A gravity update scheme using PID controller for droplet traveling at terminal velocity in air flow

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To improve the combustion efficiency in gas turbines, it will be important to find out positions of droplets and the evaporated fuel vapors in the combustion chamber. In our study, we investigate the drag coefficient of droplets, because drag force will affect droplet dynamics. In practice, simple drag correlations are commonly used in DNS, which are single-parameter dependent on Reynolds number. However, if droplets have complex interactions with the flow, more parameters should be taken into consideration. For example, in gas turbine combustion, it is natural to think that deformation, evaporation and internal circulation of droplets have impact on drag coefficient as well. Therefore, drag coefficient will have a dependence on related parameters (effective diameter, Weber number, density ratio, etc.). To reveal the dependence of drag coefficient on probable parameters, we perform simulations of an evaporating droplet traveling at its terminal velocity in high-temperature air by using the numerical framework developed by our research group. This framework uses an interface-capturing DNS for vaporizing multiphase flows. Since the drag force is dynamically changing, an algorithm which updates the gravity to balance the drag force is developed. We incorporate PID controller in our scheme to mimic the difference between gravity and drag force in a more robust manner compared to our previous work [Setiya and Palmore, ESSCI, 2020]. The resultant gravity is then used to characterize the behavior of drag coefficient.