arXiv subjects

Eduardo Martini

Publications and source records attributed to Eduardo Martini.

At least 19 recordsLinked to original sources

arXiv2024

Scalable resolvent analysis for three-dimensional flows

Resolvent analysis is a powerful tool for studying coherent structures in turbulent flows. However, its application beyond canonical flows with symmetries that can be used to simplify the problem to inherently three-dimensional flows and other large systems has been hindered by the computational cost of computing resolvent modes. In particular, the CPU and memory requirements of state-of-the-art algorithms scale poorly with the problem dimension, \ie the number of discrete degrees of freedom. In this paper, we present RSVD-$Δt$, a novel approach that overcomes these limitations by combining randomized singular value decomposition with an optimized time-stepping method for computing the action of the resolvent operator. Critically, the CPU cost and memory requirements of the algorithm scale linearly with the problem dimension. We develop additional strategies to minimize these costs and control errors. We validate the algorithm using a Ginzburg-Landau test problem and demonstrate RSVD-$Δt$'s low cost and improved scaling using a three-dimensional discretization of a turbulent jet. Lastly, we use it to study the impact of low-speed streaks on the development of Kelvin-Helmholtz wavepackets in the jet via secondary stability analysis, a problem that would have been intractable using previous algorithms.

physics.flu-dyn↗

arXiv2024

Wave reflections and resonance in a Mach 0.9 turbulent jet

This work aims to provide a more complete understanding of the resonance mechanisms that occur in turbulent jets at high subsonic Mach number, as shown by Towne et al. (J. Fluid Mech., vol. 825, 2017, pp. 1113-1152). Resonance was suggested by that study to exist between upstream- and downstream-travelling guided waves. Five possible resonance mechanisms were postulated, each involving different families of guided waves that reflect in the nozzle exit plane and at a number of downstream turning points. However, that study did not identify which of the five resonance mechanisms underpin the observed spectral peaks. In this work, the waves underpinning resonance are identified via a biorthogonal projection of Large Eddy Simulation data on eigenbases provided by a locally parallel linear stability analysis. Two of the five scenarios postulated by Towne et al. are thus confirmed to exist in the turbulent jet. The reflection-coefficients in the nozzle exit and turning-point planes are, furthermore, identified. Such information is required as input for simplified resonance-modelling strategies such as developed in Jordan et al. (J. Fluid Mech., vol. 853, 2018, pp. 333-358) for jet-edge resonance, and in Mancinelli et al. (Exp. Fluids, vol. 60, 2019, pp. 1-9) for supersonic screech.

physics.flu-dyn↗

arXiv2024

Effect of streaks on hypersonic boundary layer instability

Hypersonic boundary layers exhibit diverse transition pathways, influenced by various flow conditions and environments. Non-modal mechanisms, such as the lift-up effect, are recognized as pivotal contributors to transition, particularly over complex geometries like rough walls or blunted forebodies. In this study, we investigate the impact of steady streaks on the transition to turbulence in hypersonic boundary layers. Streaky baseflows are generated using optimal disturbances at the inlet, forming the basis for our analysis. We conduct linearized direct numerical simulations on these baseflows at Mach number $M_\infty=6.0$, using white noise forcing to trigger instabilities. An efficient extension of the SPOD method is applied to identify and track the instabilities originating from the broadband forcing on the 3D non-homogeneous baseflows. The results highlight the dominant influence of low-frequency first-mode instabilities and streak-associated instabilities in the linear regime. These findings emphasize the critical role of streaks in hypersonic boundary layer transition and provide valuable insights into this complex phenomenon.

physics.flu-dyn↗

arXiv2024

Modal decomposition of nonlinear interactions in wall turbulence

Coherent structures are found in many different turbulent flows and are known to drive self-sustaining processes in wall turbulence. Identifying the triadic interactions which generate coherent structures can provide insights beyond what is possible with linearized models. There are infinite possible interactions that may generate a given structure. Thus, a method to systematically study those, ranking them in terms of their contribution to the structure of interest, is essential. We here use the resolvent-based extended spectral proper orthogonal decomposition (RESPOD) approach (Karban, U. et al. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. Journal of Fluid Mechanics 969, A36) to rank the triadic interactions which give rise to the dominant coherent structures in minimal Couette flows at Reynolds number 400 and 1000. Our analysis identifies that six triadic interactions dominate the most energetic coherent structure, revealing the capability of the methodology to identify and rank nonlinear interactions. The approach can be used to analyse the energy exchange in turbulent flows and may guide the construction of reduced-order models based on the interplay between different flow modes. Based on this framework, we introduce a modelling strategy where the interactions increasing or reducing the energy of a given mode are grouped as sources and sinks, respectively. The effect of the sinks is embedded in the resolvent operator by using an eddy viscosity model. The sources are used for driving this modified resolvent operator and are shown to yield accurate flow predictions at zero frequency. We discuss that this strategy can be useful when analysing nonlinear interactions or modelling forcing at high-Reynolds-number flows.

