arXiv subjects

Dan S. Henningson

Publications and source records attributed to Dan S. Henningson.

At least 19 recordsLinked to original sources

arXiv2024

Direct numerical simulation of transition under free-stream turbulence and the influence of large integral length scales

Under action of free-stream turbulence (FST), elongated streamwise streaky structures are generated inside the boundary layer, and their amplitude and wavelength are crucial for the transition onset. While turbulence intensity is strongly correlated with the transitional Reynolds number, characteristic length scales of the FST are often considered to have a slight impact on the transition location. However, a recent experiment by Fransson & Shahinfar (2020} shows significant effects of FST scales. They found that, for higher free-stream turbulence levels and larger integral length scales, an increase in the length scale postpones transition, contrary to established literature. Here, we aim at understanding these results by performing a series of high-fidelity simulations. These results provide understanding why the FST integral length scale affects the transition location differently. These integral length scales are so large that the wide streaks introduced in the boundary layer have substantially lower growth in the laminar region upstream of the transition to turbulence, than streaks induced by smaller integral length scales. The energy in the boundary layer subsequently propagate to smaller spanwise scales as a result of the non-linear interaction. When the energy has reached smaller spanwise scales larger amplitude streaks results in regions where the streak growth are larger. It takes longer for the energy from the wider streaks to propagate to the spanwise scales associated with the breakdown to turbulence, than for the those with smaller spanwise scales. Thus there is a faster transition for FST with lower integral length scales in this case.

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arXiv2024

Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence

Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of the incompressible Navier-Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric non-linear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or non-linear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the non-linear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.

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arXiv2023

Instability of the optimal edge trajectory in the Blasius boundary layer

In the context of linear stability analysis, considering unsteady base flows is notoriously difficult. A generalisation of modal linear stability analysis, allowing for arbitrarily unsteady base flows over a finite time, is therefore required. The recently developed optimally time-dependent (OTD) modes form a projection basis for the tangent space. They capture the leading amplification directions in state space under the constraint that they form an orthonormal basis at all times. The present numerical study illustrates the possibility to describe a complex flow case using the leading OTD modes. The flow under investigation is an unsteady case of the Blasius boundary layer, featuring streamwise streaks of finite length and relevant to bypass transition. It corresponds to the state space trajectory initiated by the minimal seed; such a trajectory is unsteady, free from any spatial symmetry, and shadows the laminar-turbulent separatrix for a finite time only. The finite-time instability of this unsteady base flow is investigated using the 8 leading OTD modes. The analysis includes the computation of finite-time Lyapunov exponents as well as instantaneous eigenvalues, and of the associated flow structures. The reconstructed instantaneous eigenmodes are all of outer type. They map unambiguously the spatial regions of largest instantaneous growth. Other flow structures, previously reported as secondary, are identified with this method as relevant to streak switching and to streamwise vortical ejections. The dynamics inside the tangent space features both modal and non-modal amplification. Non-normality within the reduced tangent subspace, quantified by the instantaneous numerical abscissa, emerges only as the unsteadiness of the base flow is reduced.

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arXiv2023

Non-iterative vortex-based smearing correction for the actuator line method

The actuator line method (ALM) is extensively used in wind turbine and rotor simulations. However, its original uncorrected formulation overestimates the forces near the tip of the blades and does not reproduce well forces on translating wings. The recently proposed vortex-based smearing correction for the ALM is a correction based on physical and mathematical properties of the simulation that allows for a more accurate and general ALM. So far, to correct the forces on the blades, the smearing correction depended on an iterative process at every time step, which is usually slower, less stable and less deterministic than direct methods. In this work, a non-iterative process is proposed and validated. First, we propose a formulation of the non-linear lifting line that is equivalent to the ALM with smearing correction, showing that their results are practically identical for a translating wing. Then, by linearizing the lifting line method, the iterative process of the correction is substituted by the direct solution of a small linear system. No significant difference is observed in the results of the iterative and non-iterative corrections, both in wing and rotor simulations. Additional contributions of the present work include the use of a more accurate approximation for the velocity induced by a smeared vortex segment and the implementation of a free-vortex wake model to define the vortex sheet, that contribute to the accuracy and generality of the method. The results present here may motivate the adoption of the ALM by other communities, for example, in fixed-wing applications.

