arXiv subjects

William R. Wolf

Publications and source records attributed to William R. Wolf.

At least 19 recordsLinked to original sources

arXiv2025

Dissecting coherent motions in extreme wall shear stress events within adverse pressure gradient turbulent boundary layers

Coherent motions associated with extreme wall shear stress events are investigated for adverse pressure gradient turbulent boundary layers (APG-TBLs). The analyses are performed using wall-resolved large eddy simulations of a NACA0012 airfoil at angles of attack of 9 and 12 deg. and Reynolds number 400000. The suction side exhibits attached TBLs which develop under progressively stronger APGs. A quadrant decomposition of Reynolds shear stress shows that sweeps and ejections dominate the momentum exchange between the mean and fluctuating fields, with the intensity of sweeps near the wall growing more rapidly with APG strength. Probability density functions of wall shear stress reveal a higher frequency of backflow events and an increased distribution symmetry with stronger APGs. Extreme positive and backflow events are examined using space--time correlations and conditional statistics. Conditional averages show that backflow events originate from inner-layer sweep motions bringing high-momentum fluid toward the wall, followed by ejections that drive local deceleration. In such cases, the intensity of ejections is modulated by the APG strength. The dynamics of coherent turbulent structures and their interactions are examined using conditional flow field analyses. For extreme positive events, stronger APGs lead to shorter high-speed streaks, while the associated sweep motions generate spanwise velocities that increasingly influence the near-wall dynamics. In the case of backflows, stronger APGs shorten low-speed streaks and amplify high-speed structures associated with sweep motions, promoting spanwise alignment of vortical structures. Overall, APGs modify the structure and dynamics of extreme near-wall events by reshaping the balance and spatial organization of sweep- and ejection-dominated motions.

physics.flu-dyn↗

arXiv2025

Observer-based neural networks for flow estimation and control

Neural network observers (NNOs) are proposed for real-time estimation of fluid flows, addressing a key challenge in flow control: obtaining real-time flow states from a limited set of sparse and noisy sensor data. For this task, we propose a generalization of the classical Luenberger observer. In the present framework, the estimation loop is composed of subsystems modeled as neural networks (NNs). By combining flow information from selected probes and an NN surrogate model (NNSM) of the flow system, we train NNOs capable of fusing information to provide the best estimation of the states, that can in turn be fed back to an NN controller (NNC). The NNO capabilities are demonstrated for three nonlinear dynamical systems. First, a variation of the Kuramoto-Sivashinsky (KS) equation with control inputs is studied, where variables are sparsely probed. We show that the NNO is able to track states even when probes are contaminated with random noise or with sensors at insufficient sample rates to match the control time step. Then, a confined cylinder flow is investigated, where velocity signals along the cylinder wake are estimated by using a small set of wall pressure sensors. In both the KS and cylinder problems, we show that the estimated states can be used to enable closed-loop control, taking advantage of stabilizing NNCs. Finally, we present a legacy dataset of a turbulent boundary layer experiment, where convolutional NNs (CNNs) are employed to implement the models required for the estimation loop. We show that, by combining low-resolution noise-corrupted sensor data with an imperfect NNSM, it is possible to produce more accurate estimates, outperforming both the direct reconstructions via specialized super-resolution NNs and the direct model propagation from initial conditions.

physics.flu-dyn↗

arXiv2025

Characterization of boundary layers on isothermal and adiabatic curved surfaces of a supersonic turbine cascade

