experimental study of droplet clustering in polydisperse...

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Experimental study of droplet clustering in polydisperse sprays

Manish M1, Srikrishna Sahu 1,* 1: Department of Mechanical Engineering, IIT Madras, Chennai, India

* Correspondent author: [email protected]

Keywords: Droplet clustering, ILIDS, RDF, number density, turbulent flux

ABSTRACT

The clustering of droplets in a polydispersed spray is experimentally studied. The aim here is to understand

the cause of droplet clustering in sprays and study its consequence on local turbulent number flux of droplets.

Planar measurement of droplet position, number density and velocity is achieved by application of PIV technique,

while ILIDS technique is used for droplet sizing. Measurements are reported for an axial location 30 cm

downstream of the injector exit and different radial stations. Based on the measured droplet number count and

inter-droplet-distances, the length scale of the droplet clusters were quantified following two independent statistical

approaches, namely, droplet counting in a cell method and estimation of Radial Distribution function (RDF). The

results from both approaches are in agreement with each other. Towards outer region of the spray the length scale

of droplet clusters is found to be larger as well as the tendency of droplets to form clusters is higher. The

measurement area at any radial station is considered to consist of cells of same size, and both steady and turbulent

components of the average droplet number flux were calculated for cells of different sizes in comparison to the

length scale of the droplet clusters. While the steady number flux is almost independent of the cell size, the

magnitude of turbulent number flux is found to be higher for cell size similar to typical dimension of droplet

clusters in comparison to larger cell sizes. Also, relative to its steady value, the turbulent number flux increases

towards the edge of the spray. The correlation coefficient between fluctuations of droplet number density and

droplet velocity is found to be negative indicating smaller droplet velocity fluctuations for a droplet cluster for the

local drag seen by droplets within a cluster is different from individual droplets. The results show that droplet

clustering can lead to considerable local turbulent number flux especially towards the outer region of the spray.

1. Introduction

In liquid fuelled combustion, the combustion performance and emissions are mainly governed

by the atomization of the liquid fuel, the motion and evaporation of the fuel droplets and mixing

of fuel and air. So, spray dynamics studies are important to ensure efficient utilization of energy

as well as to better understand the mechanism of pollutants formation and control. Thereby,

unsteady spray behavior such as droplet clustering is of concern, for example, in problems

related to the unsteady flow of fuel into and through the combustion chamber (Heinlein and

Fritsching 2006). Droplet clustering can be caused due to unsteady disintegration of liquid


jets/sheets close to the injector. However, away from the injector due to wide range of droplet

size distribution in sprays, different dynamic behavior of droplet dispersion and interaction with

the surrounding gas lead to formation of clusters of droplets (Zimmer et al. 2003). Previous

studies on particle laden turbulent flows (Longmire & Eaton 1992; Wang and Maxey 1993;

Squires and Eaton, 1990) showed that neither large particles (with high Stokes number) nor small

particles (with very small Stokes number) exhibit the tendency to form clusters. Between these

two extremes exists a range of stokes number within which particles respond to some eddies but

not to others, and these particles tend to preferentially concentrate in certain flow structures

(Fessler et al. 1994; Ferrante and Elghobashi 2003). For a spray, the consequence of droplet

clustering can be critical since the instantaneous spatial distribution of droplets in sprays might

have dense and dilute regions, which strongly influence the subsequent evaporation of droplets,

and so the process of air-fuel mixture preparation. Sufficiently small inter-particle spacing with

in a droplet cluster prevents penetration of oxygen. Consequently, a fuel-rich mixture is formed

in which droplets do not burn individually, but rather in a group, which may affect flame

location and distributions of temperature, fuel vapor and oxygen (Chiu and Liu 1977).

The aim of the present paper is to understand the cause and consequence of droplet

clustering in isothermal sprays. A twin-fluid internal mixing air-assist atomizer is considered for

this purpose such that the liquid break-up process is completed close to the injector exit and

droplet clustering downstream is expected only due to interaction of droplets with the

surrounding air. Planar measurements of spray droplets are obtained using different laser based

diagnostic techniques. The focus of the paper is on quantifying the degree of droplet clustering

and estimation of clusters properties (cluster size and velocity, droplet size distribution).

