Mathematical Modelling of an Annealing Furnace for Process Control Applications

Transcription

1 Mathematical Modelling of an Annealing Furnace for Process Control Applications N.Depree 1, J.Sneyd 2, S.Taylor 2, M.P.Taylor 1, M.O Connor 3, J.J.J.Chen 4 1 Light Metals Research Centre, University of Auckland, New Zealand. 2 Department of Mathematics, University of Auckland, New Zealand. 3 New Zealand Steel Ltd, Mission Bush Rd, Glenbrook, New Zealand. 4 Chemical and Materials Engineering, University of Auckland, New Zealand. Keywords: Steel, Furnace, Modelling, Optimisation, Continuous Galvanising Abstract Optimisation and improved control of the annealing furnace on a continuous galvanising line was investigated by the construction of a series of mathematical models to predict furnace and strip temperature and strip recrystallisation under both steady and transient states. A modelling approach is followed due to the very poor measurability of temperatures inside the furnace, affected by strong reflected radiation. A 3D Model is used to investigate the temperature distribution of the steel strip and the furnace thermocouple probes, and information from the 3D model enables the construction of a highly simplified 1D/2D model. Combining the 1D/2D model with a steel recrystallisation calculation allows the system to be used for rapid simulation of furnace operating conditions. This is applied to the most common products processed on the plant, resulting in identification of several opportunities for increased production rate and increased energy efficiency. Introduction The metal coating line (MCL) at the New Zealand Steel company (NZS) relies on a large continuous electric radiant furnace to heat treat steel strip before hot-dip galvanising. The temperature evolution of the strip inside the furnace is vital to ensure the specified mechanical properties are met for a range of steel products including both high temperature (recrystallisation) and lower temperature (recovery) heat treatments. Strip dimensions and processing conditions are changed often due to the wide range of product types with short production runs required in the small NZ market, causing the furnace to be in a transient temperature condition up to 50% of its operating time due to its high thermal mass. Figure 1: Furnace schematic diagram showing location of Pyrometers IR1-4 and L1-L4, Induction Pre-heaters B1-C4 and Contact Thermocouple Accurate control of the strip temperature is difficult because of poor measurement capability of the pyrometers and thermocouples in the furnace, due to the strong reflected 267

2 radiation in the furnace cavity. The in-situ strip temperature pyrometers IR1-4 and L1-4 shown in Figure 1 commonly read up to C higher than the actual strip temperature as measured using a gold-cup pyrometer probe to exclude reflected radiation [2, 7]. At only one location (L1) it is possible to measure the strip temperature within a range of C higher than actual temperature due to improved installation design and location of this pyrometer. Furnace thermocouples are also affected by radiative heat transfer, being cooled by the strip passing below, causing thermocouples to read lower than the adjacent actual furnace wall temperatures. This cooling affect has been estimated to be 20 C or more by previous investigations [3, 10]. Poor understanding of furnace and strip temperature results in situations where the strip is under- or over-heated, resulting in undesirable product properties and energy wastage. This is especially problematic in transient temperature operation during changes from one product type to another with different dimensions or required heat treatment temperature. Manual furnace control combined with high thermal mass and complex temperature responses lead to large amounts of lost production due to incorrect heat treatment. Control of the furnace can be improved by modelling using fundamental heat transfer equations. This allows rapid simulation of various control alternatives to provide settings which maximise production rate, reduce energy consumption, and maintain appropriate heat treatment of the strip. Furnace Design The NZ Steel MCL Annealing furnace is a single-pass, electrically heated furnace installed in It is approximately 160m long, comprising 12 heating zones for the first 68m, and 8 longer cooling zones for the last 89m as shown in Figure 1. Radiant electric heating elements are installed in all zones, with 346kW heating capacity in the heating zones, mounted above and below the strip, and kW capacity in cooling zones, mounted below the strip only for total electric heating capacity of 4.6MW. Cooling zones also contain steel cooling tubes through which ambient air is passed to indirectly cool the strip Additional furnace equipment includes induction preheaters of 3MW capacity used to heat the strip immediately prior to furnace entry, and gas jet coolers used for rapid cooling of the strip by direct air jets in zone 14 only. There are thermocouples mounted inside sheaths projecting into the furnace cavity in each zone, and several pyrometers (L1-4, IR1-4) measuring strip temperature, however each of these is affected by reflected radiation as described above. Accurate strip temperature measurement is only available immediately prior to furnace entry, after the preheaters, using a retractable contact pyrometer which is manually actuated when required. Model Development The furnace system was first investigated using a 3D finite-element model created with COM- SOL Multiphysics software. This method enabled a model with minimal simplification of the furnace system, with 3D representations of the complex internal geometry of the furnace, including the heating elements, hearth rolls, cooling tubes and thermocouple probes. The model geometry and types and locations of heat transfer equations used are shown in Figure 2. The 3D model showed good agreement with measured thermocouple temperatures, 268