The effects of adiabatic and isothermal boundary conditions are investigated on the shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade. Special attention is given to the characterization of the incoming boundary layers over the convex and concave walls of the blade and their impact in the SBLIs. Large eddy simulations (LES) are performed for an inlet Mach number of $\mathbf{M_\infty = 2.0}$ and Reynolds number based on the axial chord $\mathbf{Re = 200\,000}$. For the isothermal condition, the wall to inlet temperature ratio is $\mathbf{T_w/T_{\infty}=0.75}$, representing a cooled wall. Different incident shock wave topologies occur on the suction and pressure sides of the airfoil. For the former, an oblique shock impinges on the boundary layer leading to a larger separation bubble. On the other hand, a normal shock from a Mach reflection induces a small separation region near the wall for the pressure side. Results are presented in terms of mean velocity and temperature contours, and the incoming boundary layers are characterized by looking at the Clauser parameter, shape factor, dilatation and turbulent kinetic energy (TKE) profiles. Inspection of the shape factors show that the adiabatic wall boundary layers are more prone to separate than the isothermal ones. This is indeed observed in the airfoil suction side, but not on the pressure side, where the flow separates in the same chord position regardless of the thermal boundary condition. This is a topic for investigation in the final version of the paper. An assessment of the dilatation and TKE profiles explains the disparities of the bubble sizes on the pressure and suction sides of the airfoil.

physics.flu-dyn↗

arXiv2025

Characterization of supersonic boundary layers of adiabatic and isothermal curved surfaces with shock interactions

Boundary layers of adiabatic and isothermal curved walls are investigated for a supersonic turbine cascade, including the effects of shock-boundary layer interactions (SBLIs). Wall-resolved large eddy simulations (LES) are performed for a linear cascade of blades with an inlet Mach number of $M_\infty = 2.0$ and Reynolds number based on the axial chord $Re_\infty = 200\,000$. The wall to inlet temperature ratio of the isothermal case is $T_w/T_{\infty}=0.75$, representing a cooled wall. An assessment of the effects of pressure gradient, thermal boundary conditions and SBLIs is presented in terms of the downstream variation of mean flow quantities such as density, temperature, and momentum profiles. The different thermal boundary conditions affect the density and temperature profiles along the boundary layer, where cooling increases the density of the gas near the wall, and reduces its temperature and viscosity. Both of these effects make the momentum profiles fuller and, hence, the boundary layer of the isothermal case is less prone to separate than that of the adiabatic wall. The mean density profiles are also affected by pressure gradients induced by the convex and concave curvatures of the blade, which lead to expansion and compression of the flow, respectively. The analysis of separate terms from the momentum balance equation explains the behavior of various physical mechanisms in the inner and outer regions of the supersonic boundary layers. The importance of mean flow advection, compressibility, and Reynolds stresses is presented in terms of flow acceleration and deceleration. The impact of the SBLIs in the momentum balance mechanisms is also investigated, showing that a combination of compressions and expansions impact the boundary layers by redirecting the flow toward the wall due to the shock formations.

physics.flu-dyn↗

arXiv2025

Pressure Field Reconstruction with SIREN: A Mesh-Free Approach for Image Velocimetry in Complex Noisy Environments

This work presents a novel approach for pressure field reconstruction from image velocimetry data using SIREN (Sinusoidal Representation Network), emphasizing its effectiveness as an implicit neural representation in noisy environments and its mesh-free nature. While we briefly assess two recently proposed methods - one-shot matrix-omnidirectional integration (OS-MODI) and Green's function integral (GFI) - the primary focus is on the advantages of the SIREN approach. The OS-MODI technique performs well in noise-free conditions and with structured meshes but struggles when applied to unstructured meshes with high aspect ratio. Similarly, the GFI method encounters difficulties due to singularities inherent from the Newtonian kernel. In contrast, the proposed SIREN approach is a mesh-free method that directly reconstructs the pressure field, bypassing the need for an intrinsic grid connectivity and, hence, avoiding the challenges associated with ill-conditioned cells and unstructured meshes. This provides a distinct advantage over traditional mesh-based methods. Moreover, it is shown that changes in the architecture of the SIREN can be used to filter out inherent noise from velocimetry data. This work positions SIREN as a robust and versatile solution for pressure reconstruction, particularly in noisy environments characterized by the absence of mesh structure, opening new avenues for innovative applications in this field.

cs.CV↗

arXiv2025

Resultant force on grains of a real sand dune: How to measure it?

