Showing papers in "Journal of Fluid Mechanics in 2017"
TL;DR: Although neural networks have been applied previously to complex fluid flows, the article featured here is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows.
Abstract: It was only a matter of time before deep neural networks (DNNs) – deep learning – made their mark in turbulence modelling, or more broadly, in the general area of high-dimensional, complex dynamical systems. In the last decade, DNNs have become a dominant data mining tool for big data applications. Although neural networks have been applied previously to complex fluid flows, the article featured here (Ling et al., J. Fluid Mech., vol. 807, 2016, pp. 155–166) is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models. As one often expects with modern DNNs, performance gains are achieved over competing state-of-the-art methods, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows.
609 citations
TL;DR: In this article, a blind deconvolution network is proposed for large eddy simulations, where the deconvolved field is computed without any pre-existing information about the filtering procedure or kernel.
Abstract: We present a single-layer feed-forward artificial neural network architecture trained through a supervised learning approach for the deconvolution of flow variables from their coarse-grained computations such as those encountered in large eddy simulations. We stress that the deconvolution procedure proposed in this investigation is blind, i.e. the deconvolved field is computed without any pre-existing information about the filtering procedure or kernel. This may be conceptually contrasted to the celebrated approximate deconvolution approaches where a filter shape is predefined for an iterative deconvolution process. We demonstrate that the proposed blind deconvolution network performs exceptionally well in the a priori testing of two-dimensional Kraichnan, three-dimensional Kolmogorov and compressible stratified turbulence test cases, and shows promise in forming the backbone of a physics-augmented data-driven closure for the Navier–Stokes equations.
184 citations
TL;DR: In this article, known structures and self-sustaining mechanisms of wall turbulence are reviewed and explored in the context of the scale interactions implied by the nonlinear advective term in the Navier-Stokes equations.
Abstract: Known structures and self-sustaining mechanisms of wall turbulence are reviewed and explored in the context of the scale interactions implied by the nonlinear advective term in the Navier–Stokes equations. The viewpoint is shaped by the systems approach provided by the resolvent framework for wall turbulence proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in which the nonlinearity is interpreted as providing the forcing to the linear Navier–Stokes operator (the resolvent). Elements of the structure of wall turbulence that can be uncovered as the treatment of the nonlinearity ranges from data-informed approximation to analysis of exact solutions of the Navier–Stokes equations (so-called exact coherent states) are discussed. The article concludes with an outline of the feasibility of extending this kind of approach to high-Reynolds-number wall turbulence in canonical flows and beyond.
176 citations
TL;DR: In this paper, a phase-field multiphase lattice Boltzmann model was developed to systematically investigate the dynamic behavior of a droplet passing through a microfluidic T-junction, especially focusing on the non-breakup of the droplet.
Abstract: We develop a phase-field multiphase lattice Boltzmann model to systematically investigate the dynamic behaviour of a droplet passing through a microfluidic T-junction, especially focusing on the non-breakup of the droplet. Detailed information on the breakup and non-breakup is presented, together with the quantitative evolutions of driving and resistance forces as well as the droplet deformation characteristics involved. Through comparisons between cases of non-breakup and breakup, we find that the appearance of tunnels (the lubricating film between droplet and channel walls) provides a precondition for the final non-breakup of droplets, which slows down the droplet deformation rate and even induces non-breakup. The vortex flow formed inside droplets plays an important role in determining whether they break up or not. In particular, when the strength of vortex flow exceeds a critical value, a droplet can no longer break up. Additionally, more effort has been devoted to investigating the effects of viscosity ratio between disperse and continuous phases and width ratio between branch and main channels on droplet dynamic behaviours. It is found that a large droplet viscosity results in a small velocity gradient in a droplet, which restricts vortex generation and thus produces lower deformation resistance. Consequently, it is easier to break up a droplet with larger viscosity. Our work also reveals that a droplet in small branch channels tends to obstruct the channels and have small vortex flows, which induces easier breakup too. Eventually, several phase diagrams for droplet flow patterns are provided, and the corresponding power-law correlations ( , where is dimensionless initial droplet length and is capillary number) are fitted to describe the boundaries between different flow patterns.