3 and predicts strip temperature within the expected offset below the recorded L1 pyrometer temperature. Figure 2: Location and types of heat transfer calculations performed in the COMSOL 3D model The 3D model was used to investigate the temperature effects described previously, such as the increased heating of strip edges. The strip edge heating effect, as shown in Figure 3, was approximately +20 C for both high and low temperature heat treatments, but up to +30 C when considering further additive effects such as thinner and rougher edges caused by the cold rolling process. This is an important consideration for low-temperature heat treatments (recovery only) where the higher edge temperature may cause localised recrystallisation and softening, forming wavy-edge defects in the product strip. The long solution time of approximately 9 hours for the 3D model however precludes its use for furnace optimisation by rapid simulation of control alternatives. The reduced-dimensionality heat transfer model with coupled metallurgical calculation (RDHT-CM model) was developed by simplifying the system as a 2D furnace body and 1D strip, with simple 1D radiative heat transfer equations and energy balances. Furnace and strip temperatures are solved using finite difference approximations to the conduction heat equation, with strip movement simulated by advection of heat in the direction of strip movement. The model schematic is shown in Figure 4, as compared to the 3D model in Figure 2. The RDHT model uses similar equations to the 3D model, and also uses a variable mesh spacing to allow correct prediction of the wall temperature response in transient simulations. The RDHT model is written using MATLAB software, and solves steady-state solutions within 10 seconds on a desktop computer. This allows it to be maintained by NZ Steel engineers, or translated to code suitable for inclusion in NZS systems. Transient model solutions are significantly faster than real-time, so that solutions could be implemented for continuous shadowing of furnace operation with prediction of current strip temperature and metallurgical condition. The simplified geometry in this model means that it cannot be used 269

4 Figure 3: 3D Model result showing edge heating effect of +20 C for mm 300MPa product for investigating spatial temperature distribution, such as strip edge heating and thermocouple probe cooling as in the 3D model. Figure 4: Schematic diagram showing geometry of the RDHT model, and the type and location of heat transfer equations used The RDHT temperature model is coupled to a simple metallurgical model, where the progressive recrystallisation of the steel strip is calculated down the length of the furnace. The recrystallisation model is based on the Arrhenius (Equation 1) and Avrami equations (Equation 2) further developed for recrystallisation during hot-rolling by Sellars et al [1, 9], Medina et al [4, 5, 6], and previous work by BHP [8]: t 0.5 = A ɛ p ɛ q D s exp Q rex ( ( ) RT n ) t X v = 1 exp t 0.5 (1) (2) 270

5 Where: t, t 0.5 = time, time required for 50% recrystallisation T = Strip Temperature R = Gas Constant ɛ = initial strain in steel (cold reduction) ɛ = strain rate during rolling D = steel initial grain size before rolling Q rex = Activation energy for recrystallisation X v = volume fraction recrystallised n = Avrami constant A, p, q, s = empirical constants The metallurgical model equations take into account the range of processing conditions experienced by different steel products and grades used at NZ Steel, including the activation energy for recrystallisation of the steel, which is a function of the steel chemistry including the process variation in content of C, Mn, Si, Mo, V and Nb. The recrystallisation equations and empirical constants are fitted to the steel types in use by NZ Steel using laboratory-conducted recrystallisation temperature experiments, and integrated into the strip temperature equations in the RDHT model. Model Results Typical temperature output from the RDHT-CM model is shown in Figure 5 for the mm strip product undergoing a full recrystallisation heat treatment to produce a ductile strip with 300MPa tensile strength. Results are presented at each furnace zone rather than distance down the furnace. The first 12 heating zones are approximately 68m long, and the final 8 cooling zones 89m long, as shown in Figure 1. The temperature results from the model show good agreement with the measured furnace thermocouple temperatures, with the understanding developed from the 3D model that model results of furnace wall temperature should be higher than the measured thermocouple temperature. The model strip temperature also agrees with the measured L1 pyrometer temperature shown, where the predicted temperature should be in the range of C below the recorded pyrometer temperature. The metallurgical model results in Figure 6 are as expected for a full recrystallisation heat treatment, where the calculation predicts that 100% recrystallisation is achieved in the furnace. Note that recrystallisation does not start occuring until the strip temperature rises above approximately 600 C, and then progresses rapidly to 100%. The calculation also provides a range of uncertainty on the calculation (RX min and RX max curves) due to variation in calculation input parameters, such as the initial steel grain size and variation in chemical composition etc. As the production rate (tonnes/hr) is fixed by the product dimensions and the MCL linespeed, the furnace power usage from the RDHT model is combined with plant measurement of preheater power usage to give the total specific heating energy requirement (kwhr/t) for any given product. The coupled metallurgical model is used to find the minimum strip 271

