arXiv subjects

Adrián Lozano-Durán

Publications and source records attributed to Adrián Lozano-Durán.

At least 37 records · Page 2Linked to original sources

arXiv2021

Self-critical machine-learning wall-modeled LES for external aerodynamics

The prediction of aircraft aerodynamic quantities of interest remains among the most pressing challenges for computational fluid dynamics. The aircraft aerodynamics are inherently turbulent with mean-flow three-dimensionality, often accompanied by laminar-to-turbulent transition, flow separation, secondary flow motions at corners, and shock wave formation, to name a few. However, the most widespread wall models are built upon the assumption of statistically-in-equilibrium wall-bounded turbulence and do not faithfully account for the wide variety of flow conditions described above. This raises the question of how to devise models capable of accounting for such a vast and rich collection of flow physics in a feasible manner. In this work, we propose tackling the wall-modeling challenge by devising the flow as a collection of building blocks, whose information enables the prediction of the stress as the wall. The model relies on the assumption that simple canonical flows contain the essential flow physics to devise accurate models. Three types of building block units were used to train the model: turbulent channel flows, turbulent ducts and turbulent boundary layers with separation. This limited training set will be extended in future versions of the model. The approach is implemented using two interconnected artificial neural networks: a classifier, which identifies the contribution of each building block in the flow; and a predictor, which estimates the wall stress via non-linear combinations of building-block units. The output of the model is accompanied by the confidence in the prediction. The latter value aids the detection of areas where the model underperforms, such as flow regions that are not representative of the building blocks used to train the model. The model is validated in a unseen case representative of external aerodynamic applications: the NASA Juncture Flow Experiment.

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arXiv2021

Toward a flow-structure-based wall-modeled large-eddy simulation paradigm

A promising and cost-effective method for numerical simulation of high Re wall-bounded flows is wall-modeled large-eddy simulation. Most wall models are formulated from the Reynolds-averaged Navier-Stokes equations (RANS). These RANS-based wall models are calibrated using mean turbulence data and make no use of the current vast knowledge on turbulent flow structure. Moreover, RANS-based models are limited to predicting the mean velocity profile, and the mean wall shear stress. Using the knowledge of the wall-normal self-similarity of high-$Re_τ$ wall-bounded turbulent flows, we present a coupling between a near-wall patch of DNS resolution fixed in inner-units and an outer LES flow field. The near-wall patch captures the near-wall self-sustaining cycle as well as the lower portion of the self-similar hierarchy of eddies. Given that both the near-wall patch and the LES capture separate portions of the self-similar hierarchy of eddies an instantaneous top boundary condition for the patch is formulated. The near-wall model is capable of predicting subgrid-scale quantities such as the wall stress, velocity fluctuations, kinetic energy spectra, and flow structure across the entire near-wall layer.

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arXiv2021

Performance of wall-modeled LES for external aerodynamics in the NASA Juncture Flow

We investigate the performance of wall-modeled LES for external aerodynamics in the NASA Juncture Flow. We characterize the errors in the prediction of mean velocity profiles and pressure coefficient for three different locations over the aircraft: the upstream region of the fuselage, the wing-body juncture, and the wing-body juncture close to the trailing-edge. The last two locations are characterized by strong mean-flow three-dimensionality and separation. The message conveyed by our error analysis is that WMLES performs as expected in regions where the flow resembles a zero-pressure-gradient flat plate boundary layer. However, there is a clear decline of the current models in the presence of wing-body junctions and, more acutely, in separated zones. The slow convergence to the solution in these regions renders the brute-force grid-refinement approach to improve the accuracy of the solution unfeasible. The results reported above pertain to the mean velocity profile predicted using the typical grid resolution for external aerodynamics applications, i.e., 5--20 points per boundary-layer thickness. The prediction of the pressure coefficient is below 5\% error for all grid sizes considered, even when boundary layers were marginally resolved. The latter accuracy can be attributed to the outer-layer nature of the mean pressure, which becomes less sensitive to flow details within the turbulent boundary layer. Finally, we show that boundary-layer-conforming grids (i.e., grids maintaining a constant number of points per boundary-layer thickness) allow for a more efficient distribution of grid points and smaller errors. Our results suggest that novel modeling venues encompassing physical insights, together with numerical and gridding advancements, must be exploited to attain predictions within the tolerance required for Certification by Analysis.

