Convective Gaseous Diffusion in Steady Axisymetric Cavity Flows

Abstract

Theoretical results on gaseous convective turbulent diffusion in steady axisymmetric flows are found to compare well with experimental results already in the literature. The investigation starts with the formulation of a highly idealized “slug-flow” model of the process for a quick estimate of the importance of turbulent boundary layer convection and for a comparison of previously published experimental and analytical results which had revealed order-of-magnitude discrepancies between calculated and measured air diffusion rates. Next, an existing two-dimensional convective diffusion model is adapted to axisymmetric cavity flow. Good agreement between experimental and calculated mass flow rates is found with a proper choice of turbulent diffusively from a Launder-Spaulding mixing-length model. The adapted “wrap around” model predicts a concentration boundary-layer thickness of the order of the cavity radius at the cavity terminus. Consequently, an axisymeetric analysis is also presented. From this it is found that the important part of the gaseous mass flow into the cavity occurs near the very front of the cavity where the concentration gradients are most severe. Downstream flow regions near the cavity are thereby depleted of dissolved air and the resulting concentration gradients are greatly reduced. Therefore the mass flow rate through downstream cavity surfaces are relatively unimportant and the simpler wrap around calculation can give useful engineering estimates of total mass flow rates.

The dynamics of partial cavity formation, shedding and the influence of dissolved and injected non-condensable gas

“…In addition, dissolved gas within the bulk flow gas can be exchanged with a partial cavity, as discussed recently by Lee et al (2016). Typically, the liquid near the cavity may be supersaturated with dissolved gas, and mass transfer will take place into the cavity at the gas-liquid cavity interface (Parkin & Ravindra, 1991) or at the interfaces of the bubbly mixture that forms the cavity (Yu & Ceccio, 1997;Lee et al, 2016). The question arises as to the effect that such gas diffusion may have on the gross dynamics of a shedding cavity, mainly in the context of changing the behavior of the bubbly flow, and this will be discussed here.…”

Scaling of Gas Diffusion Into Limited Partial Cavities

“…Table 3 presents the scaled and measured gas diffusion rates. We compare the models of Parking and Kermeen [5] (with D ¼ 2 Â 10 À5 cm 2 =s), Parkin and Ravindra [7] (with d ¼ 1 mm to approximate the typical model scale boundary layer thickness), and the slug flow model.…”

“…"PK," "B," "PR," and "SF" refer to the models of Refs. [5], [2], and [7], and the slug flow model [7], respectively. The confidence interval of the measured gas flux is 0…”

“…c O ¼ freestream dissolved gas concentration (g/m 3 ) c S ¼ saturated dissolved gas concentration at the cavity surface (g/m 3 ) c S;US ¼ saturated dissolved gas content at the cavity surface in the low-pressure region near the cavity separation (g/m 3 ) D t ¼ molecular mass diffusion coefficient (m 2 /s) k B ¼ constant used at each model (value varies by assumptions) L C ¼ partial cavity length (m) L D ¼ length scale derived from each modeling assumptions (m) L DB ¼ length scale used on model of Brennen [2] (m) L DPK ¼ length scale used on model of Parkin and Kermeen [5] (m) L DPR ¼ length scale used on model of Parkin and Ravindra [7] (m) L DSF ¼ length scale used on slug flow model [7] (m) L Dd ¼ length scale related to the diffusion boundary layer at the bubble surface within the cavity (m) m SB ¼ mass of the noncondensable gas in a single bubble (kg) _ m B ¼ net mass flux (kg/s) _ m B;Sat ¼ net mass flux in the wake of the cavity for supersaturated conditions (kg/s) _ m B;USat ¼ net mass flux in the wake of the cavity for undersaturated conditions (kg/s)…”

“…with k B ¼ 0.45. Similarly, Parkin and Ravindra [7] modified their laminar diffusion model by employing a turbulent diffusivity…”