Different statistical approaches have been developed in past (Fessler et al. 1994; Sundaram and

Collins 1999; Monchaux et al. 2010) for quantifying preferential accumulation of inertial particles

in particle-laden turbulent flows mostly in channels and wind tunnels. However, application of

such methods for quantitative measurement of droplet clustering in sprays has been considered

by few researchers in past (for example, see Lian et al. 2013; Sahu et al 2016). The present paper

also includes results for measurement of average liquid number flux (both steady and turbulent

fluxes), which is associated with the ability of the liquid fuel to react and vital for the

stability and extinction of the flames (Hardalupas et al. 1994). The correlation between droplet

number density and droplet velocity is obtained. Such correlation, which is apparently found to

be a consequence of droplet clustering, signifies spray unsteadiness. One of the purposes of the

present work is to obtain a comprehensive data set for droplet clustering statistics for different


liquid mass loading (by varying the air and the liquid volume flow rates). The results are

presented here for a water spray under ambient conditions.

2. Flow and Optical arrangement

Experiments are conducted with an air-assist internal mixing type injector (Spraying

system Co. 1/4 J series) generating a solid cone spray under ambient conditions. The flow circuit

and the optical arrangements are shown in figure 1. Water, pressurized at 1.5 bars in a pressure

vessel, was fed to the nozzle. The volume flow rates of water and air were controlled by different

rotameters with operating ranges of 20-200 ml/min and 7-70 lpm, respectively.

Measurement of droplet clusters and number density are achieved by planar laser sheet

imaging of the droplets. For this purpose, a double pulse Nd:YAG laser (Quantel, EverGreen:

145 mJ/pulse at 532 nm; 5 mm beam diameter) was used to illuminate the flow. The green laser

beam was expanded in to a sheet using a cylindrical lens (focal length: -25 mm) and a spherical

lens (focal length: +250 mm). The height and beam waist of the laser sheet were about 5 cm and 1

mm, respectively. The scattered light from droplets was collected through a lens (50 mm; f/1.8D

Nikon lens) along with a suitable band-pass optical filter. The images of focused droplets were

captured through a camera (PCO Pixelfly: 14 bit, 1,040 × 1,392pixels2) placed at an angle of 90◦

with respect to the laser sheet. The field of view was about 1.3 cm × 1.6 cm such that the spatial

resolution and magnification were 12 µm/pixel and 0.52, respectively. The droplet velocity is

measured by Particle Image Velocimetry (PIV) by capturing double frame images corresponding

to dual pulses of the laser. Since droplet size is not known, this way size-averaged droplet

velocity was measured. Thus, the first frame of each PIV image pair is used for measurement of

droplet clustering, while both frames are used for determining droplet velocity.

The droplet size is measured by the Interferometric Laser Imaging for Droplet Sizing

(ILIDS) technique. ILIDS is a planar defocusing technique based on detecting the reflected and

the first order refracted light scattered from a droplet, which, at a specific forward scattering

angle, interfere to produce parallel fringes on a defocused plane (Glover et al. 1995). The

characteristic interferogram is observed with a far field arrangement of receiving optics. The

number of fringes present in each of the recorded fringe patterns is proportional to the droplet

diameter. ILIDS has been successfully applied for droplet measurements for different spray

applications (Kawaguchi et al. 2002; Damaschke et al. 2005; Hardalupas et al. 2010). For ILIDS

measurements the camera was set at an angle of 69◦ forward scattering angle. The object distance


was about 16 cm and the collecting angle was about 10◦ resulting in diameter/fringe equals to

about 4.5 microns.

Fig. 1 Schematic of the experimental setup.

The nozzle was mounted on an aluminum frame and was traversed for measurements at

different axial and radial locations within the spray. The laser repetition rate was set to 5 Hz

such that the acquired images remained statistically uncorrelated. For each measurement

locations 1000 images are captured. In house developed image processing software‟s based on

MATLAB were used for processing the raw images from different techniques.

3. Results & Discussion

Fig. 2 Shadowgraph images of the spray for various air and water flow rates.


