A Study of the Convective Cooling of Large Industrial Billets

The thermodynamic heat-transfer mechanisms, which occur as a heated billet cools in an air environment, are of clear importance in determining the rate at which a heated billet cools. However, in finite element modelling simulations, the convective heat transfer term of the heat transfer mechanisms is often reduced to simplified or guessed constants, whereas thermal conductivity and radiative emissivity are entered as detailed temperature dependent functions. As such, in both natural and forced convection environments, the fundamental physical relationships for the Nusselt number, Reynolds number, Raleigh parameter, and Grashof parameter were consulted and combined to form a fundamental relationship for the natural convective heat transfer as a temperature-dependent function. This function was calculated using values for air as found in the literature. These functions were then applied within an FE framework for a simple billet cooling model, compared against FE predictions with constant convective coefficient, and further compared with experimental data for a real steel billet cooling. The modified, temperature-dependent convective transfer coefficient displayed an improved prediction of the cooling curves in the majority of experiments, although on occasion a constant value model also produced very similar predicted cooling curves. Finally, a grain growth kinetics numerical model was implemented in order to predict how different convective models influence grain size and, as such, mechanical properties. The resulting findings could offer improved cooling rate predictions for all types of FE models for metal forming and heat treatment operations.

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Molecular dynamics simulation of the precision machining process including radiative and convective heat transfer mechanisms

Modelling and Simulation in Materials Science and Engineering ◽

10.1088/0965-0393/2/2/004 ◽

1994 ◽

Vol 2 (2) ◽

pp. 223-237 ◽

Cited By ~ 3

Author(s):

J A Patten ◽

K Flurchick ◽

J Beeler ◽

J Strenkowski

Keyword(s):

Heat Transfer ◽

Molecular Dynamics ◽

Molecular Dynamics Simulation ◽

Convective Heat Transfer ◽

Convective Heat ◽

Machining Process ◽

Dynamics Simulation ◽

Precision Machining ◽

Transfer Mechanisms

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Hybrid Eigenfunction-Discretization Methodology for Solving Convective Heat Transfer Problems

Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer ◽

10.1115/ht2012-58336 ◽

2012 ◽

Author(s):

D. J. M. N. Chalhub ◽

L. A. Sphaier ◽

L. S. de B. Alves

Keyword(s):

Heat Transfer ◽

Convective Heat Transfer ◽

Convective Heat ◽

Integral Transform ◽

Integral Transformation ◽

Temperature Dependent ◽

Discretization Schemes ◽

Upwind Discretization ◽

Transfer Problems ◽

Approximation Parameter

This paper presents a novel methodology for the solution of problems that include diffusion and advection effects, as naturally occur in convective heat transfer problems. The methodology is based on writing the unknown temperature field in terms of eigenfunction expansions, as traditionally carried-out with the Generalized Integral Transform Technique (GITT). However, a different approach is used for handling advective derivatives. Rather than transforming the advection terms as done in traditional GITT solutions, upwind discretization schemes (UDS) are used prior to the integral transformation. With the introduction of upwind approximations, numerical diffusion is introduced, which can be used to reduce unwanted oscillations that arise at higher Péclet values. This combined methodology is termed the GITT-UDS for convective problems. The procedure is illustrated for a simple case of one-dimensional Burgers’ equation with temperature-dependent velocities. Numerical results are calculated, showing that augmenting the upwind approximation parameter can effectively reduce solution oscillations for higher Péclet values.

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Numerical and Analytical Investigation of Heat Transfer Mechanisms and Flow Phenomena in an IP Steam Turbine Blading During Startup

Volume 9: Oil and Gas Applications; Organic Rankine Cycle Power Systems; Steam Turbine ◽

10.1115/gt2020-15537 ◽

2020 ◽

Author(s):

Dieter Bohn ◽

Christian Betcher ◽

Karsten Kusterer ◽

Kristof Weidtmann

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Convective Heat Transfer ◽

Steam Turbine ◽

Heat Transport ◽

Convective Heat ◽

Thermal Design ◽

Transfer Coefficients ◽

Heat Transfer Coefficients ◽

Transfer Mechanisms

Abstract As a result of an ever-increasing share of volatile renewable energies on the world wide power generation, conventional thermal power plants face high technical challenges in terms of operational flexibility. Consequently, the number of startups and shutdowns grows, causing high thermal stresses in the thick-walled components and thus reduces lifetime and increases product costs. To fulfill the lifetime requirements, an accurate prediction and determination of the metal temperature distribution inside these components is crucial. Therefore, boundary conditions in terms of local fluid temperatures as well as heat transfer coefficients with sufficient accuracy are required. As modern numerical modeling approaches, like 3D-Conjugate-Heat-Transfer (CHT), provide these thermal conditions with a huge calculation expense for multistage turbines, simplified methods are inevitable. Analytical heat transfer correlations are thus the state-of-the-art approach to capture the heat transport phenomena and to optimize and design high efficient startup curves for flexible power market. The objective of this paper is to understand the predominant basic heat transfer mechanisms such as conduction, convection and radiation during a startup of an IP steam turbine stage. Convective heat transport is described by means of heat transfer coefficients as a function of the most relevant dimensionless, aero-thermal operating parameters, considering predominant flow structures. Based on steady-state and transient CHT-simulations the heat transfer coefficients are derived during startup procedure and compared to analytical correlations from the literature, which allow the calculation of the heat exchange for a whole multistage in an economic and time-saving way. The simulations point out that the local convective heat transfer coefficient generally increases with increasing axial and circumferential Reynolds’ number and is mostly influenced by vortex systems such as passage and horseshoe vortices. The heat transfer coefficients at vane, blade, hub and labyrinth-sealing surfaces can be modeled with a high accuracy using a linear relation with respect to the total Reynolds’ number. The comparison illustrates that the analytical correlations underestimate the convective heat transfer by approx. 40% on average. Results show that special correlation-based approaches from the literature are a particularly suitable and efficient procedure to predict the heat transfer within steam turbines in the thermal design process. Overall, the computational effort can be significantly reduced by applying analytical correlations while maintaining a satisfactory accuracy.

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