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arXiv2023

Simulating Airplane Aerodynamics with Body Forces: Actuator Line Method for Non-planar Wings

Two configurations typical of fixed-wing aircraft are simulated with the actuator line method (ALM): a wing with winglets and a T-tail. The ALM is extensively used in rotor simulations to model the blades by body forces, which are calculated from airfoil data and the relative flow velocity. This method has not been used to simulate airplane aerodynamics, despite its advantage of allowing coarser grids. This may be credited to the failure of the uncorrected ALM to accurately predict forces near the tip of wings, even for simple configurations. The recently-proposed vortex-based smearing correction shows improved results, suggesting those limitations are part of the past. For the non-planar configurations studied in this work, differences between the ALM with the original smearing correction and a non-linear lifting line method (LL) are observed near the intersection of surfaces, because the circulation generated in the numerical simulation differs from the calculated corrected circulation. A vorticity magnitude correction is proposed, which improves the agreement between ALM and LL. This second-order correction resolves the ambiguity in the velocity used to define the lift force. The good results indicate that the improved ALM can be used for airplane aerodynamics, with an accuracy similar to the LL.

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arXiv2022

The Stability of Wakes of Floating Wind Turbines

Floating offshore wind turbines (FOWTs) are subjected to platform motion induced by wind and wave loads. The oscillatory movement trigger vortex instabilities, modifying the wake structure, influencing the flow reaching downstream wind turbines. In this work, the wake of a FOWT is analysed by means of numerical simulations and comparison with linear stability theory. Two simplified models based on the stability of vortices are developed for all degrees of freedom of turbine motion. In our numerical simulations, the wind turbine blades are modeled as actuator lines and a spectral-element method with low dispersion and dissipation is employed to study the evolution of the perturbations. The turbine motion excites vortex instability modes predicted by the linear stability of helical vortices. The flow structures that are formed in the non-linear regime are a consequence of the growth of these modes and preserve some of the characteristics that can be explained and predicted by the linear theory. The number of vortices that interact and the growth rate of disturbances are well predicted by a simple stability model of a two-dimensional row of vortices. For all types of motion, the highest growth rate is observed when the frequency of motion is one and a half the frequency of rotation of the turbine; that induces the out-of-phase vortex pairing mechanism. For lower frequencies of motion, several vortices coalesce to form large flow structures, which cause high amplitude of oscillations in the streamwise velocities, that may increase fatigue or induce high amplitude motion on downstream turbines.

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arXiv2022

Stability of Two-dimensional Potential Flows Using Bicomplex Numbers

The use of the complex velocity potential and the complex velocity is widely disseminated in the study of two-dimensional incompressible potential flows. The advantages of working with complex analytical functions made this representation of the flow ubiquitous in the field of theoretical aerodynamics. However, this representation is not usually employed in linear stability studies, where the representation of the velocity as real vectors is preferred by most authors, in order to allow the representation of the perturbation as the complex exponential function. Some of the classical attempts to use the complex velocity potential in stability studies suffer from formal errors. In this work, we present a framework that reconciles these two complex representations using bicomplex numbers. This framework is applied to the stability of the von Kármán vortex street and a generalized formula is found. It is shown that the classical results of the symmetric and staggered von Kármán vortex streets are just particular cases of the generalized dynamical system in bicomplex formulation.

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arXiv2020

Optimal perturbations and transition energy thresholds in boundary layer shear flows

Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blasius boundary layer, culminating in the computation of the subcritical transition critical energy threshold and the associated fully localized critical optimum in a spatially extended configuration, the so called minimal seed. By dynamically rescaling the variables with the local boundary layer thickness, we show that the identified edge trajectory approaches the same attracting phase space region as previously reported edge trajectories, and reaches the region more efficiently.

