Development of inverse analysis method using a plate model for estimation of temperature distribution history of an elbow with thermal stratification

Abstract

Thermal fatigue may occur in a pipe with high temperature stratified flow. To avoid the fatigue damage by the stratified flow, it is important to know a history of temperature and thermal stress distribution in the pipe. This paper describes a heat conduction inverse analysis method using a plate model as a basic study for estimation of a temperature history on the inner surface of an elbow where a thermal stratification occurs. It was made clear that the relation between the surface temperature and the other surface temperature of the plate model was characterized by the reduction ratio of an amplitude R and time delay Δt dependent on the cycle of the temperature history. The reduction rate R and time delay Δt may change with the boundary condition. Therefore, it is necessary to calculate R and Δt numerically in accordance with the boundary condition. The surface temperature history was estimated by dividing the magnitude of the other surface temperature by the reduction ratio R and by advancing the time by the time delay Δt. It was found that the surface temperature history was estimated with good accuracy by the inverse analysis method proposed in this study.

Keywords

• inverse problem
• heat conduction
• stratified flow
• thermal stress
• thermal fatigue