Abstract
A method for determining time-optimum fluid temperature changes during heating of the thick walled cylinder was presented. Optimum fluid temperature changes were determined both for the cylindrical pressure vessels without holes. Heating of the hollow cylinder will be carried out in such a way that the circumferential thermal stress at the inner surface is equal to the allowable stress value. Optimum fluid temperature changes were assumed in the form of simple time functions containing unknown parameters. The unknown parameters were determined from the condition that the circumferential thermal stress at the inner surface of the hollow cylinder without holes is equal to the allowable stress at given time points. An over-determined system of nonlinear algebraic equations was solved for unknown parameters using the least squares method. At first, the thermal stress was calculated using the discrete form of the Duhamel integral. The Finite Element Method (FEM) was used to determine the circumferential thermal stress in the second method. For practical reasons the optimum temperature in the ramp form is preferred. It is possible to increase the fluid temperature stepwise at the beginning of the heating process and then increase the fluid temperature with the constant rate. Because of the possibility of practical implementation a more appropriate is the ramp function for approximating optimum fluid temperature changes.
Highlights
IntroductionOptimization of heating and cooling of thick boiler components is the subject of many studies [1,2,3,4,5,6], since too rapid heating or cooling element causes high thermal stresses
Optimization of heating and cooling of thick boiler components is the subject of many studies [1,2,3,4,5,6], since too rapid heating or cooling element causes high thermal stresses.There is a great need for reducing start-up and shut-down costs in thermal power plants
During optimum heating of the cylinder the circumferential thermal stress at the inner surface of the cylinder is equal to the allowable value
Summary
Optimization of heating and cooling of thick boiler components is the subject of many studies [1,2,3,4,5,6], since too rapid heating or cooling element causes high thermal stresses. The major limiting factor relevant to fast power plant start-ups is maximum allowable thermal stress for thickwalled components such as headers of superheaters and reheaters, boiler drums and steam turbine rotors. Estimation of the maximum thermal stress enables the optimization of the bypass mode [6] In both papers drum is considered as a thick-walled cylinder in which the temperature distribution is a function of radius and time [4,5]. A method of determining the optimum time changes of fluid temperature during heating process of boiler structural pressure elements was proposed in [10]. The optimization procedure is based on the discrete form of the Duhamel’s integral Another method for optimum heating of thick walled pressure components was presented in [11, 12]. Optimum temperature curve for a hollow cylinder without holes will be determined from the condition that the von Mises equivalent stress at the cylinder inner surface is equal to the permissible stress
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