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Interaction of droplet dispersion and evaporation in a polydispersed spray
- S. Sahu, Y. Hardalupas, A. M. K. P. Taylor
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- Journal:
- Journal of Fluid Mechanics / Volume 846 / 10 July 2018
- Published online by Cambridge University Press:
- 03 May 2018, pp. 37-81
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The interaction between droplet dispersion and evaporation in an acetone spray evaporating under ambient conditions is experimentally studied with an aim to understand the physics behind the spatial correlation between the local vapour mass fraction and droplets. The influence of gas-phase turbulence and droplet–gas slip velocity of such correlations is examined, while the focus is on the consequence of droplet clustering on collective evaporation of droplet clouds. Simultaneous and planar measurements of droplet size, velocity and number density, and vapour mass fraction around the droplets, were obtained by combining the interferometric laser imaging for droplet sizing and planar laser induced fluorescence techniques (Sahu et al., Exp. Fluids, vol. 55, 1673, 2014b, pp. 1–21). Comparison with droplet measurements in a non-evaporating water spray under the same flow conditions showed that droplet evaporation leads to higher fluctuations of droplet number density and velocity relative to the respective mean values. While the mean droplet–gas slip velocity was found to be negligibly small, the vaporization Damköhler number ( $Da_{v}$ ) was approximately ‘one’, which means the droplet evaporation time and the characteristic time scale of large eddies are of the same order. Thus, the influence of the convective effect on droplet evaporation is not expected to be significant in comparison to the instantaneous fluctuations of slip velocity, which refers to the direct effect of turbulence. An overall linearly increasing trend was observed in the scatter plot of the instantaneous values of droplet number density ( $N$ ) and vapour mass fraction ( $Y_{F}$ ). Accordingly, the correlation coefficient of fluctuations of vapour mass fraction and droplet number density ( $R_{n\ast y}$ ) was relatively high ( ${\approx}0.5$ ) implying moderately high correlation. However, considerable spread of the $N$ versus $Y_{F}$ scatter plot along both coordinates demonstrated the influence on droplet evaporation due to turbulent droplet dispersion, which leads to droplet clustering. The presence of droplet clustering was confirmed by the measurement of spatial correlation coefficient of the fluctuations of droplet number density for different size classes ( $R_{n\ast n}$ ) and the radial distribution function (RDF) of the droplets. Also, the tendency of the droplets to form clusters was higher for the acetone spray than the water spray, indicating that droplet evaporation promoted droplet grouping in the spray. The instantaneous group evaporation number ( $G$ ) was evaluated from the measured length scale of droplet clusters (by the RDF) and the average droplet size and spacing in instantaneous clusters. The mean value of $G$ suggests an internal group evaporation mode of the droplet clouds near the spray centre, while single droplet evaporation prevails near the spray boundary. However, the large fluctuations in the magnitude of instantaneous values of $G$ at all measurement locations implied temporal variations in the mode of droplet cloud evaporation.
Droplet–turbulence interaction in a confined polydispersed spray: effect of turbulence on droplet dispersion
- S. Sahu, Y. Hardalupas, A. M. K. P. Taylor
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- Journal:
- Journal of Fluid Mechanics / Volume 794 / 10 May 2016
- Published online by Cambridge University Press:
- 04 April 2016, pp. 267-309
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The effect of entrained air turbulence on dispersion of droplets (with Stokes number based on the Kolmogorov time scale, $St_{{\it\eta}}$, of the order of 1) in a polydispersed spray is experimentally studied through simultaneous and planar measurements of droplet size, velocity and gas flow velocity (Hardalupas et al., Exp. Fluids, vol. 49, 2010, pp. 417–434). The preferential accumulation of droplets at various measurement locations in the spray was examined by two independent methods viz. counting droplets on images by dividing the image in to boxes of different sizes, and by estimating the radial distribution function (RDF). The dimension of droplet clusters (obtained by both approaches) was of the order of Kolmogorov’s length scale of the fluid flow, implying the significant influence of viscous scales of the fluid flow on cluster formation. The RDF of different size classes indicated an increase in cluster dimension for larger droplets (higher $St_{{\it\eta}}$). The length scales of droplet clusters increased towards the outer spray regions, where the gravitational influence on droplets is stronger compared to the central spray locations. The correlation between fluctuations of droplet concentration and droplet and gas velocities were estimated and found to be negative near the spray edge, while it was close to zero at other locations. The probability density function of slip between fluctuating droplet velocity and gas velocity ‘seen’ by the droplets signified presence of considerable instantaneous slip velocity, which is crucial for droplet–gas momentum exchange. In order to investigate different mechanisms of turbulence modulation of the carrier phase, the three correlation terms in the turbulent kinetic energy equation for particle-laden flows (Chen & Wood, Can. J. Chem. Engng, vol. 65, 1985, pp. 349–360) are evaluated conditional on droplet size classes. Based on the comparison of the correlation terms, it is recognized that although the interphase energy transfer due to fluctuations of droplet concentration is low compared to the energy exchange only due to droplet drag (the magnitude of which is controlled by average droplet mass loading), the former cannot be considered negligible, and should be accounted in two phase flow modelling.
