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The comparative analysis of heat transfer efficiency in the conditions of formation of ash deposits in the boiler furnaces, with taking into account the crystallization of slag during combustion of coal and water-coal fuel

The results of the numerical simulation of heat transfer from the combustion products of coal and coal-water fuels (CWF) to the internal environment. The mathematical simulation has been carried out on the sample of the pipe surfaces of the combustion chamber of the boiler unit. The change in the characteristics of heat transfer (change of thermochemical characteristics) in the conditions of formation of the ash deposits have been taken into account. According to the results of the numerical simulation, the comparative analysis of the efficiency of heat transfer has been carried out from the furnace environment to the inside pipe coolant (water, air, or water vapor) from the combustion of coal and coal-water fuels. It has been established that, in the initial period of the boiler unit operation during coal fuel combustion the efficiency of heat transfer from the combustion products of the internal environment is higher than when using CWF. The efficiency of heat transfer in CWF combustion conditions is more at large times (τ≥1.5 hours) of the boiler unit. A significant decrease in heat flux from the combustion products to the inside pipe coolant in the case of coal combustion compared to CWF has been found. It has been proved that this is due primarily to the fact that massive and strong ash deposits are formed during coal combustion.


Introduction
Currently, most of the modern thermal power plants in Europe and North America use coal as the main fuel [1][2][3]. However, it is worth noting that the most significant problem of the modern boiler technology when burning coal is the formation of ash deposits [4,5] on the heating surfaces, has not been solved yet. The deposition of slag is the main negative factor in the operation of the boiler unit [6]. High thermal resistance of ash leads to a significant decrease in the efficiency of heat transfer from the furnace environment to water or vapor. It is also worth noting that the sticking of ash, as a rule, occurs unevenly over the heat exchange surface. As a result, the pipe surface is heated unevenly, and a severe corrosion occurs [7]. 1a steel pipe wall; 2a layer of ash; 3a conventional symbol for the motion of the interface of the "ash layer -intrachamber sphere" system. A number of works [8,9] is devoted to modeling of the processes of slag deposition on the pipe heat exchange surfaces. In particular, in [9], the mechanisms of adhering ash on the heat transfer surfaces have been studied in some detail. However, it should be noted that in this case, a little attention has been paid to the problems of heat transfer in the conditions of contamination of the pipes of the boiler units with ash and slag. There are known works [10,11] devoted to the problems of heat transfer as a result of ash deposits. But mainly they are devoted to the study of thermophysical properties (density (ρ), thermal conductivity (λ) and heat capacity (С)) of slag. Such studies are conducted at a constant thickness of the ash-slag layer. At the same time it is worth noting that in the process of depositing ash on the surface of heat exchange, the thickness of this layer as a rule is constantly changing. It is known [12] that the precipitation of slag proceeds under the conditions of crystallization of a liquid-slag melt. The latter is due to the presence of ash silicon oxide (SiO) and iron (FeO). The thermal effect of crystallization reaches 100 kJ/kg. Respectively, in the conditions of deposition of the ash the question arises about the appropriateness of including this heat in the simulation of heat transfer processes in the system "fluid -pipe wall and gas environment".
One of the most promising methods of "low-ash" coal combustion is water-coal fuel technology (WCF). Due to the fact that WCF contains up to 50% water, the combustion temperature of such fuel is significantly lower (Tg ≤ 1100K) than the traditional pulverized-coal torch (Tg ≥1300K). In other words, the Tg burning of the water-coal fuel is lower than the slagging start temperature. However, to date, there has been no comparative analysis of the efficiency of heat transfer from the inside of the furnace to the heat carrier during the combustion of coal and water-coal fuel, under the conditions of ash precipitation and crystallization.
The purpose of the work is mathematical modeling of heat exchange processes in the "pipe surface -furnace environment" system in the conditions of formation of ash and slag deposits formed during the combustion of coal and water-coal fuel.

Formulation of the problem
The following problem is formulated based on the known [12] regularities of formation of ash deposits.
It is assumed that at the initial time (τ = 0 s) the heat exchange surface of the superheater is heated due to convection and emission of flue gases (Fig. 1). From the time τ = τssa the process of formation of ash and slag deposits begins. In this case, the ash crystallizes. To determine the efficiency of heat transfer in the system "inner pipe environmenta pipe wallan ash layer -external environment", the heat conduction problem has been solved.
The mathematical model corresponding to the above physical formulation of the problem includes the following system of differential equations of thermal conductivity in partial derivatives: -a metal pipe The change in the outer radius of the pipe (with taking into account the sediment layer) has been calculated using the expression: Where Vrs=Wrs/ρsa linear rate of depositions formation, Wrs=f(T)a mass rate of ash formation kg / m 2 s ( [13] for WCF, [12] when burning coal). The system (1) - (2) has been solved under the following boundary conditions. Initial conditions: On the boundary of the system "pipe wallash layer" boundary the conditions of the fourth kind are fulfilled: At the interface of the system "water vapor -a pipe wall", convective heat exchange has been taken into account: At the interface of the system "pipe surfacefurnace environment", at τ = 0, the heat exchange law has been set: Similar conditions have been formulated at the boundary of the system "ash depositsthe gaseous environment" at τ> τssa, taking into account the crystallization process of the slag melt: The problem has been solved in three stages. At the first, heat exchange has been calculated in the system "flue gasesa pipe surface -a heat carrier". At the time τ = τssa, the calculation of the slag deposition on the heating surface has begun. The formation of an ash layer with high thermal resistance has been taken into account. Later, heat transfer from the gaseous environment to the heat carrier inside the pipe has occurred through a layer of ash deposits. The thermal balance of the system "flue gasesa pipe surfaceash -a heat carrier" has been calculated according to the following scheme: To analyze the efficiency of heat transfer through the ash sediments, heat has been calculated due to heat exchange from the internal surface of the pipe: The total amount of heat due to convection and radiation from the external environment to the pipe surface: