Well-resolved Large-eddy Simulations Research Articles

Active flow control of a turbulent separation bubble through deep reinforcement learning

The control efficacy of classical periodic forcing and deep reinforcement learning (DRL) is assessed for a turbulent separation bubble (TSB) at Reτ = 180 on the upstream region before separation occurs. The TSB can resemble a separation phenomenon naturally arising in wings, and a successful reduction of the TSB can have practical implications in the reduction of the aviation carbon footprint. We find that the classical zero-net-mas-flux (ZNMF) periodic control is able to reduce the TSB by 15.7%. On the other hand, the DRL-based control achieves 25.3% reduction and provides a smoother control strategy while also being ZNMF. To the best of our knowledge, the current test case is the highest Reynolds-number flow that has been successfully controlled using DRL to this date. In future work, these results will be scaled to well-resolved large-eddy simulation grids. Furthermore, we provide details of our open-source CFD–DRL framework suited for the next generation of exascale computing machines.

Features of laminar separation bubble subjected to varying adverse pressure gradients

This article describes the spatial development of a laminar separation bubble (LSB), its transition, and eventual breakdown under the influence of adverse pressure gradients (APGs) similar to those experienced by low-pressure turbine blades. The investigation combines a comprehensive experimental approach with a well-resolved large eddy simulation (LES). The streamwise pressure gradients were varied by manipulating the upper wall within the test section. The Reynolds number (Re), based on the plate length and inlet velocity, was 0.2 × 106 with a freestream turbulence intensity of 1.02%. The particle image velocimetry (PIV) and hotwire data were used to illustrate the vortex dynamics, growth of perturbations, and intermittency. The onset and end of transition progressively shift upstream, resulting in a reduction of the laminar shear layer length and bubble length with increasing APG. Interestingly, the flow features exhibit self-similarity in velocity profiles and the growth rate of velocity fluctuations when normalized against the bubble length. The formation of two-dimensional Kelvin–Helmholtz (K–H) rolls is apparent in the beginning, resulting in the selective amplification of frequency and exponential growth of fluctuations. Linear stability theory explains the most amplified frequency and phase speed of convective vortices, apart from the growth of disturbances. Analysis of LES data reveals intricate inviscid–viscous interactions that trigger shear layer breakdown. In brief, evolving perturbations within the braid region of vortices in the latter half interact with the advecting K–H rolls, culminating in the breakdown and the onset of turbulent flow downstream.

Influence of wall shear stress on the secondary flow in square ducts

We investigate turbulent duct flows with a square cross section using well-resolved large-eddy simulations (LES). A physically consistent subgrid-scale turbulence model based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES is used. The wall shear stress is artificially modified at one of the four walls to analyse the influence on the secondary flow. A direct numerical simulation (DNS) of a symmetrical duct flow is used as reference to assess the influence of a modified wall shear stress. The modification results in an asymmetrical distribution of the secondary flow source terms, affecting the momentum distribution. Further, the anisotropy of the Reynolds stress tensor, which induces the secondary flow vortices is considerably affected by the wall shear stress modulation.

Separation delay in turbulent boundary layers via model predictive control of large-scale motions

Turbulent boundary layers are dominated by large-scale motions (LSMs) of streamwise momentum surplus and deficit that contribute significantly to the statistics of the flow. In particular, the high-momentum LSMs residing in the outer region of the boundary layer have the potential to re-energize the flow and delay separation if brought closer to the wall. This work explores the effect of selectively manipulating LSMs in a moderate Reynolds number turbulent boundary layer for separation delay via well-resolved large-eddy simulations. Toward that goal, a model predictive control scheme is developed based on a reduced-order model of the flow that directs LSMs of interest closer to the wall in an optimal way via a body force-induced downwash. The performance improvement achieved by targeting LSMs for separation delay, compared to a naive actuation scheme that does not account for the presence of LSMs, is demonstrated.

Momentum boundary layers in transcritical channel flows

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. We apply a physically consistent subgrid-scale turbulence model, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. In total seven cases are computed covering different Reynolds numbers, pseudo-boiling positions and pressure values. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum layer thicknesses. All cases feature a turbulent mass flux which is essential in turbulence modelling. Furthermore, we analyse the turbulent kinetic energy budgets, perform a quadrant and octant analysis of the Reynolds shear stress and employ an invariant map to study the anisotropy in transcritical turbulent channel flows.