Dunes are bedforms found on sandy terrains shaped by fluid flow on Earth, Mars, and other celestial bodies. Despite their prevalence, understanding dune dynamics at the grain scale is challenging due to the vast number of grains involved. In this study, we demonstrate a novel approach to estimate the forces acting on individual dune grains using images. By combining subaqueous experiments, high-speed camera recordings, discrete numerical simulations, and a specially trained convolutional neural network, we can quantify these forces with high accuracy. This method represents a breakthrough in studying granular dynamics, offering a new way to measure forces not only on dune grains but also on smaller objects, such as rocks, boulders, rovers, and man-made structures, observed in satellite images of both Earth and Mars. This technique expands our ability to analyze and understand fluid-grain interactions in diverse environments.

physics.geo-ph↗

arXiv2023

Embedded shear layers in turbulent boundary layers of a NACA0012 airfoil at high angles of attack

An investigation of turbulent boundary layers (TBLs) is presented for a NACA0012 airfoil at angles of attack 9 and 12 deg. Wall-resolved large eddy simulations (LES) are conducted for a freestream Mach number M = 0.2 and chord-based Reynolds number Re = 4x10^5, where the boundary layers are tripped near the airfoil leading edge on the suction side. For the angles of attack analyzed, mild, moderate and strong adverse pressure gradients (APGs) develop over the airfoil. Despite the strong APGs, the mean flow remains attached along the entire airfoil suction side. Similarly to other APG-TBLs investigated in the literature, a secondary peak appears in the Reynolds stress and turbulence production profiles. This secondary peak arises in the outer layer and, for strong APGs, it may overcome the first peak typically observed in the inner layer. The analysis of the turbulence production shows that other components of the production tensor become important in the outer layer besides the shear term. For moderate and strong APGs, the mean velocity profiles depict three inflexion points, the third being unstable under inviscid stability criteria. In this context, an embedded shear layer develops along the outer region of the TBL leading to the formation of two-dimensional rollers typical of a Kelvin-Helmholtz instability which are captured by a spectral proper orthogonal decomposition (SPOD) analysis. The most energetic SPOD spatial modes of the tangential velocity show that streaks form along the airfoil suction side and, as the APG becomes stronger, they grow along the spanwise and wall-normal directions, having a spatial support along the entire boundary layer.

physics.flu-dyn↗

arXiv2023

Analysis of transient and intermittent flows using a multidimensional empirical mode decomposition

Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust spatial support. In this context, although widely used, methods based on singular value decomposition (SVD) may produce modes that are difficult to interpret when applied to problems dominated by intermittent and transient events. Fortunately, specific modal decomposition techniques have been recently developed to analyze such problems. However, a proper comparison between existing methods is still lacking from the literature. Therefore, this work compares two recent methods: the fast adaptive multivariate empirical mode decomposition (FA-MVEMD) and the multi-resolution dynamic mode decomposition (mrDMD). These techniques are employed here for the study of flow databases involving transient and intermittent dynamics. Specifically, the investigated problems include an SD7003 airfoil subjected to deep dynamic stall conditions, and a steady NACA0012 airfoil operating at a transitional Reynolds number. In the former case, the methods are employed to investigate the onset and evolution of the dynamic stall vortex (DSV), while in the latter case, intermittent vortex pairing is analyzed. We show that the combination of a multidimensional EMD with the Hilbert transform provides modes with superior spatial support when compared to the mrDMD, also allowing the characterization of instantaneous frequencies of coherent structures. Moreover, the EMD also condenses a larger amount of information within a single intrinsic mode function (IMF).

physics.flu-dyn↗

arXiv2023

Flow imaging as an alternative to pressure transducers through vision transformers and convolutional neural networks

