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Dropwise condensation, which collects the condensate liquid in the form of droplets, has attracted a growing interest due to much higher heat transfer coefficient. One important and challenging issue in dropwise condensation is the presence of non-condensable gas (NCG) which drastically reduces its heat transfer performance. Concerning the mechanism understanding, this thesis is aiming to investigate dropwise condensation in case of NCG by combing different methods. Firstly, convective dropwise condensation out of moist air is experimentally investigated under controllable conditions. In modeling, some crucial aspects are reasonably captured: the coupled heat and mass transfer during droplet growth by a multi-scale droplet growth model; the inter-droplet interaction defined by a distributed point sink method; the enhancement of the convective mass transfer using the droplet Sherwood number. Furthermore, a multi-component multi-phase thermal pseudopotential-based LB model is developed to advance the directly numerical simulation of dropwise condensation.