Abstract
A cooling rate affects the mechanical properties of steel which strongly depend on microstructure evolution processes. The heat transfer boundary condition for the numerical simulation of steel cooling by water jets can be determined from the local one dimensional or from the three dimensional inverse solutions in space and time. In the present study the inconel plate has been heated to about 900 °C and then cooled by six circular water jets. The plate temperature has been measured by 30 thermocouples. The heat transfer coefficient and the heat flux distributions at the plate surface have been determined in time and space. The one dimensional solutions have given a local error to the heat transfer coefficient of about 35%. The three dimensional inverse solution has allowed reducing the local error to about 20%. The uncertainty test has confirmed that a better approximation of the heat transfer coefficient distribution over the cooled surface can be obtained even for limited number of thermocouples. In such a case it was necessary to constrain the inverse solution with the interpolated temperature sensors.
Highlights
Steel products are widely present in our everyday live
H6-Mo 1 6 6 784 0.5 13.5 0.6 0.26 the norm of the dimensionless temperature gradients difference. It has been shown [35] that the objective function (13) reduces in inverse solutions the heat transfer coefficient (HTC) fluctuations resulting from the HTC maxima moving over the cooled surface in time
A prior estimation of the HTC and heat flux obtained from local 1D inverse solution at surface element nodes has given acceptable accuracy
Summary
Dimensionless scaling function defined by Eq. Function defining heat transfer coefficient distribution in space and time [W/(m2 K)]. Function defining variation of the heat transfer coefficient maximum in time [W/(m2 K)]. Unknown parameters to be determined by minimizing the objective function [W/(m2 K)] Rayleigh number, Ra = g β (Ts-Ta) H3 ρa ca / (νa λa) Heat flux (W/m2) Cooling chamber surface (m2) Plate surface (m2). Penalty coefficient coupled with the temperature sensor m, x1, x2, x3 Cartesian coordinates (m) Greek symbols βa Volume expansion coefficient of air (1/K). Εk Emissivity of the cooling chamber surface εs Emissivity of the plate surface λ. Natural coordinates of the surface element Kinematic viscosity of air (m2/s) Density (kg/m3) Air density (kg/m3)
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