In order to depict the influence of liquid mass loading on droplet dispersion in the spray few

shadowgraph images of the spray are presented in Fig. 2. Figures 2(a-e) show the images for

different air flow rates (𝑄��) while the water flow rate (𝑄��) is kept constant. As the droplet size is

expected to be smaller with increasing air flow rate for the same flow rate of water, and small

droplets show better response to the carrier flow partly induced by the spray itself, branches like

structures appear within the spray. However, as the water flow rate increases for the same air

flow (compare Fig.2f to Fig.2e), though the droplet size is expected to increase these structures

are more noticeable and droplet clustering is qualitatively more prominent. This suggests

importance of quantitative measurements of clustering in the spray.

The results presented below correspond to two different operating flow conditions where

the air flow rate is maintained constant (𝑄��= 25 ml/min and 𝑄𝑎 = 25 lpm; 𝑄��=50 ml/min and

𝑄��= 25 lpm). The measurements are obtained 30 cm downstream of the nozzle exit, and the

measurement stations are situated at different radial stations from the spray axis (denoted as R =

0 mm, 20 mm and 30 mm, respectively).

3.1 Measurement of droplet clustering

The tendency of droplets to form clusters and also the length scale of the clusters were quantified

based on two independent statistical methods viz. “droplet counting in a cell approach” and

estimation of “radial distribution function (RDF)”, respectively. For this purpose, the positions of

droplets on images must be identified. In the present work, the center of each droplet on an

image is identified following Otsu‟s method of image thresholding and subsequent reduction of

a graylevel image to a binary image. Usually before binarizing, the images are band-pass filtered

to remove the noise due to multiple reflections and current leekage from saturated pixels. We

studied the influence of the cut-off values of the employed band-pass filter using the image

processing software, ImageJ on droplet clustering measurements. It was found that for the

present measurements, the choice of those cut-off values has minimal influence on the

estimated length scale of droplet clusters. Also, though, droplet number count reduces with

increasing the cut-off values, as expected, the relative values of fluctuations to mean droplet

count is not affected. Hence, the results presented in the paper corresponds to the case of no

band-pass filtering. A typical raw image of the droplets and the identified droplet centers are

shown in Fig. 3.


(a)

(b)

Fig. 3: (a) Typical instantaneous image of the spray (b) Binarized image showing identified droplets

In the “droplet counting in a cell” approach the image is divided in to certain number of equally

sized cells (as shown in fig 3). The probability density function (PDF) of the droplet number

density is obtained by counting the number of droplets inside each cell. The ensemble averaged

PDF (over all images) is compared with that arising from a purely random distribution of

droplets (given by a Poisson distribution). The normalized difference between the standard

deviations of the PDF‟s is termed as D1 parameter, such that (D1 = 𝜎−𝜎𝑝

𝜆 , where λ is the average

droplet count in a cell). The value of D1 indicates the degree of clustering such that the box size

for which D1 is the maximum indicates the length scale of the droplet clusters (Lc). This is

demonstrated in Figure 4 for the two different operating flow conditions and same location at R

= 0 mm. Figure 4 also shows that clustering is higher for the case of larger flow rate of water

though the length scales of the droplet clusters remain nearly same (150 pixels or about 2 mm).

Similarly, D1 is evaluated for other measurement locations. Figure 5 shows radial variation of D1

for a given box size of 150 by 150 pixel2. The figure indicates greater preferential accumulation of

droplets towards the edge of the spray.

Fig. 4 Demonstration of the “droplet counting in a cell” method for the considered operating flow conditions and location R = 0 mm.

Fig. 5 Radial variation of D1


Though the droplet counting in a cell approach provides local information on droplet

clustering, the result is always ensemble averaged. On the other hand, the radial distribution

function (RDF) can provide instantaneous cluster size and the information is not local. RDF is

defined as the probability of finding a second droplet at a given separation distance from a

reference droplet compared to a case where the droplets are homogeneously distributed

