arXiv subjects

Lutz Lesshafft

Publications and source records attributed to Lutz Lesshafft.

9 recordsLinked to original sources

arXiv2026

Jet-edge interaction: linear and non-linear frequency-selection mechanisms

We consider a round turbulent jet grazing a rectangular plate angled at $45^\circ$. Through sound pressure measurements, the tonal dynamics associated with jet-edge interaction are explored in a parameter space comprising jet Mach number, $M_j$, and plate radial position, $R/D$. A variety of spectral signatures are observed and classified. The classification - based on analysis of power-spectral density and bicoherence, and on the resonance model proposed by Jordan et al. (2018) - comprises: broadband spectra; tonal spectra associated with purely linear frequency-selection mechanisms; tonal spectra associated with both linear and non-linear frequency selection. The classification identifies regions in the parameter space ($M_j$, $R/D$); and clarifies mechanisms underpinning regime changes. The linear frequency selection (LFS) regime comprises multiple tones, with no evidence of triad interaction. A regime involving non-linear frequency selection emerges from this state, with the strong amplification of one LFS tone, which then generates multiple harmonics. Intermediate regimes are identified involving weaker, non-harmonic triadic interactions where two LFS tones interact to generate a third tone. In addition to these mechanisms a mode-switching mechanism is identified at $M_j$ = 0.84 and shown to result from the cut-on of a new upstream-travelling wave at that Mach number. The mode-switch is found to be remarkably robust, occurring in a repeatable manner over a Mach-number increment of 0.01 regardless of whether the Mach number is increased or decreased (no hysteresis is observed).

physics.flu-dyn↗

arXiv2024

Onset of global instability in a premixed annular V-flame

We investigate self-excited axisymmetric oscillations of a lean premixed methane--air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies, attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction cannot be approximated as a simple distortion of the mean flow.

physics.flu-dyn↗

arXiv2022

An empirical model of noise sources in subsonic jets

Modelling the noise emitted by turbulent jets is made difficult by their acoustic inefficiency: only a tiny fraction of the near-field turbulent kinetic energy is propagated to the far field as acoustic waves. As a result, jet-noise models must accurately capture this small, acoustically efficient component hidden among comparatively inefficient fluctuations. In this paper, we identify this acoustically efficient near-field source from large-eddy-simulation data and use it to inform a predictive model. Our approach uses the resolvent framework, in which the source takes the form of nonlinear fluctuation terms that act as a forcing on the linearized Navier-Stokes equations. First, we identify the forcing that, when acted on by the resolvent operator, produces the leading spectral proper orthogonal decomposition modes in the acoustic field for a Mach 0.4 jet. Second, the radiating components of this forcing are isolated by retaining only portions with a supersonic phase speed. This component makes up less than 0.05% of the total forcing energy but generates most of the acoustic response, especially at peak (downstream) radiation angles. Finally, we propose an empirical model for the identified acoustically efficient forcing components. The model is tested at other Mach numbers and flight-stream conditions and predicts noise within 2 dB accuracy for a range of frequencies, downstream angles, and flight conditions.

physics.flu-dyn↗

arXiv2022

The effect of a flight stream on subsonic turbulent jets

This study concerns a turbulent jet at Mach number $M_j=0.9$, subject to a uniform external flow stream at $M_f=0.15$. We assess the mechanisms that underpin the reduction in fluctuation energy that is known to occur when a jet is surrounded by a flight stream. The analysis combines experimental and numerical databases, spectral proper orthogonal decomposition (SPOD) and linear modelling. The experiments involve Time-Resolved, Stereo PIV measurements at different cross-sections of the jet. A companion large-eddy simulation was performed with the same operating conditions using the "CharLES" solver by Cascade Technologies in order to obtain a complete and highly resolved 3D database. We show that the energy reduction is spread over a broad region of the frequency-wavenumber space and involves, apart from the known stabilization of the modal Kelvin-Helmholtz (KH) instability, the attenuation of flow structures associated with the non-modal Orr and lift-up mechanisms. Streaky structures, associated with helical azimuthal wavenumbers and very slow time scales, are the most strongly affected by the flight stream, in terms of energy attenuation and spatial distortion. The energy reductions are accompanied by a weakening of the low-rank behaviour of the jet dynamics revealed by previous studies. These trends are found to be consistent with results of a local linear model based on the modified mean flow in the flight stream case.

