arXiv subjects

Philipp Schlatter

Publications and source records attributed to Philipp Schlatter.

At least 55 records · Page 3Linked to original sources

arXiv2021

Recurrent neural networks and Koopman-based frameworks for temporal predictions in a low-order model of turbulence

The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show that it is possible to obtain excellent reproductions of the long-term statistics and the dynamic behavior of the chaotic system with properly trained long-short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below $1\%$. Besides, a newly developed Koopman-based framework, called Koopman with nonlinear forcing (KNF), leads to the same level of accuracy in the statistics at a significantly lower computational expense. Furthermore, the KNF framework outperforms the LSTM network when it comes to short-term predictions. We also observe that using a loss function based only on the instantaneous predictions of the chaotic system can lead to suboptimal reproductions in terms of long-term statistics. Thus, we propose a model-selection criterion based on the computed statistics which allows to achieve excellent statistical reconstruction even on small datasets, with minimal loss of accuracy in the instantaneous predictions.

physics.flu-dyn↗

arXiv2020

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

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

physics.flu-dyn↗

arXiv2020

An Uncertainty-Quantification Framework for Assessing Accuracy, Sensitivity, and Robustness in Computational Fluid Dynamics

A framework is developed based on different uncertainty quantification (UQ) techniques in order to assess validation and verification (V&V) metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator's outputs with respect to uncertain inputs and computational parameters. These parameters are divided into two groups: based on the variation of the first group, a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group. To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise structure is used. To estimate the propagated uncertainties in the simulator's outputs from first and also the combination of first and second groups of parameters, standard and probabilistic polynomial chaos expansions (PCE) are employed, respectively. Global sensitivity analysis based on Sobol decomposition is performed in connection with the computer experiment to rank the parameters based on their influence on the simulator's output. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel flow using the open-source CFD solver Nek5000. Due to the high-order nature of Nek5000 a thorough assessment of the results' accuracy and reliability is crucial, as the code is aimed at high-fidelity simulations. The detailed analyses and the resulting conclusions can enhance our insight into the influence of different factors on physics simulations, in particular the simulations of wall-bounded turbulence.

physics.comp-ph↗

arXiv2020

Optimization of Tensor-product Operations in Nekbone on GPUs

In the CFD solver Nek5000, the computation is dominated by the evaluation of small tensor operations. Nekbone is a proxy app for Nek5000 and has previously been ported to GPUs with a mixed OpenACC and CUDA approach. In this work, we continue this effort and optimize the main tensor-product operation in Nekbone further. Our optimization is done in CUDA and uses a different, 2D, thread structure to make the computations layer by layer. This enables us to use loop unrolling as well as utilize registers and shared memory efficiently. Our implementation is then compared on both the Pascal and Volta GPU architectures to previous GPU versions of Nekbone as well as a measured roofline. The results show that our implementation outperforms previous GPU Nekbone implementations by 6-10%. Compared to the measured roofline, we obtain 77 - 92% of the peak performance for both Nvidia P100 and V100 GPUs for inputs with 1024 - 4096 elements and polynomial degree 9.

cs.DC↗

arXiv2020

Near wall coherence in wall-bounded flows and implications for flow control

Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, opposition control is only realizable if there is a degree of coherence between the sensor--actuator pairs of the control system (these sensors and actuators should typically be wall-based to avoid parasitic drag). As such, we here inspect the feasibility of real-time control of the near-wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from numerical simulations at $Re_τ\approx 590$ and $ 2000$ are employed. It is shown that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region. Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers. Coherence values of 0.55 and 0.4, which are considerably lower than the maximum possible coherence 1, were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. This suggests that a closed-loop drag reduction scheme targeting near wall cycle of streaks alone will be of limited success in practice as the Reynolds number grows.

physics.flu-dyn↗

arXiv2020

SPOD and resolvent analysis of near-wall coherent structures in turbulent pipe flows

Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers $Re_τ = 180$ and $550$. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing to map out the similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing represents quasi-streamwise vortices and associated response corresponds to streaks. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.

physics.flu-dyn↗

arXiv2020

On the use of recurrent neural networks for predictions of turbulent flows

In this paper, the prediction capabilities of recurrent neural networks are assessed in the low-order model of near-wall turbulence by Moehlis {\it et al.} (New J. Phys. {\bf 6}, 56, 2004). Our results show that it is possible to obtain excellent predictions of the turbulence statistics and the dynamic behavior of the flow with properly trained long short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below $1\%$. We also observe that using a loss function based only on the instantaneous predictions of the flow may not lead to the best predictions in terms of turbulence statistics, and it is necessary to define a stopping criterion based on the computed statistics. Furthermore, more sophisticated loss functions, including not only the instantaneous predictions but also the averaged behavior of the flow, may lead to much faster neural network training.

physics.flu-dyn↗

arXiv2019

A critical point for bifurcation cascades and featureless turbulence

In this Letter we show that a bifurcation cascade and fully sustained turbulence can share the phase space of a fluid flow system, resulting in the presence of competing stable attractors. We analyse the toroidal pipe flow, which undergoes subcritical transition to turbulence at low pipe curvatures and supercritical transition at high curvatures, as was previously documented. We provide decisive evidence that the nature of the supercritical transition is of Ruelle--Takens type and that, in a narrow range of intermediate curvatures, its dynamics competes with that of sustained turbulence emerging through subcritical transition mechanisms.

physics.flu-dyn↗

arXiv2019

Edge tracking in spatially developing boundary layer flows

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

physics.flu-dyn↗

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.