(Sundaram et al 1999). Figure 6a schematically shows the method of calculation of RDF. In this

process, a series of concentric circles are considered around a droplet on an image. The droplet

count between consecutive radii (r-Δr and r+Δr) provides the number of droplets within the

annular area around a separation distance, „r‟. This is repeated for the different radial separation

distances and for all droplets on the image. The ensemble average of droplet counts for each „r‟

provides the RDF according to the following equation,

𝑅𝐷𝐹 (𝑟) = [(𝑁_𝑎𝑛𝑛𝑢𝑙𝑎𝑟 (𝑟)) ⁄ (𝐴_𝑎𝑛𝑛𝑢𝑙𝑎𝑟 (𝑟) )]/ [𝑁𝑡𝑜𝑡𝑎𝑙 ⁄ 𝐴𝑡𝑜𝑡𝑎𝑙 ]

where Ntotal/Atotal denotes average number of particles per unit area of the image. A typical RDF

corresponding to an instantaneous image is shown in Fig. 6b. RDF > 1 indicates clustering, while

RDF < 1 implies presence of voids in the image. Thus, the separation distance where RDF = 1

should provide an estimation of length scale of droplet clusters.

(a) (b)

Fig. 6: (a) Method of calculation of RDF (b) An instantaneous RDF indicating drpolet clustrs and voids.

Fig 7: RDF for different instantaneous

images calculated for 𝑄��=50 ml/min and

𝑄��= 25 lpm for R = 0 mm location.

Fig. 7 shows the RDF‟s for several instantaneous images for 𝑄��=50 ml/min and 𝑄��= 25 lpm for R

= 0 mm location. It can be observed that even if the air and water flow rates are constant the

length scale of droplet clusters (corresponding to RDF = 1) as well as the tendency of droplets to

form clusters denoted as RDFmax(maximum value of a given RDF at minimum separation


distance) vary considerably as depicted by double ended arrows in the same figure. The average

cluster length is obtained by arithmetic mean of the instantaneous values. Fig. 8a and 8b

respectively present variation of average cluster length (Lc) and average RDFmax for the two

liquid flow rates and different radial measurement locations. The error bars indicate statistical

uncertainty with 95% confidence interval. The results are in good agreement with the findings

via evaluation of the D1 parameter. It can be observed in Figure 8 that towards the edge of the

spray the droplets have greater tendency to preferentially accumulate in certain regions of the

flow which was in accordance with the trend of D1 parameter presented earlier.

Below we show in Fig. 9 the same quantities as in Fig. 8 for different cut-offs for the band-pass

filter, which confirms that such thresholding has minimal influence on droplet cluster

characteristics.

(a) (b)

Fig. 8: (a) Radial evolutionof average cluster length scale (b) average RDFmax for the two flow operating conditions.

(a) (b)

Fig. 9: Effect of band-pass filtering on average (a) cluster length scale (b) RDFmax. Here two sets of the cut-off limits

are considered for band-pass filtering (1-10 and 1-20).


3.2 Measurement of droplet size by ILIDS

A typical ILIDS image is presented in Fig. 10a, which shows circular fringe patterns

corresponding to each droplet. The images are first binarized using Otsu algorithm followed by

Hough transform to identify the centers of each droplet fringe pattern and measure its diameter.

The intensity values along a horizontal line passing through center of a circular pattern and

corresponding to a length few pixels more than its diameter are considered, whose Fourier

transform (in conjunction with Gaussian sub pixel interpolation) determines the spatial

frequency of the fringe pattern. A hanning window is used to minimize the spectral leakage. A

histogram of the droplet size measured by ILIDS corresponding to liquid flow rate of 50 lpm and

location R = 0 mm is shown in Fig. 10b. It can be observed that small droplets (20-30 µm)

dominate the size distribution. The Arithmetic Mean Diameter (AMD) was estimated to be about

30 μm, while the Sauter Mean Diameter (SMD) was about 40 μm.

(a) (b)

Fig. 10: (a) Typical ILIDS image (b) Histogram of droplet diameter 𝑄��=50 ml/min and 𝑄��= 25 lpm for R = 0 mm

location

3.3 Measurement of droplet velocity and number density

For measurement of instantaneous droplet velocity and number density each PIV image is

divided into cells of equal size and these quantities are calculated for each cell. The cell size is

always kept same for both quantities, and decided on the basis of estimated average cluster

dimension as determined in the previous section by D1 parameter and RDF. The purpose behind

this is to study the role of droplet clustering on local mean and turbulent droplet number fluxes,

which, as mentioned earlier, have significance in temporal and spatial distribution of liquid

volume in spray combustion systems. The results presented below are for interrogation window

size of 150 pixels in both directions, which is same as the estimated length scale of the droplet


clusters (Lc). The consequence of choice of window dimension either larger or smaller than the

cluster length scale will be explained later. In order to restrict the length of the paper, we present

results only for one operating flow condition ( Qw= 50 ml/min and Qa= 25 lpm)

