Transport phenomena and penetrability of solid particles in hot metal during lance injection

Abstract

The transport phenomena in injection lance and the penetrability of solid particles into liquid metal at the lance tip during injection treatment was analysed by a one-dimensional mathematical model developed in this work. Mechanic interactions and heat transfers between a solid particle, carrier gas, lance and/or hot metal have been incorporated in the model. Temperatures and velocities of carrier gas and solid particles were examined for a typical hot metal desulphurisation process by granulated magnesium injection. The temperature of gas increases by several hundred degrees, while that of solid magnesium particles only by several degrees in the lance. The gas velocity is increased by thermal expansion in lance. At the lance tip, the magnesium particle velocity is slower than the gas velocity. The penetrability of a magnesium particle into the hot metal at the lance tip was analysed.List of symbols C D drag coefficient C g heat capacity of gas, J mol 21 K 21 C p heat capacity of magnesium, J kg 21 K 21 C l p mean value of specific heat including latent heat of vapourisation for magnesium, J kg 21 K 21 D tip injection depth, m F B buoyancy force, kg m s 22 F D drag force, kg m s 22 F G gravitational force, kg m s 22 F I fluid inertia force, kg m s 22 g gravity, m s 22 h g/s heat transfer coefficient at gas-steel interface, J m 22 s 21 K 21 h p/g heat transfer coefficient at gas-particle interface, J m 22 s 21 K 21 h r/e heat transfer coefficient at refractory shellhot metal interface, J m 22 s 21 K 21 H g enthalpy of gas, J mol 21 k Mg(l) thermal conductivity of liquid magnesium, J m 21 s 21 K 21 k shell thermal conductivity of refractory shell, J m 21 s 21 K 21 k steel thermal conductivity of steel, J m 21 s 21 K 21 m p mass of magnesium particle, kg q Mg heat transfer rate from gas to magnesium particles, J s 21 q p heat flux across gas-magnesium particle interface, J s 21 q r heat flux in radial direction, J s 21 q 0 heat flux across gas-steel interface, J s 21 q 1 heat flux in steel, J s 21 q 2 heat flux in refractory shell, J s 21 q 3 heat flux across refractory shell-hot metal interface, J s 21 Q g flowrate of carrier gas, mol s 21 Q Mg feeding rate of magnesium, kg s 21 r p radius of magnesium particle, m r 0 internal radius of steel pipe, m r 1 external radius of steel pipe or internal radius of refractory shell, m r 2 external radius of lance, m r g radius of magnesium vapour bubble, m Re Reynolds number t time, s t p magnesium particle travelling time in lance, s t g gas travelling time in lance, s T g gas temperature, K T p magnesium particle temperature, K T shell temperature in refractory shell, K T steel temperature in steel pipe wall, K T ext external temperature, K T rm room temperature, K T 0 temperature at internal surface of steel pipe, K T 1 temperature at the boundary between steel pipe and refractory shell, K T 2 temperature at lance surface, K v f velocity of fluid, m s 21 Ironmaking and Steelmaking 2010 VOL 37 NO 8 599 v g velocity of gas, m s 21 v m velocity of hot metal, m s 21 v p velo...

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