SYSTEM FOR INDIRECT MEASUREMENT OF THE HEAT FLOWS A T ANNEALING OF THE STEEL COILS

Abstract The temperature of the thermal processed products i s the main variable which designates their quality and energy consumption. In aspect of the st e l coils annealing quality is necessary to known temperature inside the object. It is the plac e with the lowest temperature during annealing process. This paper deals about proposal of the “Sy stem of indirect measurement of the heat flows” in the steel coil. This system provides in t he real time information about behaviours of the inner temperatures in the coil during annealing process based on indirect measurement of the heat flows. Indirect measurement of the heat flows is based on direct measurement of the temperatures on protective hood, atmosphere tempera tur nd direct or indirect measurement of coil’s surface temperatures. This system was verifi ed in laboratory conditions. Proposed system for indirect measurement of the heat flows is exten sio of the system for indirect measurement of the inner temperatures based on direct measured atmosphere temperature.


Introduction
The annealing process is one of the important operations in production of cold rolled steel sheets, which significantly influences the final product quality of cold rolling mills.In this process, cold rolled coils are heated slowly to a desired temperature and then cooled.Modelling of annealing process (prediction of heating and cooling time and trend prediction of coil core temperature) is a very sophisticated and expensive work.Modelling of annealing process can be done by using of two-dimensional thermal models [1,2,3].Information about heat flows behaviour that fall down on heated batch is important in energetic aggregates at calculation of the heat losses, balance computations of furnaces, but also for indirect measurement of the inner temperatures at annealed batch.Heat flows can be estimated by direct with a sensor or indirect (with calculation) from another direct measured process values [4,5].In term of annealing quality of steel coils is necessary to know temperature in the batch's body, same place with a lowest temperature during annealing process [6,7].In this paper is presented comparison of two methods for indirect measurement of the heat flows at application on annealing process of the steel coils.This comparison is in term of estimation's precision of annealed coil's inner temperatures.DOI  Inputs into first method are measured temperatures on protection cover of the bell furnace and on surface of annealed coil.Inputs into second method are measured temperatures on a coil's surface.Both methods were verified with measurements performed in laboratory conditions.

Material and experimental methods
Utilized two methods for presented indirect measurement rise from elementary balances method.This method rises from dividing of the object into elementary cuboids (blocks).For each elementary cuboid is formulated balance equation and from way of its solution is possible to create explicit or implicit algorithm of the heat field's solution.This partition on elementary cuboids can be equable or unequal.However surface cuboids should have half volume and corner cuboids quarter volume.On Fig. 1 is depicted scheme of the batch partition (steel coil) into equable cuboids.At centre of each cuboid is centralized weight and temperature.At solution we regarded two dimensional temperatures field with heat energy's diffusion in direction of the axis x and y [8,9,10].

Fig.1 Steel coil´s partition into elementary cuboids
Volume of the inner elementary cuboids at two-dimensional object is following: For surface elementary cuboid of two-dimensional object in direction of y axis is valid: For surface elementary cuboid of two-dimensional object in direction of x axis is valid: And for corner elementary cuboids of two-dimensional object is valid: Where V i,j -volume of elementary cuboid at point i, j In case of two-dimensional object we regard distance ∆z = 1 m.
In accordance with orientation of the heat flows where: on the top surface fall down heat flow density marked as q oj,1j , on the left surface fall heat flow density q io,i1 , from right surface is resultant heat transfer by radiation and convection expressed with heat flow density q in,in+1 and from low surface is resultant heat transfer by radiation and convection expressed with heat flow q mj,m+1j , where α is overall coefficient of the heat transfer, we can define heat flow density between elementary cuboids after time period ∆τ by following: For elementary cuboids are valid following balance equations: Where: T i,j -temperatures at node points i, j (i = 1,...,m, j = 1,...,n), where m is a count of elementary cuboids in direction of axis y and n is number of elementary cuboids in direction of x axis [K], q ij,ij+1 -heat flow density between elementary cuboids with temperature T i,j and T i,j+1 [W.m -2 ], λ ij,ij+1 -heat conductivity between elementary cuboids with temperature T i,j and At solution two-dimensional temperature field was regarded with diffusion of thermal energy in direction of axis x and y at following margin conditions.Margin conditions can be divided into initial and boundary.At the first method at calculation of heat flow density rise from boundary condition of second type and in the second method from boundary condition of the first type [11,12,13].Both methods were verified on laboratory measurements.At verification was created laboratory steel coil as physical model.His thermophysical properties are shown in Tab. 1.Chemical composition of the steel is 0.08 % of Carbon and 0.4 % of Manganese [14,15,16,17].
Where: q S+K -heat flow density by radiation and convection [W.m -2 ], α -coefficient of the heat transfer [W.m -2 .K -1 ], T p -temperature of the cover (bell) [K], T a -temperature of the atmosphere [K], T z -temperature of the coil surface at the each node point [K], σ -Stefan-Boltzmann constant [-], ε -effective coefficient of the heat radiation.
Coefficients of radiations depend on surface and coefficients of the material's radiation where exchange of ration is incoming.When these parameters are incorrect estimated then will incorrect calculated density of the heat flow, so calculated (indirect measured) temperatures on surface and in batch inner can be loaded with error.For elimination of errors was introduced corrective coefficient of radiation marked as K, that after multiplying with radiant part decrease difference between measured and simulated temperature.
At simulation we assume space division between cover and coil into seven zones (Fig. 2).For these zones were corrected by simulation coefficients K 1 , K 2 , ..., K 7 , in order to decrease relative errors between measured and simulated temperature.At correction of coefficients was regarded its dependency on average temperature between the cover and the coil.