Each pair of double exposure PIV images were processed based on direct image cross-

correlation (Raffel et al 2013) to obtain instantaneous droplet velocity vectors. The instantaneous

PIV realizations are ensemble averaged over all images to obtain mean droplet velocity. Fig. 11

presents vector plots for the mean droplet velocity downstream measurement locations. It can be

observed in Fig 11 that as expected the mean droplet velocity is mostly axial and it reduces away

from the spray axis. The fluctuations in droplet velocities are determined by subtracting the

mean velocity from instantaneous values.

Fig. 11: Mean droplet velocity vector plots for different radial location for 𝑄��=50 ml/min and 𝑄��= 25 lpm

For measurement of instantaneous droplet number density (N), the number of identified

droplets is counted for each cell whose volume is defined by the cell area and laser sheet

thickness.

The results presented in rest of the paper correspond to the row of cells passing through the

center of a measurement location. The variation of any statistics with respect to the radial

locations is presented for the three radial measurement stations together in a single plot. The

radial variation of mean and root mean square (rms) of fluctuations of droplet axial velocity and

droplet number density are shown in figures 12a and 12b, respectively. The errorbars represent

uncertainty with 95% confidence interval. The mean and fluctuations, as expected, reduce away

from the central spray region, the fluctuations of droplet velocity and number density are

considerable (30-50%) relative to the respective mean values.


(a) (b)

Fig. 12: Radial variation of average and fluctuations of (a) droplet velocity (b) droplet number density.

In order to estimate the droplet response to gas velocity fluctuations and also compare the

droplet cluster dimension to different length scales of the surrounding turbulent flow, the air

turbulence must be characterized. Since the air velocity is not measured in our experiments, we

assume that the droplets follow the air flow faithfully since the measurement location is far

below the injector exit and we calculate the turbulent characteristics based on the fluctuations of

droplet velocity. The integral length scale is estimated as one-fifth of the spray radius. The

Kolmogorov scales are obtained via dissipation rate, which is calculated from the droplet rms

velocity and integral length scale (Tennekes & Lumley 1972). We emphasize that because of the

assumptions made above the turbulent characteristics as presented in Table 1 can only be

considered in an order of magnitude sense.

Gas velocity fluctuation≈ ur 1.25 m/s

Integral length scale ≈ 1.0 cm

Integral time scale ≈ 8.55 ms

Dissipation rate ≈ 160 m2

/s3

Kolmogorov length scale ≈ 67 µm

Kolmogorov time scale ≈ 0.31 ms

Turbulent Reynolds number ≈ 780

Particle relaxation time ≈ 4.8 ms

Table 1: Turbulent characteristics of the flow at the center of the spray

Table 1 shows that most droplets are smaller than the Kolmogorov length scale but not

negligible. The droplet Stokes numbers based on integral and Kolmogorov time scales are StL=


0.5, Stη = 15, indicating partial and poor response of droplets to large and small turbulent eddies.

Also the cluster length scale is about 30 times the Kolmogorov scale.

3.3 Measurement of droplet number flux

The droplet number flux i.e. number of droplets moving across unit area normal to the flow per

unit time is obtained as a product of droplet number density and velocity. It can be shown that

the average number flux (denoted as 𝑁𝑈 ) is the sum of the steady flux (𝑁 × 𝑈 ) and the turbulent

flux (𝑛′ × 𝑢′ ). The latter is essentially the correlation between fluctuations of droplet number

density and velocity. Though, the turbulent flux is often neglected, which is partly due to the

difficulty associated with its measurement, it can be important when droplets partially respond

to the carrier phase turbulent gas flow, as in the present case. The situation can be of even more

significance when droplets tend to form clusters as a consequence of the two-phase interaction

process since this directly affects the evaporation rate of droplets and ability of droplets to react.