167 citations
TL;DR: In this article, scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented, with the scaled data for thrust, power and efficiency all showing excellent collapse.
Abstract: Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on swimming aquatic animals.
149 citations
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TL;DR: In this article, the authors address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier-Stokes equations.
Abstract: In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier–Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for coloured-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that coloured-in-time excitation of the Navier–Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization and control design.
145 citations
TL;DR: In this article, the potential core of a subsonic jet is modeled using a linear modal analysis of the Euler equations linearized about the turbulent mean flow and acoustic modes of a cylindrical soft duct.
Abstract: The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and relate them to previously observed tones in the near-nozzle region. The waves are detected in data from a large-eddy simulation of a Mach 0.9 isothermal jet and modelled using parallel and weakly non-parallel linear modal analysis of the Euler equations linearized about the turbulent mean flow, as well as simplified models based on a cylindrical vortex sheet and the acoustic modes of a cylindrical soft duct. In addition to the Kelvin–Helmholtz instability waves, three types of waves with negative phase velocities are identified in the potential core: upstream- and downstream-propagating duct-like acoustic modes that experience the shear layer as a pressure-release surface and are therefore radially confined to the potential core, and upstream-propagating acoustic modes that represent a weak coupling between the jet core and the free stream. The slow streamwise contraction of the potential core imposes a frequency-dependent end condition on the waves that is modelled as the turning points of a weakly non-parallel approximation of the waves. These turning points provide a mechanism by which the upstream- and downstream-travelling waves can interact and exchange energy through reflection and transmission processes. Paired with a second end condition provided by the nozzle, this leads to the possibility of resonance in limited frequency bands that are bound by two saddle points in the complex wavenumber plane. The predicted frequencies closely match the observed tones detected outside of the jet. The vortex-sheet model is then used to systematically explore the Mach number and temperature ratio dependence of the phenomenon. For isothermal jets, the model suggests that resonance is likely to occur in a narrow range of Mach number, 0.82 < M < 1.
140 citations
TL;DR: In this article, a microcontinuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions, which employs a Darcy-Brinkman-Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface.
Abstract: A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions. The approach employs a Darcy–Brinkman–Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface. The methodology compares well with the arbitrary-Lagrangian–Eulerian technique. The simulation framework is validated using an experimental microfluidic device to image the dissolution of a single calcite crystal. The evolution of the calcite crystal during the acidizing process is analysed and related to the flow conditions. Macroscopic laws for the dissolution rate are proposed by upscaling the pore-scale simulations. Finally, the emergence of wormholes during the injection of acid in a two-dimensional domain of calcite grains is discussed based on pore-scale simulations.
137 citations
TL;DR: In this article, the authors investigated the hydrodynamic benefits of body-fin and fin-fin interactions in a fish model in carangiform swimming and found that the leading edge vortices produced by the caudal fin are associated with most of the thrust production in this fish model.
Abstract: Numerical simulations are used to investigate the hydrodynamic benefits of body–fin and fin–fin interactions in a fish model in carangiform swimming. The geometry and kinematics of the model are reconstructed in three-dimensions from high-speed videos of a live fish, Crevalle Jack (Caranx hippos), during steady swimming. The simulations employ an immersed-boundary-method-based incompressible Navier–Stokes flow solver that allows us to quantitatively characterize the propulsive performance of the fish median fins (the dorsal and the anal fins) and the caudal fin using three-dimensional full body simulations. This includes a detailed analysis of associated performance enhancement mechanisms and their connection to the vortex dynamics. Comparisons are made using three different models containing different combinations of the fish body and fins to provide insights into the force production. The results indicate that the fish produces high performance propulsion by utilizing complex interactions among the fins and the body. By connecting the vortex dynamics and surface force distribution, it is found that the leading-edge vortices produced by the caudal fin are associated with most of the thrust production in this fish model. These vortices could be strengthened by the vorticity capture from the vortices generated by the posterior body during undulatory motion. Meanwhile, the pressure difference between the two sides of posterior body resulting from the posterior body vortices (PBVs) helps with the alleviation of the body drag. The appearance of the median fins in the posterior region further strengthens the PBVs and caudal-fin wake capture mechanism. This work provides new physical insights into how body–fin and fin–fin interactions enhance thrust production in swimming fishes, and emphasizes that movements of both the body and fins contribute to overall swimming performance in fish locomotion.
