieved by extracting intensity profiles from images of a back-illuminated knife edge at the optical center and at radial positions 0.5d, 1.0d and 1.5d away from the center. Prior to profile evaluation, images are averaged (N=200) and normalised by a flat-field intensity image to correct sensitivity variations of the intensifier. The step response function at different image positions (see Fig. 12 left) is derived by subtracting the mean intensity of the edge profile and normalisation with the standard deviation. Differentiation of the step response function provides the line spread function whose Fourier transformation gives the modulation transfer function (MTF) shown in Fig.12, bottom left. Due to lens aberrations the resolution decreases slightly with increasing field angle. Given a magnification of 6.1 pixel/mm, the PLIF imaging system resolves spatial frequencies of 0.83 cycle/mm near the tunnels centerline, 0.75 cycle/mm at 1d distance from the center line and of 0.70 cycle/mm near the tunnel wall implying a contrast reduction of 50 %. Accordingly, the lateral cut-off wavelength is 1.2-1.4 mm. The spatial resolution achievable with PIV is coupled to the transfer function of the interrogation window. The size of the PIV interrogation window in wall-normal direction is Wz = Wy = 1.4 mm (at 50 % overlap). According to Foucaut et al. [10] the cut-off wavelength at 50 % signal reduction is equal to π/2.8W which translates into a wallnormal cut-off wavelength of 1.62 mm . Following Buch & Dahm [5], the smallest velocity gradient scale is represented by the strain limited vorticity diffusion scale λν , which is defined as −3/4

λν =  δ Reδ

,

(8)

where δ is the mean flow width and Reδ is the outer scale Reynolds number, which is defined as Reδ = U δ/ν, where U quantifies the mean shear. As discussed by Su & Clemens [28], the scaling coefficient  is flow dependent. The authors measured a value of  ≈ 15 in case of a planar turbulent jet. On the other hand, Buch & Dahm [5] measured a

Flow Turbulence Combust

1.0

counts[−]

0.8 0.6

xi=0.0d (center) xi=0.5d xi=1.0d xi=1.5d

0.4 0.2 0.0 −1.0

−0.5

0.0 x[mm]

1.0 −1.0

0.5

−0.5

0.0 x[mm]

0.5

1.0

1.0

modulation

0.8 0.6 0.4 0.2 0.0 0.0

0.5

1.0 1.5 cycles/mm

2.0

2.5

Fig. 12 Spatial resolution of the PLIF imaging system at a magnification of 6 pixel/mm ; Step response function (top left), Line spread function with Gaussian fit (top right) and modulation transfer function (bottom left)

value of  ≈ 11 for round jets. The strain-limited vorticity scale is related to the smallest strain-limited scalar diffusion scale λD by λD = λν Sc−1/2 ,

(9)

where the Schmidt number, Sc, for the acetone-air mixture is 1.42 at 293 K at atmospheric pressure (1 bar). For the present experiments we estimate the mean shear U and and the flow width δ from Fig. 13 in the x − y center plane. The outer width δ0.05 is the distance between the points where the velocity has fallen to 0.05U . Estimations of the mean shear U is based on the difference between the local maximum jet velocity and the stream wise velocity of co-flowing air at the nozzle exit. According to Su & Clemens [28] a scaling coefficient of  = 15 is used. Estimates of outer scale parameter and strain-limited diffusion scales λν and λD are provided in Table 3 for the downstream positions at x = 0.4d, 4.4d and 8.4d. For a round jet, Tsurikov & Clemens [33] estimated the relationship between the strainlimited diffusion scale and the Kolmogorov or Batchelor scale as λν = 6η and λD = 6 ηB on the basis of experimental kinetic energy dissipation data of Friehe et al. [12]. According to Friehe et al., the Taylor microscale λT in a round jet can be estimated as a function of the Reynolds number Re0 of the nozzle, based on the bulk injection velocity: −1/2

λT = 0.88 Re0

x.

(10)

Flow Turbulence Combust Fig. 13 Axial velocity in the x − y center plane normalized to the local mean shear velocity. The outer flow width δ0.05 is obtained from the distance between the points where the axial velocity has fallen to 0.05U

1.5

x=0.4d x=4.4d x=8.4d

1

y/d

0.5 0 -0.5 -1 -1.5

-0.4

0

0.4 0.8 (U-Ux=0)/ΔU

1.2

Although this relation is valid for the self-preserving region of a plane jet, it is used herein to provide a rough estimate of the characteristic turbulence length scale in Table 3. In the present study, the grid resolution of the velocity field is 0.73 mm, thus a rough estimate yields resolution of the Taylor microscale from a distance of x = 6d. Clearly, neither the strain-limited diffusion scales (see Table 3) nor the Kolmogorov or Batchelor scales can be resolved with the present measurement setup. The non-resolution of those scales leads to spatial smoothing of the smallest fluctuations. However, the large turbulent structures dominate the mixing of both streams in the near field of the jet [6]. Moreover, the experiment is designed for a field of view which extends across the full channel height to cover the mixing in the jet shear layer and near the tunnel wall. In principle, the present measurement setup is capable of resolving finer scales in exemplary small regions of the flow field if higher lens magnifications are applied.

