A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the disparity between the flow and acoustic speed. Therefore low-Mach-number flows impose mathematical and computational challenges in their description. Standard numerical methods for compressible flows, which are typically designed for problems with a single dominant spatial and temporal scale, require alternative approaches such as preconditioning techniques or solvers tailored for low-Mach-number equations. The present work introduces a simplified fluid dynamics model for flows at low Mach number, based on the fractional time-step method. The proposed approach is suitable for handling strong temperature gradients and thermal diffusion, as encountered in combustion systems. To address discontinuities at the flame front in reacting-flow cases, due to the hypothesis of infinitely fast chemistry, a regularisation procedure is employed. Additionally, the immersed boundary method (IBM) is extended to handle mass flux across the boundary surface, enabling simulations of fuel ejection from an arbitrary burner geometry, using a convenient Cartesian grid. The numerical method utilises a predictor-corrector scheme for time integration on a collocated grid, with flux interpolation to prevent numerical pressure oscillations (“odd-even decoupling”). Relevant test cases are used to verify the methods and their implementations, demonstrating correctness and robustness.

This work presents wavepacket models for supersonic round twin jets operating at perfectly expanded conditions, computed via plane-marching parabolised stability equations based on mean flows obtained from the compressible Reynolds-averaged Navier-Stokes (RANS) equations. High-speed schlieren visualisations and non-time-resolved PIV measurements are performed to obtain experimental datasets for validating the modelling strategy. The RANS solutions are found to be in good quantitative agreement with the particle image velocimetry (PIV) mean-flow measurements, confirming the ability of the approach to capture the interaction between jets at the mean-flow level. The obtained wavepackets consist of toroidal and flapping fluctuations of the twin-jet system, and show similarities with those of single axisymmetric jets. However, for the case of closely spaced jets, they exhibit deviations in the phase speed of structures travelling in the outer mixing layer and those travelling in the inner one, leading to different non-axisymmetric behaviours. In particular, toroidal twin-jet wavepackets feature tilted ring-like structures with respect to the jet axis, while flapping twin-jet wavepackets are distorted and lose the clean chequerboard pattern typically observed in $m = 1$ modes in axisymmetric jets. A quantitative comparison of the modelled wavepackets with experimentally educed coherent structures is performed in terms of their structural agreement measured through an alignment coefficient, providing a first validation of the modelling strategy. Alignment coefficients are found to be particularly high in the intermediate range of studied frequencies.

This paper introduces a modification to variational mode decomposition (VMD) by promoting mode orthogonality in the minimization problem. The main idea is to actively transmit and receive non-orthogonal signal components between the modes by imposing weak orthogonality conditions. The approach, combined with the proportional value of filter bandwidth, effectively prevents mode duplication and enhances robustness of the decomposition against over-segmentation. Experiments considering a broadband synthetic signal show the improved performance of this method in comparison to the standard Variational Mode Decomposition (VMD). The sensitivity of the method to different filter bandwidth, levels of noise, and its effectiveness in handling over-segmentation are also examined.

This work investigates the instability of recirculation bubbles formed in a non-Newtonian fluid from the Giesekus model using a global eigenmode stability analysis. The objective is to relate the parameters that control the viscoelastic contribution with characteristics of the recirculation bubble that can be decisive in the emergence of instabilities and to investigate the influence of the non-Newtonian contribution on the hydrodynamic stability of these flows.