136 citations
TL;DR: In this article, the wake of a five-bladed marine propeller at design operating condition is studied using large eddy simulation (LES), and the mean loads and phase-averaged flow field show good agreement with experiments.
Abstract: The wake of a five-bladed marine propeller at design operating condition is studied using large eddy simulation (LES). The mean loads and phase-averaged flow field show good agreement with experiments. Phase-averaged and azimuthal-averaged flow fields are analysed in detail to examine the mechanisms of wake instability. The propeller wake consisting of tip and hub vortices undergoes streamtube contraction, which is followed by the onset of instabilities as evident from the oscillations of the tip vortices. Simulation results reveal a mutual-induction mechanism of instability where, instead of the tip vortices interacting among themselves, they interact with the smaller vortices generated by the roll-up of the blade trailing edge wake in the near wake. It is argued that although the mutual-inductance mode is the dominant mode of instability in propellers, the actual mechanism depends on the propeller geometry and the operating conditions. The axial evolution of the propeller wake from near to far field is discussed. Once the propeller wake becomes unstable, the coherent vortical structures break up and evolve into the far wake, composed of a fluid mass swirling around an oscillating hub vortex. The hub vortex remains coherent over the length of the computational domain.
127 citations
TL;DR: In this paper, the Strouhal number, phase angle between heave and pitch at the trailing edge, and angle of attack are principal parameters for a single fish and a pair of hydrodynamically interacting fish.
Abstract: We establish through numerical simulation conditions for optimal undulatory propulsion for a single fish, and for a pair of hydrodynamically interacting fish, accounting for linear and angular recoil. We first employ systematic two-dimensional (2-D) simulations to identify conditions for minimal propulsive power of a self-propelled fish, and continue with targeted 3-D simulations for a danio-like fish; all at Reynolds number 5000. We find that the Strouhal number, phase angle between heave and pitch at the trailing edge, and angle of attack are principal parameters. For 2-D simulations, imposing a deformation based on measured displacement for carangiform swimming provides, at best, efficiency of 35 %, which increases to 50 % for an optimized motion; for a 3-D fish, the efficiency increases from 22 % to 34 %. Indeed, angular recoil has significant impact on efficiency, and optimized body bending requires maximum bending amplitude upstream of the trailing edge. Next, we turn to 2-D simulation of two hydrodynamically interacting fish. We find that the upstream fish benefits energetically only for small distances. In contrast, the downstream fish can benefit at any position that allows interaction with the upstream wake, provided its body motion is timed appropriately with respect to the oncoming vortices. For an in-line configuration, one body length apart, the efficiency of the downstream fish can increase from 50 % to 60 %; for an offset arrangement it can reach 80 %. This proves that in groups of fish, energy savings can be achieved for downstream fish through interaction with oncoming vortices, even when the downstream fish lies directly inside the jet-like flow of an upstream fish.
TL;DR: In this paper, the authors define a path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number).
Abstract: Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a uni-dimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number . We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.
TL;DR: In this article, a global linear stability analysis based on the turbulent mean flow was conducted to identify trapped acoustic waves in the potential core of a high-subsonic jet, which can be unambiguously identified by a local dispersion relation.
