FONDATĂ 1976 THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. FASCICLE IX. METALLURGY AND MATERIALS SCIENCE N0. 4 – 2010, ISSN 1453 – 083X DIMENSIONLESS NUMBERS IN THE ANALYSIS OF HYDRODYNAMIC INSTABILITY OF INTERFACE STEEL - SLAG AT MICROSCALE IN REFINING PROCESSES Petre Stelian NITA ”Dunarea de Jos” University of Galati email: pnita @ugal.ro ABSTRACT In evaluation of the local hydrodynamics of interface, in steel-slag refining processes influenced by solutal effects, adequate scales of length and time satisfying certain conditions are necessary to get a correct and suggestive image of the weight of factors possible to be used in industrial technologies. These could be obtained based on already established common dimensionless numbers but carefully applied in a specific manner, taking into consideration particularities of the established interface and the main involved process. Based of the general philosophy of building dimensionless artificial conglomerates, a new dimensionless group Ni = Ma ⋅ Bo is proposed in this paper as a consequence of needs to evaluate particularly the effects of capillarity actions at interface, especially of solutal origin, in presence of other physico-chemical and physical actions, especially when the effects of capillarity prevail over all others. KEYWORDS: steel refining, hydrodynamic instability of interface, length scale, time scale, dimensionless numbers. 1. Introduction extend because of the final purpose of the applied treatments which is to provide a certain appreciable Despite the fact that capillarity is recognized as high amount of refined steel, presenting a high level an important phenomenon in hydrodynamics of of purity concerning harmful elements. Oxygen, interface, only extremely rare and more than prudent sulphur and phosphorus are the most frequently target approaches of this subject are present in scientific and elements of treatments applied to steels using slags. technical papers dealing with process at interfaces in Several problems in analyzing the influence exerted metallurgical systems steel-slag. Therefore in the by the presence of surface active solute in the liquid following paragraphs there is a short introduction in phases composing the refining system steel-slag are the specific problems and aspects of this class of analyzed in a simplified manner due to their low systems and this represents an attempt of the author to specific concentrations [1][2]. open in a certain measure new doors in the At low levels of concentrations of surface active fundamentals of some new metallurgical processes of solutes, their influence on density is insignificant, also refining based on the advanced knowledge. As a main the corresponding aspects of buoyancy due to approach, specific dimensionless numbers are variations of density. Up to values of maximal presented and comments are made on the connections concentrations of 2 mass% sulphur in slags and 0.02% with the hydrodynamics of interface steel-slag. mass% sulphur in steel, which are specific to Solutocapillarity plays an important and desulphurization process at industrial scale, there are particular role in the hydrodynamics of interface not reported sensible variations of density in the between liquid phases of technological interest in respective liquid phases, compared to the densities of steel refining under slags. the same liquids in absence of sulphur. Therefore it is The amplitude of the local fluctuations of possible that aspects of buoyancy could be totally concentrations at interface between steel and slag is neglected. limited compared to the possible local fluctuations of The solutocapillarity due to surface tension temperature in other systems or when strong gradients gradient produced by perturbation of concentration is of temperature are imposed externally by special a factor of instability while the surface tension acts to techniques or devices. Supplementary, the depths of stabilize the interface; viscosity, diffusion and the layers of steel and slag are of a certain established gravitation are also stabilizing actions. Viscous - 89 - FONDATĂ 1976 THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. FASCICLE IX. METALLURGY AND MATERIALS SCIENCE N0. 4 – 2010, ISSN 1453 – 083X diffusion acts to dampen the concentration decomposed into normal components (normal stress fluctuations and the associated fluid flow. The gravity and pressure) and a tangential component (shear acts physically to flatten the interface and thus to stress). Boundary conditions at interface lead to the stabilize the deformational perturbations. The following physical considerations [3]: presence of a heavier liquid phase below a lighter one 1. jump in fluid pressure is balanced by interface (as it is the case of steel under slag) is also a tension; stabilizing factor. 2. jump in fluid stress is balanced by surface If it is intended to put in evidence the absolute gradient of interface tension (gradient along the role of the destabilizing factor–solutocapillarity in interface) ∇Sσi . promoting flow, it is necessary that other destabilizing Macroscopic interfacial no-slip conditions break factors or factors damping the solutocapillarity effects when at microscale, processes due to surface tension to be minimized at certain level, bellow a certain gradient, become relevant as magnitude. Analysis of threshold value of the involved parameter. This could this class of processes could be performed in be performed selecting or imposing values of different conditions of the existence of a deformable interface parameters in a physically acceptable range and but which doesn’t deform because of the small weight leading finally to an adequate time scale. Several of factors leading to deformations. This situation general remarks regarding properly named operations could be encountered at least in the incipient state of in scaling and in its preliminary stages and considered flow, or during time intervals where considerations are useful by their close relation with required conditions are accomplished. This is the case the technological and physical reality and utility. In when physical actions producing deformations are not this sense, in an such analysis principle of in acts a dominant in comparison to others. It results that, in certain incertitude; imposing too restrictive conditions conditions of adequate scaling of length and time of to obtain favorable conditions of prevalence of a different actions, computations of parameters certain physical action, compared to another, not only regarding the resulting particular and specific flow are that this could not serve too much, but it could block realistic and possible to be made. the utility of the respective scale. For example, the The known dimensionless numbers are limited as characteristic time scale which is dependent upon the possibilities to give a good image of the physical characteristic length at different powers. These reality in the problems mentioned in title. Several of negative aspects could be totally avoided by a correct them use a characteristic length with a certain scaling operation based on a correct meaning of the specificity which differs from a phenomenon to processes and on an adequate selection of the another (it is well known that there are different dimensionless numbers used in these cases. Further independent scales of length). In fact, the main going there is also the possibility to introduce a new problem in the analysis of local instability produced dimensionless number taking into account the need to by different actions, including the mass transfer of a evaluate the simultaneous complex action of many surface active element, consists in a correct and several forces involved in interfacial flow and specific scaling of length, velocity and time. It is dynamics as it is more and more encountered in known that every physical or physicochemical action literature. is characterized by scales of length, time and velocity which are almost independent among them, but when 2. Dimensionless numbers involved in the actions are simultaneous, the fastest action has the interfacial hydrodynamic instability largest probability to occur. If it is analyzed the occurrence of a certain physical or a physicochemical 2.1 Principles and particularities action it is necessary to scale the time and the Technological systems in steel refining under conditions when it is the dominant action with a slags could be included in the class of complex certain high degree of certitude. This is usually made process of multi-phase flow, where a fluid interface establishing the condition when the time scale is separates immiscible phases, presenting a certain shorter with at lest an order of magnitude, compared surface tension(σ ,σ ) and leading to certain to other concurrent actions. From this condition a steel slag characteristic length scale results, and in certain interface tension(σ i ).The fluid interface is conditions, also a velocity scale results. Other times it deformable, it has an unlimited extend, reported to the is possible to start the scaling from velocity, instead dimensions of the interfacial layer thickness and it is of time and then the characteristic length and time unbounded at wall, that means the interface is in the result on this base. free-slip condition. This is generally valid if the This kind of analysis is often the single way to get friction at interface could be neglected or included in some information on the possible behavior of a other quantified physical factors.