Determination of Wall Pressure and Stress an Blast Furnace using Finite Element and SPH Method

Transcription

1 Determination of Wall Pressure and Stress an Blast Furnace using Finite Element and SPH Method Mukul Mandal Bhaskar Sengupta Manager, Tech cell Head, Tech cell M&M, L&T Construction M&M, L&T Construction 6 th Floor, Technopolis 6 th Floor, Technopolis Saltlake India Saltlake , India mukulm@lntecc.com bhaskarsg@lntecc.com Abbreviations: FEA- Finite element analysis, SPH Smoothed particle hydrodynamics, DP - Drucker-Prager Keywords: Blast furnace, SPH, Finite element, Drucker-Prager Abstract Distribution of wall pressure and stresses of an iron blast furnace containing granular material is calculated using finite element method. Granular material inside the furnace is assumed as a continuous media and Drucker-Prager elastic, perfectly plastic material model is used to approximate the behaviour or iron ore and pellet inside the blast furnace. A mesh less numerical technique known as SPH method combined with finite element method has been adopted to solve the governing equations using explicit integration scheme. Model takes into account internal friction inside the bulk material. Interaction between bulk material and steel wall is modelled using a frictional interface with proper co-efficient of friction between them. An attempt is also made to study dynamic wall stress assuming a continuous flow of burden material inside the furnace. Introduction Blast furnace is large counter current heat exchanger where heat exchange takes place between upward moving hot gases and downward moving charge material. Hot air is injected through the tuyers which are placed circumferentially in the bottom region of the furnace. Charge materials consisting iron ore and coke are fed through the top of the furnace using CBLT hopper system. Hot air reacts with coke to form hot reducing gas which ascends through the top of the furnace. Reactions takes place between iron ore and hot gases which reduces iron oxide into liquid iron which is then collected in the bottom of the furnace called hearth [1, ]. To meet the requirement of higher production rate, blast furnace size has been increased over the years. At the same time efforts are on to increase the campaign life of the furnace. This leads to better and more efficient design of furnace shell along with other parts. A blast furnace is typically divided into different zones: hearth, bosh, belly, stack, throat and top cone. Furnace wall is made of silica/alumina/carbon block. Circumscribing the furnace wall is a self supported steel shell which gives strength and rigidity to the whole structure. Cooling staves are also supported by this steel shell. Top part of the furnace known as top cone supports the top structure of the furnace. Therefore for structural strength and stability of the furnace this outer shell plays an important role and it should be checked with respect to structural strength. 1

2 Steel shell of a blast furnace is subjected to different types of mechanical and structural loads. Amongst mechanical loads, pressure load due to burden material is an important load to be considered for designing of blast furnace shell. In the current study an attempt has been made to evaluate the pressure and stresses under static and dynamic condition to find areas which need special attention due to high local pressure at the initial design stage of furnace shell. The study is performed in finite element solver RADIOSS using HYPERMESH as pre-processing tool. Process Methodology SPH method has been used for this analysis due to its certain inherent advantages in dealing with large deformation non-linear problems. The study also emphasizes in deriving the material model for burden material. The burden is essentially a granular material with zero cohesion between the particles. Also internal friction inside the material plays an important role to define behaviour of such material. Drucker-Prager material model (law 1 in RADIOSS) is used here to approximate the behaviour of burden material. A brief description on SPH method and material model is given below. Smoothed Particle Hydrodynamic Method: Smoothed particle hydrodynamic is a mesh free particle method based on Lagrangian formulation. The basic steps which are followed in any SPH method are summarized as below: Geometry creation Node generation Shape function based on nodes in a local support domain Discretized system equations Solution of field variables Post processing The method uses the same basic approach followed in any finite element analysis except in mesh generation and approximation of field variables using shape functions. Instead of generating mesh the problem domain is represented using a set of independent points known as SPH particles and then kernel and particle approximation is applied to approximate the field variables and its derivatives. The discrete equations are then formulated to solve for the unknown field variables. For details of SPH formulation refer to reference [3, 4].

3 Drucker-Prager Material Model: In material with internal friction such as sand, soils, rocks and concrete the slip surfaces are rough and the shear stress needed to activate slip is affected by the stress normal to the slip plane. For such materials, often called pressure-sensitive materials, it is not possible to neglect the effect of the first invariant I1 on the yield condition. This pressure sensitive yield criterion is known as Drucker-Prager yield criterion which can be describes using the equation below: f I, J ) = αi + J τ 0 (1) ( = In which α and τ0 are material parameters and J is the second invariant of the deviatoric stress. Drucker-Prager yield criterion is modified Von-Mises yield criterion which states yield occurs when second deviatoric stress invariant reaches a critical value. It is pressure independent whereas Drucker-Prager yield criterion states that plastic yielding begins when the invariant of the deviatoric stress tensor and the hydrostatic pressure reach a critical combination given in equation 1. The yield surfaces for both criterions are illustrated in figure 1. s s 1 = s = s 3 Drucker-Prager Von Mises s 1 s 3 Figure 1: Drucker-Prager and Von-Mises yield surface The material parameters which define the behavior of the above model needs to evaluated using shear and compression test of iron ore. This has been kept as a future scope of this study. For the current study the material parameters are taken from reference 1. The yield function described by equation 1 can be rewritten as a function of pressure (p) and Von-Mises stress as given in reference [5]: 1/ [ 3( a + a p + a )] 0 f ( I1, J ) = σ vm p = () Where a0, a1, a are yield surface parameters and svm is provisional Von-Mises flow stress which is in terms of principal stress becomes: σ vm = ( σ σ ) + ( σ σ 3) + ( σ 1 3 σ1 ) (3) 3

