Estimation of solid-liquid phase moving front position during metal casting with mold

The air-gap formation between the casting and the metal mold during the casting of metal creates a thermal resistance; in order to calculate the solid-liquid phase moving front position, one needs to predict the mold-casting interface condition beforehand. In this work, inverse solution methodologies based on the optimal regularization method and conjugate gradient method are developed, respectively, to estimate the unknown interface condition with time from the transient simulated temperature measurements taken at the outer mold surface. Then, the solid-liquid phase front is calculated by using the estimated interface condition as the boundary condition. The advantages and disadvantages of using the optimal regularization method and conjugate gradient method will be discussed systematically. Moreover, statistical analysis based on the optimal regularization method is performed to determine the 99% confidence bounds for the estimated function. The validity of the bounds can be proved from the inverse solution using the conjugate gradient method since they always lie within these confidence limits.