Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France

On the impact of large–scale coherent structureson scalar mixing in swirling jets

J. Frohlich���, M. Garcıa-Villalba �, W. Rodi�

�Institute for Technical Chemistry and Polymer Chemistry,University of Karlsruhe, 76128 Karlsruhe, Germany

�Institute for Hydromechanics, University of Karlsruhe, 76128 Karlsruhe, Germany�Email: froehlich@ict.uni-karlsruhe.de

ABSTRACT

The paper presents large eddy simulations of co-annular swirling jets into an open domain. In each of thejets a passive scalar is introduced and its transport is computed. If the exit of the pilot jet is retractedstrong coherent flow structures are generated. Average and instantaneous fields are discussed. A conditionalaveraging technique is devised and applied to velocity and scalars. The results show the strong impact ofthe coherent structures on the mixing process.

I NTRODUCTION AND CONFIGURA TION

Swirling annular and co–annular jets are widelyused in combustion devices such as gas tur-bine burners to stabilize the flame by meansof a swirl–induced recirculation zone. Previ-ous experimental and numerical studies havedemonstrated, however, that such flows are oftenprone to fluid mechanical instabilities generatinglarge–scale coherent vortical structures [9,2,11].These have a substantial impact on the mixing ofscalar quantities such as fuel and oxidizer or hotand cold gas. This process hence substantiallyimpacts on the combustion, possibly triggeringhighly detrimental combustion instabilities [10].

The paper presents results of large eddy sim-ulations (LES) of such turbulent flows in theconstant–density case, i.e. without combustion,and focuses on the pure mixing process. Theentire simulation model, consisting of numericaldiscretization scheme, choice of grid, subgrid–scale modelling and boundary conditions, hasbeen validated in previous work [7,4]. In these

Fig. 1. Visualization of coherent vortex structures bymeans of iso-surfaces of instantaneous pressure per-turbation. Left: no retraction, right: with retraction.Light colour: structures in the inner shear layer ex-hibiting a small angle with the��axis, darker colour:structures in the outer shear layer, exhibiting a largerangel with the��axis.

studies the generation of coherent structures(CS) was investigated together with their depen-dence on various aspects. The strongest struc-tures were observed in simulations with the pilotjet retracted into a surrounding tube, so that thiscase is considered here. In the case without re-traction which is taken for comparison, the CSare destroyed by a pilot jet [5]. Both cases areillustrated by snapshots in Fig.1. The presentpaper is devoted to the interaction between the

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Fig. 2. Two-dimensional streamlines and mean con-centration���� in the centerplane. Left: no retraction,right: with retraction.

large–scale coherent structures and the scalarmixing process.

The geometry, shown in Fig. 1, features two an-nular jets exiting into still ambient. The outermain jet accounts for 90% and the inner jet for10% of the mass flux. The Reynolds number is��� � �����, based on the bulk velocity of themain jet and its outer radius�. The total swirlnumber is� � ����, the swirl number of thepilot jet alone is 2 at��� � �����. All condi-tions are identical for both cases, apart from theretraction of the inner jet to������ � ������ inthe second case. Geometry and parameters corre-spond to an experiment conducted at the Univer-sity of Karlsruhe [1]. To investigate the mixingprocesses, two scalars were introduced,�� in theinner and�� in the outer jet. An additional equa-tion is solved for each of them using an eddy dif-fusion model with turbulent Schmidt number of��� [3]. The origin of the��coordinate in stream-wise direction is located at the end of the outertube (see Fig. 2).

RESULTS FOR AVERAGE AND INSTANTA -NEOUS FLOW

Fig. 2 shows two-dimensional streamlines in thecenterplane (� � ��plane) for both cases. Withretraction, the average recirculation zone does notreach upstream to the exit of the jets and is shorterand broader. Also, the spreading angle of the jetis larger than in the reference case. Details of theflow field are discussed in [8]. With retraction,the mean concentration of�� close to the axisis substantially larger and also increased at the

Fig. 3. Snapshots of instantaneous concentration. Top:centerplane, bottom:� � ����. Left: no retraction,right: with retraction. The thin white circle is locatedat � � �.

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Fig. 4. PDF of scalar�� at two different positions.Left: ��� � ���, ��� � ����, right: ��� � ����,��� � ����. - - - - no retraction, —— with retraction.

outer edge, i.e. around��� � �, ��� � �.

