The following paper presents the method for solving one-dimensional inverse boundary heat conduction problems. The method is used to estimate the unknown thermal boundary condition on inner surface of a thick-walled Y-branch. Solution is based on measured temperature transients at two points inside the element's wall thickness. Y-branch is installed in a fresh steam pipeline in a power plant in Poland. Determination of an unknown boundary condition allows for the calculation of transient temperature distribution in the whole element. Next, stresses caused by non-uniform transient temperature distribution and by steam pressure inside a Y-branch are calculated using the finite element method. The proposed algorithm can be used for thermal-strength state monitoring in similar elements, when it is not possible to determine a 3-D thermal boundary condition. The calculated temperature and stress transients can be used for the calculation of element durability. More accurate temperature and stress monitoring will contribute to a substantial decrease of maximal stresses that occur during transient start-up and shut-down processes.
Heating surfaces in power boilers are exposed to very high heat flux. For evaporator protection against overheating, internally helically ribbed tubes are used. The intensification of the heat transfer and the maintenance of the thin water layer in the intercostal space, using ribbed tubes, enables better protection of the power boiler evaporator than smooth pipes. Extended inner surface changes flow and thermal conditions by influencing the linear pressure drop and heat transfer coefficient. This paper presents equations that are used to determine the heat transfer coefficient. The results of total heat transfer, obtained from CFD simulations, for two types of internally ribbed and plain tubes are also presented.
The paper presents the results of numerical computations performed for the furnace chamber waterwalls of a supercritical boiler with a steam output of 2400 × 103 kg/h. A model of distributed parameters is proposed for the waterwall operation simulation. It is based on the solution of equations describing the mass, momentum and energy conservation laws. The aim of the calculations was to determine the distribution of enthalpy, mass flow and fluid pressure in tubes. The balance equations can be brought to a form where on the left-hand side space derivatives, and on the right-hand side – time derivatives are obtained. The time derivatives on the right-hand side were replaced with backward difference quotients. This system of ordinary differential equations was solved using the Runge-Kutta method. The calculation also takes account of the variable thermal load of the chamber along its height. This thermal load distribution is known from the calculations of the heat exchange in the combustion chamber. The calculations were carried out with the zone method.
The paper presents the solution to a problem of determining the heat flux density and the heat transfer coefficient, on the basis of temperature measurement at three locations in the flat sensor, with the assumption that the heat conductivity of the sensor material is temperature dependent. Three different methods for determining the heat flux and heat transfer coefficient, with their practical applications, are presented. The uncertainties in the determined values are also estimated.
In this paper a mathematical model enabling the analysis of the heat-flow phenomena occurring in the waterwalls of the combustion chambers of the boilers for supercritical parameters is proposed. It is a one-dimensional model with distributed parameters based on the solution of equations describing the conservation laws of mass, momentum, and energy. The purpose of the numerical calculations is to determine the distributions of the fluid enthalpy and the temperature of the waterwall pipes. This temperature should not exceed the calculation temperature for particular category of steel. The derived differential equations are solved using two methods: with the use of the implicit difference scheme, in which the mesh with regular nodes was applied, and using the Runge-Kutta method. The temperature distribution of the waterwall pipes is determined using the CFD. All thermophysical properties of the fluid and waterwall pipes are computed in real-time. The time-spatial heat transfer coefficient distribution is also computed in the on-line mode. The heat calculations for the combustion chamber are carried out with the use of the zone method, thus the thermal load distribution of the waterwalls is known. The time needed for the computations is of great importance when taking into consideration calculations carried out in the on-line mode. A correctly solved one-dimensional model ensures the appropriately short computational time.