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arXiv2020

The edge as a Lagrangian Coherent Structure in a high-dimensional state space

Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a dividing manifold called the edge, which separates trajectories attracted by the laminar state from those reaching the turbulent state. We apply here concepts and tools from Lagrangian data analysis to investigate this edge manifold. This approach is carried out in the state space of automous arbitrarily high-dimensional dissipative systems, in which the edge manifold is re-interpreted as a Lagrangian Coherent Structure (LCS). Two different diagnostics, finite-time Lyapunov exponents and Lagrangian Descriptors, are used and compared with respect to their ability to identify the edge and to their scalability. Their properties are illustrated on several low-order models of subcritical transition of increasing dimension and complexity, as well on well-resolved simulations of the Navier-Stokes equations in the case of plane Couette flow. They allow for a mapping of the global structure of both the state space and the edge manifold based on quantitative information. Both diagnostics can also be used to generate efficient bisection algorithms to approach asymptotic edge states, which outperform classical edge tracking.

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arXiv2020

A model for the collapse of the edge when two transitions routes compete

The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical systems concept of edge manifold has been suggested in the subcritical case to explain the partition of the state space of the system. This investigation is devoted to the evolution of the edge manifold when a linear stability is added in such subcritical systems, a situation poorly studied despite its prevalence in realistic fluid flows. In particular the fate of the edge state as a mediator of transition is unclear. A deterministic three-dimensional model is suggested, parametrised by the linear instability growth rate. The edge manifold evolves topologically, via a global saddle-loop bifurcation, from the separatrix between two attraction basins to the mediator between two transition routes. For larger instability rates, the stable manifold of the saddle point increases in codimension from 1 to 2 after an additional local saddle node bifurcation, causing the collapse of the edge manifold. As the growth rate is increased, three different regimes of this model are identified, each one associated with a flow case from the recent hydrodynamic literature. A simple nonautonomous generalisation of the model is also suggested in order to capture the complexity of spatially developing flows.

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arXiv2020

The colour of forcing statistics in resolvent analyses of turbulent channel flows

The cross-spectral density (CSD) of the non-linear forcing in resolvent analyses is here quantified for the first time for turbulent channel flows. Direct numerical simulations (DNS) at $Re_τ =179$ and $Re_τ =543$ are performed. The CSDs are computed for highly energetic structures typical of buffer-layer and large-scale motions, for different temporal frequencies. The CSD of the non-linear forcing is shown not to be uncorrelated (white) in space, which implies the forcing is structured. Since the non-linear forcing is non-solenoidal by construction and the velocity of an incompressible flow is affected only by the solenoidal part of the forcing, this solenoidal part is evaluated. It is shown that the solenoidal part of the non-linear forcing is the combination of oblique streamwise vortices and a streamwise component which counteract each other, as in a destructive interference. It is shown that a rank-2 approximation of the forcing, with only the most energetic SPOD (spectral proper orthogonal decomposition) modes, leads to the bulk of the response. The projections of the non-linear forcing onto the right-singular vectors of the resolvent are evaluated. The left-singular vectors of the resolvent associated with very low-magnitude singular values are non-negligible since the non-linear forcing term has a non-negligible projection onto the linear sub-optimals of resolvent analysis. The same projections are computed when the forcing is modelled with an eddy-viscosity approach. It is clarified that this modelling improves the accuracy of the prediction since the projections are closer to those associated with the non-linear forcing from DNS data.