Droplet–turbulence interaction in a confined polydispersed spray: effect of droplet size and flow length scales on spatial droplet–gas velocity correlations
- S. Sahu, Y. Hardalupas, A. M. K. P. Taylor
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- Journal:
- Journal of Fluid Mechanics / Volume 741 / 25 February 2014
- Published online by Cambridge University Press:
- 07 February 2014, pp. 98-138
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This paper discusses the interaction between droplets and entrained turbulent air flow in the far-downstream locations of a confined polydispersed isothermal spray. Simultaneous and planar measurements of droplet and gas velocities in the spray along with droplet size are obtained with the application of a novel experimental technique, developed by Hardalupas et al. (Exp. Fluids, vol. 49, 2010, pp. 417–434), which combines interferometric laser imaging for droplet sizing (ILIDS) with particle image velocimetry (PIV). These measurements quantified the spatial correlation coefficients of droplet–gas velocity fluctuations ($R_{dg}$) and droplet–droplet velocity fluctuations ($R_{dd}$) conditional on droplet size classes, for various separation distances, and for axial and cross-stream velocity components. At the measurement location close to the spray edge, with increasing droplet size, $R_{dg}$ was found to increase in axial direction and decrease in cross-stream direction. This suggests that as the gas-phase turbulence becomes more anisotropic away from the spray axis, the gravitational influence on droplet–gas correlated motion tends to increase. The effective length scales of the correlated droplet–gas motion were evaluated and compared with that for gas and droplet motion. The role of different turbulent eddies of the gas flow on the droplet–gas interaction was examined. The flow structures were extracted using proper orthogonal decomposition (POD) of the instantaneous gas velocity data, and their contribution on the spatial droplet–gas velocity correlation was evaluated, which quantified the momentum transfer between the two phases at different length scales of the gas flow. The droplets were observed to augment turbulence for the first three POD modes (larger scales) and attenuate it for the rest of the modes (smaller scales). It has been realized that apart from droplet Stokes number and mass loading, the dynamic range of length scales of the gas flow and the relative turbulent kinetic energy content of the flow structures (POD modes) must be considered in order to conclude if the droplets enhance or reduce the carrier-phase turbulence especially at the lower wavenumbers.
Electromagnetically controlled multi-scale flows
- L. ROSSI, J. C. VASSILICOS, Y. HARDALUPAS
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- Journal:
- Journal of Fluid Mechanics / Volume 558 / 10 July 2006
- Published online by Cambridge University Press:
- 04 July 2006, pp. 207-242
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We generate a class of multi-scale quasi-steady laminar flows in the laboratory by controlling a quasi-two-dimensional shallow-layer brine flow by multi-scale Lorentz body forcing. The flows' multi-scale topology is invariant over a broad range of Reynolds numbers, $\hbox{\it Re}_{2D}$ from 600 to 9900. The key multi-scale aspects of this flow associated with its multi-scale hyperbolic stagnation-point structure are highlighted. Our multi-scale flows are laboratory simulations of quasi-two-dimensional turbulent-like flows, and they have a power-law energy spectrum $E(k)\,{\sim}\,k^{-p}$ over a range $2\pi/L\,{<}\,k\,{<}\,2\pi/\eta$ where $p$ lies between the values 5/3 and 3 which are obtained in a two-dimensional turbulence that is forced at the small scale $\eta$ or at the large scale $L$, respectively. In fact, in the present set-up, $p\,{+}\,D_{s}\,{=}\,3$ in agreement with a previously established formula; $D_s\,{\approx}\,0.5$ is the fractal dimension of the set of stagnation points and $p\,{\approx}\,2.5$. The two exponents $D_s$ and $p$ are controlled by the multi-scale electromagnetic forcing over the entire range of scales between $L$ and $\eta$ for a broad range of Reynolds numbers with separate control over $L/\eta$ and Reynolds number. The pair dispersion properties of our multi-scale laminar flows are also controlled by their multi-scale hyperbolic stagnation-point topology which generates a sequence of exponential separation processes starting from the smaller-scale hyperbolic points and ending with the larger ones. The average mean square separation $\overline{\Delta^{2}}$ has an approximate power law behaviour ${\sim}t^{\gamma}$ with ‘Richardson exponent’ $\gamma\,{\approx}\,2.45$ in the range of time scales controlled by the hyperbolic stagnation-points. This exponent is itself controlled by the multi-scale quasi-steady hyperbolic stagnation-point topology of the flow.