Slow-growth approximation for near-wall patch representation of wall-bounded turbulence

Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however. They can cause significant variation of the mean flow in the streamwise direction. For such situations, we perform asymptotic analysis of the Navier–Stokes equations to inform a model for the effect of mean flow growth on near-wall turbulence in a small domain localized to the boundary. The asymptotics are valid whenever the viscous length scale is small relative to the length scale over which the mean flow varies. To ensure the correct momentum environment, a dynamic procedure is introduced that accounts for the additional sources of mean momentum flux through the upper domain boundary arising from the asymptotic terms. Comparisons of the model's low-order, single-point statistics with those from direct numerical simulation and well-resolved large eddy simulation of adverse-pressure-gradient turbulent boundary layers indicate the asymptotic model successfully accounts for the effect of boundary layer growth on the small-scale near-wall turbulence.

Experimental and numerical investigation into the drag performance of dimpled surfaces in a turbulent boundary layer

Although several previous studies have reported a potential drag-reducing effect of dimpled surfaces in turbulent boundary layers, there is a lack of replicability across experiments performed by different research groups. To contribute to the dialogue, we scrutinize one of the most studied dimple geometries reported in the literature, which has a dimple diameter of 20 mm and a depth of 0.5 mm. There is no general consensus in literature on the drag-reduction performance of this particular dimple geometry, with some studies suggesting a drag reduction, while others report a drag increase. The present combined experimental and numerical study comprises two sets of wind tunnel experiments and a well-resolved large-eddy simulation. The wind tunnel experiments and the large-eddy simulation both depict a total drag increase of around 1%–2% compared to the flat reference case. This finding agrees with a recent study by Spalart et al. (2019). Furthermore, the present wind tunnel experiments have shed light on a plausible reason behind the discrepancy between the study by Spalart et al. (2019) and earlier results from van Nesselrooij et al. (2016). Lastly, the large-eddy simulation results reveal that the pressure drag is the main contributor to the increase in the total drag of the dimpled surface. We believe that these results will contribute to a new consensus on the drag performance of this dimple geometry.

Injector spacing influences on flame blow-off in a linear array

Lean premixed flame stabilization at atmospheric conditions, in a linear array of five swirl injectors, was modeled using well-resolved large eddy simulation (LES) and chemical kinetics that were accurate both for ignition and flame speed. The effects of injector spacing were studied by selectively blocking injectors in the array to obtain five (F), two (T) and single (S) injector configurations. Each of these was simulated at well-anchored as well as near blow-off conditions. Experiments indicated a blow-off trend that was non-monotonic with spacing: the two-injector configuration exhibited the greatest resistance to blow-off, followed by the single-injector setup. The five-injector configuration proved to be the least resistant (by far) in comparison. In an earlier computational study [1], preferential blow-off in configuration F was successfully modeled and strong flame-flame interference could be investigated. This work is continued to assess the ability of a numerical model to study flames near blow-off, but with varying levels of flame-flame interaction. Passive scalar tracking was used to relate cross-injector transport of material to a given injector’s flame-holding ability. The non-monotonic blow-off trend could not be explained by stretch and heat release rate trends, but well-stirred reactor (WSR) theory was found to be more relevant as trends in recirculation zone residence times correlate well with blow-off sequences. In addition, cross-injector transport was studied due to the multi-injector scenario to assess how flameholding zones may be diluted. This work is expected to be useful for analyzing part-load behavior in multi-injector power-generating gas turbine combustion systems, and helps to characterize injector performance towards extending the range of lean operability.

Unsteady mechanisms in shock wave and boundary layer interactions over a forward-facing step

The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\langle C_f \rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations.

Aerodynamic noise from long circular and non-circular cylinders using large eddy simulations

Flow-induced aerodynamic noise from four cylindrical shapes of infinite length at a low subcritical flow regime is studied using Large Eddy Simulation (LES) and acoustic analogy. Numerical simulations are performed for short-span (length to diameter ratio of 3) cylinders, and a sound correction method based on equivalent/spatial coherence length has been applied to estimate noise from long-span cylinders. An attempt is made to compare spatial coherence lengths of four cross-sections at the same Reynolds number (Re). The sound correction method that is well established for circular cylinders proved effective for non-circular cross-sections also. Owing to the limitation in computational capacity, a well-resolved LES is still unachievable for higher Re flows and long-span cylinders without adopting a sound correction methodology. A grid resolution based on the characteristic length and velocity scale was adopted in simulation and proved effective for computing aerodynamic and aeroacoustic characteristics. An ‘effective frequency band’ of sound pressure level-frequency curve is proposed that predicts over 99.5% of the overall sound pressure level, and features of this band for four cross-sections are presented.

Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows

Modal-decomposition techniques are computational frameworks based on data aimed at identifying a low-dimensional space for capturing dominant flow features: the so-called modes. We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow data useful for flow analysis, reduced-order modeling and flow control. Our approach is based on β-variational autoencoders (β-VAEs) and convolutional neural networks (CNNs), which enable extracting non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flow-field data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions, where the energy percentage captured by the proposed method from five modes is equal to 87.36% against 32.41% of the POD. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes with the determinant of the correlation matrix equal to 0.99, which may lead to interpretability.