physics.flu-dyn↗

arXiv2024

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved data sets. In this work, a linearised Ginzburg-Landau model is considered in order to study the method's convergence. SPOD modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg-Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and span-wise velocity components along the stream-wise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

physics.flu-dyn↗

arXiv2024

Reactive experimental control of turbulent jets

We present an experimental study of reactive control of turbulent jets. We target axisymmetric disturbances associated with coherent structures, which are known to underpin the peak sound radiation of turbulent jets. We first consider a forced jet flow case, such that the coherent structures can be amplified above background levels, which makes it easier to detect them by the sensors. We then consider the more challenging case of a natural jet, i.e., without artificial forcing. The control strategy explores linear convective mechanisms in the initial jet region, which justifies application of linear control theory. The control law is constructed in the frequency domain, based on empirically determined transfer functions. The Wiener-Hopf formalism is used to enforce causality, providing an optimal causal solution, thus, preventing the drop in performance that may be observed in flow control applications that use simpler wave-cancellation methods. With this approach, we could improve the control performance of forced turbulent jets compared to results obtained in previous studies, attaining order-of-magnitude attenuation of power spectra of velocity fluctuations. Furthermore, we could obtain substantial levels of attenuation of natural turbulent jets, of about 60% in power spectra for the most amplified frequencies. These results open new directions for the control of turbulent flows.

physics.flu-dyn↗

arXiv2024

Experimental control of Tollmien-Schlichting waves using the Wiener-Hopf formalism

Reactive flow control has been shown as a promising tool to improve, among other aspects, the aerodynamic characteristics of an aircraft. This paper focuses on the use of reactive flow control to attenuate Tollmien-Schlichting (TS) waves over a wing profile. TS waves are an instability mechanism that is one of the first stages of boundary layer transition to turbulence. The Wiener-Hopf technique was used in this work for the experimental boundary layer control. The approach improves previous wave-cancellation techniques that, by constructing control kernels in the frequency domain, lead to control kernels with a non-causal part, i.e., actuation would need future sensor information to be constructed. In practical applications, it is unfeasible to access this type of information. Ignoring the non-causal part of the kernel leads to suboptimal solutions that might significantly degrade the performance of the controller. The Wiener-Hopf formalism allows us to take into account causality constraints in the formulation of the control problem, leading to an optimal realistic solution and a control kernel that is causal by construction. Moreover, it is possible to construct the control strategy based only on the power and cross-spectra obtained experimentally, in a data-driven approach. The present work shows how to apply experimentally the Wiener-Hopf resolvent-based formalism using signals from a wind tunnel experiment, demonstrating that the Tollmien-Schlichting waves can be effectively attenuated via a Wiener-Hopf based controller, which yielded better results than a typical wave-cancellation approach.

physics.flu-dyn↗

arXiv2023

Perturbation amplification near the stagnation point of blunt bodies

Different transition to turbulence routes for the flow around blunt bodies are possible. Non-modal amplification of perturbations via the lift-up effect has recently been explored to explain transition near the stagnation point in axisymmetric bodies. However, only perturbations already present in the boundary layer can be amplified, and the mechanisms by which free-stream perturbations enter the boundary layer have not yet been fully explored. In this study, we present an investigation of how disturbances enter the boundary layer via the stagnation point. This linear mechanism is expected to dominate over non-linear mechanisms previously identified on the formation of boundary layer perturbations at low turbulence intensity levels. A parametric investigation is presented, revealing trends with Reynolds and Mach numbers.

physics.flu-dyn↗

arXiv2023

Modeling closed-loop control of installation noise using Ginzburg-Landau equation