Abstract: Coherent features of a turbulent Mach 0.9, Reynolds number 10^6 jet are educed from a high-fidelity large eddy simulation. Besides the well-known Kelvin–Helmholtz instabilities of the shear layer, a new class of trapped acoustic waves is identified in the potential core. A global linear stability analysis based on the turbulent mean flow is conducted. The trapped acoustic waves form branches of discrete eigenvalues in the global spectrum, and the corresponding global modes accurately match the educed structures. Discrete trapped acoustic modes occur in a hierarchy determined by their radial and axial order. A local dispersion relation is constructed from the global modes and found to agree favourably with an empirical dispersion relation educed from the simulation data. The product between direct and adjoint modes is then used to isolate the trapped waves. Under certain conditions, resonance in the form of a beating occurs between trapped acoustic waves of positive and negative group velocities. This resonance explains why the trapped modes are prominently observed in the simulation and as tones in previous experimental studies. In the past, these tones were attributed to external factors. Here, we show that they are an intrinsic feature of high-subsonic jets that can be unambiguously identified by a global linear stability analysis.
TL;DR: In this paper, the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction with strong mean-flow separation were analyzed for grid-converged large-eddy simulations.
Abstract: We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by. The Reynolds number based on the incoming boundary-layer thickness of is considerably higher than in previous LES studies. The very long integration time of allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Gortler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Gortler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.
TL;DR: In this article, a pairwise interaction extended point-particle (PIEP) model was proposed to account for the hydrodynamic influence of the neighbouring particles in an Eulerian-Lagrangian simulation.
Abstract: This study introduces a new point-particle force model that attempts to account for the hydrodynamic influence of the neighbouring particles in an Eulerian–Lagrangian simulation. In previous point-particle models the force on a particle depends only on Reynolds number and mean volume fraction. Thus, as long as the mean local volume fraction is the same, the force on different particles will be estimated to be the same, even though the precise arrangement of neighbours can be vastly different. From direct numerical simulation (DNS) it has been observed that in a random arrangement of spheres that were distributed with uniform probability, the particle-to-particle variation in force can be as large as the mean drag. Since the Reynolds number and mean volume fraction of all the particles within the array are the same, the standard models fail to account for the significant particle-to-particle force variation within the random array. Here, we develop a model which can compute the drag and lateral forces on each particle by accounting for the precise location of a few surrounding neighbours. A pairwise interaction is assumed where the perturbation flow induced by each neighbour is considered separately, then the effects of all neighbours are linearly superposed to obtain the total perturbation. Faxen correction is used to quantify the force perturbation due to the presence of the neighbours. The single neighbour perturbations are mapped in the vicinity of a reference sphere and stored as libraries. We test the pairwise interaction extended point-particle (PIEP) model for random arrays at two different volume fractions of and 0.21 and Reynolds numbers in the range . The PIEP model predictions are compared against drag and lift forces obtained from the fully resolved DNS simulations performed using the immersed boundary method. Although not perfect, we observe the PIEP model prediction to correlate much better with the DNS results than the classical mean drag model prediction.
TL;DR: In this paper, the authors dealt with turbulent boundary layers under adverse pressure gradients and well-resolved large-eddy simulations were performed to assess the influence of the streamwise pressure develo...
Abstract: This study deals with turbulent boundary layers under adverse-pressure gradients. Well-resolved large-eddy simulations (LES) were performed to assess the influence of the streamwise pressure develo ...
TL;DR: In this article, a detailed parametric study is performed to investigate the sensitivity of the noise reductions to the serration amplitude and wavelength, and an optimum serration wavelength is identified whereby maximum noise reductions are obtained, corresponding to when the transverse integral length scale is approximately one-fourth the serral wavelength.
Abstract: This paper presents the results of a detailed experimental investigation into the effectiveness of sinusoidal leading edge serrations on aerofoils for the reduction of the noise generated by the interaction with turbulent flow. A detailed parametric study is performed to investigate the sensitivity of the noise reductions to the serration amplitude and wavelength. The study is primarily performed on flat plates in an idealized turbulent flow, which we demonstrate captures the same behaviour as when identical serrations are introduced onto three-dimensional aerofoils. The influence on the noise reduction of the turbulence integral length scale is also studied. An optimum serration wavelength is identified whereby maximum noise reductions are obtained, corresponding to when the transverse integral length scale is approximately one-fourth the serration wavelength. This paper proves that, at the optimum serration wavelength, adjacent valley sources are excited incoherently. One of the most important findings of this paper is that, at the optimum serration wavelength, the sound power radiation from the serrated aerofoil varies inversely proportional to the Strouhal number , where , and are frequency, serration amplitude and flow speed, respectively. A simple model is proposed to explain this behaviour. Noise reductions are observed to generally increase with increasing frequency until the frequency at which aerofoil self-noise dominates the interaction noise. Leading edge serrations are also shown to reduce aerofoil self-noise. The mechanism for this phenomenon is explored through particle image velocimetry measurements. Finally, the lift and drag of the serrated aerofoil are obtained through direct measurement and compared against the straight edge baseline aerofoil. It is shown that aerodynamic performance is not substantially degraded by the introduction of the leading edge serrations on the aerofoil.
