Two-phase air-water flows: Scale effects in physical modeling

Physical modeling represents probably the oldest design tool in hydraulic engineering together with analytical approaches. In free surface flows, the similitude based upon a Froude similarity allows for a correct representation of the dominant forces, namely gravity and inertia. As a result fluid flow properties such as the capillary forces and the viscous forces might be incorrectly reproduced, affecting the air entrainment and transport capacity of a high-speed model flow. Small physical models operating under a Froude similitude systematically underestimate the air entrainment rate and air-water interfacial properties. To limit scale effects, minimal values of Reynolds or Weber number have to be respected. The present article summarizes the physical background of such limitations and their combination in terms of the Morton number. Based upon a literature review, the existing limits are presented and discussed, resulting in a series of more conservative recommendations in terms of air concentration scaling. For other air-water flow parameters, the selection of the criteria to assess scale effects is critical because some parameters (e.g., bubble sizes, turbulent scales) can be affected by scale effects, even in relatively large laboratory models.