In this work, we propose a framework whereby flow imaging data is leveraged to extract relevant information from flowfield visualizations. To this end, a vision transformer (ViT) model is developed to predict the unsteady pressure distribution over an airfoil under dynamic stall from images of the flowfield. The network is capable of identifying relevant flow features present in the images and associate them to the airfoil response. Results demonstrate that the model is effective in interpolating and extrapolating between flow regimes and for different airfoil motions, meaning that ViT-based models may offer a promising alternative for sensors in experimental campaigns and for building robust surrogate models of complex unsteady flows. In addition, we uniquely treat the image semantic segmentation as an image-to-image translation task that infers semantic labels of structures from the input images in a supervised way. Given an input image of the velocity field, the resulting convolutional neural network (CNN) generates synthetic images of any corresponding fluid property of interest. In particular, we convert the velocity field data into pressure in order to subsequently estimate the pressure distribution over the airfoil in a robust manner.

physics.flu-dyn↗

arXiv2023

Dynamic Mode Decomposition of High Reynolds Number Supersonic Jet Flows

Current design constraints have encouraged the studies of aeroacoustic fields around compressible jet flows. The present work addresses the numerical study of unsteady turbulent jet flows as a preparation for future aeroacoustic analyses of main engine rocket plumes. An in-house large eddy simulation tool is used in order to reproduce high fidelity results of compressible jet flows. The large eddy simulation formulation is written using a second order numerical scheme for a finite difference spatial discretization. Numerical simulations of perfectly expanded jets are performed and the results are compared to the literature. Dynamic mode decompositions (DMD) of the jet flow, using large size three-dimensional snapshots, are performed. Three variables are analyzed, namely, the velocity magnitude, the vorticity magnitude and the divergence of velocity. In particular, two frequencies are identified and they are linked to flow structures observed in experiments performed by other authors in the literature. The spatial shapes of the corresponding dynamic modes are also discussed.

physics.flu-dyn↗

arXiv2022

Influence of different subgrid-scale models in low-order LES of supersonic jet flows

The present work is concerned with a study of large eddy simulations (LES) of unsteady turbulent jet flows. In particular, the present analysis is focused on the effects of the subgrid-scale modeling used when a second-order spatial discretization methodology is employed for the numerical simulations. The present effort addresses perfectly expanded supersonic jets, because the authors want to emphasize the effects of the jet mixing phenomena. The LES formulation is discretized using the finite difference approach, after the equations are rewritten in a generalized coordinate system. Both space and time discretizations are second-order accurate and an explicit time march is adopted. Special care is dedicated to the discretization of the energy equation to appropriately model the set of filtered equations appearing in the LES formulation. The classical Smagorinsky, the dynamic Smagorinsky and the Vreman models are the subgrid-scale closures selected for the present work. The computational results are compared to data in the literature to validate the present simulation tool. Results indicate that the characteristics of numerical discretization can be as important as the effects of the subgrid-scale models for such low-order spatial discretization schemes. A detailed analysis is presented for the performance of each subgrid closure in the numerical context here considered.

physics.flu-dyn↗

arXiv2022

Unsteadiness of Shock-Boundary Layer Interactions in a Mach 2.0 Supersonic Turbine Cascade

The physics of shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade at Mach 2.0 and Reynolds number 395,000, based on the axial chord, is investigated through a wall-resolved large eddy simulation. Special attention is given to the characterization of the low-frequency dynamics of the separation bubbles using flow visualization, spectral analysis, space-time cross correlations, and flow modal decomposition. The mean flowfield shows different shock structures formed on both sides of the airfoil. On the suction side, an oblique shock impinges on the turbulent boundary layer, whereas a Mach reflection interacts with the pressure side boundary layer. The interactions taking place in the present turbine cascade show similarities and discrepancies with respect to more canonical cases. For example, the characteristic frequencies of the shock/bubble motions are comparable to those described in the literature of canonical cases. However, the suction side bubble leads to compression waves that do not coalesce into a separation shock, and a thin bubble forms on the pressure side despite the strong normal shock from the Mach reflection. Instantaneous flow visualizations illustrate elongated streamwise structures on the incoming boundary layers and their interactions with the shocks and separation bubbles. The space-time cross-correlations reveal that the near-wall streaks drive the motion of the suction side separation bubble, which in turn promotes oscillations of the reattachment shock and shear layer flapping. Organized motions in the SBLIs and their corresponding characteristic frequencies and spatial support are identified using proper orthogonal decomposition.

