0 Introduction The gasifier furnace body is composed of various refractory bricks and shells. Its temperature distribution not only affects the service life of the fire bricks, but also affects the safe operation of the gasifiers. It is to extend the service life of the fire bricks. Important research topics for safe operation of gasifiers. In this paper, the finite element method is applied to the above complex heat transfer calculations. Compared with the finite difference method, arbitrary nodes and networks can be arranged, which has stronger adaptability and flexibility for complex regional and boundary problems.
1 Mathematical model In the Cartesian coordinate system, for the general three-dimensional problem, the field variable T(x, y, z, t) of the transient temperature field should satisfy the following differential equations in Cartesian coordinates: first, second, third The term is the amount of heat transferred into the microbody from the x, y, and z directions; the fourth term is the heat generated by the heat source in the micro body; and the last item is the amount of heat required for the microbody to heat up. Differential equations indicate that the heat required for the microbody to heat up should be balanced with the heat transferred to the microbody and the heat generated by the microbody heat source.
If it is a constant, equation (1) becomes a simpler formula: =k/c, which is called the thermal conductivity or thermal diffusivity. For a material without an internal heat source, equation (2) becomes a Fourier equation under steady state. ,t/=0, equation (2) is transformed into Poisson's equation. Finally, if q=0, then equation (4) is simplified to Laplace's equation as a special case. If the thermal conductivity changes linearly with temperature, B, In the steady state, when there is no internal heat source, substituting equation (1), we have: Since it is a known constant, the above equation translates to the fact that by transforming the variable t into (k), a non-linear, thermally conductive differential equation can be made. For linearization, analytical solutions can be obtained. In addition, the temperature field distribution in the solution domain should satisfy the boundary conditions.
The boundary conditions can be divided into three types, which are expressed as follows: The boundary temperature T(t) above the boundary is called the first type boundary condition, it is a forced boundary condition, and the heat flux density q(t) is given on the boundary. ), known as the second kind of boundary condition, when q=0, it is the adiabatic boundary condition; the convection heat transfer condition given on the boundary is called the third kind of boundary condition, and the second and the third kind of boundary condition is the natural boundary condition. .
The heat transfer between the outer surface of the furnace shell and the surrounding medium includes natural convection heat transfer and radiative heat transfer. The corresponding heat transfer coefficient can be calculated according to the following empirical formula: Implementation of the finite element method The finite element method is based on variational principle and partial interpolation. A numerical method, which firstly uses the variational principle to transform the differential equation of the required boundary value problem into an equivalent functional variational problem for extremum, and then divides the continuous area of ​​definite solution into finite subunits. And using the partial difference to approximate the variational problem into the multivariate function for the extremum problem, to obtain the linear algebraic equations called finite element equations, which can solve the numerical solution of the original boundary value problem.
The functional of the first type of boundary conditions is the functional of the second type of boundary conditions and the functional of the third type of boundary conditions. In order to discretize the variational problem into a numerical calculation problem, it is necessary to divide the definite solution region (including the boundary). For a limited number of unit regions that do not overlap each other, the shape of the unit can in principle be arbitrary, but the simplest and most practical is a triangular unit. In this way, the variational calculation can be performed in each local grid cell, and finally it is synthesized into the global linear algebraic equations for solving. In the variational calculation of the unit, the selection of the unknown approximation function T is an important problem. The simplest method in the finite element method is the linear interpolation function. As long as the unit is small enough, the error of the linear interpolation function is small enough.
3 Calculation example 3.1 Furnace temperature distribution Using the above mathematical model, the temperature distribution of the gasifier can be calculated under different structural parameters, different lining materials and different furnace temperature conditions. An example of calculating the temperature field distribution of a certain structural gasifier furnace using this model is given below. The calculation conditions are: Outer shell material: Plain carbon steel, thickness 96mm Dome Large flange Material: Stainless steel Gasification furnace Furnace wall temperature: 1300°C～1500°C Gasification furnace ambient air temperature: 20°C Typical Texaco Gasification Furnace structure.
As the temperature of the inner wall of the gasification furnace rises, the temperature of the outer wall rises linearly; ambient temperature changes will affect the temperature of the furnace body of the gasifier, and the ambient temperature is low, then the surface temperature of the gasification furnace coal conversion in 2003 is low; ambient temperature High, then the surface temperature of the gasifier is also high, the actual operation is indeed the case, the theoretical calculation and the actual production data basically in line with.
3.2 Boiler bottom temperature distribution The weight of gasifier stove bricks acts on the bottom of the pan through fireproof brackets. If the temperature of the bottom of the boiler is too high, the mechanical strength of the metal material will be reduced, making it unable to fully withstand the weight of the fire bricks. Bricks will collapse and cause production accidents. By theoretically analyzing the influencing factors of the temperature distribution at the bottom of the pot, measures are proposed to maintain a reasonable temperature at the bottom of the pot in order to guide the production process.
The bottom temperature is very uneven, there is a temperature point. It can be seen from the figure that the temperature change of the inner wall of the gasifier has little effect on the change of the bottom temperature. When the temperature in the oven of the gasifier changes from 1200°C to 1450°C, it increases by 250°C, and the highest point of the bottom of the pot The temperature increased from the corresponding 258.51 °C to 261.57 °C, only an increase of 3.06 °C. The gas flow state in the quench chamber causes the convective heat transfer coefficient to change, and the change of convection heat transfer coefficient has a certain influence on the temperature of the bottom of the pot, but the effect is not significant. From Figure 5, it can be seen that the convection heat transfer, the highest point of the bottom of the pot temperature from 265.9 °C to 257.43 °C, a decrease of 8.47 °C. Thus, it can be seen that the arrangement of the refractory bricks determines the temperature distribution of the bottom of the pan. Whether the temperature in the furnace rises or the convection in the quench chamber deteriorates, the bottom temperature will not rise too high.
4 Conclusions The heat transfer model of the gasifier has been established, and the finite element method has been used to solve the solution by variation. Taking the Texaco gasifier as an example, the temperature distributions of the furnace body and the bottom of the gasifier are calculated, and the influence of temperature, ambient temperature, and convection heat transfer coefficient on the temperature distribution is discussed. The mathematical model can be used to calculate the temperature of any point on the gasifier furnace, providing a theoretical basis for the design, operation and maintenance of the gasifier.
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