physics.flu-dyn↗

arXiv2022

Global linear stability analysis of a flame anchored to a cylinder

This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct numerical simulation performed with a simple one-step reaction scheme in the low Mach number limit. Furthermore, the linear analysis predicts a strong stabilising effect of flame ignition, consistent with documented experiments and numerical simulations. Instability in ignited wake flows is, however, found to set in at sufficiently high Reynolds number, and a linear wavemaker analysis characterises this instability as being driven by hydrodynamic mechanisms of a similar nature as in non-reacting wake flows. The frequency of nonlinear limit-cycle flame oscillations in this unstable regime is retrieved accurately by linear eigenmode analysis performed on the time-averaged mean flow, under the condition that the full set of the reacting flow equations is linearised. If, on the contrary, unsteadiness in the density and in the reaction rate are excluded from the linear model, then the congruence between linear and nonlinear dynamics is lost.

physics.flu-dyn↗

arXiv2019

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↗

arXiv2018

Resolvent-based modelling of coherent wavepackets in a turbulent jet

Coherent turbulent wave-packet structures in a jet at Reynolds number 460000 and Mach number 0.4 are extracted from experimental measurements and are modeled as linear fluctuations around the mean flow. The linear model is based on harmonic optimal forcing structures and their associated flow response at individual Strouhal numbers, obtained from analysis of the global linear resolvent operator. These forcing-response wave packets ("resolvent modes") are first discussed with regard to relevant physical mechanisms that provide energy gain of flow perturbations in the jet. Modal shear instability and the nonmodal Orr mechanism are identified as dominant elements, cleanly separated between the optimal and suboptimal forcing-response pairs. A theoretical development in the framework of spectral covariance dynamics then explicates the link between linear harmonic forcing-response structures and the cross-spectral density (CSD) of stochastic turbulent fluctuations. A low-rank model of the CSD at given Strouhal number is formulated from a truncated set of linear resolvent modes. Corresponding experimental CSD matrices are constructed from extensive two-point velocity measurements. Their eigenmodes (spectral proper orthogonal or SPOD modes) represent coherent wave-packet structures, and these are compared to their counterparts obtained from the linear model. Close agreement is demonstrated in the range of "preferred mode" Strouhal numbers, around a value of 0.4, between the leading coherent wave-packet structures as educed from the experiment and from the linear resolvent-based model.

physics.flu-dyn↗

arXiv2017

Artificial eigenmodes in truncated flow domains

Whenever linear eigenmodes of open flows are computed on a numerical domain that is truncated in the streamwise direction, artificial boundary conditions may give rise to spurious pressure signals that are capable of providing unwanted perturbation feedback to upstream locations. The manifestation of such feedback in the eigenmode spectrum is analysed here for two simple configurations. First, explicitly prescribed feedback in a Ginzburg-Landau model is shown to produce a spurious eigenmode branch, named the 'arc branch', that strongly resembles a characteristic family of eigenmodes typically present in open shear flow calculations. Second, corresponding mode branches in the global spectrum of an incompressible parallel jet in a truncated domain are examined. It is demonstrated that these eigenmodes of the numerical model depend on the presence of spurious forcing of a local k+ instability wave at the inflow, caused by pressure signals that appear to be generated at the outflow. Multiple local k+ branches result in multiple global eigenmode branches. For the particular boundary treatment chosen here, the strength of the pressure feedback from the outflow towards the inflow boundary is found to decay with the cube of the numerical domain length. It is concluded that arc-branch eigenmodes are artifacts of domain truncation, with limited value for physical analysis. It is demonstrated, for the example of a non-parallel jet, how spurious feedback may be reduced by an absorbing layer near the outflow boundary.

physics.flu-dyn↗

arXiv2015

Identifying the active flow regions that drive linear and nonlinear instabilities

A new framework for the analysis of unstable oscillator flows is explored. In linear settings, temporally growing perturbations in a non-parallel flow represent unstable eigenmodes of the linear flow operator. In nonlinear settings, self-sustained periodic oscillations of finite amplitude are commonly described as nonlinear global modes. In both cases the flow dynamics may be qualified as being endogenous, as opposed to the exogenous behaviour of amplifier flows driven by external forcing. This paper introduces the endogeneity concept, a specific definition of the sensitivity of the global frequency and growth rate with respect to variations of the flow operator. The endogeneity, defined both in linear and nonlinear settings, characterizes the contribution of localized flow regions to the global eigendynamics. It is calculated in a simple manner as the local point-wise inner product between the time derivative of the direct flow state and an adjoint mode. This study demonstrates for two canonical examples, the Ginzburg-Landau equation and the wake of a circular cylinder, how an analysis based on the endogeneity may be used for a physical discussion of the mechanisms that drive a global instability. The results are shown to be consistent with earlier 'wavemaker' definitions found in the literature, but the present formalism enables a more detailed discussion: a clear distinction is made between oscillation frequency and growth rate, and individual contributions from the various terms of the flow operator can be isolated and separately discussed. [Truncated]

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