We consider closed-loop control of a two-dimensional supersonic boundary layer at M = 4.5 that ai... more We consider closed-loop control of a two-dimensional supersonic boundary layer at M = 4.5 that aims at reducing the linear growth of second Mack mode instabilities. These instabilities are first characterized with local spatial and global resolvent analyses, which allow us to refine the control strategy and to select appropriate actuators and sensors. After linear input-output reduced-order models have been identified, multi-criteria structured mixed H 2 /H ∞ synthesis allows us to fix beforehand the controller structure and to minimize appropriate norms of various transfer functions: the H 2 norm to guarantee performance (reduction of perturbation amplification in nominal condition), and the H ∞ norm to maintain performance robustness (with respect to sensor noise) and stability robustness (with respect to uncertain free-stream velocity/density variations). Both feedforward and feedback set-ups, i.e. with estimation sensor placed respectively upstream/downstream of the actuator, allow us to maintain the local perturbation energy below a given threshold over a significant distance downstream of the actuator, even in the case of noisy estimation sensors or free-stream density variations. However, the feedforward set-up becomes completely ineffective when convective time delays are altered by free-stream velocity variations of ±5 %, which highlights the strong relevance of the feedback set-up for performance robustness in convectively unstable flows.
HAL (Le Centre pour la Communication Scientifique Directe), Jul 1, 2019
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 12, 2021
Transition to turbulence in a boundary layer at supersonic speeds leads to an increase in heat fl... more Transition to turbulence in a boundary layer at supersonic speeds leads to an increase in heat flux and skin friction, becoming a constraint for aircraft design. The present study deals with linear growth control of the second Mack mode in a 2D boundary layer at Ma ∞ = 4.5. Beyond its compressible component, the novelty of this study is twofold: to obtain a robust controller by using a feedback sensor placed downstream of the actuator and to use modern synthesis methods to guarantee both stability and performance robustness. This differs from most previous research in the case of the incompressible boundary layer flow which focused on performance using a feedforward setup. Although these two designs both manage not to exceed a given local perturbation energy threshold over a distance downstream of the actuator, the feedback setup offers the best solution for the robustness to performance due to its ability to perform in off-design conditions.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 23, 2016
Fluid Dynamics (CFD) has deeply transformed aerodynamic engineering, which now relies heavily on ... more Fluid Dynamics (CFD) has deeply transformed aerodynamic engineering, which now relies heavily on computations. There is a consensus today that a critical area in this field is the ability to adequately predict viscous turbulent flows with the possible presence of a boundary layer transition and flow separation . As CFD progresses, experiments become scarce and more comprehensive. However, they remain unavoidable for exploring the borders of the parameter space that they previously secured. Thus, testing will long remain essential to CFD, the success of which still depends on the best compromise between efficient software, physical knowledge and reliable measurement availability. The case of the transonic buffet described in this paper provides a good illustration of the collaboration between these various research domains, which has shaped thirty years of aerodynamics in an institution like ONERA. 1 At the time of the 70 th anniversary of ONERA, an emblematic example is the satellite MICRO-SCOPE launched by Soyuz on April 29 th 2016 from the French Guiana Space Center, and which contains some world-class ONERA technologies. This satellite is aimed at improving the confirmation of the equivalence between inertial mass and gravitational mass, an important verification of Einstein's relativistic theory of gravitation, see .
2021 Symposium on Design, Test, Integration & Packaging of MEMS and MOEMS (DTIP), 2021
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
The evolution of any complex dynamical system is described by its state derivative operators. How... more The evolution of any complex dynamical system is described by its state derivative operators. However, the extraction of the exact N-order state derivative operators is often inaccurate and requires approximations. The open-source CFD code called BROADCAST discretises the compressible Navier-Stokes equations and then extracts the linearised Nderivative operators through Algorithmic Differentiation (AD) providing a toolbox for laminar flow dynamic analyses. Furthermore, the gradients through adjoint derivation are extracted either by transposition of the linearised operator or through the backward mode of the AD tool. The software includes base-flow computation and linear global stability analysis via eigen-decomposition of the linearised operator or via singular value decomposition of the resolvent operator. Sensitivity tools as well as weakly nonlinear analysis complete the package. The numerical method for the spatial discretisation of the equations consists of a finite-difference high-order shock-capturing scheme applied within a finite volume framework on 2D curvilinear structured grids. The stability and sensitivity tools are demonstrated on two cases: a cylinder flow at low Mach number and a hypersonic boundary layer.
