Comparison of experimental and numerical studies of turbulent collision of inertial droplets and the resulting droplet size distribution

The effect of air turbulence on droplet size spectrum broadening is poorly understood and modeled within the process of warm rain formation. This is one of the main sources of uncertainty in numerical weather prediction and climate modeling. Growth of cloud droplets by turbulent collision-coalescence has been studied in recent years to better understand warm rain initiation (Wang and Grabowski 2009). The central issue under study is to what extent the effect of air turbulence on the dynamics of inertial droplets can enhance the probability of collision-coalescence relative to the gravitational mechanism alone. This is equivalent to the question of how much does air turbulence alter the radial relative velocity and normalized local pair density (i.e., the radial distribution function or RDF) of cloud droplets. We study this problem through a combination of numerical simulation and experiments. A hybrid direct numerical simulation (HDNS) is applied to quantify these pair statistics of sedimenting cloud droplets in a grid generated turbulence where experimental measurements of similar statistics are being made. Both gravitational settling and droplets inertia are considered.

Pair statistics of droplets with radius in the 1-50 µm range are injected in a wind tunnel with grid generated turbulence and measured through Phase Doppler Particle Analysis (PDPA) and planar flow visualization. Because of the droplet size and the low volume fraction, droplet interactions at short range, leading to collision and coalescence, are infrequent (volumetrically) in cloud simulating conditions and building converged statistics of these events is very difficult. Some recent efforts in active grid turbulence using point-based phase-Doppler interferometer (Saw et al. 2008) or box turbulence using sophisticated 3D digital holography (Salazar et al. 2008) have been made to measure statistics related to RDF. In those experiments, the gravity effect is assumed to be negligible. In our experiments, we have increased the droplet volume fraction to between 10^(-5)-10^(-4), equivalent to a liquid water content of 10-100 g/m^3, to augment the probability of collisions while keeping the flow dilute enough that the droplets do not significantly modulate the turbulence statistics. Similarly, the dissipation rate of turbulent kinetic energy is relatively high (ϵ≈0.01-1 m^2/s^-3) with respect to usual values in cumulus clouds, which allows us to reach high Reynolds numbers in a laboratory setting (Re_λ=200-400) and further increase the probability of collisions. Additionally, we have a low mean convective velocity in the wind tunnel (≈1 m/s) so that the droplets residence time is long enough for collisions to significantly alter the size distribution inside the measurement test section. We will present the comparison of our experimental results with HDNS under closely matched conditions: decaying homogenous and isotropic turbulence generated in a low speed wind tunnel, in a parameter range (flow dissipation rate and droplet size) that partially overlaps with those of atmospheric clouds. The 1D RDF obtained from the PDPA and the 2D RDF obtained from flow visualizations will be compared to the same quantities obtained from the 3D HDNS. This information allows us to relate the experimentally determined quantities to the full three dimensional RDF and collision kernel. The change in the Droplet Size Distribution (DSD) as the droplets are convected downstream, measured from the PDPA data, can then be used in conjunction with the 3D information from the HDNS to develop and validate turbulent collision kernels and to evaluate collision-coalescence efficiencies.

References

Ayala O., Grabowski W.W., Wang L.-P., A hybrid approach for simulating turbulent collisions of hydrodynamically- interacting particles, J. Comp. Phys., Vol. 225, pp. 51-73, 2007.

Rosa B. and Wang L.-P., Parallel implementation of particle tracking and collision in a turbulent flow. PPAM2009, Wroclaw (Poland), September 13-16, 2009.

Salazar J.P.L.C., De Jong J., Cao L.J., Woodward S.H., Meng H. and Collins L.R., Experimental and numerical investigation of inertial particle clustering in isotropic turbulence, J. Fluid Mech., Vol. 600, pp. 245-256, 2008.

Saw E.W., Shaw R.A., Ayyalasomayajula S., Chuang P.Y., Gylfason A., Inertial clustering of particles in high- Reynolds-number turbulence, Phys. Rev. Lett., Vol. 100, 214501, 2008.

Wang L.-P. and Grabowski W.W., The role of air turbulence in warm rain initiation, Atmos. Sci. Lett., Vol. 10, pp. 1-8, 2009.