A FREESTREAM CORRECTION ALGORITHM BASED ON DATA ASSIMILATION FOR HYPERSONIC WIND TUNNELS AND VALIDATION

Accurately measuring the freestream parameters in hypersonic wind tunnels presents a significant challenge. The rigorous accuracy of these critical parameters severely constrains the computational precision of freestream-sensitive numerical flow fields. Building upon the foundation of the traditional Ensemble Kalman Filter (EnKF) data assimilation algorithm, and focusing on wind tunnel freestream parameters as the primary research subject, a novel Thermodynamics-Regularized Ensemble Kalman Filter (TEnKF) data assimilation algorithm is proposed for hypersonic wind tunnels. Utilizing sparse wall physical quantities experimentally measured on the test model surface alongside prior ensemble numerical flow fields, the proposed TEnKF algorithm additionally incorporates freestream fluid stagnation parameters as essential regularization terms within both the objective function and the update step. This strategic formulation effectively constrains the specific physical subspace spanned by the posterior ensemble of freestream parameters, thereby comprehensively addressing the inherent ill-posedness problem frequently encountered in the traditional EnKF. Comprehensive case corrections meticulously conducted across various distinct types of hypersonic wind tunnels consistently demonstrate that the performance of the TEnKF algorithm substantially outperforms the standard EnKF approach. Specifically, the corresponding reconstructed flow fields exhibit significantly smaller overall errors compared to experimental data, and the corrected freestream results strictly guarantee necessary compatibility with the prior stagnation parameters. Furthermore, detailed analyses concerning both parameter sensitivity and the algorithmic correction process clearly reveal that this thermodynamic regularization successfully mitigates the detrimental impact of freestream-wall sensitivity imbalances on final correction results. Concurrently, it indirectly introduces a vital damping term into the structure of the Kalman filter. Consequently, the ensuing correction process becomes remarkably more stable and highly conducive to rapid convergence, while simultaneously circumventing the highly problematic issue of isolated, independent corrections among interacting freestream parameters. Therefore, the TEnKF successfully provides a significantly more reliable and robust numerical correction algorithm for hypersonic wind tunnel freestreams, effectively improving computational prediction accuracy while substantially reducing associated uncertainties.