A model problem for thermo-diffusive instabilities on planar laminar flames is considered, which studies flames stabilized in the proximity of a cold burner in a co-flow mixing layer between fuel and oxidizer streams. It accounts for the driving mechanisms for the onset of thermo-diffusive instability, but assumes constant density and neglects flow or pressure gradients. A premixedness parameter characterizes the transverse gradient of the mixture fraction at the upstream boundary. By varying the premixedness parameter from zero to unity, different flame structures are recovered covering the complete spectrum from non-premixed edge flames to fully-premixed planar flames, through partially-premixed triple flames. A modal linear stability analysis is presented. The equations governing small-amplitude flame fluctuations are recast as an eigenvalue problem, in which the eigenfunctions describe two-dimensional flow field variables with arbitrary spatial dependence, and the eigenvalues describe the oscillation frequency and temporal growth rate. For all partially-premixed flames, a pair of complex eigenvalues are found, corresponding to upstream-downstream pulsations of the flame leading edge. These eigenmodes are unstable for a bounded region in the Premixedness-Damk & ouml;hler space. Fully-premixed flames present multiple pairs of unstable eigenmodes; the most unstable pair corresponds to an upstream-downstream oscillation of the flame without distortion along the transverse direction, while the subsequent ones describe wavy deformations of the flame structure consistent with the formation of cellular patterns. The predictions of the linear stability analysis compare well with results from nonlinear simulations. Novelty and significance statement A novel methodology is presented for the instability analysis of laminar flames that considers linear eigenmodes with arbitrary dependence on two spatial directions. The computationally-inexpensive approach allows to perform vast parametric studies of the influence of the physical parameters, thus providing new physical insights. Here, it is applied to a model problem for thermo-diffusive instability, that allows studying the complete range of flames possible in a co-flow configuration in a unified set up. A wide range of Damk & ouml;hler numbers a premixedness parameters are analyzed and the instability maps are reported, which is a novelty in the literature. The methodology proposed can be directly applied to other 2D configurations and can incorporate more complex phenomena like the coupling between the thermodiffusive instability and flow and pressure gradients, and differential diffusivity.

The incompressible flow around a circular cylinder, positioned at the center of an unconfined planar counterflow, is studied by means of numerical solutions of the conservation equations and linear stability analysis. The flow is completely defined by the Reynolds number (Re)-based on the cylinder radius, the strain rate defining the counterflow, and the kinematic viscosity. For very low values of Re, the flow is steady, two-dimensional, and fully attached to the cylinder wall. Increasing Re above Re-s approximate to 16.86, the flow separates, giving rise to two symmetric, counter-rotating recirculation regions on each side of the cylinder. Further increasing Re leads to a progressive enlargement of the recirculation regions and the appearance of multiple recirculation centers, akin to Moffatt eddies. However, the convective acceleration imposed by the counterflow limits their size. An oscillatory mode becomes linearly unstable at Rec approximate to 4146. This mode gives rise to a sinuous meandering of the wake flow on each side of the cylinder, being analogous to the well-known von K & aacute;rm & aacute;n instability. The frequency of this mode is directly proportional to the strain rate defining the counterflow.

Linear global stability analysis is performed on a laminar separation bubble formed due to surface waviness. The eigenspectrum shows a globally unstable mode, responsible for the three-dimensionalisation of the bubble, and a family of low-frequency globally stable modes. An adjoint sensitivity analysis shows high sensitivity of the stable modes upstream of the bubble’s reattachment point. Direct numerical simulation (DNS) alongside with a linear impulse response analysis are performed. DNS shows that, when transition occurs due to self-excited mechanisms, low-frequency upstream propagating waves form inside the bubble; this is not the case in linear impulse analysis. It is conjectured that these upstream propagating waves correspond to the low-frequency stable modes in the spectrum which become active through nonlinearity when transition occurs.

This study examines the flow over a wall-bounded bump geometry using wall-modeled large-eddy simulations (WMLES) in the limit of very thin wall resolution. The geometry and flow conditions are based on an experimental investigation of a canonical geometry designed to replicate diffusion rates similar to those in low-pressure turbine blades. The high subsonic Mach and low Reynolds number upstream of the bump generate strong pressure gradients, both favorable and adverse. As the incoming turbulent boundary layer encounters the bump surface, it undergoes relaminarization, shock-wave interaction and subsequent separation. An inadequate grid resolution near the wall is found to suppress the formation of streamwise vortices during relaminarization, resulting in a different mixing process within the separated boundary layer and a longer separation bubble. To prevent this, extending the spatial region of high refinement to at least 3 delta 99 of the relaminarization region is recommended. The study also investigates the impact of freestream isotropic turbulence on the pressure distribution and separation, revealing that even a small variation in inflow turbulence intensity is sufficient to induce relevant changes in the mean flow results.