An adverse-pressure-gradient turbulent boundary layer with nearly constant up to

In this study, a new well-resolved large-eddy simulation of an incompressible near-equilibrium adverse-pressure-gradient (APG) turbulent boundary layer (TBL) over a flat plate is presented. In this simulation, we have established a near-equilibrium APG over a wide Reynolds-number range. In this so-called region of interest, the Rotta–Clauser pressure-gradient parameter $\beta$ exhibits an approximately constant value of around 1.4, and the Reynolds number based on momentum thickness reaches ${\textit {Re}}_{\theta }=8700$ . To the best of the authors’ knowledge, this is to date the highest ${\textit {Re}}_{\theta }$ achieved for a near-equilibrium APG TBL under an approximately constant moderate APG. We evaluated the self-similarity of the outer region using two scalings, namely the Zagarola–Smits and an alternative scaling based on edge velocity and displacement thickness. Our results reveal that outer-layer similarity is achieved, and the viscous scaling collapses the near-wall region of the mean flow in agreement with classical theory. Spectral analysis reveals that the APG displaces some small-scale energy from the near-wall to the outer region, an effect observed for all the components of the Reynolds-stress tensor, which becomes more evident at higher Reynolds numbers. In general, the effects of the APG are more noticeable at lower Reynolds numbers. For instance, the outer peak of turbulent-kinetic-energy (TKE) production is less prominent at higher $Re$ . Although the scale separation increases with ${\textit {Re}}$ in zero-pressure-gradient TBLs, this effect becomes accentuated by the APG. Despite the reduction of the outer TKE production at higher Reynolds numbers, the mechanisms of energisation of large scales are still present.

Evaluation of LES, IDDES and URANS for prediction of flow around a streamlined high-speed train

The turbulent flow past a simplified Intercity-Express 3 high-speed train at ReH=6×104 is investigated by a combination of wind tunnel experiments and numerical simulations using the large-eddy simulation (LES), the improved delayed detached eddy simulation (IDDES) and the unsteady Reynolds-averaged Navier-Stokes (URANS) simulation. This work aims to compare the predictive capabilities of LES, IDDES and URANS for the flow over a streamlined high-speed train. Numerical simulations are compared to experimental data for validation. Results show that the well-resolved LES is more accurate among the numerical methods used. Compared to the well-resolved LES, IDDES and URANS using the coarser mesh can produce similar mean flow, although IDDES and URANS are found to be slightly inaccurate for the coherent wake structures near the wall. However, for the near-wall flow instability concerning wake dynamics, Reynolds stresses, turbulence kinetic energy and the fluctuation of pressure, IDDES is found to be inapplicable. Overall, this study suggests that the well-resolved LES is appropriate to the flow of a streamlined high-speed train. Moreover, IDDES and URANS are proved to apply to the mean field of the studied flow.

Spanwise-coherent hydrodynamic waves around flat plates and airfoils

We investigate spanwise-coherent structures in the turbulent flow around airfoils, motivated by their connection with trailing-edge noise. We analyse well-resolved large-eddy simulations (LES) of the flow around NACA 0012 and NACA 4412 airfoils, both at a Reynolds number of 400 000 based on the chord length. Spectral proper orthogonal decomposition performed on the data reveals that the most energetic coherent structures are hydrodynamic waves, extending over the turbulent boundary layers around the airfoils with significant amplitudes near the trailing edge. Resolvent analysis was used to model such structures, using the mean field as a base flow. We then focus on evaluating the dependence of such structures on the domain size, to ensure that they are not an artefact of periodic boundary conditions in small computational boxes. To this end, we performed incompressible LES of a zero-pressure-gradient turbulent boundary layer, for three different spanwise sizes, with the momentum-thickness Reynolds number matching those near the airfoils trailing edge. The same coherent hydrodynamic waves were observed for the three domains. Such waves are accurately modelled as the most amplified flow response from resolvent analysis. The signature of such wide structures is seen in non-premultiplied spanwise wavenumber spectra, which collapse for the three computational domains. These results suggest that the spanwise-elongated structures are not domain-size dependent for the studied simulations, indicating thus the presence of very wide structures in wall-bounded turbulent flows.

Distinctions between single and twin impinging jet dynamics.

