SCALAR-SOURCE IDENTIFICATION AND OPTIMAL SENSOR PLACEMENT IN TURBULENT CHANNEL FLOW

The spreading of a released pollutant in a turbulent environment has severe consequences. The ability to identify the unknown source location from remote sensor data is greatly obfuscated by turbulence. This work discusses effective scalar-source localization algorithms in a turbulent channel by exploiting adjoint and ensemble methods, and by utilizing the growing power of high-fidelity simulations. To reconstruct the spatial distribution of the source, a cost functional is defined based on the difference between the true sensor observations and their model predictions. Forward-adjoint simulations provide the gradient of the cost functional to the source distribution, and the source estimation is iteratively updated. When a single sensor is directly downstream, the reconstruction is accurate in the cross-stream directions but elongated in streamwise direction. Using more sensors improves the performance demonstrably. We therefore seek the optimal sensor placement that improves the prediction in streamwise direction, by minimizing the condition number of the Hessian matrix of the cost functional. An iterative approach is adopted that gradually adjusts the sensor(s) while tracking the principal subspace of the Hessian. For a single sensor, the optimal location is near the edge of the scalar plume. This placement distinguishes signals for adjacent sources much more than sensor directly downstream. For fast identification of the source location and intensity, an eigen-ensemble-variational algorithm is formulated, which relies on the left and right singular vectors, or eigen-sources and eigen-measurements of the scalar impulse-response system. The projection of the true source onto an eigen-source is proportional to the projection of the sensor signal onto the corresponding eigen-measurement. The unknown source is identified by minimizing its deviation from this proportionality. We demonstrate effective ways to use an ensemble of trial sources to estimate the pre-requisite eigen-sources and accurately predict the source location. Furthermore, the effect of sensor noise can be evaluated when Gaussian noise is added to the measurement. All together, the developed algorithms provide effective strategies for reconstruction of unknown scalar sources and optimization of sensor networks. The resulting data provide an important benchmark for future research on olfactory search strategies in fully turbulent environments

Reconstructing velocity and pressure from sparse noisy particle tracks using Physics-Informed Neural Networks

Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from sparse and noisy particle tracks obtained experimentally remains a significant challenge. We introduce a new method for this reconstruction, based on Physics-Informed Neural Networks (PINNs). The method uses a Neural Network regularized by the Navier-Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method [1]. Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions

Multigrid sequential data assimilation for the large-eddy simulation of a massively separated bluff-body flow

The potential for data-driven applications to scale-resolving simulations of turbulent flows is assessed herein. Multigrid sequential data assimilation algorithms have been used to calibrate solvers for Large Eddy Simulation for the analysis of the high-Reynolds-number flow around a rectangular cylinder of aspect ratio 5:1. This test case has been chosen because of a number of physical complexities which elude accurate representation using reduced-order numerical simulation. The results for the statistical moments of the velocity and pressure flow field show that the data-driven techniques employed, which are based on the Ensemble Kalman Filter, are able to significantly improve the predictive features of the solver for reduced grid resolution. In addition, it was observed that, despite the sparse and asymmetric distribution of observation in the data-driven process, the data augmented results exhibit perfectly symmetric statistics and a significantly improved accuracy also far from the sensor location

Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database

We study the applicability of tools developed by the computer vision community for features learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis, the capability of Convolutional Neural Networks embedded in a Deep Generative Adversarial Model (Deep-GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two-dimensional damaged snapshots extracted from a large database of numerical configurations of 3d turbulence in the presence of rotation, a case with multi-scale random features where both large-scale organised structures and small-scale highly intermittent and non-Gaussian fluctuations are present. Second, following a reverse engineering approach, we aim to rank the input flow properties (features) in terms of their qualitative and quantitative importance to obtain a better set of reconstructed fields. We present two approaches both based on Context Encoders. The first one infers the missing data via a minimization of the L2 pixel-wise reconstruction loss, plus a small adversarial penalisation. The second searches for the closest encoding of the corrupted flow configuration from a previously trained generator. Finally, we present a comparison with a different data assimilation tool, based on Nudging, an equation-informed unbiased protocol, well known in the numerical weather prediction community. The TURB-Rot database, http://smart-turb.roma2.infn.it, of roughly 300K 2d turbulent images is released and details on how to download it are given