The coherent structures visualized in Fig. 1 sub-stantially impact on the scalar mixing as shownin Fig. 3. Without retraction, the distribution ismore symmetric in the centerplane and regular incircumferential direction in the lower plot. Withretraction, large spots of high concentration ap-pear in plots at��� � ���� reflected by asym-metry in the centerplane plot. The spots are gen-erated by the coherent structures visible in theright plot of Fig. 1. It has previously been foundthat they are correlated with a local excess in ax-ial velocity [6] and this brings along undilutedscalar from the jet exit as shown by correspond-ing plots in planes� � ���� (not reproducedhere).

This issue has been investigated also by meansof the probability density function (PDF) of bothscalars at various points. Fig. 4 shows two rep-resentative plots. The dashed line corresponds tothe reference case and the continuous line to thecase with retraction. The left plot was generatedfor a point in the inner structure. Without retrac-tion, the concentration�� is fairly uniform as re-flected by the narrow shape of the PDF. With re-traction, the coherent structures are related to al-most unmixed scalar during some instants whileat other instants more diluted flow is present lead-ing to a bimodal shape of the PDF. Similar obser-vations are made at the outer border of the jet inthe right plot of Fig. 4. The point of investigationis the same for both curves but the spreading an-gle of the jet is different in both cases. Hence, thejet is somewhat more remote from the point inthe case without retraction. Further downstream,i.e. for � � ��, the shape of the PDF from bothcases is similar, but mean and variance still differ.

CONDITIONAL AVERAGING

The coherent structures observed in Fig. 1 ro-tate around the axis at a relatively constant rate.They are however not totally stable due to thehigh Reynolds number and can, for example, dis-integrate into several structures or change theirshape to a certain extent. It has been shown thatthe inner structures trigger the outer ones [5] sothat the following conditional averaging strategywas devised. Due to the cylindrical symmetryof the geometry all angular positions are statis-tically equivalent. In over 180 stored flow fieldsthe position of the strongest inner structure wasdetected and its center assigned zero angular co-ordinate. The resulting rotated fields of velocityand scalars were ensemble averaged and are iden-tified by a tilde in the following. This procedurewas applied for the case with retraction only sincein the reference case the observed structures arevery weak.

Fig. 5. Conditional averages of flow field and scalarsfor the retracted case. In both graphs an iso-surfaceof �� � ��� showing the inner and the outer vortexstructure is depicted. The left plot also shows aniso-surface of��� and the right plot an iso-surface of���.

Fig. 5 provides the conditionally averaged vortexstructures by means of pressure-perturbation iso-surfaces, similarly to Fig. 1. Included in the twoplots are iso-surfaces of�� (left) and �� (right).They demonstrate how the coherent vortices in-fluence the concentration of the scalar quantities.The maximum of �� is found in the interiourof the inner structure while�� has small valuesthere. Due to its position of intrusion,�� essen-tially depends on the inner structures. The mixingof �� with the ambient fluid, on the other hand, isdetermined by the outer structures as evidencedby the second graph in Fig. 5. The distortion ofthe iso-surface of its conditionally averaged con-centration by the outer structure is very well vis-ible.

In a further step it was investigated to whichextent the coherent structures contribute to thefluctuations of the scalar. This is illustrated inFig. 6. The top graph shows the total fluctua-tions ��� � �����

��. Fluctuations generated byhighly ordered regular structures are determinedas����������

��. The bottom plot in Fig. 6 showsthe ratio of these two quantities. In almost the en-tire region with� �, more than 40% of the fluc-tuations result from organized motion. The fluc-tuations themselves are not very strong, though,as visible in the right plot of the figure. Anothermaximum of the ratio is observed in the outershear layer with 30-40% around��� � ��� � � � �and��� � ��� due to the outer structures. Here,also the fluctuations attain large values.

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Fig. 6. Analysis of fluctuations of�� in the center-plane for the retracted case. Top: total fluctuations,bottom: percentage of fluctuations generated by con-ditionally averaged structures.

CONCLUSIONS

The analysis of instantaneous and statistical datademonstrates the strong impact of the coherentstructures generated by retraction of the pilot jeton the mixing process. In a reacting flow thiswould alter considerably the entire combustionprocess. The technique devised for conditionalaveraging yields smooth and reliable data whichcharacterize the regular part of large-scale fea-tures in the velocity and scalar field. Note thatthis procedure can also be applied to non-swirlingflows of round jets since the same argumentsgiven in the text hold for such configurations aswell.

Acknowledgments: This work was supportedby the German Research Foundation throughSFB 606, www.sfb606.uni-karlsruhe.de. The ref-erences of the authors can be obtained there. Thecalculations were carried out on the HP XC6000Cluster of the University of Karlsruhe ComputerCentre.

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