TL;DR: In this paper, a detailed analysis of the flame area, its local thickness and their rates of change in isosurface following reference frames, quantities that are intimately connected, is presented.
Abstract: This article reports an analysis of the first detailed chemistry direct numerical simulation (DNS) of a high Karlovitz number laboratory premixed flame. The DNS results are first compared with those from laser-based diagnostics with good agreement. The subsequent analysis focuses on a detailed investigation of the flame area, its local thickness and their rates of change in isosurface following reference frames, quantities that are intimately connected. The net flame stretch is demonstrated to be a small residual of large competing terms: The positive tangential strain term and the negative curvature stretch term. The latter is found to be driven by flame speed-curvature correlations and dominated in net by low probability highly curved regions. Flame thickening is demonstrated to be substantial on average, while local regions of flame thinning are also observed. The rate of change of the flame thickness (as measured by the scalar gradient magnitude) is demonstrated, analogously to flame stretch, to be a competition between straining tending to increase gradients and flame speed variations in the normal direction tending to decrease them. The flame stretch and flame thickness analyses are connected by the observation that high positive tangential strain rate regions generally correspond with low curvature regions; these regions tend to be positively stretched in net and are relatively thinner compared with other regions. High curvature magnitude regions (both positive and negative) generally correspond with lower tangential strain; these regions are in net negatively stretched and thickened substantially.
TL;DR: Tan et al. as mentioned in this paper investigated the evaporation of mixture droplets in more detail, by successively increasing the mixture complexity from pure water over a binary water-ethanol mixture to the ternary Ouzo mixture (water, ethanol and anise oil).
Abstract: The Greek aperitif Ouzo is not only famous for its specific anise-flavoured taste, but also for its ability to turn from a transparent miscible liquid to a milky-white coloured emulsion when water is added. Recently, it has been shown that this so-called Ouzo effect, i.e. the spontaneous emulsification of oil microdroplets, can also be triggered by the preferential evaporation of ethanol in an evaporating sessile Ouzo drop, leading to an amazingly rich drying process with multiple phase transitions (Tan et al., Proc. Natl Acad. Sci. USA, vol. 113 (31), 2016, pp. 8642-8647). Due to the enhanced evaporation near the contact line, the nucleation of oil droplets starts at the rim which results in an oil ring encircling the drop. Furthermore, the oil droplets are advected through the Ouzo drop by a fast solutal Marangoni flow. In this article, we investigate the evaporation of mixture droplets in more detail, by successively increasing the mixture complexity from pure water over a binary water-ethanol mixture to the ternary Ouzo mixture (water, ethanol and anise oil). In particular, axisymmetric and full three-dimensional finite element method simulations have been performed on these droplets to discuss thermal effects and the complicated flow in the droplet driven by an interplay of preferential evaporation, evaporative cooling and solutal and thermal Marangoni flow. By using image analysis techniques and micro-particle-image-velocimetry measurements, we are able to compare the numerically predicted volume evolutions and velocity fields with experimental data. The Ouzo droplet is furthermore investigated by confocal microscopy. It is shown that the oil ring predominantly emerges due to coalescence.
TL;DR: In this article, a simulation of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream is presented, and the authors compare measurements and simulations when the foil is forced with pitching oscillations, and find a close correspondence between flow visualisations using thickness variations in the soap film and numerically determined vortex structures.