Several decades of research on laminar separation bubbles (LSBs) have amassed evidence of an scenario dominated by the convective amplification of incoming disturbances by the inflectional instability. However, some LSBs present dynamics suggesting that additional, self-excited instability mechanisms are also present. This paper reviews some theoretical/numerical results on self-excited instability, and revisits recent low-Tu wind tunnel experiments which provide evidence of the global instabilities. It is concluded that self-excited mechanisms might have been present and overlooked in many previous studies; some considerations are suggested for future research to allow for their identification.

Fluid motion, especially at relatively high Reynolds numbers, often presents non-stationary dynamics characterized by the evolution of the statistical description of the flow and its fluctuations over time, which may arise from external changes in the flow configuration or from the presence of intermittent or transient physical processes. Variational mode decomposition (VMD) is a time–frequency analysis framework that separates a scalar signal into independent amplitude- and frequency-modulated components, each characterized by a finite frequency bandwidth. This paper extends the VMD with two refinements, found to be necessary to ensure the robustness of the technique when applied to fluid flows: (i) the incorporation of orthogonality-promoting objectives into the determination of the modes and (ii) the determination of each mode's frequency bandwidth based on the data. The proposed method, multivariate orthogonalized variational mode decomposition (OVMD), is applied to different cases, including the transient development of a cylinder wake and separated flow over a wall-mounted bump under a harmonic change of the inlet bulk velocity. Each case corresponds to a different scenario of non-stationary flow dynamics. The results illustrate the potential of OVMD in analyzing and modeling flows involving non-stationary dynamical processes.

Three-dimensional laminar boundary layers over swept wings are susceptible to crossflow instabilities, manifesting as stationary and traveling crossflow vortices. The boundary layer distorted by these vortices is prone to the growth of secondary instabilities. Discrepancies between direct numerical simulation (DNS) and stability methodologies on the development of secondary perturbations of stationary crossflow vortices over swept wings have been reported in the literature. To shed light on the origin of these inconsistencies, a comparison of DNS and linear stability theory is provided here. Secondary disturbances of finite-amplitude stationary crossflow vortices are analyzed for two frequencies: [Formula: see text] (Type III secondary instability) and [Formula: see text] (Type I secondary instability). Results from linear stability theory (LST-2D) and linear parabolized stability equations (PSE-3D) formulated in a suitable nonorthogonal coordinate system correlate well with DNS data in terms of perturbation shape and location relative to the stationary crossflow vortices. Employing a nonorthogonal coordinate system is crucial for PSE-3D to fulfill slow variation along the streamwise direction and spanwise periodicity, whereas LST-2D, assuming parallel flow, can also use periodic boundary conditions in a vortex-aligned orthogonal coordinate system. However, the LST-2D results underestimate the integrated growth rate, whereas the PSE-3D computations closely match the DNS, highlighting the importance of including streamwise gradients and upstream history in the instability computations.

The importance of wavepackets in the generation of mixing noise in twin jets is expected by extrapolation of the insights previously obtained from the study of single isolated jets. This work presents wavepacket models for supersonic round twin jets operating at perfectly-expanded conditions, computed via plane-marching parabolized stability equations based on mean flows obtained from the compressible RANS equations. High-speed schlieren visualizations and non-time-resolved PIV measurements are performed to obtain experimental datasets for validating the modelling strategy. The RANS solutions are found to be in good quantitative agreement with the PIV mean-flow measurements, confirming the ability of the approach to capture the interaction between jets at the mean-flow level. The obtained wavepackets consist of toroidal and flapping fluctuations of the twin-jet system, and show similarities with those of single axisymmetric jets. However, for the case of closely-spaced jets, they exhibit deviations in the phase speed of structures travelling in the outer mixing layer and those travelling in the inner one, leading to different non-axisymmetric behaviours. In particular, toroidal twin-jet wavepackets feature tilted ring-like structures with respect to the jet axis, while flapping twin-jet wavepackets are distorted and lose the clean checkerboard pattern typically observed in m = 1 modes in axisymmetric jets. A quantitative comparison of the modelled wavepackets with experimentally-educed coherent structures is performed in terms of their structural agreement measured through an alignment coefficient, providing a first validation of the modelling strategy. Alignment coefficients are found to be particularly high in the intermediate range of studied frequencies.

