Inverse boundary problem in estimating heat transfer coefficient of a round pulsating bubbly jet: design of experiment

Abstract

An inverse algorithm is developed to estimate the transient convective coefficient distribution of a pulsating bubbly jet impinging on a cylindrical thermal mass. Cooling of the thermal mass is simulated by solving the two-dimensional transient heat equation in a cylindrical coordinate system using the finite difference method. The sum of squared differences between calculated and measured temperature data is the objective functional. As this is a nonlinear IHCP, the adjoint method is employed to derive the gradient components of the objective function, needed for the implementation of CGM. The procedure is carried out for six gas Reynolds numbers changing continuously through ten seconds of the jet impingement. The inverse scheme is validated using noiseless temperature data. The accuracy and convergence rate of the algorithm is then assessed by simulating the cooling process of thermal mass with four different materials. Moreover, the effects of sensors’ location, as well as initial guess on the estimation, are evaluated. Time-varying heat transfer coefficients are then estimated in the presence of Gaussian noise, having four standard deviations. Results demonstrate that, despite the estimation is affected by the noise level, the adjoint method is most efficient and rapidly convergent for the thermal mass with moderate thermal conductivity having a noisy temperature field of $ \sigma $ $ \lt $ 1 $ ^{\circ}{\rm C} $ .

Keywords

• boundary value problem
• pulsating bubbly impinging jet
• time-varying local convective heat transfer coefficient estimation
• nonlinear inverse heat conduction problem
• adjoint method
• conjugate gradient method