Inner and outer flow of an adhering droplet in shear flow. (August 2022)

• Record Type: Journal Article
• Authors: Burgmann, Sebastian; Krämer, Veronika; Rohde, Martin; Dues, Michael; Janoske, Uwe
• Is Part Of: International journal of multiphase flow. Volume 153(2022)
• Publication Date: 2022-08
• Subjects: Sessile drop in shear flow -- Laser-optical flow measurement -- Numerical VOF simulation -- Inner flow reversal -- Wake flow with recirculation zone -- Increase of pressure difference; Multiphase flow -- Periodicals; Écoulement polyphasique -- Périodiques; Multiphase flow; Periodicals; 620.1064
• DOI: 10.1016/j.ijmultiphaseflow.2022.104140
• Languages: English
• ISSNs: 0301-9322

Abstract

Highlights: Laser-optical flow measurements of the inner and outer flow of a drop in shear flow. Numerical simulation with modified VOF- model taking into account contact angle hysteresis effects. Correlation of recirculation flow in the wake with flow reversal inside the drop. Upstream movement of separation point in contrast to similar rigid surface structure. Correlation of size of recirculation zone with pressure-difference along the drop. Abstract: Adhering droplets in shear flow start to move downstream when a critical velocity ucrit is reached, i.e. the adhesion force is overcome by aerodynamic force. It is still not clear, whether drag-coefficient-estimation based on an approximation of the droplet as a rigid spherical cap is a valid approach. In contrast to rigid hemispheres there is a gas-liquid-interface, i.e. the velocity of the interface is not zero by all means. Therefore, there is a fluid transport inside the drop that depends on the outer flow structure. We report on a combined numerical and experimental investigation to find out the characteristic inner and outer flow structure of an adhering droplet in shear flow in order to evaluate the rigid-hemisphere-approach. The inner flow structure of the droplet is measured by particle-image velocimetry (PIV) while the wake flow of the droplet in the gas-phase is measured by a modified laser-doppler-velocimeter (laser-doppler profile sensor). Numerical simulations of a droplet have been carried out using a modified volume of fluid (VOF) model taking into account contact angle hysteresis effects in OpenFOAM®. The complete two-phase fluid motion of the liquid droplet and surrounding gas phase is simulated, i.e. the inner and outer flow of the droplet are captured with a three-dimensional simulation model. Experimental and numerical results agree very well concerning flow pattern inside and outside the droplet. There is a strong connection between the inner and outer flow of the droplet. For lower Reynolds numbers based on droplet diameter (Red < 800) the flow inside the droplet rotates in direction of the channel flow. On the leeward side of the droplet there is a small wake flow with slightly decreased flow velocity. At higher Reynolds numbers (Red ≥ 800) the flow pattern inside the droplet changes completely: A strong reverse flow close to the droplet surface appears. Concurrently a strong recirculation zone emerges in the wake of the droplet. This is due to the roll-up process of a separated shear layer originating from the droplet. Due to the coupling of the inner flow with the outer flow via the gas-liquid-interface our data show that at higher Reynolds numbers flow separation takes place on the windward half of the droplet. This is in contrast to the case of a rigid hemisphere, where the separation is located at approximately 90°, i.e. the top of the droplet, and does not move upstream with increasing Reynolds number. The height of the separation zone increases up to 1.29 times the droplet height, which is not observed for rigid hemispheres. Since the pressure field around an obstacle is governed by the flow separation location and the corresponding size of the recirculation zone, the coupling of the inner and outer flow changes the pressure distribution around the droplet with respect to a similar rigid structure. This will affect the aerodynamic forces acting on the droplet, which is why the approximation by a rigid spherical cap does not seem to be a suitable approach. Nevertheless, additional experimental and numerical efforts need to be done to assess the flow structures, pressure distributions and forces acting on the droplet in a suitable precision also considering possible aero-elastic effects.