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Proceedings of the 7th International and 45th National Conference on Fluid Mechanics and Fluid Power (FMFP)December 10-12, 2018, IIT Bombay, Mumbai, India.
FMFP2018 - PAPER NO.Experimental Study of Turbulent Non-Turbulent Interface in a Planar
Mixing Layer using Kinetic Energy Criteria.
G. Balamurugan
Dept. of Aerospace Engg,IIT Kanpur
A. Rodda
Dept. of Aerospace Engg,IIT Kanpur
J. Philip
Dept. of Mechanical Engg,The University of Melbourne
A. C. Mandal
Dept. of Aerospace Engg,IIT Kanpur
AbstractUsing kinetic energy (KE) criteria, the Turbulent Non-Turbulent Interface (TNTI) in a planar mixing layer hasbeen identified and studied in this paper. The mixing layeris generated in a simple way by blocking the top halfof the wind tunnel test section with a mesh of suitablesolidity. High resolution particle image velocimetry (PIV)is used to acquire the velocity data. The threshold foridentifying the interface is obtained using the area al-gorithm suggested by [2]. The mean and rms profilesof velocity and the spanwise vorticity with respect tothe TNTI show finite jump at the interface location. Thefractal dimension of the KE interface based on the boxcounting method is found to be ∼1.2.
Keywords: Mixing layer; Turbulent flows; TurbulentNon-Turbulent Interface
I. INTRODUCTIONTurbulent flows are separated from the irrotational
laminar flows by sharp and highly distorted surfaceswhich are generally called Turbulent Non-Turbulent In-terface (TNTI). The study of TNTI has increased recentlybecause of their role in the combustion, entrainment andmixing of turbulent flows. To understand the physicalprocesses associated with entrainment of irrotational fluidin practical flows, TNTIs in canonical flows such asboundary layers, jets, wakes and mixing layers havebeen studied. In numerical studies, such interfaces areusually identified using vorticity due to the availabilityof three velocity components or a passive scalar suchas concentration or temperature. In experiments, TNTIsare identified using either the Kinetic energy from PIVdata [4,8] or the concentration of a passive dye from asimultaneous PIV-LIF measurements [5,12]. These earlierstudies reveal that there exists a jump in the stream-wise velocity and vorticity at the interface, and the TNTIthickness is of the order of Taylor microscale [5].
Generally, a mixing layer is constituted of two TNTIs,one above and another below the centerline and they
are being exposed to two different free stream veloci-ties. Hence one can expect an asymmetric entrainmentbetween the top and the bottom TNTIs for a mixinglayer [11]. In this study we compare the geometric andkinematic features of the upper and lower interfaces. Thisis different from the earlier works on turbulent wakes, jetsand boundary layers.
II. EXPERIMENTAL SETUP
Figure 1: A schematic of the wind tunnel test sectionwith the mesh.
Experiments were carried out in a low-speed windtunnel at the Department of Aerospace Engineering, IITKanpur. The top half of the tunnel test section wasblocked using a mesh of suitable solidity which deceler-ates the flow behind it to a lower velocity than the flow inbottom half thereby creating a planar two stream velocitymixing layer, similar to the work by [7]. The experimentalsetup with the mesh mounted inside the test section isschematically shown in figure 1. Further details aboutthe mesh and the tunnel are given in tables 1 and 2, re-spectively. The PIV measurements were carried out usinga Nd:YAG laser and two high resolution CCD cameraswith a field of view centered at 50 cm from the mesh. Atotal of 1800 frames were acquired at 1Hz. The acquired
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Table 1: Details of the mesh used in the study.