In this article, we propose a methodology to reconstruct, in a single step, the mean-and unsteady... more In this article, we propose a methodology to reconstruct, in a single step, the mean-and unsteady properties of a flow from very few time-resolved measurements. The procedure is based on the a priori alignement of Fourier-and Resolvent-modes over energetic frequencies, which is a common feature in shear-dominated transitional flows. Hence, the Reynolds-stresses, which determine the mean-flow, may be approximated from a series of Resolvent modes, which discretize the fluctuation field in the frequency space and whose amplitudes can be tuned thanks to few measurements. In practice, we solve a nonlinear optimization problem (with only few parameters) based on a model coupling strongly the equations governing the mean-flow and the Resolvent modes. The input data for the assimilation procedure may be very sparse, typically one or two pointwise measurements. This technique is applied to two distinct physical configurations, one "oscillator" flow with periodic fluctuations (squared-section cylinder) and one "noise amplifier" flow with a broadband frequency spectrum (backward-facing step).
Theoretical and Computational Fluid Dynamics, 2020
The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent ... more The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent jet. A flowfield dataset is first obtained from a LES simulation including chemical reactions. The spatial reduction is accomplished by performing successively a Fourier transform in the azimuthal direction and a proper orthogonal decomposition (POD), while the temporal reduction is obtained through a selection of Fourier modes in the leading temporal POD modes (chronos). A prior low-pass temporal filter has been used to eliminate a significant portion of high-frequency content, the resulting reduced-order model (ROM) focusing only on the low-frequency, large-scale structures of the jet. The leading axisymmetric (m = 0) POD mode describes a very low-frequency pulsation of the shock cells. The second and third axisymmetric POD modes are paired and describe a wave packet amplified along the potential core and with a rapid decay downstream. The two leading helical (m = 1) POD modes, which are complex modes, appear to be mixed and together describe convecting wave packets of a longer wavelength and a lower frequency. They can be associated to the instability of the shear layer downstream of the potential core. Strong global cross-correlations are observed between the mass fractions and the axial velocity and temperature fields, which lead to similar energy decay rates and POD modes when they are included in the POD. The temporal reduction of the leading sets of chronos via an energy-based selection of Fourier modes has been shown to complement efficiently the spatial reduction, providing a complete spatiotemporal ROM of the flowfield. Keywords Reduced-order model • Proper orthogonal decomposition • Turbulent jet • Reacting flows Communicated by Daniel J. Bodony.
The transonic flow field around a supercritical airfoil is investigated. The objective of the pre... more The transonic flow field around a supercritical airfoil is investigated. The objective of the present paper is to enhance the understanding of the physical mechanics behind two-dimensional transonic buffet. The paper is composed of two parts. In the first part, a global stability analysis based on the linearized Reynolds-averaged Navier–Stokes equations is performed. A recently developed technique, based on the direct and adjoint unstable global modes, is used to compute the local contribution of the flow to the growth rate and angular frequency of the unstable global mode. The results allow us to identify which zones are directly responsible for the existence of the instability. The technique is firstly used for the vortex-shedding cylinder mode, as a validating case. In the second part, in order to confirm the results of the first part, a selective frequency damping method is locally used in some regions of the flow field. This method consists of applying a low-pass filter on sele...
The response of a laminar premixed methane-air flame subjected to flow perturbations around a ste... more The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated.
Nonlinear model reduction for large-scale flows is an essential component in many fluid applicati... more Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIMapproximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated the flow about an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.
This article provides theoretical conditions for the use and meaning of a stability analysis arou... more This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this freque...