Figure 13a and 13b show, respectively, the radial variation of the steady and the turbulent

components of the average number flux, which reduce away from the central region of the

spray. It can also be observed that the correlation between fluctuations of droplet number

density and velocity is negative and non-negligible at the present measurement locations as its

importance relative to the steady flux (ratio between the two quantities) increases towards the

spray edge from about 5% to about 50%. The correlations normalized with rms values (or the

correlation coefficients) are presented in figures 14a and 14b for both axial and radial velocity

components. For both cases the correlation coefficients are negative and increase towards the

edge of the spray. This is attributed to droplet clustering for the drag on droplets in a cluster is

different from the case when droplets are transported individually. Thus, the gas velocity

fluctuations are smaller (𝑢′< 0) for a group of droplets passing through the measurement

location (𝑛′>0), and positive (𝑢′> 0) after the passage of the droplet group (𝑛′<0), hence the

correlation is negative. Since the significance of radial transport of droplets is realized away from

the spray axis, the correlation coefficient for radial velocity component is high (≈ 0.5) near the

spray boundary though the magnitude of correlation is much lower in comparison to that for the

axial velocity. The above result signifies that the average droplet number flux is overestimated if

the turbulent flux is not taken in to account.


(a)

(b)

Fig. 13 : Radial variation of (a) steady number flux and (b) turbulent number flux

(a)

(b)

Fig. 14 : Radial variation of (a) normalized axial flux, 𝑛′ × 𝑢′ and (b) normalized radial flux, 𝑛′ × 𝑣′

3.3.1 Effect of cell size on droplet number flux

Since droplet clustering occurs predominantly at viscous scales, while transport of clusters are

affected by large scale eddies, the turbulent number flux of droplets is a scale variant quantity.

Hence, the measured droplet statistics are obtained for different cell sizes relative to the

estimated length scale of the droplet clusters (cell size ranging from half of the cluster dimension

(0.5×Lc) up to 8 times the dimension of clusters (8×Lc)). In general, the uncertainty for the

smallest cell size is higher. The largest cell size nearly corresponds to the whole measurement

window.


(a) (b)

Fig. 15: Radial variation of (a) steady number flux. (b) turbulent number flux for various cell sizes.

Figures 15a and 15b present the steady and the turbulent number flux for cells of different sizes.

The respective statistical uncertainties with 95% confidence interval are about 3 - 8% and 27 - 30

%. The uncertainty is higher for smaller cell sizes due to less number of droplets present within a

cell. It is observed that the steady flux is nearly independent of the cell size though it is

consistently higher for cell size equal to Lc. Though not shown here similar observation was

found for the mean droplet number density, which was higher for cell size equal to Lc especially

for locations away from the spray axis, and this trend is in agreement with the results based on

D1 parameter and RDF. However, the mean droplet velocity was nearly independent of the cell

size, which is in accordance with the vector plots in Fig. 11. Thus, the trends in figure 15a are

justified. However, the fluctuations of droplet number density was found to reduce for larger

cells consistently (not shown here). The droplet velocity fluctuations were nearly independent of

the cell size though the uncertainty was higher for the smaller cell size. Figure 15b shows that for

cell sizes larger than the dimension of clusters the turbulent number flux is smaller. The results

presented here indicate that preferential accumulation of droplets can lead to turbulent mass

flux when measured over a length scale of the order of dimension of droplet clusters and

especially for near spray boundary region, and hence may not be considered negligible.

4. Conclusion

The present work focuses on quantitative measurement of droplet clustering in sprays

with an aim to study some of the important consequence of clustering including uneven

distribution of liquid fuel mass within the spray and increased significance of turbulent mass

flux. Experiments were conducted for a polydispersed spray generated by a twin fluid air-assist

atomizer. Droplet number density and droplet velocity measurements were obtained by the


application of planar laser sheet imaging of the spray droplets, while droplet sizing was

achieved by ILIDS technique. Two independent statistical methods are used to quantify the

length scales of droplet clusters as well as the tendency of droplets to form clusters. The

measurement area at any radial station is considered to consist of cells of same size, and results

including measurements of basic spray characteristics and droplet number flux are presented for

row of cells through the center of the measurement area. The statistical uncertainties of the

measured quantities are also presented. The effect of the choice of intensity cut-off values while

band-pass filtering the images was found to negligibly affect the measured droplet clustering

statistics.