Installation noise is a dominant source associated with aircraft jet engines. Recent studies show that linear wavepacket models can be employed for prediction of installation noise, which suggests that linear control strategies can also be adopted for mitigation of it. We present here a simple model to test different control approaches and highlight the potential restrictions on a successful noise control in an actual jet. The model contains all the essential elements for a realistic representation of the actual control problem: a stochastic wavepacket is obtained via a linear Ginzburg-Landau model; the effect of the wing trailing edge is accounted for by introducing a semi-infinite half plane near the wavepacket; and the actuation is achieved by placing a dipolar point source at the trailing edge, which models a piezoelectric actuator. An optimal causal resolvent-based control method is compared against the classical wave-cancellation method. The effect of the causality constraint on the control performance is tested by placing the sensor at different positions. We demonstrate that when the sensor is not positioned sufficiently upstream of the trailing edge, which can be the case for the actual control problem due to geometric restrictions, causality reduces the control performance. We also show that this limitation can be moderated using the optimal causal control together with modelling of the forcing.

physics.flu-dyn↗

arXiv2022

Solutions to aliasing in time-resolved flow data

Avoiding aliasing in time-resolved flow data obtained through high fidelity simulations while keeping the computational and storage costs at acceptable levels is often a challenge. Well-established solutions such as increasing the sampling rate or low-pass filtering to reduce aliasing can be prohibitively expensive for large data sets. This paper provides a set of alternative strategies for identifying and mitigating aliasing that are applicable even to large data sets. We show how time-derivative data, which can be obtained directly from the governing equations, can be used to detect aliasing and to turn the ill-posed problem of removing aliasing from data into a well-posed problem, yielding a prediction of the true spectrum. Similarly, we show how spatial filtering can be used to remove aliasing for convective systems. We also propose strategies to prevent aliasing when generating a database, including a method tailored for computing nonlinear forcing terms that arise within the resolvent framework. These methods are demonstrated using a non-linear Ginzburg-Landau model and large-eddy simulation (LES) data for a subsonic turbulent jet.

physics.flu-dyn↗

arXiv2022

Unbiased two-windows approach for Welch's method

Periodogram methods are widely used for the estimation of power- and cross-spectra, of which Welch's method is the most popular. Previous studies have analyzed the variance of the power spectra estimates and developed analytical probability functions, showing that the approach is unbiased when applied to white-noise signals or in the limit of infinite window lengths. However, no explicit expression for the estimation bias is available for more complex signals when finite windows are used. In this study, we show that, for finite window lengths, Welch's method is biased for all signals other than the white-noise signal. A novel two-window approach that is unbiased when applied to signals with bounded correlation lengths is proposed. Numerical experiments are used to illustrate the advantages of the novel approach.

physics.data-an↗

arXiv2022

Resolvent-based tools for optimal estimation and control via the Wiener-Hopf formalism

The application of control tools to complex flows frequently requires approximations, such as reduced-order models and/or simplified forcing assumptions, where these may be considered low-rank or defined in terms of simplified statistics (e.g. white noise). In this work, we propose a resolvent-based control methodology with causality imposed via a Wiener-Hopf formalism. Linear optimal causal estimation and control laws are obtained directly from full-rank, globally stable systems with arbitrary disturbance statistics, circumventing many drawbacks of alternative methods. We use efficient, matrix-free methods to construct the matrix Wiener-Hopf problem, and we implement a tailored method to solve the problem numerically. The approach naturally handles forcing terms with space-time colour; it allows inexpensive parametric investigation of sensor/actuator placement in scenarios where disturbances/targets are low rank; it is directly applicable to complex flows disturbed by high-rank forcing; it has lower cost in comparison to standard methods; it can be used in scenarios where an adjoint solver is not available; or it can be based exclusively on experimental data. The method is particularly well-suited for the control of amplifier flows, for which optimal control approaches are typically robust. Validation of the approach is performed using the linearized Ginzburg-Landau equation. Flow over a backward-facing step perturbed by high-rank forcing is then considered. Sensor and actuator placement are investigated for this case, and we show that while the flow response downstream of the step is dominated by the Kelvin-Helmholtz mechanism, it has a complex, high-rank receptivity to incoming upstream perturbations, requiring multiple sensors for control.