This review article is concerned with the design of linear reduced-order models and control laws ... more This review article is concerned with the design of linear reduced-order models and control laws for closed-loop control of instabilities in transitional flows. For oscillator flows, such as open-cavity flows, we suggest the use of optimal control techniques with Galerkin models based on unstable global modes and balanced modes. Particular attention has to be paid to stability–robustness properties of the control law. Specifically, we show that large delays and strong amplification between the control input and the estimation sensor may be detrimental both to performance and robustness. For amplifier flows, such as backward-facing step flow, the requirement to account for the upstream disturbance environment rules out Galerkin models. In this case, an upstream sensor is introduced to detect incoming perturbations, and identification methods are used to fit a model structure to available input–output data. Control laws, obtained by direct inversion of the input–output relations, are ...
Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbat... more Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. Th...
Numerical simulations and perturbation analysis of a radially imploding laminar premixed flame ar... more Numerical simulations and perturbation analysis of a radially imploding laminar premixed flame are used to study the mechanisms responsible for the generation of pressure fluctuations at flame fronts for various Lewis numbers. The relative importance of mechanisms based on unsteady heat release and on vorticity is investigated using an optimization methodology. Particular attention is paid to the influence of non-axisymmetric conditions and local flame curvature. It is shown that vorticity-based noise generation prevails for high-wavenumber, non-axisymmetric disturbances at all curvatures, while heat-release-driven noise generation dominates the axisymmetric and low-wavenumber regimes. These results indicate that short-wavelength vorticity waves actively participate in flame acoustic activity and can surpass acoustic output mechanisms based on heat-release fluctuations in the vicinity of the flame front.
In data-based control design, system-identification techniques are used to extract low-dimensiona... more In data-based control design, system-identification techniques are used to extract low-dimensional representations of the input–output map between actuators and sensors from observed data signals. Under realistic conditions, noise in the signals is present and is expected to influence the identified system representation. For the subsequent design of the controller, it is important to gauge the sensitivity of the system representation to noise in the observed data; this information will impact the robustness of the controller and influence the stability margins for a closed-loop configuration. Commonly, full Monte Carlo analysis has been used to quantify the effect of data noise on the system identification and control design, but in fluid systems, this approach is often prohibitively expensive, due to the high dimensionality of the data input space, for both numerical simulations and physical experiments. Instead, we present a framework for the estimation of statistical properties ...
We consider closed-loop control of a two-dimensional supersonic boundary layer at M = 4.5 that ai... more We consider closed-loop control of a two-dimensional supersonic boundary layer at M = 4.5 that aims at reducing the linear growth of second Mack mode instabilities. These instabilities are first characterized with local spatial and global resolvent analyses, which allow us to refine the control strategy and to select appropriate actuators and sensors. After linear input-output reduced-order models have been identified, multi-criteria structured mixed H 2 /H ∞ synthesis allows us to fix beforehand the controller structure and to minimize appropriate norms of various transfer functions: the H 2 norm to guarantee performance (reduction of perturbation amplification in nominal condition), and the H ∞ norm to maintain performance robustness (with respect to sensor noise) and stability robustness (with respect to uncertain free-stream velocity/density variations). Both feedforward and feedback set-ups, i.e. with estimation sensor placed respectively upstream/downstream of the actuator, allow us to maintain the local perturbation energy below a given threshold over a significant distance downstream of the actuator, even in the case of noisy estimation sensors or free-stream density variations. However, the feedforward set-up becomes completely ineffective when convective time delays are altered by free-stream velocity variations of ±5 %, which highlights the strong relevance of the feedback set-up for performance robustness in convectively unstable flows.