Mesh solidity U1 U2 Uc Ud Reλ
0.3 6.3 3.4 4.8 2.9 142
Table 2: Tunnel specifications and PIV details
Property ValueTurbulent intensity 0.1%
Test section 0.61 m x 0.61 mPIV ROI 0.12 m x 0.16 m
Number of vectors 236x405PIV Resolution 0.41 mm
images were stitched and processed using the open sourcesoftware, PIVlab [9] with a 32×32 pixel interrogationwindow and 50% overlap. In the following, streamwise,transverse and spanwise directions are denoted by x, yand z respectively and the corresponding instantaneous,ensemble averaged and fluctuating velocities are denotedby (u, v, w), (U, V,W ) and (u′, v′, w′) respectively. Themean and fluctuations with respect to the interface co-ordinates are denoted by (〈U〉, 〈V 〉, 〈W 〉) and (u, v andw) respectively.
III. RESULTS AND DISCUSSION
Figure 2: Transverse profiles of (a) streamwise velocity(b) x-component and (c) y-component of the normalReynolds stress and (d) tangential Reynolds stress insimilarity coordinates. Symbols: x= �, 0.43 m;©, 0.49m; 4, 0.55 m; N, Hot-wire data of [1] at x=0.573 m.
A. Mean flow dataThe streamwise mean velocity and Reynolds stress
profiles, in similarity coordinates, at three differentstreamwise locations spanning the region of interest areplotted in figure 2. One can notice that the profiles areself similar inside our measurement field. The data alsocompare well with the hot-wire data of [6]. This isinteresting because the mixing layer in the present workis generated in a completely different manner unlike theusual way of using a splitter plate (e.g.,[6]).
B. Interface identification
Figure 3: (a) A sample interface identified usingkinetic energy criteria. Arrow indicates the positivedirection for conditional profiles. (b) Area used in(c) to obtain the threshold. Blue contour, top area;orange contour, bottom Area. (c) Variation of areawith threshold. (d) Slope of the area curve in (c).
Fluctuating kinetic energy (equation 1), defined withrespect to the characteristic velocity (Uc), is used toidentify TNTI because the mean velocities are differentfor the top and bottom streams. This resulted in lower
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Figure 4: (a) PDF of the interface position, yi. , meanposition of the interface, solid lines —–, Gaussianfit for the PDF. (b) Length of the interface, LTNTI
normalized with the streamwise length of data fieldfor different PIV frames. , top interface; , bottominterface; - - - -, Cumulative mean of the interfacelength over all frames.
values of relative kinetic energy inside the turbulent zone(see figure 3(a)). A typical PIV realization using thecontours of relative kinetic energy and the associatedtop and bottom TNTIs are shown. The threshold valueis obtained based on the area algorithm suggested by [2].Here, the TNTI is identified as the solid white lines withcontour levels close to 7. One can see that the valuesare consistent with the region of slope change in figure3(c). The area values plotted in figure 3(c) are calculatedas the region inside the blue and the orange lines forthe top and bottom interfaces respectively as shown infigure 3(b) for a given threshold. The PDF of the interfaceposition and the interface length for each PIV realizationare plotted in figure 4. It is found that PDF for boththe top and the bottom interfaces follow the Gaussiandistribution similar to results in other shear flows. Theinterface length LTNTI calculated as the sum of thelinear distances between the consecutive interface pointsfrom first to last interface point is around 1.6 times thestreamwise extent. This value is different from the usualvalue of 3 reported in earlier 2D-PIV studies. This can beeither due to the lower value of Reynold number in thepresent or the use of KE criteria for interface detection.
K =100
U2c
[(u− Uc)2 + v2];Uc = 0.5 ∗ (U1 + U2). (1)
C. Conditional StatisticsThe mean profiles of the spanwise vorticity, the
streamwise and transverse velocities with respect to theTNTI are plotted in figure 5 and the corresponding rmsvalues in figure 6. The direction towards the irrotationalregion is taken as positive for both the top and the
Figure 5: Conditional profiles of (a) streamwise meanvelocity (b) transverse velocity and (c) spanwise vortic-ity in super-layer co-ordinates for the top and bottominterfaces. δ, mixing layer thickness from an errorfunction fit; and Ud = U1 − U2.