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

The influence of surface roughness on transition to turbulence in a Mach 4.5 boundary layer is studied using direct numerical simulations. Transition is initiated by the nonlinearly most dangerous inflow disturbance, which causes the earliest possible breakdown on a flat plate for the prescribed inflow energy and Mach number. This disturbance is primarily comprised of two normal second-mode instability waves and an oblique first mode. When localized roughness is introduced, its shape and location relative to the synchronization points of the inflow waves are confirmed to have a clear impact on the amplification of the second-mode instabilities. The change in modal amplification coincides with the change in the height of the near-wall region where the instability wave-speed is supersonic relative to the mean flow; the net effect of a protruding roughness is destabilizing when placed upstream of the synchronization point and stabilizing when placed downstream. Assessment of the effect of the roughness location is followed by an optimization of the roughness height, abruptness and width with the objective of achieving maximum transition delay. The optimization is performed using an ensemble-variational (EnVar) approach, while the location of the roughness is fixed upstream of the synchronization points of the two second-mode waves. The optimal roughness disrupts the phase of the near-wall pressure waves, suppresses the amplification of the primary instability waves, and mitigates the nonlinear interactions that lead to breakdown to turbulence. The outcome is a sustained non-turbulent flow throughout the computational domain

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet, which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet by predicting five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a "plug-and-play" mode.Comment: 30 pages, 17 figure

Estimation of upstream instability waves from wall-pressure measurements in separated high-speed flows

Flow separation and reattachment have a profound impact on the performance of flight vehicles, yet are probed using only a small number of discrete wall sensors. As the flow crosses the onset of separation, the spectra of the incident disturbances change significantly. As a result, the accuracy of interpreting wall-pressure data is sensitive to sensor placement, whether it is positioned upstream of the separation or within the reverse-flow region. This research investigates the challenges of flow estimation within a separated high-speed flow. The impact of separation on the accuracy of flow estimation from wall measurements is first quantified in a compression ramp configuration with a six-degree ramp angle. At freestream Mach $5.59$, this configuration produces a sufficiently strong compression which leads to separation upstream of the corner and downstream reattachment on the ramp. An ensemble variational (EnVar) data assimilation technique is used to perform two flow estimations: the first is conducted with sensor observations taken upstream of the separation, and the second with sensor observations taken from within the separated region. This study adopts numerical observations in lieu of experimental measurements. Whether the sensor data are extracted upstream or within separation, the non-linear optimization improves the error in the initial estimate of the boundary layer instability waves. However, to a lesser extent when the flow estimation utilizes observations from within the separated region. A comparison of the two flow estimations reveals increased errors in the disturbance spectra, as well as in instantaneous wall-pressure observations for the estimate derived from observations in the separated region. Sensor sensitivity to flow disturbances directly impacts to the efficacy of the EnVar procedure. A lack of sensitivity results in an inaccurate or inconclusive assimilation. The difference in the accuracy of the two estimations is interpreted/explained in terms of sensor sensitivity. The sensor sensitivity analysis is conducted using two methods: an ensemble-based approach termed the normalized gradient and an adjoint-based method. Results from both approaches are consistent and reveal a decrease in sensor sensitivity within the separated region to the most unstable boundary layer modes. This decrease leads to increased errors in reconstructing the upstream spectra. The compression-ramp study is the proof-of-concept prior to conducting a first-of-its-kind flow estimation over a cone-flare configuration, using experimental observations. The same EnVar data-assimilation technique is employed, with sensors placed throughout the domain: upstream, within, and downstream of the separated region. The outcome of the flow estimation is consistent with the results from the compression-ramp study. The EnVar technique is successful in improving the initial estimate, and reduces the error in peak spectral content and intensity at each sensor location. However, residual errors remain, predominantly at the downstream sensor locations. Sensor sensitivity analysis highlights adequate sensitivity to the most unstable planar waves that diminishes at higher frequencies. The sensitivity of the sensors to harmonics of the most unstable modes, generated nonlinearly within the domain, is adequate prior to the onset of separation. However, post separation and reattachment, the sensitivity degrades, leading to larger errors in the estimated harmonic modes