Abstract: We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream. We explore pure pitching and pure heaving, and contrast these two generic types of kinematics. We compare measurements and simulations when the foil is forced with pitching oscillations, and we find a close correspondence between flow visualisations using thickness variations in the soap film and the numerically determined vortex structures. Numerically, we determine wake maps spanned by oscillation frequency and amplitude, and we find qualitatively similar maps for pitching and heaving. We determine the drag–thrust transition for both pitching and heaving numerically, and we discuss it in relation to changes in wake structure. For heaving with low oscillation frequency and high amplitude, we find that the drag–thrust transition occurs in a parameter region with wakes in which two vortex pairs are formed per oscillation period, in contrast to the common transition scenario in regions with inverted von Karman wakes.
TL;DR: In this article, Zhang et al. analyzed the stability of a hypersonic boundary layer on a flared cone for the same flow conditions as in earlier experiments, and the nonlinear parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Gortler mode or the first mode).
Abstract: The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Gortler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Gortler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.
TL;DR: In this paper, a spectral coherence analysis of the turbulent boundary layer flow structure is carried out through a spectrogram of two-point streamwise velocity signals at a near-wall reference position and a range of wall-normal positions spanning a Reynolds-number range.
Abstract: An assessment of the turbulent boundary layer flow structure, which is coherent with the near-wall region, is carried out through a spectral coherence analysis. This spectral method is applied to datasets comprising synchronized two-point streamwise velocity signals at a near-wall reference position and a range of wall-normal positions spanning a Reynolds-number range . Within each dataset, a self-similar structure is identified from the coherence between the turbulence in the logarithmic region and at the near-wall reference position. This self-similarity is described by a streamwise/wall-normal aspect ratio of , where and are the streamwise wavelength and wall-normal distance respectively.
TL;DR: In this article, the first and higher harmonic components of the resonant fluid response in the gap between two identical fixed rectangular boxes are experimentally investigated in a wave basin and it is shown that for an incident group with appropriate frequency content, the linear gap response may be substantially smaller than the second-harmonic component, which is strongly driven via quadratic coupling of the linear terms from the incident wave and occurs in gap resonant modes.
Abstract: The first- and higher-harmonic components of the resonant fluid response in the gap between two identical fixed rectangular boxes are experimentally investigated in a wave basin. Gap response is excited by transient wave groups (being based on scaled versions of the autocorrelation function of sea state spectra, representing NewWaves, the average shape of large waves in a sea state). Several different wave groups with different maximum surface elevations, spectral peak frequencies and bandwidths are used, while the bilge shape of the boxes and approach angle of the waves are also varied. Unlike a simple regular wave, it is complicated to separate the harmonic components for a transient wave group due to non-linear wave-wave and wave-structure interactions. A four-phase combination methodology is used to separate the first four harmonic components, and this also allows higher-harmonic components to be isolated with simple digital frequency filtering. Harmonic components up to 14th order in the incident wave amplitude have been extracted. It is shown that for an incident group with appropriate frequency content, the linear gap response may be substantially smaller than the second-harmonic component, which is strongly driven via quadratic coupling of the linear terms from the incident wave and occurs in the gap resonant modes. Double frequency excitation may have important practical implications for offshore operations. Fourth and zeroth (long wave) harmonics in the gap are further driven via quadratic coupling of the second-harmonic itself. Linear damping coefficients for the first few modes of the gap resonant response are derived from measured time series using a numerical fit and shown to be higher than those from linear diffraction calculations.
TL;DR: In this article, the statistical properties of the kinetic and thermal energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh-Benard (RB) convection were investigated.