Large eddy simulation data of a bluff-body stabilized flame are analyzed using spectral proper orthogonal decomposition (SPOD) to investigate: (i) the role of flame-vortex interactions in the dominant flow dynamics and (ii) how the proper choice of the cross-spectral density (CSD) defining SPOD can assist in identifying the underlying dynamics. Bluff-body flame holders aim to achieve stable flames under lean premixed conditions to minimize pollutant emissions. The recirculation region induced by the body promotes the mixing of hot combustion products with unburnt gases, preventing the global blowoff. However, the coupling between the shear layers and flame-induced vorticity sources can result in large flow structures that either contribute to increased flame stability or exhibit features typical of the early stages of flame blowout. SPOD is a data-driven technique remarkably powerful in extracting low-dimensional models. For each frequency, it computes a basis of orthogonal modes that maximizes the content of a predefined CSD in the leading modes. By choosing physically relevant variables to construct the CSD, different physics can be explored, which is used here to investigate the coupled dynamics between the flame-induced baroclinic torque, vortical structures, and the temperature field. The results show that the vorticity and temperature fields exhibit low-dimensional dynamics characterized by a narrowband frequency and its harmonics; these dynamics are varicose oscillations of the flame region, governed by the baroclinic torque. Sinuous oscillations typical of wake instability for nonreactive flows are also present, suggesting a competition between them.

The instability characteristics and laminar–turbulent transition of a series of laminar separation bubbles (LSBs) formed due to a single sinusoidal surface waviness are investigated in the absence of external disturbances or forcing. A scaling based on the geometrical parameters of the waviness and flow Reynolds number is found that enables the prediction of flow separation on the wall leeward side. The analysis of three-dimensional instabilities of two-dimensional base flows reveals a relation between the number of changes in the curvature sign of the recirculating streamlines and the number of unstable centrifugal modes that coexist for the same flow. When multiple curvature changes occur, in addition to the usual steady mode reported for two-dimensional recirculation bubbles, a new self-excited mode with a higher growth rate emerges, localised near the highest streamline curvature, close to the reattachment point. A detailed analysis of the mode growth and saturation using DNS reveals that the localised mode only disturbs the LSB locally, while the usual one leads to a global distortion of the bubble in the spanwise direction; this has a distinctive impact on the self-excited secondary instabilities. Then, the complete transition scenario is studied for two selected LSB cases. The first one only presents an unstable eigenmode, namely the usual centrifugal mode in recirculating flows. The second case presents three unstable eigenmodes: two centrifugal eigenmodes (the usual and the localised ones) and a two-dimensional eigenmode associated with the self-sustained Kelvin–Helmholtz waves. These results show how completely different transition scenarios can emerge from subtle changes in the LSB characteristics.

Pressure fluctuations at the shear-layer boundary of a supersonic round twin jet are measured by means of a phased microphone array. Measurements are taken one streamwise position at a time using 8 microphones distributed around the twin jet and placed at the boundary of the external shear layer of each jet, following mean-flow streamwise-velocity contours from RANS calculations. The spectral signature of the measured fluctuations captures the broadband mixing-layer noise component which dominates for perfectly-expanded jets, as well as the broadband shock-cell noise component and the screech resonance tones which are typical of imperfectly-expanded supersonic jets. More importantly, at frequencies where mixing noise is the dominant mechanism, the streamwise evolution of the measured pressure signals exhibits a region of linear growth that is consistent with the development of wavepackets in the twin jet flow field. The decomposition of the microphone signals into the four possible combinations (families) of symmetric and antisymmetric pressure fluctuations illustrates that symmetric fluctuations with respect to the plane containing both jets are generally more energetic than their antisymmetric counterparts, especially farther downstream from the nozzle exit, whereas symmetric and antisymmetric fluctuations with respect to the symmetry plane between both jets generally show similar energy levels. For perfectly-expanded conditions, local SPOD analyses based on the symmetric family of pressure signals reveal that the most energetic symmetric oscillation mode in the studied twin-jet system is a toroidal fluctuation, confirming the findings of previous investigations based on schlieren visualizations. For the first time, quantitative comparisons between plane-marching PSE wavepacket models and experimentally-measured pressure fluctuations are performed for the twin jet at perfectly-expanded conditions, finding a reasonable agreement between the PM-PSE mode SS0 and the symmetric experimental pressure signals for the higher frequencies of the mixing-noise region analyzed.