Lecture 38 Modeling of steelmaking processes

Transcription

1 Lecture 38 Modeling of steelaking processes Contents Introduction Physical odel Design of a physical odel for fluid flow in steel elt Key words: Physical odeling, water odeling, tundish etallurgic Introduction With the globalization, steel arket has becoe copetitive both with respect to quality and cost of steel. Steel industry is required to produce quality steel at a reasonable cost so that it reains copetitive with the world arket. For this purpose constant and continuous efforts are required to introduce either new steelaking technology or to iprove the process technologies in the existing steel processing vessels like converter, ladle, continuous casting tundish and old. In order to eet these objectives, a sustainable research and developent activities ust be carried out in the plant to address the quality issues in the steel product and then to introduce changes in the steel processing line, that is product- process integration approach. One of the research tools is to design the odel of the actual process (here after we call proto type) so that specific studies can be ade. The results of these studies can then be ipleented for the desired objectives. A odel of the process can either be physical or atheatical. The present lecture deals with soe issue related to design of physical odels of steelaking processes. Physical odel In physical odeling, the odel reactor and experients are designed based on the siilarity criteria between the prototype and odel. Both, odel and prototype, ust be siilar geoetrically, dynaically, cheically and therally. Two systes are said to be geoetrically siilar when for every point in the odel, there exists a corresponding point in the prototype. This can be achieved by aintaining a constant ratio between the linear diensions of the systes. This is called scale factor λ. λ = D D p = L L p (1) The above relation suggests that two systes following the geoetrical siilarly should have the sae aspect ratio of the vessel. The value of scale factor indicates how big or sall odel would be. For exaple, a scale factor of 0.2 eans that diaeter of the odel cylindrical vessel is 1 5 of the diaeter of the actual vessel, if the actual vessel is cylindrical in shape. For a rectangular vessel all the linear diensions of the odel vessel are 1/5 of the actual ones.

2 Dynaic siilarity requires that the corresponding forces acting at corresponding tie and location ust bear the sae ratio between the odel and the prototype. In steelaking the inertial, viscous and surface tension forces are of relevance. The ratio between inertial and viscous force is called Reynold s nuber Re = inertial force = ρ ul = ul viscous force μ γ (2) Where u is velocity, L is characteristic linear diension and γ is kineatic viscosity. Reynold s nuber characterize the type of flow, that is whether lainar or turbulent. The ratio between inertia and gravity force is Froude nuber (Fr) (Fr) = u2 gl Modified Froude nuber FFFF 1 is ore relevant than siple Froude nuber Fr 1 = ρ g u 2 aerodynaic force = ρ l ρ g gl gravitational force (3) ρ g is the density of gas and ρρ ll is density of liquid. Froude nuber deterines the iportance of aerodynaics force and gravitational force when gas jet either ipinges the bath or suberged into the bath. Froude nuber siilarity is very iportant to odel the cheically active or inert gas injection in steelaking processes. Weber nuber (We) is the ratio of aerodynaic to surface tension force We = ρu2 L σ (4) σ is surface tension of liquid. The dynaic siilarity requires Re = Re p (5) Fr = Fr p or Fr 1 1 = Fr p and (6) We = We p (7) The siilarity in Reynold s nuber requires that, u o = γ γ p 1 λ (8) The subscript denotes odel and p denotes prototype. The siilarity in Froude nuber requires that. u o = λ 0.5 (9) And Weber nuber requires that,

3 u o = ρ p ρ σ σ p λ 0.5 (10) Weber nuber is relevant when droplet foration occurs in the actual syste. Design of a physical odel for fluid flow in steel elt In steelaking, fluid flow in steel elt controls ixing and ass transfer reactions in converter and ladle. Fluid flow in the tundish of a continuous caster is also iportant to evaluate the perforance of the tundish with reference to its ability to distribute olten steel in all olds at constant superheand to reove inclusions during the process of continuous casting. Experient in full scale size of the steelaking vessel with olten steel is very difficult and pose practical difficulties. Suitably designed odels are very helpful to conduct large nuber of experients to arrive at optiu results. These optiu results can be verified in the prototype selectively. i. Selection of odel vessel The prototype vessels in steelaking are converter, ladle and tundish. Converters and ladles are ore or less cylindrical in shape. Whereas tundish is a rectangular with side walls inclined. Model vessel is designed by geoetric siilarity. A scale factor =1 represents full scale odel. Full scale odels ay becoe difficult to handle since the diensions involved would be large. We select scale factor λ = 0.2for the purpose of illustration. If the industrial ladle has a diaeter of 4, odel vessel diaeter would be 80c, while the aspect ratio (bath height/bath diaeter) for both vessels will be sae. The aspect ratio of industrial ladle is 0.9. Therefore odel bath height is 72c. siilarly we can design odel converter and odel tundish by selecting a suitable scale factor. ii. Selection of odel steel elt phase In order to copare the results of two geoetrically siilar systes it is essential that transport echaniss should be siilar in both the systes. For exaple if flow is turbulent in the prototype then turbulent flow should also prevail in odel liquid. Density and viscosity of the fluid are the two iportant fluid properties that govern fluid flow behavior. Density represents inertia of fluid against an applied force and viscosity is internal friction of fluid. The ratio of density to viscosity, that is γ = μ ρ (11) is called kineatic viscosity of fluid. Kineatic viscosity represents the diffusion of oentu flux into the liquid and governs the fluid flow behavior. Though absolute value of viscosity and density of steel elt ay differ fro the odel liquid, siilarity in kineatic viscosity in both the fluids ensures siilar fluid flow behavior. In this connection water is the fluid whose kineatic viscosity is /s which is very close to that of olten steel elt. Thus water can be selected as odel liquid. In fact water odel has been very widely used to investigate the behavior of steel elt. Soe references are given at the end of the lecture.

4 iii) Selection for odel slag phase It is in fact very difficult to find a low teperature odel slag which is siilar to actual slag. Density of slag in prototype is around 0.4 ties that of olten steel. Slag floats on steel. Transitory and peranent contact of slag phase with olten steel are the principle refining echaniss. In transitory contact, the refining occurs by rising olten slag droplets. Due to large difference in the density of olten slag and steel, transitory contact ode is difficult to odel. Peranent contact ode can be odeled. Several organic oils like paraffin, ineral oil can be used as a odel slag to study the physics of slag/ etal interface. iv) Selection of odel velocity of gas In steelaking processes, gas is used to stirr the olten phases Dynaic siilarity ust be observed between odel and prototype, that (Re) = (Re) p (Fr) = (Fr) and (We) = (We) p Substituting the quantitative value of the diensionless nubers, we get. ρul = ρul μ μ p u2 = u2 gl gl p ρu2 L σ = L ρu2 σ p 12) Fro equations 12 we get for Reynold s nuber siilarity u = γ γ p 1 λ (13) For Froude nuber siilarity u = σ 0.5 σ p (14) For Weber nuber siilarity u = ρ p 0.5 σ 0.5 ρ σ p λ 0.5 (15)

5 The Weber nuber siilarity can be neglected since the inertial forces in the prototype are very large as copared to surface tension forces. Froude and Reynold s nuber siilarity can be obtained in a aqueous odel only when λ = 1. This lecture highlights soe of the iportant aspects of physical odeling of steelaking processes. In the past several years physical odeling or ore precisely water odeling has becoe a very iportant tool to investigate the physical effects in steelaking caused by either ipinging or suberged gas jets. The references are given at the end of the lecture 39.