Data assimilation and resolvent analysis of turbulent flow behind a wall-proximity rib

This study aims to detect the unsteady features of the turbulent flow behind a wall-proximity rib using resolvent analysis, based on the mean flow field determined using an adjoint-based data assimilation (ABDA) model. The rib is located at gap ratios G/d = 0.25 and 0.50 with a flow Reynolds number Re = 7600 based on the rib size (d = 10 mm) and the free-stream velocity U0. The split fiber measurements at x/d = −0.25, 1.25, 4.25, and 9.25 are solely used as observational data, while the temperature sensitive paint and particle image velocimetry (PIV) results are used as the complement for the analysis and validation. First, the mean flows at both gap ratios are reproduced with the ABDA model using the streamwise velocity constraint of the observational data. It is shown that the global fields are accurately recovered, including the wall jet originating from the gap, which is absent from the PIV results. This finding indicates substantial heat transfer enhancement immediately behind the rib. Subsequently, the resolvent modes at Strouhal numbers St = 0.02, 0.05, 0.15, and 0.30 are obtained from the mean flows using a stochastic approach instead of performing the singular value decomposition directly on the resolvent operator, due to the large matrix size. With the help of the power spectral density of the split fiber measurement, the resolvent analysis identifies the large-scale flapping motion and the wall-jet fine scales that enhance the heat transfer in the case of G/d = 0.25, in addition to the Karman vortex shedding, which makes little contribution to the wall heat transfer in the case of G/d = 0.50. The flow dynamical features in both cases are reconstructed using the leading five resolvent modes at St = 0.15, showing good agreement with the proper orthogonal decomposition modes.