Dimension Reduction Analysis Of Heat Transfer On Blast Furnace Hearth Erosion

Blast furnace is a very important equipment in steel production. It takes huge cost to build a blast furnace or maintenance it. Blast furnace hearth is the reactor of hige temperature melted iron and it is made up of Refractory lining of laying body, Coolers and Steel shell. Because the blast furnace hearth directly contacts with high temperature melted iron, so it is inevitable to be eroded. The chemical and physical impact, flow scour and thermal expansion of the structure make erosion and damage to the lining, and it will get worse with the time extension of steel production. If the erosion reachs a certain degree, the blast furnace hearth will burst and it is a very serious accident. If the factory stop using the blast furnace too early, it will be waste.On the basis of heat transfer, a mathematical model can be established. This is a very useful method to use the computer as the tool to make numerical calculation in the blast furnace safety production. The corrosion will destroy the original approximate axis-symmension and complicate the shape of the container. Since the increase of complexity of geometry leads to the increase of complexity of computation, when solve this kind of inverse problem numerically a lot of direct problems with flexible boundary often need to be solved. Especially, when deal with a high-dimension problem,the sick increase of complexity and amount of computation lead to great difficulty in solving the problem.A combination of perturbation method and expansion with eigenfunction is a new method to solve high-dimension erosion problem. It can transfer high-dimension problem into low-dimension problem. Through perturbation method, the problem can be transfered into a problem with fixed boundary and axis-symmetric domain. Then the boundary condition is not axis-symmetric and expansion with eigenfuncton can be used to transfer it into a group of lower-dimension problems. Using this method, a two-dimension problem with unknown boundary can be transfered into a group of one-dimension axis-symmetric problems. So the difficulty of geometrical complexity and high-dimension caculation complexity can be solved.In this paper, the perturbation method is used and parametric computer program with MATLAB is made to reduce the dimension of the problem. This paper gives the precision boundaries through the examples under different hearth and different thermal parameter. Then points out the shortage of the perturbation method in judging sunk erosion. When the error is big, this paper gives two precision correction methods through a lot of examples:artificial cooling correction and boundary moving correction. Then checks the feasibility of the precision correction methods through examples and it is a improvement of the perturbation method. At last, this paper gives the erosion form construction method on the basis of database in the cross section of the hearth.