The dynamic balances of dissolved air and heat in natural cavity flows

Abstract

In steady, fully developed and unventilated cavity flows occurring in practice, air (originally dissolved in the water) and heat are diffused through the fluid towards the interface providing a continuous supply of air and vapour to the cavity. This must be balanced by the rate of entrainment of volume of air and vapour away from the cavity in the wake. These equilibria which determine respectively the partial pressure of air within the cavity and the temperature differences involved in the flow are studied in this paper. The particular case of the cavitating flow past a spherical headform has been investigated in detail. Measurements indicate a near-linear relation between the partial pressure of air in the cavity and the total air content of the water. From a second set of experiments, designed to estimate the volume rates of entrainment under various conditions by employing artificial ventilation, it appears that this is a function only of tunnel speed and cavity size within the range of the experiments. A simplified theoretical approach involving the turbulent boundary layer on the surface of the cavity is then used to estimate the rates of diffusion into the cavity. The resulting air balance yields a partial pressure of air/air content relation compatible with experiment. The water vapour or heat balance suggests that the temperature differences involved are likely to be virtually undetectable experimentally.

Cavitation and Bubble Dynamics

“…One of the consequences of the balance between the supply of noncondensable gas (air) and its removal by entrainment is the inherent regulation of the partial pressure of the noncondensable gas (air) in the cavity. Brennen (1969) put together a simplified model of these processes and showed that the results for the partial pressure of air were in rough agreement with experimental measurements of that partial pressure. Moreover, there is an analogous balance of heat in which the latent heat removed by the entrainment process must be balanced by the heat diffused to the cavity through the interfacial layer.…”

“…Instead, a pair of counter-rotating vortices with gas/vapor cores form in the closure region (Cox and Claydon 1956); this type of closure is much steadier and less turbulent than the reentrant jet type, which is prevalent at higher Froude numbers. The rate at which vapor/gas can be entrained by the counter-rotating vortex closure is much higher than for the reentrant jet closure (Brennen 1969).…”

“…Such will be the case when the Froude number based on cavity length, , F r = U ∞ (g ) 1 2 , is less than some critical value denoted by F r c . For bodies of small aspect ratio (such as axisymmetric headforms) it appears that F r c ≈ 2.5 (Brennen 1969) and, when F r < F r c , the reentrant jet structure no longer occurs. Instead, a pair of counter-rotating vortices with gas/vapor cores form in the closure region (Cox and Claydon 1956); this type of closure is much steadier and less turbulent than the reentrant jet type, which is prevalent at higher Froude numbers.…”

“…Measurements of the volume rate of entrainment for large cavities with the steady, reentrant jet type of closure (for example, Brennen 1969) suggest that the volume rate increases with velocity as U n ∞ where n is a little larger than unity. Using axisymmetric headforms of different size, b, Billet and Weir (1975) showed that though the volume entrainment rate scaled approximately with U ∞ b 2 , there was a significant variation with cavitation number, σ, the volume rate increasing substantially as σ decreased and the cavity became larger.…”

Possibility of Quantitative Prediction of Cavitation Erosion Without Model Test

“…Therefore, the air flow rate of a ventilated cavity has often been measured instead, under the assumption that the flow rate necessary to maintain a certain length of cavity should be same for a vapor cavity and a ventilated cavity. (Brennen, 1969;Billet and Weir, 1975).…”