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arXiv2020

Requirements and sensitivity analysis of RANS-free wall-modeled LES

We study the sensitivity of wall model input variables to the modeling choices of the outer LES. This work is motivated by sensitivities observed in dynamic slip wall models. These dynamic wall models use variables from the near-wall LES solution as inputs to predict the wall stress without relying on a priori coefficients or equilibrium assumption. Mitigating the sensitivities in the wall model inputs allows development of robust dynamic wall models. The effects of SGS model, boundary condition type, numerics, and mesh topology are assessed through a series of WMLES calculations of turbulent channels. Probability density functions are computed from planes of the WMLES solutions at a wall-normal sampling height and are used as a metric for sensitivity. Sensitivity to SGS model is alleviated when the fraction of total wall stress carried by the SGS model is held constant. Use of hexagonal close-packed grids mitigated numerical sensitivities.

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arXiv2020

Information transfer between turbulent boundary layer and porous media

The interaction between the flow above and below a permeable wall is a central topic in the study of porous media. While previous investigations have provided compelling evidence of the strong coupling between the two regions, few studies have quantitatively measured the directionality, i.e., causal-and-effect relations, of this interaction. To shed light on the problem, we use transfer entropy as a marker to evaluate the causal interaction between the free turbulent flow and the porous media using interface-resolved direct numerical simulation. Our results show that the porosity of the porous medium has a profound impact on the intensity, time scale and spatial extent of surface-subsurface interactions. For values of porosity equal to 0.5, top-down and bottom-up interactions strongly are asymmetric, the former being mostly influenced by small near-wall eddies. As the porosity increases, both top-down and bottom-up interactions are dominated by shear-flow instabilities.

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arXiv2020

Cause-and-effect of linear mechanisms sustaining wall turbulence

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in theoretical and conceptual arguments. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean-flow ($\bf U$) to the fluctuating velocities ($\bf u'$). We use cause-and-effect analysis based on interventions. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from $\bf U$ to $\bf u'$ is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes, and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow. Finally, we demonstrate that an ensemble of simulations with various frozen-in-time $\bf U$ arranged so that only transient growth is active, can faithfully represent the energy transfer from $\bf U$ to $\bf u'$ as in realistic turbulence. Our approach provides direct cause-and-effect evaluation of the linear energy-injection mechanisms from $\bf U$ to $\bf u'$ in the fully nonlinear system and simplifies the conceptual model of self-sustaining wall turbulence.

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arXiv2020

The coherent structure of the kinetic energy transfer in shear turbulence

The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex shaped as an inverted hairpin followed by an upright hairpin. The asymmetry between the forward and backward cascade arises from the opposite flow circulation within the hairpins, which triggers reversed patterns in the flow.

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arXiv2020

On the evolution of the velocity gradient tensor in transitional boundary layers

We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the Q-criterion. To that end, we have derived transport equations based on several invariants of the velocity gradient tensor to obtain integral budgets spanning the different stages of transition from laminar to turbulent flow. We have also discussed which quantity would be the most appropriate in our study, while keeping in mind the potential for future modeling applications.

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arXiv2020

Wall-modeled large-eddy simulation of non-equilibrium turbulent boundary layers

We conducted WMLES to examine the performance of a simple and widely used ODE-based equilibrium wall model in a spatially-developing 3D TBL inside a bent square duct (Schwarz and Bradshaw 1994) and 3D separated flows behind a skewed bump (Ching et al. 2018a,b; Ching and Eaton 2019). From the square duct simulation, the mean velocity profiles and crossflow angles in the outer region were predicted with high accuracy for all the considered mesh resolutions. Some disagreement was observed in the crossflow angles in the bend region where the non-equilibrium effect is most significant. Also, the simulation for the wall-mounted skewed bump showed that this simple ODE-based equilibrium wall model along with an adequate grid resolution around the 3D separation point resulted in reasonable predictions of 3D separating and reattaching flows, including mean velocity distributions, separation bubbles, and vortex structures in the bump wake.

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arXiv2019

Computational model discovery with reinforcement learning

The motivation of this study is to leverage recent breakthroughs in artificial intelligence research to unlock novel solutions to important scientific problems encountered in computational science. To address the human intelligence limitations in discovering reduced-order models, we propose to supplement human thinking with artificial intelligence. Our three-pronged strategy consists of learning (i) models expressed in analytical form, (ii) which are evaluated a posteriori, and iii) using exclusively integral quantities from the reference solution as prior knowledge. In point (i), we pursue interpretable models expressed symbolically as opposed to black-box neural networks, the latter only being used during learning to efficiently parameterize the large search space of possible models. In point (ii), learned models are dynamically evaluated a posteriori in the computational solver instead of based on a priori information from preprocessed high-fidelity data, thereby accounting for the specificity of the solver at hand such as its numerics. Finally in point (iii), the exploration of new models is solely guided by predefined integral quantities, e.g., averaged quantities of engineering interest in Reynolds-averaged or large-eddy simulations (LES). We use a coupled deep reinforcement learning framework and computational solver to concurrently achieve these objectives. The combination of reinforcement learning with objectives (i), (ii) and (iii) differentiate our work from previous modeling attempts based on machine learning. In this report, we provide a high-level description of the model discovery framework with reinforcement learning. The method is detailed for the application of discovering missing terms in differential equations. An elementary instantiation of the method is described that discovers missing terms in the Burgers' equation.