physics.flu-dyn↗

arXiv2021

Including acoustic modes in the vortex-sheet eigenbasis of a jet

Vortex-sheet models of jets are widely used to describe the dynamics of modes, such as the Kelvin-Helmholtz instability and guided acoustic waves. However, it is seldom pointed out in the literature the absence of the free-stream acoustic modes in the vortex-sheet spectrum. This indicates that free-stream sound waves are not eigensolutions of the parallel jet. This family of modes is important if, for example, one is interested in problems of sound emission or flow-acoustic interactions. In this work we show how a distantly-confined jet may be used as a surrogate problem for the free jet, in which free-stream acoustic waves appear as a set of discrete modes. Comparing the modes observed in the free jet with those of the distantly-confined jet, we show that, other than the free-stream acoustic modes, the eigenvectors and eigenvalues converge with wall distance. The proposed surrogate problem thus efficiently reproduces the dynamics of the original problem, while allowing to account for the dynamics of free-stream acoustic modes.

physics.flu-dyn↗

arXiv2021

Reflection and transmission of a Kelvin-Helmholtz wave incident on a shock in a jet

Screech tones in supersonic jets are underpinned by resonance between downstream-travelling Kelvin-Helmholtz waves and upstream-travelling acoustic waves. Specifically, recent work suggests that the relevant acoustic waves are guided within the jet and are described by a discrete mode of the linearised Navier-Stokes equations. However, the reflection mechanism that converts downstream-travelling waves into upstream-travelling waves, and vice versa, has not been thoroughly addressed, leading to missing physics within most resonance models. In this work we investigate the reflection and transmission of waves generated by the interaction between a Kelvin-Helmholtz wave and a normal shock in an under-expanded jet using a mode-matching approach. Both vortex-sheet and finite-thickness shear-layer models are explored, quantifying the impact of the shear layer in the reflection process. This approach could enable more quantitative predictions of resonance phenomena in jets and other fluid systems.

physics.flu-dyn↗

arXiv2021

Resolvent-based estimation of turbulent channel flow using wall measurements

We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, A2) showed that the resolvent-based estimator is optimal when the true space-time forcing statistics are utilized, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterize these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models - an eddy-viscosity model and white-noise forcing - and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer-layer, but only using the true forcing statistics allows accurate estimation of large-scale log-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

physics.flu-dyn↗

arXiv2020

Accurate Frequency Domain Identification of ODEs with Arbitrary Signals

The difficulty in frequency domain identification is that frequency components of arbitrary inputs and outputs are not related by the system's transfer function if signals are windowed. When rectangular windows are used, it is well known that this difference is related to transient effects that can be estimated alongside the systems' parameters windows. In this work, we generalize the approach for arbitrary windows, showing that signal windowing introduces additional terms in the system's equations. The formalism is useful for frequency-domain input-output analysis of a system, and also for system identification. For the latter application, the approach considerably reduces aliasing effects and allows the computation of the associated correction terms, reducing the number of parameters that need to be estimated. The system identification approach has features of the modulating-function technique, filtering out the effects of initial conditions while retaining the spectral interpretation of frequency-domain methods.

eess.SP↗

arXiv2020

Closed-loop control of forced turbulent jets

Closed-loop control of turbulent flows is a challenging problem with important practical and fundamental implications. We perform closed-loop control of forced, turbulent jets based on a wave-cancellation strategy. The study is motivated by the success of recent studies in applying wave cancellation to control instability waves in transitional boundary layers and free-shear flows. Using a control law obtained through a system-identification technique, we successfully implement wave-cancellation-based, closed-loop control, achieving order-of-magnitude attenuations of velocity fluctuations. Control is shown to reduce fluctuation levels over an extensive streamwise range.

physics.flu-dyn↗

arXiv2020

Efficient computation of global resolvent modes

Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows with large gain separation. Direct computation of force and response modes using a singular value decomposition of the full resolvent matrix is feasible only for simple problems; despite recent progress, the cost of resolvent analysis for complex flows remains considerable. In this paper, we propose a new matrix-free method for computing resolvent modes based on integration of the linearized equations and the corresponding adjoint system in the time domain. Our approach achieves an order of magnitude speedup when compared to previous matrix-free time stepping methods by enabling all frequencies of interest to be computed simultaneously. Two different methods are presented: one based on analysis of the transient response, providing leading modes with fine frequency discretization; and another based on the steady-state response to a periodic forcing, providing optimal and suboptimal modes for a discrete set of frequencies. The methods are validated using a linearized Ginzburg-Landau equation and applied to the three dimensional flow around a parabolic body.

physics.flu-dyn↗