bottom interfaces as shown in figure 3(a). The conditionalvorticity profiles in figure 4(a) shows a clear discontinuityat the interface, as the vorticity value is almost zeroin the irrotational region and then it sharply increasesto a maximum value at the interface, which happensover a distance of the order of Taylor microscale, (λ),and reaches a nearly constant value inside the turbulentregion. This suggests that smaller length scales play a rolein the dynamics close to the TNTI even in a plane mixinglayer. This is consistent with the observations reportedfor other shear flows (e.g. [3,4,5]). Another importantfeature that is observed in the transverse velocity profileis that the top and the bottom interfaces show oppositetrends at the TNTI. This is because of the differencein the entrainment direction for the top and bottominterfaces. The conditional streamwise and transverse
Figure 6: Conditional profiles. (a-c) Reynolds stresscomponents and (d) fluctuating spanwise vorticity.
velocity and their rms profiles also exhibit a jump close to
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the interface. These conditional profiles corroborate thepresence of super-layer, across which sharp changes inproperties occur. Another complementary way to showthe presence of super-layer at the TNTI is by plotting themean velocities conditioned with the interface location,as shown in figure 6. This shows that the jump happensat that particular y position where the interface is locatedthereby confirming the earlier results.
Figure 7: Conditional profiles of (a) streamwise and(b) cross-stream mean velocity conditioned also withthe transverse location of interface, yi.
D. Fractal Characteristics of TNTI
Figure 8: Box counting method to find the fractaldimension of the interface. – – – –, Linear fit witha slope of 1.2.
The multi-scale nature of the TNTI can be explainedby its fractal dimension [1], which is usually obtained byusing the box counting method. Here, the slope, as shownin figure 8, between the number of boxes (Nb) requiredto completely cover the TNTI against box size (∆b). Thefractal dimension for the top and bottom interfaces is≈1.2. This value obtained in a plane mixing layer is closeto the value of 1.3 in other TNTI experiments (e.g., [1,8]).
IV. CONCLUSIONSThe statistics associated with the TNTI is studied in a
planar mixing layer using 2D-PIV data. The mixing layeris generated by simply blocking a portion of the tunneltest section with a mesh of suitable solidity. The meandata in the similarity coordinates follows the hotwire dataof [6]. The TNTI is identified using the fluctuating kineticenergy as the detector function. The threshold value isobtained based on the area algorithm suggested by [2].The PDF of the transverse interface location found by thekinetic energy criteria follows the Gaussian distributionbut the interface length is only 1.6 times the streamwiseextent. Similarly the super-layer profiles displayed a finitejump at the TNTI location but the fractal dimension is nottoo far from the values reported in the literature. Henceone needs to either apply the Kinetic energy criteria athigh Reynolds number or look for other interface detectorfunctions such as spanwise vorticity similar to numericalsimulations.
Acknowledgements
ACM, GB and AR thankfully acknowledge the financialsupport from IIT Kanpur for the PIV system and are alsograteful to Prof. D. Das and Prof. S. Mittal for providingtheir CCD cameras. The comments on a initial poster ofthe present work, by the participants of the discussionmeeting “Turbulence from Angstroms to Light years”held at ICTS, Bengaluru is also thankfully acknowledged.ACM would also like to thank Dr. Phani Kumar forpointing out a key reference in this work.
REFERENCES
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Minerva Access is the Institutional Repository of The University of Melbourne
Author/s:
Balamurugan, G; Rodda, A; Philip, J; Mandal, AC
Title:
Experimental Study of Turbulent Non-Turbulent Interface in a Planar Mixing Layer using
Kinetic Energy Criteria
Date:
2018
Citation:
Balamurugan, G., Rodda, A., Philip, J. & Mandal, A. C. (2018). Experimental Study of
Turbulent Non-Turbulent Interface in a Planar Mixing Layer using Kinetic Energy Criteria.
FMFP.
Persistent Link:
http://hdl.handle.net/11343/220299
File Description:
Published version