cs.LG↗

arXiv2019

Causality of energy-containing eddies in wall turbulence

Turbulent flows in the presence of walls may be apprehended as a collection of momentum- and energy-containing eddies (energy-eddies), whose sizes differ by many orders of magnitude. These eddies follow a self-sustaining cycle, i.e., existing eddies are seeds for the inception of new ones, and so forth. Understanding this process is critical for the modelling and control of geophysical and industrial flows, in which a non-negligible fraction of the energy is dissipated by turbulence in the immediate vicinity of walls. In this study, we examine the causal interactions of energy-eddies in wall-bounded turbulence by quantifying how the knowledge of the past states of eddies reduces the uncertainty of their future states. The analysis is performed via direct numerical simulation (DNS) of turbulent channel flows in which time-resolved energy-eddies are isolated at a prescribed scale. Our approach unveils, in a simple manner, that causality of energy-eddies in the buffer and logarithmic layers is similar and independent of the eddy size. We further show an example of how novel flow control and modelling strategies can take advantage of such self-similar causality.

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arXiv2019

Wall turbulence without modal instability of the streaks

Despite the nonlinear nature of wall turbulence, there is evidence that the mechanism underlying the energy transfer from the mean flow to the turbulent fluctuations can be ascribed to linear processes. One of the most acclaimed linear instabilities for this energy transfer is the modal growth of perturbations with respect to the streamwise-averaged flow (or streaks). Here, we devise a numerical experiment in which the Navier--Stokes equations are sensibly modified to suppress these modal instabilities. Our results demonstrate that wall turbulence is sustained with realistic mean and fluctuating velocities despite the absence of streak instabilities.

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arXiv2019

Coherent structures and secondary flow in turbulent square duct

The aim of the present work is to investigate the role of coherent structures in the generation of the secondary flow in a turbulent square duct. The coherent structures are defined as connected regions of flow where the product of the instantaneous fluctuations of two velocity components is higher than a threshold based on the long-time turbulence statistics, in the spirit of the three-dimensional quadrant analysis proposed by Lozano-Durán et al. (J. Fluid Mech., vol. 694, 2012, pp. 100-130). We consider both the direct contribution of the structures to the mean in-plane velocity components and their geometrical properties. The instantaneous phenomena taking place in the turbulent duct are compared with turbulent channel flow at Reynolds numbers of $Re_τ=180$ and $360$, based on friction velocity at the center-plane and channel half height. In the core region of the duct, the fractional contribution of intense events to the wall-normal component of the mean velocity is in very good agreement with that in the channel, despite the presence of the secondary flow in the former. Additionally, the shapes of the three-dimensional objects do not differ significantly in both flows. On the other hand, in the corner region of the duct, the proximity of the walls affects both the geometrical properties of the coherent structures and the contribution to the mean component of the vertical velocity, which is less relevant than that of the complementary portion of the flow not included in such objects. Our results show however that strong Reynolds shear-stress events, despite the differences observed between channel and duct, do not contribute directly to the secondary motion, and thus other phenomena need to be considered instead.

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arXiv2019

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1,000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressure-strain correlation which ultimately inhibits the generation of Reynolds stress. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium, three-dimensional flows.