6 Figure 5: Temperature results for RDHT-CM model simulation of mm strip at 140m/min linespeed Figure 6: Recrystallisation results for RDHT-CM model simulation of mm strip at 140m/min linespeed temperature and hence the amount of heating power required for any product to achieve complete recrystallisation, or in the case of unrecrystallised products, ensures strip temperatures are not high enough to cause recrystallisation. Furnace Control Simulation and Optimisation Results The RDHT-CM model is used for rapid simulation of furnace operation and control. This model was applied to common MCL products, representing over 50% of total annual production, to simulate the existing situation as well as a number of alternative possible control schemes for each product. This primarily involves alternatives with faster or slower strip speeds, directly affecting plant throughput, or different combinations of heating from the induction preheaters and the furnace electric heaters, which affects the overall heating power and energy efficiency. The model results from this investigation showed that in general, increased strip speed 272

7 Table 1: Comparison of selected alternatives for mm 300MPa Strip Measurement 130m/min 140m/min 125m/min Strip Entry Temp, C Electric Heating, kw Preheating, kw Recrystallisation 100% 100% 100% Production Rate, T/hr Specific Energy, kwhr/t gave both higher production rate and also improved energy efficiency in cases where the induction preheaters were not required, typical of thin-gauge products and low temperature (recovery only) heat treatments. For cases such as thick gauge products, or high temperature heat treatments (causing full recrystallisation) utilising the induction preheaters, it was found that the preheaters are very inefficient, and large increases in energy efficiency could be realised by reducing strip speed to a point which does not require preheating to maintain the desired heat treatment. Table 1 shows several simulations for one product type, where alternatives to the base case of 130m/min strip speed were found which enabled either higher production rate (at 140m/min) or increased energy efficiency at the expense of reduced production (125m/min). Conclusions Temperature prediction capability for the NZ Steel MCL annealing furnace has been improved by developing a full 3D model of the furnace to examine strip and furnace temperature measurements, which are strongly affected by reflected radiation. The 3D model allows investigation of the effects of reflected radiation on the existing temperature measurement devices, and understanding of the temperature distribution within the furnace. This enabled the construction of a simplified model which is able to solve quickly and efficiently the heat transfer equations using a finite difference method. This RDHT-CM model numerically solves PDEs representing 1D strip and 2D furnace walls, as well as simple radiative heat transfer equations and energy balances. This was shown to agree closely with the furnace and strip temperature results from the 3D model, and is capable of rapid solution of steady state and transient simulations of the MCL furnace. This RDHT-CM model is coupled to a metallurgical model to calculate strip recrystallisation during the heat treatment process, which has been fitted to the steel types in use at NZ Steel using laboratory results of recrystallisation temperature. The RDHT-CM model was applied to the most common products processed by the MCL furnace, comprising over 50% of total production. It was able to predict furnace temperature and strip temperature and recrystallisation for any operating conditions, and is used to rapdily simulate alternative options to find cases with increased production rate or energy efficiency. It was found that for strips not requiring pre-heating, it is both more energy efficient and more productive to run the strip at the highest speed possible, applicable to thin-gauge and high strength products which do not undergo recrystallisation. For pre-heated products, such as heavy-gauge or ductile products that require recrystallisation, it was found that productivity can be increased while maintaining the desired heat treatment, however increasing 273

8 energy efficiency requires lower line speeds to reduce the need for pre-heating. The model is also able to simulate transient temperature situations, such as changes to strip dimensions or heating temperatures, which can be difficult for operators to manually control, resulting in product wastage due to incorrect heat treatment. Simulation of these changes in advance will assist operators in adjusting furnace controls appropriately, or the model may be integrated into a dynamic control system. The model is also suitable for maintenance and modification by NZ Steel engineers if required due to the accessibility of the programming language and the fundamental heat transfer equations used. References [1] Barraclough, D., and Sellars, C. Static recrystallization and restoration after hot deformation of type 304 stainless steel. Metal Science, 13 (1979). [2] Jinks, D. Pyrometer temperature measurement for horizontal annealing furnaces. the experience at NZ Steel. BlueScope Steel TechNote BSR/N/2004/045 (2004). [3] McGuinness, M., and Taylor, S. Strip temperature in a metal coating line annealing furnace. Australian and New Zealand Mathematics in Industry Study Group, [4] Medina, S., and Lopez, V. Static recrystallization in austenite and its influence on microstructural changes in c-mn steel and vanadium microalloyed steel at the hot strip mill. ISIJ International 33, 5 (1993). [5] Medina, S., and Mancilla, J. Static recrystallisation modelling of hot deformed steels containing several alloying elements. ISIJ International 36, 8 (1996), [6] Medina, S., and Quispe, A. Improved model for static recrystallisation kinetics of hot deformed austenite in low alloy and nb/v microalloyed steels. ISIJ International 41, 7 (2001). [7] Morrison, B., Jinks, D., and Edmonds, I. NZ Steel MCL furnace - gold cup temperature measurements. BlueScope Steel TechNote SRL/N/2003/038 (2003). [8] Renshaw, W. A recrystallisation model for continuous heat treatment of low carbon aluminium killed steels. Tech. Rep. BHPR/SF/R/011, The Broken Hill Proprietary Company Ltd, [9] Sellars, C., and Whiteman, J. Recrystallisation and grain growth in hot rolling. Metal Science, 13 (1979). [10] Wang, S. Radiative heat transfer analysis. Work in progress,