We have developed a nonlinear inversion scheme for retrieving collision kernels of droplets from the time evolution of droplet size distributions in turbulent air flows. In order to obtain reference data to validate the scheme, we have performed three-dimensional direct numerical simulations (DNS) of colliding droplets in isotropic steady turbulent flows. In the DNS, air turbulence is calculated using a quasi-spectral method, and droplet motions are tracked by a Lagrange method. The collision kernels retrieved by the nonlinear inversion scheme are compared with those obtained by the DNS for flows with various Reynolds numbers. The collision kernels retrieved from our previous linear scheme are also compared to the reference data. The results show that both the linear and nonlinear schemes can retrieve the collision kernels with fair accuracy in low Reynolds number flows. In higher Reynolds number flows, however, retrieval errors of the linear scheme become larger but those of the nonlinear scheme stay small. Thus, the present nonlinear scheme is more robust than our earlier linear scheme.