5 Results and Discussion 5.1 Experimental results with steady isothermal injection The single shot of mass fraction and velocity shown in Fig. 14 provides an impression of the turbulent character of the flow. Large vortices in the upper shear layer indicate large scale mixing. These vortices break up into small-scale velocity fluctuations which accelerate the mixing and diffusion. Table 3 Strain limited diffusion scales of the confined jet and Taylor micro scale of a round jet at Re0 = 32000; estimates of the flow width δ0.05 and mean shear U are obtained from Fig. 13; values in brackets are based on a mean axial velocity profile which differs strongly from that of a round jet y/d

U [m/s]

δ0.05 [m]

Reδ

λν [ μm ]

λD [ μm ]

λT [μ m]

0.4

(18.5)

(0.029)

(35400)

(160)

(140)

49

4.4

11.1

0.047

35000

270

230

540

8.4

8.36

0.052

28700

340

280

1030

Flow Turbulence Combust

Fig. 14 Snapshot of concentration field with isothermal steady injection, positive z/d values represent the outer part of the bend; left overview, right enlarged region with overlayed velocity field after subtraction of the bulk inlet velocity

Ensemble averages over 500 single shots provided in Fig. 15 give a qualitative overview of the global velocity and mass fraction fields at Re0 = 32000 and De = 20000. Velocity data is normalized with the bulk injection velocity provided in Table 1. In Fig. 15 (top, left) the deformation of the jet potential core towards the outer region of the jet (z/d > 0) is clearly visible. This deformation originates from the asymmetric velocity distribution inside the bend also evident from recent LES results by R¨ohrig et al. [24] which were obtained at comparable conditions (Re0 = 34000, De = 19000). The 90◦ -curvature causes a velocity decrease close to the convex inner bend wall and a velocity increase near the concave

0.4d

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

/u0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 5.6d 3.0d 8.0d

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1 0 -1

/u1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

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z/d

1 0 -1

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0

y/d

1

-0.72d -1 0

2

4

x/d

6

8

0

2

4

x/d

6

8

Fig. 15 Isothermal axial velocity normalized by the bulk injection velocity (left) and concentration fields (right) with steady isothermal injection in both center-planes and at y = −0.72d middle (Average over 500 samples); vertical lines correspond to positions where profile measurements are conducted

Flow Turbulence Combust

inner bend wall (naming according to Fig. 3). The centrifugal forces act stronger on the fluid above the center axis and thus the potential core is deflected towards the outer region. Faster mixing occurs in the inner region of the jet (z/d < 0) compared with the outer regions (z/d > 0) and can be observed in both x − z planes shown in Fig. 15 (right, middle and bottom). This is based on a number of reasons. Under given operation conditions the centrifugal force causes higher velocity fluid to move toward the concave inner wall, while slow-moving fluid close to the pipe sides travels towards the convex inner wall. This eventually leads to a well-known secondary flow motion in the form of a pair of counter-rotating vortices, the so-called Dean vortices (see also [15, 24]). These Dean vortices induce positive wall normal velocities in the center-plane causing enhanced entrainment of ambient air. Furthermore, at a bulk Reynolds number of 34000, Dean vortices are unsteady and may ¨ u [15]), thus yielding increased turoscillate between divergent states (see Kalpakli and Orl¨ bulence in the lower region of the jet also evident from rms plots shown in Fig. 9. Another reason might be the wake of the lower portion of the bend which induces additional out-ofplane (or span-wise) motion, resembling vortex shedding behind a cylinder. With increasing axial distance, the turbulent region in the inner shear layer grows stronger in comparison to the outer shear layer leading to enhanced mixing in the lower region of the channel flow. 1.5

0.4d

3.0d

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8.0d

1

z/d

0.5 0

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0

0.1 0.2

/u0

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0

0.1 0.2

/u0

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0

0.1 0.2

/u0

Fig. 16 Normalized mean streamwise (top) and wall normal (bottom) velocities in the x − z center plane at different axial positions; Black line,  : exp. κ = 0.37, Re0 = 32000, De = 20000; Green line, : exp. data obtained from hot-wires [25] at x = 0.5d, κ = 0.21, Re0 = 34000, De = 15500; Red dash dot line: RANS simulation [18]

