Macroscopic flow phenomena play important roles not only for improving productivity and energy efficiency but also for achieving the stable operation in metallurgical and chemical reactors. This review paper deals with flow phenomena of four fluids which are single-phase or multi-phase flow of gas, fine particles, liquid and packed particles. In some previous researches on the multi-phase flow, fundamental equations were derived for a continuous fluid phase and dispersed phases with different types of modeling. However, in this paper, continuous flow was assumed for each phase in the derivation of the equation of motion for obtaining the numerical solution. The model has been applied to the simulation of not only four phase flows but also one to three phase flows. Typical examples for application will be described for several processes.

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To achieve a pulverized coal rate of more than 200 kg/t, a technology is needed by which the combustion zone in front of tuyeres can be properly controlled in terms of the combustibility of pulverized coal. It is, especially, necessary to quantify the combustion behavior inside the tuyeres and raceway. Experiments were conducted on off-line models with and without coke to investigate the pyrolysis and combustion behavior of pulverized coal in order to analyze the influence of blast conditions and coal properties on their combustibility.
(1) The final volatile yield of pulverized coal increases with the rise in blast temperature, and rise in O₂ content accelerates the devolatilization rate.
(2) With the progress of pyrolysis, the pulverized coal became spherical and a large number of pores formed in the particles. Thus the reactivity of char is estimated to be higher than that of coke.
(3) Rising blast temperature is effective to improve the combustion efficiency of pulverized coal in the raceway, presumably a little effective to improve with the addition of steam. O₂ enrichment at constant air ratio requires enhancement of the gas and particle mixture.
(4) Q-factor that determined the final volatile yield can be shown by the blast temperature and C content in coal, and devolatilization rate parameters can also be learned by C content in coal. A practical equation representing the devolatilization rate inside tuyeres with various kinds of coal are presented.

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A two-dimensional mathematical model is developed to describe transport phenomena in a packed bed of coke in front of blast furnace tuyere with and without pulverized coal injection (PCI). The model consists of two sub-models, one is pulverized coal (PC) combustion model in the blowpipe where the turbulent fluctuation in the gas phase is considered and the other is combustion model in the packed bed of coke. In this model coke particles in the raceway are treated as a continuous phase and both phases of gas and coke particles are calculated by using the Eulerian approach.
This model is applied to practical operating conditions. When PC is injected into tuyere, more oxygen is consumed and higher temperature rise appears at the region closer to tuyere tip in the raceway and lower temperature is represented in the coke bed than those of all coke operation. Residence time of PC particles in the blowpipe is quite short, so its burn-off in the blowpipe is very low and the PC particles mainly burn in the raceway cavity. The burn-off of PC particle increases with the volatile matter content, but some particles reach to inner wall of tuyere when high volatile coal is used.

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The motion of solid particles flowing into the raceway and the behaviours of the raceway and deadman were studied on the basis of the flow patterns obtained using a two-dimensional and a three-dimensional cold models. The lower part of the blast furnace consisted of the three characteristic regions, the converging, fast flow region with smooth steam and time lines, the deadman with motionless particles, and the quasi-stagnant region situated over the deadman, in which the particles moved very slowly with zigzag, complicated stream line. The quasi-stagnant region was formed by the particles fed within a small, limitted area near the center at the top of the bed. The radius of the area was expressed as a function of burden descending velocity only. It was suggested that the size of deadman changes depending on whether the furnace operation is carried out with all-coke or injection of pulverized coal. The periodic expansion and contraction of the raceway, therefore, the unstable burden flow in the converging flow channel, occurred when the tuyeres were not inserted into the inerior of the bed. The burden flow became more stable with higher blast gas. The boundary conditions of the fast moving region and deadman around the raceway were discussed. The plasticity theory was applicable to simulate the boundaries of such characteristic regions.

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Solid descending flow due to gravity is frequently applied to industrial processes. Several kinds of models have been proposed like the plug flow model, the potential flow model, the kinematic model, etc. In this study, a viscous flow model based on the Navier-Stokes equation has been developed and was compared with the potential flow and the kinematic models. Both two and three dimensional experimental apparatuses have been constructed to observe the velocity fields.
The concept of solid viscosity was quoted to describe the friction between particles and the value was obtained from the experimental data. Slip boundary condition was used at the wall and the friction between particles and the wall or the dead zone was expressed by the Fanning equation.
Navier-Stokes equation was applied to simulate the solid flow. The good agreement between the observed and computed results was obtained in different scale apparatuses at different solid descending velocities. The computation results gave about 0.07 Pa·s as the solid viscosity of sand particles with the diameter of 0.001-0.002 m. The solid-gas countercurrent flow was also simulated by the Navier-Stokes equation with the same value of solid viscosity.

