Graduate Seminar in Fluid Mechanics
4:10 pm Presentation
“State Estimation in Turbulent Circular-Couette Flows”
Presented by MENGZE WANG (Adviser: Prof. Zaki)
The flow state of turbulent circular-Couette flow is very sensitive to initial conditions and the start-up process. For example, slowly increasing the rotational speed or suddenly accelerating it to the target value can lead to different transitional flow structures, such as stationary and wavy Taylor vortices, which persist in the turbulent regime. As a result, in numerical simulations, it is difficult to prescribe appropriate initial conditions that achieve a target flow state. Furthermore, due to the chaotic nature of turbulence, quantitative comparison between experimental measurements and simulations is challenging. This problem is addressed using an adjoint-variational state-estimation algorithm. By combining simulations with limited measurements, we predict the appropriate initial condition that tracks the correct flow state. A symmetric projector is proposed to guarantee that the initial condition is divergence free. We first consider estimation of turbulent flow with noise-free coarse-grained velocity data. The algorithm achieves more than 50% error reduction compared to space-time interpolation, with a better prediction of large-scale structures and vorticity. We subsequently demonstrate that the estimation accuracy is robust to measurement noise. Finally, a more challenging case is investigated, in which the measurements are composed of the velocity field far from the wall and the wall shear stress.
“Numerical Simulation of the Non-Equal Sized Coalescence-Induced Self-Propelled Droplets”
Presented by XIANYANG (TOM) CHEN (Adviser: Prof. Tryggvason)
In general, external energy is needed to remove liquid from a solid wall during cooling by dropwise condensation. However, experiments have shown that in some cases droplets can propel themselves from the wall, without any external energy, due to the coalescence-induced conversion of surface energy to kinetic energy. Several authors have reported scaling analysis combined with an energy balance of kinetic energy, surface energy and viscous energy, to estimate whether the droplets can be self-propelled or not. Here, we uses numerical simulation to describe the coalescence and self-propelling for non-equal sized droplets, based on a finite-volume/front-tracking method and the Generalized Navier Boundary Condition (GNBC) to model the moving contact lines. We find that a slightly smaller contact angle (165°) will give a larger out-of-plane jumping velocity than superhydrophobic surface (with a contact angle of 180°). Further decreasing the contact angles is believed to result in “immobile coalescence”. The speed of the moving contact line does not influence the spontaneous removal process as long as it is large enough to let the contact areas detach in time. Non-equal sized drops are much more difficult to be spontaneously removed from a wall compared to equal-sized ones. Two spherical drops with a diameter ratio of 2.0, possesses 60% usable energy compared of equal- sized ones and only 0.5% of the total released energy can be effectively used for out-of-plane jumping.