physics.flu-dyn↗

arXiv2022

Switch of tonal noise generation mechanisms in airfoil transitional flows

Large eddy simulations are performed to study tonal noise generation by a NACA0012 airfoil at an angle of attack ${α= 3}$ deg. and freestream Mach number of ${M_{\infty} = 0.3}$. Different Reynolds numbers are analyzed spanning ${0.5 \times 10^5 \le Re \le 4 \times 10^5}$. Results show that the flow patterns responsible for noise generation appear from different laminar separation bubbles, including one observed over the airfoil suction side and another near the trailing edge, on the pressure side. For lower Reynolds numbers, intermittent vortex dynamics on the suction side results in either coherent structures or turbulent packets advected towards the trailing edge. Such flow dynamics also affects the separation bubbles on the pressure side, which become intermittent. Despite the irregular occurrence of laminar-turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. Increasing the Reynolds number leads to a permanent turbulent regime on the suction side that reduces the coherence level causing only small scale turbulent eddies to be observed. Furthermore, the laminar separation bubble on the suction side almost vanishes while that on the pressure side becomes more pronounced and permanent. As a consequence, the dominant noise generation mechanism becomes the vortex shedding along the wake.

physics.flu-dyn↗

arXiv2022

Transition, intermittency and phase interference effects in airfoil secondary tones and acoustic feedback loop

A large eddy simulation is performed to study secondary tones generated by a NACA0012 airfoil at angle of attack of $α= 3^{\circ}$ with freestream Mach number of $M_{\infty} = 0.3$ and Reynolds number of $Re = 5 \times 10^4$. Laminar separation bubbles are observed over the suction side and near the trailing edge, on the pressure side. Flow visualization and spectral analysis are employed to investigate vortex shedding aft of the suction side separation bubble. Vortex interaction results in merging or bursting such that coherent structures or turbulent packets are advected towards the trailing edge leading to different levels of noise emission. Despite the intermittent occurrence of laminar-turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. To understand the role of flow instabilities on the tones, the linearized Navier-Stokes equations are examined in its operator form through bi-global stability and resolvent analyses, and by time evolution of disturbances using a matrix-free method. These linear global analyses reveal amplification of disturbances over the suction side separation bubble. Non-normality of the linear operator leads to further transient amplification due to modal interaction among eigenvectors. Two-point, one time autocovariance calculations of pressure along the spanwise direction elucidate aspects of the acoustic feedback loop mechanism in the non-linear solutions. This feedback process is self-sustained by acoustic waves radiated from the trailing edge, which reach the most sensitive flow location between the leading edge and the separation bubble, as identified by the resolvent analysis. Leading edge disturbances arising from secondary diffraction and phase interference among the most unstable frequencies computed in the eigenspectrum are also shown to have an important role in the feedback loop.

physics.flu-dyn↗

arXiv2020

Calibration of projection-based reduced-order models for unsteady compressible flows

An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel calibration strategy is proposed for the LSPG method and two test cases are analyzed. The first consists of a subsonic airfoil flow where boundary layer instabilities are responsible for trailing-edge noise generation and the second comprises a supersonic airfoil flow with a transient period where a detached shock wave propagates upstream at the same time that shock-vortex interaction occurs at the trailing edge. Results show that calibration produces stable and long-time accurate for both cases. In order to reduce the computational costs of the LSPG models, an accelerated greedy missing point estimation (MPE) algorithm is employed for hyper-reduction. For the first case investigated, LSPG solutions obtained with hyper-reduction show good comparison with those obtained by the full order model. However, for the supersonic case the transient features of the flow need to be properly captured by the sampled points. Otherwise, the dynamics of the moving shock wave are not fully recovered. The impact of different time-marching schemes is also assessed and, differently than reported in literature, Galerkin models are shown to be more accurate than those computed by LSPG when the non-conservative form of the Navier-Stokes equations are solved. For the supersonic case, the Galerkin and LSPG models (without hyper-reduction) capture the overall dynamics of the detached and oblique shock waves along the airfoil. However, when shock-vortex interaction occurs at the trailing-edge, the Galerkin ROM is able to capture the high-frequency fluctuations from vortex shedding while the LSPG presents a more dissipative solution, not being able to recover the flow dynamics.

