Droplet growth processes in a cumulus cloud, beginning from its inception at sub-micron scale up to drizzle drop size of few hundred microns, in an average duration of about half hour, has been a topic of intense research. In particular role of turbulence in aiding droplet growth in clouds has been of immense interest. Motivated by this question, we have performed experiments in which turbulent natural convection coupled with phase change is set up inside a tall vertical insulated tube, by heating water located at tube bottom and circulating cold air at tube top. The resulting moist turbulent natural convection flow in the tube is expected to be axially homogeneous. Mixing of air masses of differing temperature and moisture content leads to condensation of water vapor into droplets, on aerosols available inside the tube. We there-fore have droplets in a turbulent flow, in which phase change is coupled to turbulence dynamics, just as in clouds. We obtain a linear mean-temperature pro le in the tube away from its ends. Because there is net flux of water vapor through the tube, there is a weak mean axial flow, but which is small compared to turbulent velocity fluctuations. We have experimented with two setups, the major difference between them being that in one setup, called AC setup, tube is open to atmosphere at its top and hence has higher aerosol concentration inside the tube, while the other setup, called RINAC setup, is closed to atmosphere and due to presence of aerosol filters has lower aerosol concentration inside the tube. Also in the latter setup, cold air temperature at tube top can be reduced to sub-zero levels. In both setups, turbulence attains a stationary state and is characterized by Rayleigh number based on temperature gradient inside the tube away from its ends, which is 107. A significant result from our experiments is that in RINAC setup, we obtain a broadened droplet size distribution at mid-height of tube which includes a few droplets of size 36 m, which in real clouds marks the beginning of rapid growth of droplets due to collisions among them by virtue of their interaction with turbulence. This shows that for broadening of droplet size distribution, high turbulence levels prevalent in clouds is not strictly necessary. Second part of our study comprises two pieces of theoretical work. First, we deal with the problem of a large collector drop settling amidst a population of smaller droplets whose spatial distribution is homogeneous in the direction of fall. This problem is relevant to the last stage of droplet growth in clouds, when the droplets have grown large enough that they interact weakly with turbulence and begin to settle under gravity. We propose a new method to solve this problem in which collision process is treated as a discrete stochastic process, and reproduce Telford's solution in which collision is treated as a homogeneous Poisson process. We then show how our method may be easily generalized to non-Poisson collision process. Second, we propose a new method to detect droplet clusters in images. This method is based on nearest neighbor relationship between droplets and does not employ arbitrary numerical criteria. Also this method has desirable invariance properties, in particular under the operation of uniform scaling of all distances and addition/deletion of empty space in an image, which therefore renders the proposed method robust. This method has advantage in dealing with highly clustered distributions, where cluster properties vary over the image and therefore average of properties computed over the entire image could be misleading.