Temporal super-resolution using smart sensors for turbulent separated flows

Abstract

Particle image velocimetry (PIV) data of high Reynolds number unsteady turbulent flows are often undersampled in time; this leads to aliasing of important spectral content. The present work proposes a novel data-driven estimation technique that uses oversampled sparsely placed surface-mounted pressure sensors and long short-term memory neural networks to resolve the aliased transient velocity dynamics from undersampled PIV data. The method leverages the time-resolved pressure dynamics to estimate the temporal evolution of a proper orthogonal decomposition-based low-dimensional subspace of the velocity field. The proposed approach is demonstrated on a PIV dataset of a high Reynolds number turbulent separated flow over a Gaussian speed-bump benchmark geometry ($\text{Re}_{H}=2.26\times 10^{5}$, where H is the Bump height). The 15 Hz PIV data is super-resolved to 2 kHz, and spectral analysis of the flowfields is conducted to educe the originally aliased unsteady dynamics of the turbulent separation bubble. The estimator is shown to accurately reconstruct the Reynolds shear stress from unseen sensor data, demonstrating its generalizability to resolve the coherent motions. The estimated velocity spectra show distributions consistent with those of other separated flows.

Appendix A Hyperparameter search

Various configurations of $(N_{\text {train}},\,n,\,f_{\text {cut-off}})$ used in the hyperparameter study are summarized along with the other relevant network parameters and corresponding error metrics in Table 1.

Table 1 Abridged hyperparameter study for input pressure sequence duration (n), training dataset size ($N_{\text {train}}$) and effect of pressure cut-off frequency ($f_{\text {cut-off}}$). Resultant input sequence length (S) also tabulated. Corresponding domain-averaged Reynolds shear stress ($\epsilon ^{(\Omega )}_{\overline{u'w'}}\,(\%)$) and time-averaged total instantaneous errors ($\overline{e(t)}$) tabulated