Assimilation of wall-pressure measurements in high-speed flow over a cone

Abstract

A nonlinear ensemble-variational data assimilation is performed in order to estimate the unknown flow field over a slender cone at Mach 6, from isolated wall-pressure measurements. The cost functional accounts for discrepancies in wall-pressure spectra and total intensity between the experiment and the prediction using direct numerical simulations, as well as our relative confidence in the measurements and the estimated state. We demonstrate the robustness of the predicted flow by direct propagation of posterior statistics. The approach provides a unique first look at the flow beyond the sensor data, and rigorously accounts for the role of nonlinearity, unlike previous efforts that adopted ad hoc inflow syntheses. Away from the wall, two- and three-dimensional assimilated states both show rope-like structures, qualitatively similar to independent schlieren visualizations. Despite this resemblance, and even though the planar second modes are the most unstable upstream, three-dimensional waves must be included in the assimilation in order to accurately reproduce the wall-pressure measurements recorded in the AFRL Ludwieg Tube facility. The results highlight the importance of three-dimensionality of the field and of the base-state distortion on the instability waves in this experiment, and motivate future measurements that probe the three-dimensional nature of the flow field.

ML for fast assimilation of wall-pressure measurements from hypersonic flow over a cone

“…We estimate the upstream instability waves, quantitatively reproduce the wall-pressure spectra, and discover the full spatio-temporal flow field that led to the measured data. We compare our results with the recent and only known solution, by Buchta et al 34 , and show that within the time needed for EnVar to solve one data assimilation problem our approach computes about 2000 solutions, with commensurate accuracy.…”

“…In this work, we introduce a strategy that exploits deep learning to expedite the interpretation of experimental observations. The measurements are wall-pressure spectra acquired from PCB sensors on a 7-degree cone, at free-stream Mach number , as in Buchta et al 34 . We estimate the upstream instability waves, quantitatively reproduce the wall-pressure spectra, and discover the full spatio-temporal flow field that led to the measured data.…”

“…The major advantage of our proposed approach, relative to the previous ensemble-variational method 34 , is the significant reduction in computational expense. Including the initial training cost, we are able to perform approximately 2000 data-assimilation problems in the same wall-clock time that was required to solve just one inverse problem using EnVar.…”

Optimal two-dimensional roughness for transition delay in high-speed boundary layer

“…In addition, unlike adjoint methods which may place limits on the time horizon of the flow solution (Zaki & Wang 2021), EnVar is perfectly suited for long-time integration and evaluation of statistical cost functions (Mons, Wang & Zaki 2019; Mons, Du & Zaki 2021). EnVar has successfully been adopted in high-speed boundary layers for assimilation of measurements into flow simulations (Buchta & Zaki 2021; Buchta, Laurence & Zaki 2022) and optimization (Jahanbakhshi & Zaki 2021). The reader is referred to those studies for the details of the algorithm.…”

Optimal experiment design with adjoint-accelerated Bayesian inference

“…This is true of typical sampling methods such as Markov Chain Monte Carlo, which can require hundreds of thousands of model evaluations to calculate the posterior. Recent work has, however, demonstrated sampling-free methods for variational data assimilation (Mons and Zaki, 2021; Buchta et al, 2022) and approximate Bayesian inference (MacKay, 2003; Isaac et al, 2015; Juniper and Yoko, 2022; Kontogiannis et al, 2022; Yoko and Juniper, 2024). These methods reduce the required model evaluations, making Bayesian inference feasible for computationally expensive models.…”