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arXiv2019

Turbulent windprint on a liquid surface

We investigate the effect of a light turbulent wind on a liquid surface, below the onset of wave generation. In that regime, the liquid surface is populated by small disorganised deformations elongated in the streamwise direction. Formally identified recently by Paquier et al. (2015), the deformations that occur below the wave onset were named wrinkles. We provide here a theoretical framework for this wrinkle regime, using the viscous response of a free surface liquid submitted to arbitrary normal and tangential interfacial stresses at its upper boundary. We relate the spatio-temporal spectrum of the surface deformations to that of the applied interfacial pressure and shear stress fluctuations. For that, we evaluate the spatio-temporal statistics of the turbulent forcing using Direct Numerical Simulation of a turbulent air channel flow, assuming no coupling between the air and the liquid flows. Combining theory and numerical simulation, we thus obtain synthetic wrinkles that reproduce previous experimental investigations. We show that the wrinkles are a multi-scale superposition of random wakes generated by the turbulent fluctuations. They result mainly from the nearly isotropic pressure fluctuations generated in the boundary layer, rather than from the elongated shear stress fluctuations. The wrinkle regime described in this paper naturally arises as the viscous-saturated asymptotic of the inviscid growth theory of Phillips (1957). Experiments indicate that the onset of exponential wave growth depends on the liquid viscosity. Our theory suggests that the empirical criterion for the onset is satisfied when the wrinkle amplitude reaches a given fraction of the viscous sublayer thickness. It indicates that the turbulent fluctuations near the onset may play a role in the triggering of exponential wave growth.

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arXiv2019

Error scaling of large-eddy simulation in the outer region of wall-bounded turbulence

We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of turbulent channel flows in which the no-slip condition at the wall is replaced by a Neumann condition supplying the exact mean wall-stress. The statistics investigated are the mean velocity profile, turbulence intensities, and kinetic energy spectra. The errors follow $(Δ/L)^αRe_τ^γ$, where $Δ$ is the characteristic grid resolution, $Re_τ$ is the friction Reynolds number, and $L$ is the meaningful length-scale to normalize $Δ$ in order to collapse the errors across the wall-normal distance. We show that $Δ$ can be expressed as the $L_2$-norm of the grid vector and that $L$ is well represented by the ratio of the friction velocity and mean shear. The exponent $α$ is estimated from theoretical arguments for each statistical quantity of interest and shown to roughly match the values computed by numerical simulations. For the mean profile and kinetic energy spectra, $α\approx1$, whereas the turbulence intensities converge at a slower rate $α<1$. The exponent $γ$ is approximately $0$, i.e. the LES solution is independent of the Reynolds number. The expected behavior of the turbulence intensities at high Reynolds numbers is also derived and shown to agree with the classic log-layer profiles for grid resolutions lying within the inertial range. Further examination of the LES turbulence intensities and spectra reveals that both quantities resemble their filtered counterparts from direct numerical simulation (DNS) data, but that the mechanism responsible for this similarity is related to the balance between the input power and dissipation rather than to filtering.

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arXiv2019

Characteristic scales of Townsend's wall attached eddies

Townsend (1976) proposed a structural model for the logarithmic layer (log-layer) of wall turbulence at high Reynolds numbers, where the dominant momentum-carrying motions are organised into a multi-scale population of eddies attached to the wall. In the attached eddy framework, the relevant length and velocity scales of the wall-attached eddies are the friction velocity and the distance to the wall. In the present work, we hypothesise that the momentum-carrying eddies are controlled by the mean momentum flux and mean shear with no explicit reference to the distance to the wall and propose new characteristic velocity, length, and time scales consistent with this argument. Our hypothesis is supported by direct numerical simulation (DNS) of turbulent channel flows driven by non-uniform body forces and modified mean velocity profiles, where the resulting outer-layer flow structures are substantially altered to accommodate the new mean momentum transfer. The proposed scaling is further corroborated by simulations where the no-slip wall is replaced by a Robin boundary condition for the three velocity components, allowing for substantial wall-normal transpiration at all lengths scales. We show that the outer-layer one-point statistics and spectra of this channel with transpiration agree quantitatively with those of its wall-bounded counterpart. The results reveal that the wall-parallel no-slip condition is not required to recover classic wall-bounded turbulence far from the wall and, more importantly, neither is the impermeability condition at the wall.

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arXiv2019

Wall turbulence with constrained energy extraction from mean flow

We study the mechanism of energy injection from the mean flow to the fluctuating velocity necessary to maintain wall turbulence. This process is believed to be correctly represented by the linearized Navier--Stokes equations, and three potential linear mechanisms have been considered, namely, modal instability of the streamwise mean cross-flow $U(y,z,t)$, non-modal transient growth, and non-modal transient growth supported by parametric instability. We have designed three numerical experiments of plane turbulent channel flow with additional forcing terms aiming to neutralize one or various linear mechanisms for energy extraction. From our preliminary experiments, only cases with mean cross-flows capable of supporting modal instabilities were found to sustain turbulence. However, the question whether such a new turbulence complies with the same physical mechanisms as those occurring in actual (unforced) turbulence remains unanswered. On the other hand, cases exclusively supported by transient growth decayed until laminarization.

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