HAL (Le Centre pour la Communication Scientifique Directe), Jul 1, 2019
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 12, 2021
Transition to turbulence in a boundary layer at supersonic speeds leads to an increase in heat fl... more Transition to turbulence in a boundary layer at supersonic speeds leads to an increase in heat flux and skin friction, becoming a constraint for aircraft design. The present study deals with linear growth control of the second Mack mode in a 2D boundary layer at Ma ∞ = 4.5. Beyond its compressible component, the novelty of this study is twofold: to obtain a robust controller by using a feedback sensor placed downstream of the actuator and to use modern synthesis methods to guarantee both stability and performance robustness. This differs from most previous research in the case of the incompressible boundary layer flow which focused on performance using a feedforward setup. Although these two designs both manage not to exceed a given local perturbation energy threshold over a distance downstream of the actuator, the feedback setup offers the best solution for the robustness to performance due to its ability to perform in off-design conditions.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 23, 2016
Fluid Dynamics (CFD) has deeply transformed aerodynamic engineering, which now relies heavily on ... more Fluid Dynamics (CFD) has deeply transformed aerodynamic engineering, which now relies heavily on computations. There is a consensus today that a critical area in this field is the ability to adequately predict viscous turbulent flows with the possible presence of a boundary layer transition and flow separation . As CFD progresses, experiments become scarce and more comprehensive. However, they remain unavoidable for exploring the borders of the parameter space that they previously secured. Thus, testing will long remain essential to CFD, the success of which still depends on the best compromise between efficient software, physical knowledge and reliable measurement availability. The case of the transonic buffet described in this paper provides a good illustration of the collaboration between these various research domains, which has shaped thirty years of aerodynamics in an institution like ONERA. 1 At the time of the 70 th anniversary of ONERA, an emblematic example is the satellite MICRO-SCOPE launched by Soyuz on April 29 th 2016 from the French Guiana Space Center, and which contains some world-class ONERA technologies. This satellite is aimed at improving the confirmation of the equivalence between inertial mass and gravitational mass, an important verification of Einstein's relativistic theory of gravitation, see .
2021 Symposium on Design, Test, Integration & Packaging of MEMS and MOEMS (DTIP), 2021
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
The evolution of any complex dynamical system is described by its state derivative operators. How... more The evolution of any complex dynamical system is described by its state derivative operators. However, the extraction of the exact N-order state derivative operators is often inaccurate and requires approximations. The open-source CFD code called BROADCAST discretises the compressible Navier-Stokes equations and then extracts the linearised Nderivative operators through Algorithmic Differentiation (AD) providing a toolbox for laminar flow dynamic analyses. Furthermore, the gradients through adjoint derivation are extracted either by transposition of the linearised operator or through the backward mode of the AD tool. The software includes base-flow computation and linear global stability analysis via eigen-decomposition of the linearised operator or via singular value decomposition of the resolvent operator. Sensitivity tools as well as weakly nonlinear analysis complete the package. The numerical method for the spatial discretisation of the equations consists of a finite-difference high-order shock-capturing scheme applied within a finite volume framework on 2D curvilinear structured grids. The stability and sensitivity tools are demonstrated on two cases: a cylinder flow at low Mach number and a hypersonic boundary layer.
In this article, we propose a methodology to reconstruct, in a single step, the mean-and unsteady... more In this article, we propose a methodology to reconstruct, in a single step, the mean-and unsteady properties of a flow from very few time-resolved measurements. The procedure is based on the a priori alignement of Fourier-and Resolvent-modes over energetic frequencies, which is a common feature in shear-dominated transitional flows. Hence, the Reynolds-stresses, which determine the mean-flow, may be approximated from a series of Resolvent modes, which discretize the fluctuation field in the frequency space and whose amplitudes can be tuned thanks to few measurements. In practice, we solve a nonlinear optimization problem (with only few parameters) based on a model coupling strongly the equations governing the mean-flow and the Resolvent modes. The input data for the assimilation procedure may be very sparse, typically one or two pointwise measurements. This technique is applied to two distinct physical configurations, one "oscillator" flow with periodic fluctuations (squared-section cylinder) and one "noise amplifier" flow with a broadband frequency spectrum (backward-facing step).
Theoretical and Computational Fluid Dynamics, 2020
The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent ... more The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent jet. A flowfield dataset is first obtained from a LES simulation including chemical reactions. The spatial reduction is accomplished by performing successively a Fourier transform in the azimuthal direction and a proper orthogonal decomposition (POD), while the temporal reduction is obtained through a selection of Fourier modes in the leading temporal POD modes (chronos). A prior low-pass temporal filter has been used to eliminate a significant portion of high-frequency content, the resulting reduced-order model (ROM) focusing only on the low-frequency, large-scale structures of the jet. The leading axisymmetric (m = 0) POD mode describes a very low-frequency pulsation of the shock cells. The second and third axisymmetric POD modes are paired and describe a wave packet amplified along the potential core and with a rapid decay downstream. The two leading helical (m = 1) POD modes, which are complex modes, appear to be mixed and together describe convecting wave packets of a longer wavelength and a lower frequency. They can be associated to the instability of the shear layer downstream of the potential core. Strong global cross-correlations are observed between the mass fractions and the axial velocity and temperature fields, which lead to similar energy decay rates and POD modes when they are included in the POD. The temporal reduction of the leading sets of chronos via an energy-based selection of Fourier modes has been shown to complement efficiently the spatial reduction, providing a complete spatiotemporal ROM of the flowfield. Keywords Reduced-order model • Proper orthogonal decomposition • Turbulent jet • Reacting flows Communicated by Daniel J. Bodony.
