Modeling of Steelmaking Processes - Steel Making - Lecture Notes, Study notes of Metallurgy

Download Modeling of Steelmaking Processes - Steel Making - Lecture Notes and more Study notes Metallurgy in PDF only on Docsity! Lecture 38 Modeling of steelmaking processes Contents Introduction Physical model Design of a physical model for fluid flow in steel melt Key words: Physical modeling, water modeling, tundish metallurgic Introduction With the globalization, steel market has become competitive both with respect to quality and cost of steel. Steel industry is required to produce quality steel at a reasonable cost so that it remains competitive with the world market. For this purpose constant and continuous efforts are required to introduce either new steelmaking technology or to improve the process technologies in the existing steel processing vessels like converter, ladle, continuous casting tundish and mold. In order to meet these objectives, a sustainable research and development activities must 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 model of the actual process (here after we call proto type) so that specific studies can be made. The results of these studies can then be implemented for the desired objectives. A model of the process can either be physical or mathematical. The present lecture deals with some issue related to design of physical models of steelmaking processes. Physical model In physical modeling, the model reactor and experiments are designed based on the similarity criteria between the prototype and model. Both, model and prototype, must be similar geometrically, dynamically, chemically and thermally. Two systems are said to be geometrically similar when for every point in the model, there exists a corresponding point in the prototype. This can be achieved by maintaining a constant ratio between the linear dimensions of the systems. This is called scale factor λ. λ = Dm Dp = Lm Lp (1) The above relation suggests that two systems following the geometrical similarly should have the same aspect ratio of the vessel . The value of scale factor indicates how big or small model would be. For example, a scale factor of 0.2 means that diameter of the model cylindrical vessel is 1 5⁄ of the diameter of the actual vessel, if the actual vessel is cylindrical in shape. For a rectangular vessel all the linear dimensions of the model vessel are 1/5 of the actual ones. Docsity.com Dynamic similarity requires that the corresponding forces acting at corresponding time and location must bear the same ratio between the model and the prototype. In steelmaking the inertial, viscous and surface tension forces are of relevance. The ratio between inertial and viscous force is called Reynold’s number Re = inertial force viscous force = ρ uL μ = uL γ (2) Where u is velocity, L is characteristic linear dimension and γ is kinematic viscosity. Reynold’s number characterize the type of flow, that is whether laminar or turbulent. The ratio between inertia and gravity force is Froude number (Fr) (Fr) = u 2 gL Modified Froude number 𝐹𝐹𝐹𝐹1 is more relevant than simple Froude number Fr1 = ρg u 2 �ρl−ρg �gL = aerodynamic force gravitational force (3) ρg is the density of gas and 𝜌𝜌𝑙𝑙 is density of liquid. Froude number determines the importance of aerodynamics force and gravitational force when gas jet either impinges the bath or submerged into the bath. Froude number similarity is very important to model the chemically active or inert gas injection in steelmaking processes. Weber number (We) is the ratio of aerodynamic to surface tension force We = ρu 2L σ (4) σ is surface tension of liquid. The dynamic similarity requires Rem = Rep (5) Frm = Frp or Frm1 = Frp1 and (6) Wem = Wep (7) The similarity in Reynold’s number requires that, uom uop = γm γp × 1 λ (8) The subscript m denotes model and p denotes prototype. The similarity in Froude number requires that. uom uop = λ0.5 (9) And Weber number requires that, Docsity.com