Flow Turbulence Combust

Figure 16 (top) shows axial velocity profiles within the x − z center plane of the mixing zone normalised with the bulk velocity. Positive z/d values represent the outer part of the bend. Shortly behind the nozzle exit (x = 0.4d) the axial velocity is higher in the outer region of the bend, as expected. Results are in good agreement with hot-wire measurements by Shirvan [25] which were obtained without co-flow and at slightly different conditions: x = 0.5d, κ = 0.21, Re0 = 34000, De = 15500. The velocity minimum near the center is less pronounced in the measurement data of Shirvan probably due to the smaller bend curvature and a measurement position which is located 0.1d further downstream. A preliminary RANS simulation of the present configuration (see [18]) largely reproduces the stream-wise velocity profile. With increasing distance from the injection point, the low velocity region in the inner part starts to accelerate and the mean axial velocity profile tends to recover a symmetric turbulent velocity profile at x = 8.0d. This re-stabilisation is accompanied by the break down of the Dean vortices [25]. Near the nozzle exit, the wall-normal velocities in the center plane are positive across the nozzle exit as expected (see Fig. 16 (bottom)). In addition there is a peak of negative wall normal velocity at z/d = −0.6 which conveys slow moving fluid toward the lower channel wall. With increasing distance from the nozzle the negative peak is broadening. Figure 17 shows the mean mass fraction at various downstream positions. Faster mixing in the lower region of the channel leads to a skewed mass fraction distribution within x = 0.4−5.6d. Further downstream at x = 8d the concentration distribution arranges symmetrically with respect to the channel center. The mean stream-wise turbulence component obtained with PIV at x = 0.4d is compared against hot-wire results by Shirvan [25] (see Fig. 18). The characteristic peak of enhanced turbulence production near the center of the bend exit (also visible in Fig. 9, top ) stems from the interaction between low momentum inner wall flow and high momentum core flow (c.f. [24]). The peak exhibits, however, a considerably higher magnitude compared with the hot-wire result. The reasons for this may be that the hot-wire data is captured at different experimental conditions (smaller bend curvature, κ = 0.21) and 0.1d further downstream of the bend exit. Aside from the convective transport, turbulent diffusion strongly influences the mixing process. As mentioned above, the turbulent diffusion is described by the turbulent mass flux vector. Components are obtained by averaging the instantaneous covariances of velocity components and mass fraction that are normalised by the bulk injection velocity u0 . The 1.5

3.0d

0.4d

5.6d

8.0d

1

z/d

0.5 0

-0.5 -1 -1.5 0

0.5



1

0

0.5



1

0

0.5



1

0

0.5

1



Fig. 17 Mean mass fraction in the x − z center plane at different axial positions; Black line,  : exp. κ = 0.37, Re0 = 32000, De = 20000

Flow Turbulence Combust 1.5 0.4d

3.0d

8.0d

5.6d

1

z/d

0.5 0 -0.5 -1 -1.5 0

0.02

0.04 0

/u²0

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/u²0

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0

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-0.01

0

0.01

/u²0

-0.01

0

0.01

/u²0

-0.01

0

0.01

/u²0

Fig. 18 Normalized Reynolds stress components in the x −z center plane during steady isothermal injection; Black line,  : exp. κ = 0.37, Re0 = 32000, De = 20000; Green line, : exp. data obtained from hot-wires by Shirvan [25] at x = 0.5d, κ = 0.21, Re0 = 34000, De = 15500

evolution of the mean stream-wise and wall-normal components of the turbulent mass flux at different downstream positions is shown in Fig. 19. The stream-wise turbulent mass flux u c  has a symmetric orientation while the wall-normal flux w c  has a antisymmetric orientation with respect to the tunnel’s centerline. Near the jet exit the stream-wise turbulent mass flux is larger than the wall-normal mass flux. Further downstream at x = 3.0d the

Flow Turbulence Combust 1.5 0.4d

3.0d

5.6d

8.0d

1

z/d

0.5 0 -0.5 -1 -1.5 0

0.01

0.02

/u0

0

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0

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0.5 0 -0.5 -1 -1.5 0

/u0

0.02

0

/u0

0.02

0

0.02

/u0

0

0.02

/u0

Fig. 19 Normalized mean stream wise (top) and wall normal (bottom) turbulent mass flux in the x − z center plane at different axial positions during steady isothermal injection; Black line,  : exp. κ = 0.37, Re0 = 32000, De = 20000

turbulent mass flux (and turbulent diffusion) grow more strongly in the upper shear layer while it spreads along the z axis in the lower shear layer. A comparison of experimental data with RANS simulations using various state-of-the-art turbulence models is provided in [18] and shows the difficulty to model the turbulent mass flux by an isotropic formulation of the mass flux model.