4 Following material properties are used for the current analysis which is taken from reference [5]. G (MPa) K (MPa) a0 (Pa ) a1 (Pa) a E Relation between pressure and volumetric strain is also taken from reference [5]. εv p (KPa) Table 1: Material properties of iron ore material Results & Discussions Two separate analyses have been performed to study the behaviour of steel shell under static and dynamic condition. First study gives the static pressure inside the furnace when it is filled-in with iron ore and coke. In the second part dynamic pressure inside the furnace is evaluated assuming constant inflow and outflow of burden material. Determination of static pressure: Static pressure is calculated when the furnace is completely filled-in with burden material. Burden material approximated as SPH particles are allowed to fall freely inside the furnace under gravity. Instead of filling the material from the inlet of the furnace with zero initial velocity, it was assumed the furnace is pre-filled up to belly height and an initial velocity gh is applied to all SPH particles. This approach saves a lot of computation time because iron ore particles traverse less distance before it comes into contact with the furnace bottom wall. The figure below illustrates the process in details. When velocity of all particles becomes zero which corresponds to static state of the furnace, the pressure inside the furnace is evaluated. 4

5 Iron ore particles Steel shell 0.94 m Simulation start (t=0) Belly 1.85 m Initial velocity 4.3 m/s Bosch Figure : Set-up for static pressure calculation Contour plot for normal contact pressure and Von Mises stress distribution for the steel shell has been given in the below figures when all SPH particles settle down and their velocities becomes zero. Maximum contact pressure is found to be in the bottom and bosh region of the furnace which indicates a major part of the weight is supported by this two zones. Maximum Von-Mises stresses are found in the bosh and belly region because of higher load in this area. Figure 3: Normal contact pressure Figure 4: Von-Mises stress contour Determination of dynamic pressure: The SPH particles are fed through the inlet and the particles are discharged through the annular space in the bottom of the furnace as shown in figure 5. In the bottom central portion of the furnace placed a stopper which restricts the motion of the particles and particles velocities become zero. A zone thus created having zero velocities corresponds to deadman zone of an actual furnace. Inlet velocity and density of the particles are prescribed at inlet. The furnace is assumed to be fully filled with burden material when the analysis starts 5

6 because SPH generation approach to fill the whole furnace takes huge time. The interaction between the particles is automatically taken care by RADIOSS. Iron ore particles are fed through inlet Initial velocity 5 m/s Inlet Inlet Steel shell Belly 1.85 m Bosch Outlet Outlet Figure 5: Set-up for dynamic pressure calculation Figure below shows the contour plot for normal contact pressure and Von Mises stress distribution for the steel shell. Maximum contact pressure is found to be in the bottom region of the furnace which is expected. Von-Mises stresses are higher in the bosh belly transition region because of high normal loads caused due to high burden weight supported by this region. Figure 6: Normal contact pressure Figure 7: Von-Mises stress contour 6

7 Benefits Summary Continuum mechanics approach has been used to solve the problem. Due to large deflection associated with this kind of problem mesh distortion poses a huge challenge while using conventional finite element method. To counter that problem a mesh less technique has been used. Special capability of RADIOSS is also used to define boundary between bulk material and solid FE mesh. Though simple, the Druck-Prager material model seems to be best suited for this type of material. Challenges Blast furnace being a huge structure the computational domain is large which requiring a large number of nodes/elements to discretize the domain. This poses difficulties related to computational resource requirements in terms of time and cost. Another challenge is to characterize the iron ore and coke material behavior. As the size, shape and composition of this material change their behavior changes drastically that requires material testing to be performed for different type of material. Future Plans Experimental methods to be developed to find the material properties of iron ore and coke. The computational study could be extended to a real size blast furnace with more number of SPH particles. Conclusions A computational method has been used for evaluating static and dynamic pressure inside a furnace. A scaled down model of a furnace has been used to reduce the computational cost. If applied to a real furnace the results can be used as inputs for better designing of a blast furnace. ACKNOWLEDGEMENTS The authors would like to thank Subir Roy, Prashanth Kulkarni of Altair Engineering for their help during the development of this project and submission of paper in the ATC015. REFERENCES [1] M. Geerdes, H. Toxopeus, C. van der Vliet, Modern Blast Furnace Ironmaking, Verlog Stahleisen GmbH. [] Anil K. Biswas, Principle of Blast Furnace Ironmaking, Cootha publishing house. [3] M.B. Liu. G.R. Liu, "Smoothened Particle Hydrodynamics (SPH): An Overview and Recent Developments, Arch Comput Methods Eng (010) 17: [4] G.R. Liu, Y.T. GU, An introduction to Meshfree Methods and Their Programming Published by Springer. [5] Gustaf Gustafsson, "Simulation of Iron Ore Pellets and Powder Flow Using Smoothened Particle Method," Luleå University of Technology, Department of Applied Physics and Mechanical Engineering, Division of Solid Mechanics. 7