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Bubble formation during horizontal gas injection into downward-flowing liquid

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Abstract

Bubble formation during gas injection into turbulent downward-flowing water is studied using high-speed videos and mathematical models. The bubble size is determined during the initial stages of injection and is very important to turbulent multiphase flow in molten-metal processes. The effects of liquid velocity, gas-injection flow rate, injection hole diameter, and gas composition on the initial bubble-formation behavior have been investigated. Specifically, the bubble-shape evolution, contact angles, size, size range, and formation mode are measured. The bubble size is found to increase with increasing gas-injection flow rate and decreasing liquid velocity and is relatively independent of the gas injection hole size and gas composition. Bubble formation occurs in one of four different modes, depending on the liquid velocity and gas flow rate. Uniform-sized spherical bubbles form and detach from the gas injection hole in mode I for a low liquid speed and small gas flow rate. Modes III and IV occur for high-velocity liquid flows, where the injected gas elongates down along the wall and breaks up into uneven-sized bubbles. An analytical two-stage model is developed to predict the average bubble size, based on realistic force balances, and shows good agreement with measurements. Preliminary results of numerical simulations of bubble formation using a volume-of-fluid (VOF) model qualitatively match experimental observations, but more work is needed to reach a quantitative match. The analytical model is then used to estimate the size of the argon bubbles expected in liquid steel in tundish nozzles for conditions typical of continuous casting with a slide gate. The average argon bubble sizes generated in liquid steel are predicted to be larger than air bubbles in water for the same flow conditions. However, the differences lessen with increasing liquid velocity.

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Abbreviations

D :

instantaneous equivalent bubble diameter (mm)

D N :

diameter of nozzle bore (mm)

d :

gas injection hole diameter (mm)

d :

subscript referring to instant of detachment, stage 2

e :

elongation factor, L/D

e :

subscript referring to end of expansion, stage 1

F B :

buoyancy force for a bubble (Newton)

F D :

drag force acting on a bubble from flowing liquid (Newton)

F s :

surface-tension force on a bubble (Newton)

F Sz :

vertical component of the surface-tension force on a bubble (Newton)

f :

frequency of bubble formation (s−1)

f θ :

contact-angle function, f θ=sin θ 0(cos θ−cos θ a )

L :

elongation length at instant of detachment,= e dDd (mm)

P b :

pressure in the bubble (Pascals)

P g :

gas-injection pressure in Eq. [28] (Pascals)

Q g :

gas-injection flow rate/hole (mL/s)

r :

horizontal radius of an ellipsoidal bubble (mm)

Rebub :

Reynolds number of a bubble, uD/v

t :

time during bubble formation

U :

average liquid velocity in the nozzle (m/s)

u :

liquid-velocity profile across the nozzle bore, u(y) (m/s)

ū :

average liquid velocity across the bubble (m/s)

V b :

bubble volume (equal to πD 3/6) (mL)

y, z :

horizontal and vertical coordinate directions (m)

μ g, μl :

molecular viscosity of the gas and liquid respectively (kg/ms)

θ 0 :

static contact angle (deg)

θ a, θr :

advancing and receding contact angles of a forming bubble, respectively (deg)

ρ g, ρl :

density of the gas and liquid, respectively (kg/m3)

σ :

liquid surface tension (Newton/m)

ν :

kinematic viscosity of the liquid,=μ l/ρl (m2/s)

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Authors and Affiliations

  1. the Dow Chemical Company, 77541, Freeport, TX

    Hua Bai (Senior Research Engineer)

  2. the Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 61801, Urbana, IL

    Brian G. Thomas (Professor)

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  1. Hua Bai
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  2. Brian G. Thomas
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Bai, H., Thomas, B.G. Bubble formation during horizontal gas injection into downward-flowing liquid. Metall Mater Trans B 32, 1143–1159 (2001). https://doi.org/10.1007/s11663-001-0102-y

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