5.2 Experimental results with pulsed isothermal injection Figure 20 shows single shots of the mass fraction during pulsed operation in the x − z center plane: (1) Beginning of injection, (2) strong injection and asymmetric vortex growing on the edges, (3) flow breakdown leaving behind small vortices and (4) again strong injection and forming of a large asymmetric vortex ring. Phase averaging of single shot PLIF-PIV measurements in the x − z center plane gives insight into the temporal shear layer and vortex evolvement during a pulsation cycle. Therefore, phase sorting of the single shot measurements is performed on the data using 36 equidistant bins (10◦ bin size). The bin size is a compromise of having a sufficiently large sample count per bin (100 samples on average) while keeping the spatial smoothing due vortex motion to a minimum. According to convergence tests (c.f. Section 4.6) the random

Flow Turbulence Combust

-2-

-1-

-3-

-4-

1

z/d

0.5

0

-0.5

-1

0

0.5

x/d

1

0

0.5

x/d

1

0

0.5

x/d

1

0

0.5

1

x/d

Fig. 20 Snapshots of the concentration distribution in the x − z center plane near the bend exit with pulsed injection

uncertainty of mean velocity and concentration on the basis of 100 samples would be in the order of 5-6 %. At this state of work the stability of operation conditions would not allow to significantly extend the sample size. Figure 21 shows phase averaged velocity and concentration fields at the beginning of injection (top) and during flow breakdown (bottom). Vortex centers and strength are detected using the λ2 discriminant of non-linear eigenvalues of the velocity gradient tensor as described in [34]. At ( = 320◦ ) small vortices occur immediately downstream of the nozzle exit. At ( = 340◦ ) the outer vortex has moved almost twice the distance as the inner vortex which leads to stronger growth due to entrainment. This effect supports stronger mixing and diffusion in the outer shear layer in comparison to the inner shear layer. During flow breakdown velocities in the lower region (0 > z > −0.5) are not only reduced but also exhibit directional changes (forward at = 160◦ , upward at = 200◦ ) including partial flow reversal ( = 240◦ , red box in Fig. 21). Flow stagnation and reversal is accompanied by a wave-like variation of the concentration field at = 240◦ . To enable a better insight into the temporal evolvement of velocity and concentration fields in both center planes, animations of phase averages over a pulsation cycle are provided in the web version of this article (filenames: pulsed injection xz.gif and pulsed injection xy.gif ). The temporal evolvement of axial velocity provided in these animations could also be used to gain information about the velocity amplitude over the pulsation period. Figure 22 compares the mean mass fraction at three downstream positions within the x − z center plane during pulsed and steady injection. Averaging reveals that at x = 0.4d the mean concentration field is skewed toward the upper channel side in comparison with steady injection due to the asymmetric vortex growing and enhanced diffusion. Although the mean mass flow rates are equal during pulsed and steady injection, the mean mass

Flow Turbulence Combust

Fig. 21 Phase averaged mass fraction and velocity in the x −z center plane; Top: beginning of injection; Bottom: flow breakdown with partial flow reversal (red box), for animations of phase-averages over a pulsation cycle the reader is referred to the web version of this article

1.5

steady pulsating

1 0.4d

3.0d

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z/d

0.5 0 -0.5 -1 -1.5 0

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0.8

1

0

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0.8

1

0

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Fig. 22 Evolution of mean isothermal mass fraction during pulsed and steady injection in the x − z center plane at different axial positions

Flow Turbulence Combust 1.5

Tjet=293K Tjet=343K Tjet=393K

0.4d

1

4.4d

8.4d

y/d

0.5 0

-0.5 -1 -1.5 0

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/uo

1.2

1.6 0

0.4

0.8

/u0

1.2

1.6 0

0.4

0.8

/u0

1.2

1.6

Fig. 23 Evolution of axial velocity profiles in the x − y center plane at different axial positions and different jet temperatures

fraction at x = 0.4d stays below the flat top profile obtained from steady injection. The reason for this is that most of the time during valve revolution little or no mass is injected at low or even zero speed while the bulk of mass is injected with high speed during the a relatively short valve opening time when c = 1. This becomes clearly visible in the aforementioned animations available in the web version of this article. Figure 22 reveals that stronger mixing and diffusion occurs within the outer shear layer and the concentration field is skewed toward the upper channel side. Further downstream at x = 8d the concentration field exhibit a clearly asymmetric distribution in comparison to steady injection.