The second method
At this method was elementary balances method modified for boundary condition of the first type where input to this method were directly measured temperatures on the coil's surface.By utilization of elementary balances method was simulated temperature field inside the coil.After acquisition of the temperature field at everyone time step ∆τ was calculated heat flow flatling on the coil's surface at everyone node point thus in everyone surface elementary cuboid.For adequate silken partition of the object into elementary cuboids we consider that density of the heat flow flatling on corner of the object is equals in direction of axis x and y.Orientation of the heat flows density is depicted on Fig. 1 where solution of the heat field rises from system of equations ( 6).The results are equations ( 9) for calculation of the heat flow density.
For corner elementary block with index i = 1, j =1 is heat flow density: For corner elementary block with index i = m, j =1 is heat flow density: For corner elementary block with index i = 1, j =n is heat flow density: For corner elementary block with index i = m, j =n is heat flow density:  For surface elementary blocks with index i = 2,3, ...,m-1, j = 1, is heat flow density: For surface elementary blocks with index i = 2,3, ...,m-1, j = N is heat flow density: For surface elementary blocks with index i = 1, j = 2,3, ...,n-1 is heat flow density: For surface elementary blocks with index i = m, j = 2,3, ...,n-1 is heat flow density: After substitution into equations (9) we get from the model at boundary conditions of the first type heat flow density flatling on the coil surface at the each surface elementary cuboid.This density inputs into heat field calculation at boundary conditions of the second type, like at the first method.So as the first method so at the second method we consider, that heat flow density ( 7) is flatling on the coil and this density may be effected by error at incorrect estimation of the radiation parameters.This problem we solve by application of the corrective coefficients K, that were determined for everyone node point especially: Where q is heat flow density calculated by equations (9).At calculation we consider dependency of the corrective coefficients on average temperature between the cover (bell) and the coil.Simulations were performed on the second laboratory measurement.

Results and discussion
Deviations of the single measurement for the first and the second method were expressed by calculation of relative error [18,19,20,21]:

Conclusion
In this paper is semi finished methodics for indirect measurement of the heat flows density impinging on annealed batch.Indirect measured heat flow densities inputs to the elementary balances method, which calculates heat field of annealed batch during annealing process.In term of annealing quality is needed, so that the batch in the total volume achieves recrystallization temperature.Calculated heat field of annealed batch gives information about this temperature.There were prepared two methods that solve calculation of heat flow density from two terms with a different initial boundary condition included in calculations.After performed simulations on data from laboratory measurements we can state, that the first method is preferable for creation of indirect measurement system of the heat flows.At this method found corrective

Fig. 2 Fig. 3
Fig.2 Positions of thermocouples in a cut of the coil

Fig. 4 Fig. 5
Fig.4 Temperature T 4 from the second measurement

Fig. 6 Fig. 7
Fig.6 Temperature T 3 from the second measurement

Table 1
Thermophysical properties of annealed steel 2.1 The first methodAt solution with conditions of the second type the total density of the heat flow was calculated by following equation: DOI 10.12776/ams.v19i2.95p-ISSN 1335-1532 e-ISSN 1338-1156

Table 2
Comparison of relative error

Table 3
Comparison of the relative error at the second method