physics.comp-ph↗

arXiv2020

Strong Scaling of Numerical Solver for Supersonic Jet Flow Configuration

Acoustics loads are rocket design constraints which push researches and engineers to invest efforts in the aeroacoustics phenomena which is present on launch vehicles. Therefore, an in-house computational fluid dynamics tool is developed in order to reproduce high-fidelity results of supersonic jet flows for aeroacoustic analogy applications. The solver is written using the large eddy simulation formulation that is discretized using a finite-difference approach and an explicit time integration. Numerical simulations of supersonic jet flows are very expensive and demand efficient high-performance computing. Therefore, non-blocking message passage interface protocols and parallel input/output features are implemented into the code in order to perform simulations which demand up to one billion degrees of freedom. The present work evaluates the parallel efficiency of the solver when running on a supercomputer with a maximum theoretical peak of 127.4 TFLOPS. Speedup curves are generated using nine different workloads. Moreover, the validation results of a realistic flow condition are also presented in the current work.

cs.CE↗

arXiv2020

On the scalability of CFD tool for supersonic jet flow configurations

New regulations are imposing noise emissions limitations for the aviation industry which are pushing researchers and engineers to invest efforts in studying the aeroacoustics phenomena. Following this trend, an in-house computational fluid dynamics tool is build to reproduce high fidelity results of supersonic jet flows for aeroacoustic analogy applications. The solver is written using the large eddy simulation formulation that is discretized using a finite difference approach and an explicit time integration. Numerical simulations of supersonic jet flows are very expensive and demand efficient high-performance computing. Therefore, non-blocking message passage interface protocols and parallel Input/Output features are implemented into the code in order to perform simulations which demand up to one billion grid points. The present work addresses the evaluation of code improvements along with the computational performance of the solver running on a computer with maximum theoretical peak of 2.727 PFlops. Different mesh configurations, whose size varies from a few hundred thousand to approximately one billion grid points, are evaluated in the present paper. Calculations are performed using different workloads in order to assess the strong and weak scalability of the parallel computational tool. Moreover, validation results of a realistic flow condition are also presented in the current work.

cs.DC↗

arXiv2019

On Secondary Tones Arising in Trailing-Edge Noise at Moderate Reynolds Numbers

Direct numerical simulations are carried out to investigate the flow features responsible for secondary tones arising in trailing-edge noise at moderate Reynolds numbers. Simulations are performed for a NACA 0012 airfoil at freestream Mach numbers 0.1, 0.2 and 0.3 for angle of incidence 0 deg. and for Mach number 0.3 at 3 deg. angle of incidence. The Reynolds number based on the airfoil chord is fixed at $Re_c=10^5$. Flow configurations are investigated where noise generation arises from the scattering of boundary layer instabilities at the trailing edge. Results show that noise emission has a main tone with equidistant secondary tones, as discussed in literature. An interesting feature of the present flows at zero incidence is shown; despite the geometric symmetry, the flows become non-symmetric with a separation bubble only on one side of the airfoil. A separation bubble is also observed for the non-zero incidence flow. For both angles of incidence analyzed, it is shown that low-frequency motion of the separation bubbles induce a frequency modulation of the flow instabilities developed along the airfoil boundary layer. When the airfoil is at 0 deg. angle of attack an intense amplitude modulation is also observed in the flow quantities, resulting in a complex vortex interaction mechanism at the trailing edge. Both amplitude and frequency modulations directly affect the velocity and pressure fluctuations that are scattered at the trailing edge, what leads to secondary tones in the acoustic radiation.

physics.flu-dyn↗