The transonic flow field around a supercritical airfoil is investigated. The objective of the pre... more The transonic flow field around a supercritical airfoil is investigated. The objective of the present paper is to enhance the understanding of the physical mechanics behind two-dimensional transonic buffet. The paper is composed of two parts. In the first part, a global stability analysis based on the linearized Reynolds-averaged Navier–Stokes equations is performed. A recently developed technique, based on the direct and adjoint unstable global modes, is used to compute the local contribution of the flow to the growth rate and angular frequency of the unstable global mode. The results allow us to identify which zones are directly responsible for the existence of the instability. The technique is firstly used for the vortex-shedding cylinder mode, as a validating case. In the second part, in order to confirm the results of the first part, a selective frequency damping method is locally used in some regions of the flow field. This method consists of applying a low-pass filter on sele...
The response of a laminar premixed methane-air flame subjected to flow perturbations around a ste... more The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated.
Nonlinear model reduction for large-scale flows is an essential component in many fluid applicati... more Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIMapproximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated the flow about an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.
This article provides theoretical conditions for the use and meaning of a stability analysis arou... more This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this freque...
This review article is concerned with the design of linear reduced-order models and control laws ... more This review article is concerned with the design of linear reduced-order models and control laws for closed-loop control of instabilities in transitional flows. For oscillator flows, such as open-cavity flows, we suggest the use of optimal control techniques with Galerkin models based on unstable global modes and balanced modes. Particular attention has to be paid to stability–robustness properties of the control law. Specifically, we show that large delays and strong amplification between the control input and the estimation sensor may be detrimental both to performance and robustness. For amplifier flows, such as backward-facing step flow, the requirement to account for the upstream disturbance environment rules out Galerkin models. In this case, an upstream sensor is introduced to detect incoming perturbations, and identification methods are used to fit a model structure to available input–output data. Control laws, obtained by direct inversion of the input–output relations, are ...
Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbat... more Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. Th...
Numerical simulations and perturbation analysis of a radially imploding laminar premixed flame ar... more Numerical simulations and perturbation analysis of a radially imploding laminar premixed flame are used to study the mechanisms responsible for the generation of pressure fluctuations at flame fronts for various Lewis numbers. The relative importance of mechanisms based on unsteady heat release and on vorticity is investigated using an optimization methodology. Particular attention is paid to the influence of non-axisymmetric conditions and local flame curvature. It is shown that vorticity-based noise generation prevails for high-wavenumber, non-axisymmetric disturbances at all curvatures, while heat-release-driven noise generation dominates the axisymmetric and low-wavenumber regimes. These results indicate that short-wavelength vorticity waves actively participate in flame acoustic activity and can surpass acoustic output mechanisms based on heat-release fluctuations in the vicinity of the flame front.
In data-based control design, system-identification techniques are used to extract low-dimensiona... more In data-based control design, system-identification techniques are used to extract low-dimensional representations of the input–output map between actuators and sensors from observed data signals. Under realistic conditions, noise in the signals is present and is expected to influence the identified system representation. For the subsequent design of the controller, it is important to gauge the sensitivity of the system representation to noise in the observed data; this information will impact the robustness of the controller and influence the stability margins for a closed-loop configuration. Commonly, full Monte Carlo analysis has been used to quantify the effect of data noise on the system identification and control design, but in fluid systems, this approach is often prohibitively expensive, due to the high dimensionality of the data input space, for both numerical simulations and physical experiments. Instead, we present a framework for the estimation of statistical properties ...
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