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Maximum ellipsoidal magnitude of the droplet is an important basic parameter for calculating drag force, droplets axial-velocity and dispersed-phase pressure gradient in an annular-mist pipe flow. An analytical correlation to predict the maximum ellipsoidal magnitude of a low-viscosity droplet in a parallel gas stream based on energy conservation and volume conservation. Stagnant pressure distribution on droplet surface is revised from Flachsbart's formula. The proposed correlation has clear physical meaning and easy to use. The correlation captures the deformation mechanism with an average absolute percent error of 9.53%. The effect of stagnant pressure distribution on the proposed correlation's accuracy is discussed.

Calculation of the hydraulic gradient due to the upward flow of a large size particles.water mixture in a swaying vertical pipe is a central problem in the design of systems for deep-sea mining of manganese modules. Here, the problem is investigated experimentally and with a mathematical model. An experimental apparatus that mimics the deep-sea mining system was built to investigate the effects of swaying on the hydraulic gradient. The experimental results reveal that the hydraulic gradient in a swaying vertical pipe is greater than in a fixed vertical pipe (for the same flow and solid-loading conditions) as a result of the instantaneous particle-wall collisions and the solids sliding over the pipe wall. A mathematical model for the mixture flows is suggested based on a Lagrangian simulation technique. The model results offer additional insight into the dynamics of this complex flow and agree well with the new laboratory data.

The calculation of the hydraulic gradient due to the upward flow of a large size particles—water mixture in a vertical pipe is a central problem in the design of systems for deep-sea mining of manganese nodules. Here, the problem is investigated experimentally and with a new calculation method. An experimental apparatus that mimics the deep-sea mining system was built to measure the hydraulic gradient due to the mixture upward flow, the settling velocity of a single manganese nodule, and to explore the relationship between the concentration of fluidized manganese nodules and the solid slip velocity. Experimental relations are found. Also, a formula to compute the total hydraulic gradient of the mixture flow under different flow and solid-loading conditions is developed; the formula accounts for the hydraulic gradients produced by the liquid phase, the solid phase, and the inter-particle collisions. The predictions obtained with the derived equation are compared with experimental data readily available and with the newly acquired laboratory data; these predictions agree very well with the empirical data and demonstrate the value of the model as a design tool.@DOI: 10.1115/1.1641385#