T. Telejko

Inverse method implementation to heat transfer coefficient determination over the plate cooled by water spray

The three-dimensional (3D) inverse solution to water spray cooling from 925 °C to room temperature of the AISI 309 steel plate has been presented. The finite element method with linear and nonlinear shape function has been employed in forward simulations of the plate temperature and in the inverse solutions. The forward finite element solvers have been first compared with the analytical solution to the plate cooling. The reduced finite element models have been compared with the reference model for plate cooling under variable in time and space heat transfer coefficient (HTC) and for the temperature-dependent thermophysical properties of steel. It has been shown that the reduced finite element model with only 216 degrees of freedom which utilizes nonlinear shape functions has given the inverse solution to the heat transfer at the cooled surface with the accuracy of 1.6%. The influence of the thermocouple location uncertainty and the temperature dependence of thermophysical properties have been tested in inverse solutions. The implementation of the reduced finite element heat conduction models and the function specification method in space and time have allowed to achieve the 3D inverse solution to the overall heat transfer at the cooled surface with the accuracy of 2%. The developed 3D inverse solution has been employed to the determination of the HTC distribution over the AISI 309 steel plate cooled by the water spray nozzle. The thermal characteristic of the full cone swirl spray nozzle has been developed.

Implementation of the Axially Symmetrical and Three Dimensional Finite Element Models to the Determination of the Heat Transfer Coefficient Distribution on the Hot Plate Surface Cooled by the Water Spray Nozzle

Plate and strip hot rolling lines are equipped with water cooling systems used to control the deformed material temperature. This system has a great importance in the case of thermal - mechanical deformation of steel which is focused on formation a proper microstructure and mechanical properties. The desired rate of cooling is achieved by water spray or laminar cooling applied to the hot surface of a strip. The water flow rate and pressure can be changed in a wide range and it will result in a very different heat transfer from the cooled material to the cooling water. The suitable cooling rate and the deformed material temperature can be determined based on numerical simulations. In this case thermal boundary conditions have to be specified on the cooled surface. The determination of the heat transfer coefficient distribution in the area of the water spray nozzle would improve numerical simulations significantly. In the paper an attempt is made to determine the heat transfer coefficient distribution on the hot plate surface cooled by the water spray nozzle. In the inverse method direct axially symmetrical and three dimensional solutions to the plate temperature field have been implemented. The computation time and the achieved accuracy have been compared for five cases. The studied cases differed in the maximum value of the heat transfer coefficient in nozzle spray axis and its distribution in the cooling time.

Numerical model of a shaft furnace operation

Purpose The model of a shaft furnace operation is presented in this paper. Aim of this model is to predict concentrations of carbon monoxide and dioxide, the temperature of the lava and the heat losses. Design/methodology/approach The mathematical model is based on 1D mass and heat balance laws for flue gas, coke and four materials used in a mineral wool production. Process parameters should be optimized for the minimal heat loss and the carbon monoxide concentration while keeping the prescribed lava temperature. The model consists of heterogeneous and homogeneous reactions for coke combustion, dolomite decomposition, rock and coke heating and a rock-melting model. The resulting system of partial differential equations is discretized by the finite volume method and solved with the explicit Euler scheme together with the point-implicit preconditioning of sources in species balance equations. Findings Numerical results are compared with the measured data on the pilot-scale device and show good agreement. It is found that in the lower region of the furnace, the large amount of carbon monoxide is present despite high oxygen levels. Practical/implications Based on the numerical model, the parameters of the secondary air stream could be studied (position, volume flux, oxygen enrichment and temperature) to decrease levels of carbon monoxide emissions while keeping lava temperature at needed levels. Originality/value The paper includes mathematical and numerical model needed for simulation of shaft furnaces in mineral wool industry. It can be used as a valuable tool for design engineers and furnace operators during research or redesign of existing devices.

Heat transfer coefficient distribution over the inconel plate cooled from high temperature by the array of water jets

The industrial rolling mills are equipped with systems for controlled water cooling of hot steel products. A cooling rate affects the final mechanical properties of steel which are strongly dependent on microstructure evolution processes. In case of water jets cooling the heat transfer boundary condition can be defined by the heat transfer coefficient. In the present study one and three dimensional heat conduction models have been employed in the inverse solution to heat transfer coefficient. The inconel plate has been heated to about 900oC and then cooled by one, two and six water jets. The plate temperature has been measured by 30 thermocouples. The heat transfer coefficient distributions at plate surface have been determined in time of cooling.