An adaptive fluid-solid coupling time step control algorithm for unsteady conjugate heat transfer

Unsteady simulation with conjugate heat transfer has to tackle the stiffness issue that originates from the wide disparate time scales between fluid and solid heat transfer. In the loosely coupled framework, challenges remain in determining the optimal coupling time step between the fluid and solid solvers, in terms of efficiency and accuracy. This study formulates a correlation for the coupling error, together with the Proportional-Integral-Derivative (PID) control method, to propose an adaptive fluid-solid coupling time step algorithm, which dynamically adjusts the coupling time step such that the computational efficiency can be improved without sacrificing accuracy. The proposed algorithm has been tested in a 1D conjugate heat transfer application with typical operating conditions of a real engine, and the performance of different controllers (I, PI, PID) has been analyzed and compared. Results show that with the closed-loop control, all controllers can ensure the error control below the user specified tolerance at the cost of reducing efficiency. Meanwhile, with the open-loop control which is of more interest to practical applications, controllers suffer from instability issues when a conventional algorithm based on integration error is employed. The proposed coupling-error-based algorithm successfully tackles the instability issues. Compared with the baseline algorithm of the constant coupling time step, the proposed algorithm can reduce approximately 40%–90% computational cost for the 1D cases considered.