A Systematic Methodology to Develop Scaling Laws for Thermal Features of Temperature Field Induced by a Moving Heat Source

  • Author / Creator
    Lu, Yi
  • A systematic methodology is developed to formulate scaling laws in closed-form for thermal features of moving line heat source and Gaussian heat source problems, with wide generality, high accuracy and practical simplicity, from fundamental principles. The expressions are written in form of a simple solution for the dominant factor and correction factors for secondary phenomena. In this thesis, the simple solutions are derived from asymptotic analysis of dimensionless models, and the correction factors are achieved with blending technique which is a standardized approach to generate a global approximation based on asymptotic solutions. The 1-D blending technique is modified to extend its scope of application and increase its accuracy. A systematic 2-D blending method is proposed to capture all possible cases of two independent variables. This thesis presents explicit, predictive and simple expressions for vital thermal features of moving line heat source and Gaussian heat source, that are general to different materials, processes and operating parameters. Based on the Rosenthal's moving line heat source model, expressions for 13 thermal features are tabulated, including: isotherm half-width, location of the half-width, isotherm trailing length, centerline cooling rate, isotherm leading length, centerline heating rate, maximum temperature, gradients of maximum temperature, isotherm aspect ratio, melting efficiency, cooling time from 800 ℃ to 500 ℃, solidification time, and thickness of the heat affected zone. All expressions are obtained with modified 1-D blending on one dimensionless group, Ro number that represents the intensity of heat source (except for maximum temperature), and are accurate to 8 % of the analytical solutions, except heating rate at 16 %. By employing the proposed 2-D blending method, correction factors of surface heat losses are established for isotherm half-width and its location, isotherm trailing length, and centerline cooling rate, resulting in errors within 12 %, with the introduction of the second dimensionless group h*. For isotherms around the heat source, the energy distribution of the heat source affects the temperature field significantly. The correction factors of Gaussian heat source distribution are developed with the proposed 2-D blending method for isotherm half-width. A comprehensive survey of published experiments and simulations is conducted to validate the proposed engineering expressions. The comparisons illustrate good agreements between predictions from the proposed expressions and collected data for a broad range of materials, processes, and parameters. The engineering expressions for all thermal features of moving line heat source and Gaussian heat source are simple enough to be evaluated with a calculator or spreadsheet conveniently, and are useful for a broad range of diverse materials or processes. The expressions provide design guidelines for engineers and practitioners, bring physical intuitions and insights, and speed up designing cycles especially at conceptual stage in design and development of new technologies by inspiring creativity and filtering infeasible or inferior designing options by evaluating many optional parameters and processes. The blending method can be adopted in broader engineering problems since it captures the inherent essence of complex physical phenomena based on the governing equations.

  • Subjects / Keywords
  • Graduation date
    Spring 2021
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.