Abstract: We investigate the statistical properties of the kinetic and thermal energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh–Benard (RB) convection. Direct numerical simulations were carried out in a box with unit aspect ratio in the Rayleigh number range for Prandtl numbers and 5.3. The probability density functions (PDFs) of both dissipation rates are found to deviate significantly from a log-normal distribution. The PDF tails can be well described by a stretched exponential function, and become broader for higher Rayleigh number and lower Prandtl number, indicating an increasing degree of small-scale intermittency with increasing Reynolds number. Our results show that the ensemble averages and scale as , which is in excellent agreement with the scaling estimated from the two global exact relations for the dissipation rates. By separating the bulk and boundary-layer contributions to the total dissipations, our results further reveal that and are both dominated by the boundary layers, corresponding to regimes and in the Grossmann–Lohse (GL) theory (J. Fluid Mech., vol. 407, 2000, pp. 27–56). To include the effects of thermal plumes, the plume–background partition is also considered and is found to be plume dominated. Moreover, the boundary-layer/plume contributions scale as those predicted by the GL theory, while the deviations from the GL predictions are observed for the bulk/background contributions. The possible reasons for the deviations are discussed.
TL;DR: In this article, the authors examined the onset of turbulence in Waleffe flow, the planar shear flow between stress-free boundaries driven by a sinusoidal body force, and demonstrated that the equilibrium turbulence fraction increases continuously from zero above a critical Reynolds number.
Abstract: We examine the onset of turbulence in Waleffe flow – the planar shear flow between stress-free boundaries driven by a sinusoidal body force. By truncating the wall-normal representation to four modes, we are able to simulate system sizes an order of magnitude larger than any previously simulated, and thereby to attack the question of universality for a planar shear flow. We demonstrate that the equilibrium turbulence fraction increases continuously from zero above a critical Reynolds number and that statistics of the turbulent structures exhibit the power-law scalings of the (2+1)D directed percolation universality class.
TL;DR: In this paper, the authors investigate the interaction between a large wind farm that has a fetch of 15 km and a conventionally neutral boundary layer (CNBL) in typical offshore conditions and find that the height of the inflow boundary layer has a significant impact on the wind farm flow development.
Abstract: While neutral atmospheric boundary layers are rare over land, they occur frequently over sea. In these cases they are almost always of the conventionally neutral type, in which the neutral boundary layer is capped by a strong inversion layer and a stably stratified atmosphere aloft. In the current study, we use large-eddy simulations (LES) to investigate the interaction between a large wind farm that has a fetch of 15 km and a conventionally neutral boundary layer (CNBL) in typical offshore conditions. At the domain inlet, we consider three different equilibrium CNBLs with heights of approximately 300 m, 500 m and 1000 m that are generated in a separate precursor LES. We find that the height of the inflow boundary layer has a significant impact on the wind farm flow development. First of all, above the farm, an internal boundary layer develops that interacts downwind with the capping inversion for the two lowest CNBL cases. Secondly, the upward displacement of the boundary layer by flow deceleration in the wind farm excites gravity waves in the inversion layer and the free atmosphere above. For the lower CNBL cases, these waves induce significant pressure gradients in the farm (both favourable and unfavourable depending on location and case). A detailed energy budget analysis in the turbine region shows that energy extracted by the wind turbines comes both from flow deceleration and from vertical turbulent entrainment. Though turbulent transport dominates near the end of the farm, flow deceleration remains significant, i.e. up to 35 % of the turbulent flux for the lowest CNBL case. In fact, while the turbulent fluxes are fully developed after eight turbine rows, the mean flow does not reach a stationary regime. A further energy budget analysis over the rest of the CNBL reveals that all energy available at turbine level comes from upwind kinetic energy in the boundary layer. In the lower CNBL cases, the pressure field induced by gravity waves plays an important role in redistributing this energy throughout the farm. Overall, in all cases entrainment at the capping inversion is negligible, and also the work done by the mean background pressure gradient, arising from the geostrophic balance in the free atmosphere, is small.
TL;DR: In this paper, a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values is performed, and several approaches to reduce the translational symmetry of the system are outlined.
Abstract: The chaotic dynamics of low-dimensional systems, such as Lorenz or Rossler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier–Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics – specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier–Stokes equations as they do in lower-dimensional systems – is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at , and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics.
TL;DR: In this paper, the authors used spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake.
