Thermoelastic stresses in thick-walled vessels under an arbitrary thermal transient via the inverse route

Research output: Contribution to journalConference article

Abstract

A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same, time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

Original languageEnglish (US)
Article numberPVP2005-71054
Pages (from-to)487-493
Number of pages7
JournalAmerican Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
Volume3
DOIs
StatePublished - Dec 22 2005
Event2005 ASME Pressure Vessels and Piping Conference, PVP2005 - Denver, CO, United States
Duration: Jul 17 2005Jul 21 2005

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Inverse problems
Polynomials
Boundary conditions
Thermal shock
Thermal stress
Temperature
Stress concentration
Temperature distribution
Thermodynamic properties
Pipe
Hot Temperature
Fluxes

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

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title = "Thermoelastic stresses in thick-walled vessels under an arbitrary thermal transient via the inverse route",
abstract = "A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same, time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.",
author = "Segall, {Albert Eliot}",
year = "2005",
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N2 - A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same, time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

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