5.3 Experimental results with elevated jet temperature PLIF-PIV measurements are obtained at jet temperatures of Tj et = 243 K and 293 K leading to mean temperature gradients of T = 50 K and 100 K between the jet and the unmixed air. The mass flow rate remains the same as for isothermal measurements.

1.5

Tjet=293K Tjet=343K Tjet=393K

0.4d

1

8.4d

4.4d

y/d

0.5 0

-0.5 -1 -1.5 0

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0.6



0.8

1

0

0.2

0.4

0.6



0.8

1

0

0.2

0.4

0.6



0.8

1

Fig. 24 Evolution of mass fraction profiles in the in the x − y center plane at different axial positions and different jet temperatures

Flow Turbulence Combust

The increased jet temperature leads to higher velocities within the jet due to decreasing air density at a constant mass flow rate. This is confirmed by PIV measurements of the axial velocity in the x − y center plane shown in Fig. 23. In Fig. 24, mass fraction profiles at three different jet temperatures are presented. Shortly downstream of the nozzle exit (x = 0.4d) the mass distribution remains almost unchanged at each jet temperature. At maximum injection temperature a slight decrease of mass fraction occurs near the jet edge but is not accompanied by mass redistribution beyond the strong concentration gradient. Possibly the dynamic range of mass fraction measurements is insufficient to determine such small mass redistributions due to the inherent fluorescence background (see Section 4.2). Downstream at x = 4.4d, enhanced mixing is not evident at Tj et = 343 K . Increased mixing is barely noticeable by further increasing the temperature to Tj et = 393 K . At the downstream position x = 8.4d, the temperature rise to Tj et = 343 K leads to a slightly wider mass distribution with the increased jet temperature of Tj et = 393 K further enhancing the diffusion process.

6 Conclusions A combined PLIF and PIV system is developed to simultaneously measure mass fraction and velocity of turbulent jet mixing downstream of a 90◦ pipe bend in a turbulent duct flow at atmospheric pressure. Measurements are conducted at steady isothermal injection, pulsed isothermal injection and steady injection with elevated jet temperatures. Additional stereoscopic PIV measurements upstream of the mixing port indicate a flat top velocity profile of the incoming duct flow with isotropic turbulence present outside of the boundary layers of the square duct. The spatial resolution of the intensified PLIF imaging system was verified by the knife-edge technique is found to be comparable to the spatial resolution of PIV velocity measurements. Sets of up to 3600 measurements are used to extract wall normal profiles of mean velocity, concentration and turbulent mass fluxes at several downstream positions with respect to the jet exit. The uncertainty of time-averaged velocity, mass fraction, Reynolds stress and turbulent mass flux over the number of samples is estimated in the turbulent shear layer at three downstream positions using an empirical bootstrapping approach. For 3000 samples the statistical error of time-averaged velocity components and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components ranges around 5-6 %. The systematical error due to density and temperature dependency of acetone fluorescence is discussed for measurements at elevated jet temperature. Compensation of the error is proposed on the basis of estimates of the local mixing temperature. Experimental results obtained during steady isothermal injection show the expected deformation of the jet potential core towards the outer region of the jet. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements reported in the literature if slightly different experimental conditions are taken into account. Profiles of axial turbulence intensity show enhanced turbulence production in the inner and outer shear as well as in a region near the jet center due to interaction between low momentum inner flow and high momentum core flow of the jet. Mass fraction profiles reveal enhanced mixing in the jet region below the core and a skewed mass fraction distribution which rearranges symmetrically further downstream. Experimental results during pulsed jet injection show a strong asymmetric growth of shear layer vortices which lead to a more skewed mass fraction profile in comparison with steady

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injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10◦ . Results at steady injection with increased jet temperature indicate slightly enhanced mixing from 6 nozzle diameters onward. On the whole the collected experimental data provide a comprehensive database for the development and validation of enhanced turbulence models with improved prediction of mass fraction.

Acknowledgments Part of the work reported in this paper is funded by the Daimler AG Stuttgart whose support is gratefully acknowledged. In this context we would like to thank Valentin Mayer for the good cooperation and for providing numerical simulations and the 3D graphic of the experimental setup. Also the authors would like to thank Manfred Beversdorff for his help during construction of the windtunnel and the pulser and Wolfgang F¨orster for development and programming of the phase angle acquisition system. Special thanks go to Johannes Heinze for his support during preparation of the PLIF setup and data evaluation. Finally we like to thank the reviewers for helpful comments and detailed discussion on the content on the earlier version of the manuscript.

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