The preferential accumulation of droplets was found to be higher towards the spray boundary,

where the length scale of the droplet clusters was also larger. As a consequence, the turbulent

number flux was negative and its magnitude was comparable to the steady number flux

especially away from the spray axis. Also, importantly, the turbulent number flux was smaller

for cell sizes larger than the estimated cluster dimension. The presented results are also of

significance for two-phase flow models for spray simulations.

The authors would like to acknowledge the support given by IITM for the conduct of the

research. MM acknowledges his teammates Abhijeet, Shirin, Kumari, Sai, Chaithanya, Visnu and

Azhivazhagan for all the help provided.

References

Aliseda, A., Cartellier, A., Hainaux, F., Lasheras, J. C., 2002. Effect of preferential concentration

on the settling velocity of heavy particles in homogeneous isotropic turbulence. Journal of Fluid

Mechanics 468, 77–105.

Chiu, H., Liu, T., 1977. Group combustion of liquid droplets. Combustion Science and

Technology 17 (3-4), 127 142.

Damaschke, N., Nobach, H., Nonn, T. I., Semidetnov, N., Tropea, C., 2005. Multi-dimensional

particle sizing techniques. Experiments in fluids 39 (2), 336–350.

Eaton, J. K., Fessler, J., 1994. Preferential concentration of particles by turbulence. International

Journal of Multiphase Flow 20, 169–209.


Ferrante, A., Elghobashi, S., 2003. On the physical mechanisms of two-way coupling in particle-

laden isotropic turbulence. Physics of Fluids (1994-present) 15 (2), 315–329.

Hardalupas, Y., Sahu, S., Taylor, A. M., Zarogoulidis, K., 2010. Simultaneous planar

measurement of droplet velocity and size with gas phase velocities in a spray by combined ilids

and piv techniques. Experiments in fluids 49 (2), 417–434.

Hardalupas, Y., Taylor, A., Whitelaw, J., 1994. Mass flux, mass fraction and concentration of

liquid fuel in a swirl-stabilized flame. International journal of multiphase flow 20, 233–259.

Heinlein, J., Fritsching, U., 2006. Droplet clustering in sprays. Experiments in Fluids 40 (3), 464–

472.

Kawaguchi, T., Akasaka, Y., Maeda, M., 2002. Size measurements of droplets and bubbles by

advanced interferometric laser imaging technique. Measurement Science and Technology 13 (3),

308.

Lian, H., Charalampous, G., Hardalupas, Y., 2013a. Preferential concentration of poly-dispersed

droplets in stationary isotropic turbulence. Experiments in fluids 54 (5), 1–17.

Longmire, E. K., Eaton, J. K., 1992. Structure of a particle-laden round jet. Journal of Fluid

Mechanics 236, 217-257.

Monchaux, R., Bourgoin, M., Cartellier, A., 2012. Analyzing preferential concentration and

clustering of inertial particles in turbulence. International Journal of Multiphase Flow 40, 1–18.

Raffel, M., Willert, C. E., Kompenhans, J., et al., 2013. Particle image velocimetry: a practical

guide.Springer.

Sahu, S., Hardalupas, Y., Taylor, A., 2016. Droplet–turbulence interaction in a confined

polydispersedspray: effect of turbulence on droplet dispersion. Journal of Fluid Mechanics 794,

267–309.


Squires, K. D., Eaton, J. K., 1990. Particle response and turbulence modification in isotropic

turbulence. Physics of Fluids A: Fluid Dynamics (1989-1993) 2 (7), 1191–1203.

Sundaram, S., Collins, L. R., 1999. A numerical study of the modulation of isotropic turbulence

by suspended particles. Journal of Fluid Mechanics 379, 105–143.

Tennekes, H., Lumley, J. L., 1972. A first course in turbulence. MIT press.

Wang, L.-P., Maxey, M. R., 1993. Settling velocity and concentration distribution of heavy

particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics 256, 27–68.

Zimmer, L., Ikeda, Y., 2003. Simultaneous laser-induced fluorescence and mie scattering for

droplet cluster measurements. AIAA journal 41 (11), 2170–2178.

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