Abstract: We present experimental data to demonstrate that the far wake of a vertical-axis wind turbine (VAWT) exhibits features that are quantitatively similar to that of a circular cylinder with the same aspect ratio. For a fixed Reynolds number (Re ≈ 0.8 × 10^5) and variable tip-speed ratio, two-dimensional particle image velocimetry (PIV) is used to measure the velocity field in the wake of four different laboratory-scale models: a 2-bladed, 3-bladed and 5-bladed VAWT, as well as a circular cylinder. With these measurements, we use spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake. In all cases, we observe three distinct regions in the VAWT wake: (i) the near wake, where periodic blade vortex shedding dominates; (ii) a transition region, where growth of a shear-layer instability occurs; (iii) the far wake, where bluff-body wake oscillations dominate. We define a dynamic solidity parameter, σ_D , that relates the characteristic scales of the flow to the streamwise transition location in the wake. In general, we find that increasing σ_D leads to an earlier transition, a greater initial velocity deficit and a faster rate of recovery in the wake. We propose a coordinate transformation using σ_D in which the minimum velocity recovery profiles of the VAWT wake closely match that of the cylinder wake. The results have implications for manipulating VAWT wake recovery within a wind farm.
TL;DR: In this paper, the authors investigated the aeroacoustic feedback loop establishing in a supersonic round jet impinging on a flat plate by combining compressible large-eddy simulations and modelling of that loop.
Abstract: The aeroacoustic feedback loop establishing in a supersonic round jet impinging on a flat plate normally has been investigated by combining compressible large-eddy simulations and modelling of that loop. At the exit of a straight pipe nozzle of radius r0, the jet is ideally expanded, and has a Mach number of 1.5 and a Reynolds number of 60000. Four distances between the nozzle exit and the flat plate, equal to 6r0, 8r0, 10r0 and 12r0, have been considered. In this way, the variations of the convection velocity of the shear-layer turbulent structures according to the nozzle-to-plate distance are shown. In the spectra obtained inside and outside of the flow near the nozzle, several tones emerge at Strouhal numbers in agreement with measurements in the literature. At these frequencies, by applying Fourier decomposition to the pressure fields, hydrodynamic-acoustic standing waves containing a whole number of cells between the nozzle and the plate and axisymmetric or helical jet oscillations are found. The tone frequencies and the mode numbers inferred from the standing-wave patterns are in line with the classical feedback-loop model, in which the loop is closed by acoustic waves outside the jet. The axisymmetric or helical nature of the jet oscillations at the tone frequencies is also consistent with a wave analysis using a jet vortex-sheet model, providing the allowable frequency ranges for the upstream-propagating acoustic wave modes of the jet. In particular, the tones are located on the part of the dispersion relations of the modes where these waves have phase and group velocities close to the ambient speed of sound. Based on the observation of the pressure fields and on frequency–wavenumber spectra on the jet axis and in the shear layers, such waves are identified inside the present jets, for the first time to the best of our knowledge, for a supersonic jet flow. This study thus suggests that the feedback loop in ideally expanded impinging jets is completed by these waves.
TL;DR: In this paper, a turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at Reτ ≈ 3900.
Abstract: A turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at Reτ ≈ 3900.. The three velocity components resulting from this experiment reveal a pronounced spanwise periodicity in all single-point velocity statistics. Consistent with previous hot-wire studies over similar-type riblets, we observe a weak time-average secondary flow in the form of δ-filling streamwise vortices. The observed differences in the surface and secondary flow characteristics, compared to other heterogeneous-roughness studies, may suggest that different mechanisms are responsible for the flow modifications in this case. Observations of instantaneous velocity fields reveal modified and rearranged turbulence structures. The instantaneous snapshots also suggest that the time-average secondary flow may be an artefact arising from superpositions of much stronger instantaneous turbulent events enhanced by the surface texture. In addition, the observed instantaneous secondary motions seem to have promoted a free-stream-engulfing behaviour in the outer layer, which would indicate an increase turbulent/non-turbulent flow mixing. It is overall demonstrated that the presence of large-scale directionality in transitional surface roughness can cause a modification throughout the entire boundary layer, even when the roughness height is 0.5 % of the layer thickness.