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arXiv2020

Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow

An analysis of the statistics of the non-linear terms in resolvent analysis is performed in this work for turbulent Couette flow at low Reynolds number. Data from a direct numerical simulation of a minimal flow unit, at Reynolds number 400, is post-processed using Fourier analysis in both time and space, leading to the covariance matrix of the velocity. From the same data, we computed the non-linear terms of the Navier-Stokes equations (treated as forcing in the present formulation), which allowed us to compute the covariance matrix of the forcing for this case. The two covariances are related exactly by the resolvent operator; based on this, we explore the recovery of the velocity statistics from the statistics of the forcing as a function of the components of the forcing term. This is carried out for the dominant structures in this flow, which participate in the self-sustaining cycle of turbulence: (i) streamwise vortices and streaks, and (ii) spanwise coherent fluctuations of spanwise velocity. The present results show a dominance by four of the non-linear terms for the prediction of the full statistics of streamwise vortices and streaks; a single term is seen to be dominant for spanwise motions. A relevant feature observed in these cases is that forcing terms have significant coherence in space; moreover, different forcing components are also coherent between them. This leads to constructive and destructive interferences that greatly modify the flow response, and should thus be accounted for in modelling work.

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arXiv2019

Global stability of rigid-body-motion fluid-structure-interaction problems

A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion et al. (2000) vanish at the FSI interface in a first-order approximation. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and non-linear equations when the base flow is perturbed by identical small-amplitude perturbations. In all cases both the growth rate and angular frequency of the instability matches within $0.1\%$ accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter-plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero-frequency linearly unstable mode of the coupled fluid-structure-interaction system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.

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arXiv2019

Edge tracking in spatially developing boundary layer flows

Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien--Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.

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arXiv2019

Unsteady aerodynamic effects in small-amplitude pitch oscillations of an airfoil

High-fidelity wall-resolved large-eddy simulations (LES) are utilized to investigate the flow-physics of small-amplitude pitch oscillations of an airfoil at Re = 100,000. The investigation of the unsteady phenomenon is done in the context of natural laminar flow airfoils, which can display sensitive dependence of the aerodynamic forces on the angle of attack in certain "off-design" conditions. The dynamic range of the pitch oscillations is chosen to be in this sensitive region. Large variations of the transition point on the suction-side of the airfoil are observed throughout the pitch cycle resulting in a dynamically rich flow response. Changes in the stability characteristics of a leading-edge laminar separation bubble has a dominating influence on the boundary layer dynamics and causes an abrupt change in the transition location over the airfoil. The LES procedure is based on a relaxation-term which models the dissipation of the smallest unresolved scales. The validation of the procedure is provided for channel flows and for a stationary wing at Re = 400,000.

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arXiv2019

A realizable data-driven approach to delay bypass transition with control theory

The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence via active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer via a high level of free-stream turbulence (FST). The occurring disturbances are measured via localized wall sensors and damped via near-wall actuators resembling plasma actuators. The time-varying amplitude of the signal of each actuator is computed by processing signals from the sensors. This processing is the result of two control laws: the Linear Quadratic Gaussian regulator (LQG) and the Inverse Feed-Forward Control technique (IFFC). The use of the first, LQG, requires a state-space representation of the system dynamics, so the flow is described via an operator that captures only the most relevant information of the dynamics and results in a reduced order model (ROM). The ROM is computed via the eigensystem realization algorithm, based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering FST because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, in a data-driven approach that would be realizable in experiments. Finally, the effectiveness of the technique in delaying bypass transition is shown. The work (i) presents a systematic way to deal with high dimensional disturbances to build ROMs for a control technique, and (ii) shows that even when considering constraints such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in literature.

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arXiv2019

On the role of actuation for the control of streaky structures in boundary layers

This work deals with the closed-loop control of streaky structures induced by free-stream turbulence in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator which aims to induce the exact structures which are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition mode, and an actuator that maximizes the energy of induced downstream structures. Two free-stream turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and closed-loop control is applied in large-eddy simulations of transitional boundary layers. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the free-stream turbulence levels. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer. However, it is shown that even with the actuator located downstream of the input measurement it may become impossible to cancel incoming disturbances in a causal way, depending on the wall-normal position of the output and on the actuator considered, which limits sensor and actuator placement capable of good closed-loop performance.

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arXiv2019

On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at friction Reynolds number Re$_τ$ = 1007. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associated to the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes.

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