Impinging jets are characterized by an acoustic feedback resonance capable of generating intense tones. This investigation examines changes in single impinging jet (SIJ) dynamics when another jet is added alongside to form a dual impinging jet (DIJ) arrangement of interest in vertical takeoff and landing applications. The emphasis is on the hydrodynamic and acoustic coupling in the region between the jets, which affects aircraft surface loading. Well-resolved large eddy simulations of SIJ and DIJ are employed with under-expanded Mach 1.27 jets; the nozzle exits are placed 4 diameters from the ground plane and, for the DIJ, separated 4.3 diameters from each other to mimic ongoing experiments. Three different SIJ feedback harmonics of the fundamental frequency are identified using two-point space-time correlations. Using spectral proper orthogonal decomposition, these tones are classified as either asymmetric or axisymmetric modes in the SIJ. Each individual jet in the DIJ configuration also exhibits these nominal tones. However, differences are observed on the inboard sides between the jets, where coupling effects engender an azimuthally localized Kelvin-Helmholtz instability and impingement mechanism. The global coupling between the two jets manifests as counter-rotating helical modes, which reinforce the lowest of the three identified SIJ impinging tones.

Aerodynamic Free-Flight Conditions in Wind Tunnel Modelling through Reduced-Order Wall Inserts

Parallel sidewalls are the standard bounding walls in wind tunnels when making a wind tunnel model for free-flight condition. The consequence of confinement in wind tunnel tests, known as wall-interference, is one of the main sources of uncertainty in experimental aerodynamics, limiting the realizability of free-flight conditions. Although this has been an issue when designing transonic wind tunnels and/or in cases with large blockage ratios, even subsonic wind tunnels at low-blockage-ratios might require wall corrections if a good representation of free-flight conditions is intended. In order to avoid the cumbersome streamlining methods especially for subsonic wind tunnels, a sensitivity analysis is conducted in order to investigate the effect of inclined sidewalls as a reduced-order wall insert in the airfoil plane. This problem is investigated via Reynolds-averaged Navier–Stokes (RANS) simulations, and a NACA4412 wing at the angles of attack between 0 and 11 degrees at a moderate Reynolds number (400 k) is considered. The simulations are validated with well-resolved large-eddy simulation (LES) results and experimental wind tunnel data. Firstly, the wall-interference contribution in aerodynamic forces, as well as the local pressure coefficients, are assessed. Furthermore, the isolated effect of confinement is analyzed independent of the boundary-layer growth. Secondly, wall-alignment is modified as a calibration parameter in order to reduce wall-interference based on the aforementioned assessment. In the outlined method, we propose the use of linear inserts to account for the effect of wind tunnel walls, which are experimentally simple to realize. The use of these inserts in subsonic wind tunnels with moderate blockage ratio leads to very good agreement between free-flight and wind tunnel data, while this approach benefits from simple manufacturing and experimental realization.

Spectral-Element Simulation of the Turbulent Flow in an Urban Environment

The mean flow and turbulence statistics of the flow through a simplified urban environment, which is an active research area in order to improve the knowledge of turbulent flow in cities, is investigated. This is useful for civil engineering, pedestrian comfort and for health concerns caused by pollutant spreading. In this work, we provide analysis of the turbulence statistics obtained from well-resolved large-eddy simulations (LES). A detailed analysis of this database reveals the impact of the geometry of the urban array on the flow characteristics and provides for a good description of the turbulent features of the flow within a simplified urban environment. The most prominent features of this complex flow include coherent vortical structures such as the so-called arch vortex, the horseshoe vortex and the roof vortex. These structures of flow have been identified by an analysis of the turbulence statistics. The influence of the geometry of urban environment (and particularly the street width and the building height) on the overall flow behavior has also been studied. Finally, the well-resolved LES results were compared with an available experimental database to discuss differences and similarities between the respective urban configurations.

Low-frequency unsteadiness mechanisms in shock wave/turbulent boundary layer interactions over a backward-facing step

Abstract

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.

The skin-friction coefficient of a turbulent boundary layer modified by a large-eddy break-up device

A computational study based on well-resolved large-eddy simulations is performed to study the skin friction modification by a large-eddy breakup device (LEBU) in a zero-pressure-gradient turbulent boundary layer. The LEBU was modeled using an immersed boundary method. It is observed that the presence of the device leads to the generation of wake vortices, which propagate downstream from the LEBU and toward the wall. A skin friction decomposition procedure is utilized to study different physical mechanisms of the observed skin friction reduction. From the skin friction decomposition, it is found that the skin friction reduction can be characterized by three universal regions of different changes for the skin friction contributions. The first region is predominantly associated with the formation of the wake vortices and the reduction of Reynolds shear stress. In the second region, the mean streamwise velocity fields show that a region of velocity deficit formed downstream of the LEBU propagates toward the wall and leads to turbulence reduction due to wake wall interactions, which also induces a local maximum skin friction reduction. In the third region, the dissipation of wake vortices leads to the regeneration of Reynolds shear stress. A quadrant analysis of the Reynolds shear stress contribution reveals that the LEBU increases the Q2 and Q4 contributions and attenuates the Q1 and Q3 contributions in the first region, followed by an onset of Reynolds shear stress further downstream.