Modulation of forced isotropic turbulence by an anchored droplet with near-Kolmogorov diameter and varying volatility

Abstract

Utilizing a fan-stirred chamber and two-dimensional particle image velocimetry, we analyse the modification of homogeneous and isotropic turbulence ( $50 \leq Re_\lambda \leq 140$ , with supplementary data out to $Re_\lambda = 310$ , where $Re_\lambda$ is the longitudinal Taylor Reynolds number) induced by both a non-volatile (water) and a volatile (ethanol) isolated and anchored droplet in the range $(0.3 \leq d/\eta \leq 5.1)$ , where $d/\eta$ is the ratio of droplet diameter to the Kolmogorov length scale. The dissipation rate, $\varepsilon$ , is calculated via the corrected spatial gradient method, and the resultant fields of both turbulent kinetic energy, $k$ , and $\varepsilon$ are presented as spatial heat maps and as shell averages, ${\overline {k_{\Delta r}}}$ and ${\overline {\varepsilon _{\Delta r}}}$ , vs the radial coordinate normalized by the droplet radius, $r/R$ . The dissipation rate near the water droplet surface may exceed the corresponding unladen flow value by a factor of twenty or more. The normalized radius of recovery, $r^*$ , which designates the radial location where ${\overline {k_{\Delta r}}}$ or ${\overline {\varepsilon _{\Delta r}}}$ has returned to within 10 % of the unladen value, is reasonably expressed as $r^* \propto (d/\lambda )^{-C_2}$ in either case, where $\lambda$ is the longitudinal Taylor microscale and $C_2$ is a positive empirical fitting parameter. Recovery of ${\overline {k_{\Delta r}}}$ and ${\overline {\varepsilon _{\Delta r}}}$ may take up to 14 normalized radii when $d/\lambda$ is small. Trend line extrapolation suggests that the attenuation region becomes negligible as $d/\lambda \to 1$ . Ethanol, which evaporates up to five times faster than water, induces a much smaller dissipation spike near the surface. The mass ejection phenomenon appears to reduce the strong near-surface damping of the radial root-mean-square component. However, the radius of recovery trend for fields surrounding a volatile ethanol droplet falls directly in line with the non-volatile water droplet data for both $k$ and $\varepsilon$ , indicating that droplet vaporization has little effect on the far-field return to isotropy.