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In order to comprehend phenomena of particle movement and accumulation around a dead man in a blast furnace, they were modeled by segregation of solids mixture over an inclined heap surface under multi-point feed. Utilizing a two-dimensional vessel, the flow and packing characteristics over the dead man were experimentally and analytically investigated with the lapse of operational time. Thus, varying the feed rate along the heap surface and the composition of the feed mixture, the distributions of the flowing-down velocity and the composition, and its change in the packed zone inside the heap were measured by means of a video system.
According to the experiments, the multi-point feed creates increase in the flowing-down velocity along the heap surface and upwards. In case of a static heap, the fraction of a segregating component of lower flowability such as smaller or denser particles exhibits the maximum along the surface inside the heap and increases with higher initial mixing fraction and lower feed rate. While, in case of a descending heap, the fractional peak shifts downwards and gets broad with higher descending velocity. Those trends become conspicuous with larger difference in particle size and density.
The effects of the feed rate, the feed composition, and the descending speed of the heap were quantitatively explained on the segregation pattern inside the dead man by expanding Shinohara's screening-layer model for one-point feed to the present situation of multi-point one.

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High permeability of the gas and molten materials in the dropping zone of a blast furnace is the major factor for achieving stable furnace operation with high productivity. Basic studies of the flow behaviour of liquids in a packed bed are required to grasp the effect of various operational changes on conditions in the dropping zone.
Experimental work and mathematical modelling were carried out for a liquid flow in the structured packed bed with different size particles which is frequently observed in the dropping zone in actual furnaces. Small particles were introduced into the central region, which was 0.07 m in radius and 0.2 m in height, and coarse particles were packed into the remaining area in order to reproduce the structure in the lower part of a blast furnace. The bed consists of two regions, the central region with small particles and the surrounding region with coarse particles of 6 mm in diameter. A liquid was supplied at the centre of the bed surface and radial distribution of liquid mass velocities were measured at the bottom of the bed. The size reduction of small particles shows a lower mass velocity at the centre, although the liquid profiles exhibit their maximum at the centre. Liquid dispersion in a structured packed bed was modelled by a new method, taking into account the statistical dispersion process and the effect of the physical properties of the liquid on permeability. The model was validated against measured data on the radial distribution of mass velocities and the effect of small particles diameters.

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In the upper part of the dropping zone in a blast furnace, gas and liquid flow upwards downwards and the flow behavior has been investigated by using fixed beds. However, burden continually descends there. In the present work, liquid hold-up and gas pressure loss in fixed and moving beds were measured to examine the effect of solid movement.
(1) Measured pressure losses in both dry beds are smaller than those calculated from the Ergun equation. This is considered to be caused by the following facts: Large ratio of particle to column diameter is chosen (ca. 1/6) so that the influence of particle movement may reach the column inside, and hence the flow near the wall affects pressure loss relatively largely; stainless steel balls used as packing material are of high order of sphericity and have smooth surface.
(2) As solid velocity increases, total, static and dynamic hold-ups (H_t, H_s, H_d) decrease, while H_d/H_t slightly increases. The solid movement increases pressure loss in irrigated bed.
(3) The following empirical correlations for pressure loss in fixed bed ΔP_F, total hold-up in moving bed H_tM and pressure loss in moving bed ΔP_M are obtained:
ΔP_wF/ΔP_dF={(ε–H_tF)/ε}^–1.90
H_tM=2.38(v_S/v_L)^0.188·H_tF^0.420
ΔP_wM/ΔP_dM=1+(v_L/v_G)^0.136{0.895+204(v_S/v_G)^0.669}
where, H_tF: total hold–up in fixed bed,
ΔP_d, ΔP_w: pressure losses in dry and irrigated beds,
v_G, v_L, v_S: velocities of gas, liquid and solid,
ε: void fraction of beds.
These equations reproduce experimental results within errors of ±15, ±10 and ±15%. The last one also reproduces those for fixed bed within an error of ±15%.

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Effective thermal conductivity of metallurgical coke was measured in the temperature range from 100 to 1 400°C by using the laser flash method. Effective thermal conductivity k of coke increased with a rise of temperature, and decreased with an increase of porosity of coke. The effect of radiation in the pore of coke on the value of effective thermal conductivity of coke was very small. The following empirical equation was obtained for the determination of effective thermal conductivity k (W/m K) as a function of temperature T(K) and porosity ε(–) of coke.k={0.973+6.34×10^–3(T–273)}(1–ε^2/3)

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For obtaining the convective heat transfer coefficient between gas and particles at high temperature, heat transfer experiments and mathematical model simulation were carried out both for a single sphere and for a counter-current moving bed. If the radiative heat transfer should be evaluated quantitatively, the convective heat transfer coefficient based on the previously empirical equations reported by Ranz and other researchers were available for the evaluation of convective heat transfer around a single sphere. From the experiments and the mathematical model simulation with heat transfer of the moving bed, the following empirical equation was obtained as the equation for determining the convective heat transfer coefficient in the moving bed.Nu=2.0+0.39Re_ρ^1/2Pr^1/3

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