physics.flu-dyn↗

arXiv2019

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

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

physics.flu-dyn↗

arXiv2019

The vanishing of strong turbulent fronts in bent pipes

Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio $δ= D/d = 0.01$ at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half times the value in the core and that the average cross-flow fluctuations at the front are up to three times lower if compared to a straight pipe, while attaining similar values in the core. Localised turbulence can be sustained at smaller energies through a redistribution of turbulent fluctuations and vortical structures by the in-plane Dean motion of the mean flow. This asymmetry determines a strong localisation of TKE production near the outer bend, where linear and nonlinear mechanisms optimally amplify perturbations. We further observe a substantial reduction of the range of Reynolds numbers for long-lived intermittent turbulence, in agreement with experimental data from the literature. Moreover, no occurrence of nucleation of spots through splitting could be detected in the range of parameters considered. Based on the present results, we argue that this mechanism gradually becomes marginal as the curvature of the pipe increases and the transition scenario approaches a dynamical switch from subcritical to supercritical.

physics.flu-dyn↗

arXiv2018

Reynolds-number effects in turbulent boundary layers around wing sections

Four well-resolved LESs of the turbulent boundary layers around a NACA4412 wing section, with Rec ranging from 100,000 to 1,000,000, were performed at 5 degree angle of attack. By comparing the turbulence statistics with those in ZPG TBLs at approximately matching Re_tau, we find that the effect of the adverse pressure gradient (APG) is more intense at lower Reynolds numbers. This indicates that at low Re the outer region of the TBL becomes more energized through the wall-normal convection associated to the APG. This is also reflected in the fact that the inner-scaled wall-normal velocity is larger on the suction side at lower Reynolds numbers. In particular, the wing cases at Rec = 200,000 and 400,000 exhibit wall-normal velocities 40% and 20% larger, respectively, than the case with Rec = 1,000,000. Consequently, the outer-region energizing mechanism associated to the APG is complementary to that present in high-Re TBLs.

physics.flu-dyn↗

arXiv2018

Assessment of uncertainties in hot-wire anemometry and oil-film interferometry measurements for wall-bounded turbulent flows

In this study, the sources of uncertainty of hot-wire anemometry (HWA) and oil-film interferometry (OFI) measurements are assessed. Both statistical and classical methods are used for the forward and inverse problems, so that the contributions to the overall uncertainty of the measured quantities can be evaluated. The correlations between the parameters are taken into account through the Bayesian inference with error-in-variable (EiV) model. In the forward problem, very small differences were found when using Monte Carlo (MC), Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow velocity measurements with HWA, the results indicate that the estimated uncertainty is lower when the correlations among parameters are considered, than when they are not taken into account. Moreover, global sensitivity analyses with Sobol indices showed that the HWA measurements are most sensitive to the wire voltage, and in the case of OFI the most sensitive factor is the calculation of fringe velocity. The relative errors in wall-shear stress, friction velocity and viscous length are 0.44%, 0.23% and 0.22%, respectively. Note that these values are lower than the ones reported in other wall-bounded turbulence studies. Note that in most studies of wall-bounded turbulence the correlations among parameters are not considered, and the uncertainties from the various parameters are directly added when determining the overall uncertainty of the measured quantity. In the present analysis we account for these correlations, which may lead to a lower overall uncertainty estimate due to error cancellation. Furthermore, our results also indicate that the crucial aspect when obtaining accurate inner-scaled velocity measurements is the wind-tunnel flow quality, which is more critical than the accuracy in wall-shear stress measurements.

physics.flu-dyn↗

arXiv2017

Edge state modulation by mean viscosity gradients

Motivated by the relevance of edge state solutions as mediators of transition, we use direct numerical simulations to study the effect of spatially non-uniform viscosity on their energy and stability in minimal channel flows. What we seek is a theoretical support rooted in a fully non-linear framework that explains the modified threshold for transition to turbulence in flows with temperature-dependent viscosity. Consistently over a range of subcritical Reynolds numbers, we find that decreasing viscosity away from the walls weakens the streamwise streaks and the vortical structures responsible for their regeneration. The entire self-sustained cycle of the edge state is maintained on a lower kinetic energy level with a smaller driving force, compared to a flow with constant viscosity. Increasing viscosity away from the walls has the opposite effect. In both cases, the effect is proportional to the strength of the viscosity gradient. The results presented highlight a local shift in the state space of the position of the edge state relative to the laminar attractor with the consequent modulation of its basin of attraction in the proximity of the edge state and of the surrounding manifold. The implication is that the threshold for transition is reduced for perturbations evolving in the neighbourhood of the edge state in case viscosity decreases away from the walls, and vice versa.

physics.flu-dyn↗

arXiv2017

The three-dimensional structure of swirl-switching in bent pipe flow

Swirl-switching is a low-frequency oscillatory phenomenon which affects the Dean vortices in bent pipes and may cause fatigue in piping systems. Despite thirty years worth of research, the mechanism that causes these oscillations and the frequencies that characterise them remain unclear. Here we show that a three-dimensional wave-like structure is responsible for the low-frequency switching of the dominant Dean vortex. The present study, performed via direct numerical simulation, focuses on the turbulent flow through a 90 \degree pipe bend preceded and followed by straight pipe segments. A pipe with curvature 0.3 (defined as ratio between pipe radius and bend radius) is studied for a bulk Reynolds number Re = 11 700, corresponding to a friction Reynolds number Re_τ\approx 360. Synthetic turbulence is generated at the inflow section and used instead of the classical recycling method in order to avoid the interference between recycling and swirl-switching frequencies. The flow field is analysed by three-dimensional proper orthogonal decomposition (POD) which for the first time allows the identification of the source of swirl-switching: a wave-like structure that originates in the pipe bend. Contrary to some previous studies, the flow in the upstream pipe does not show any direct influence on the swirl-switching modes. Our analysis further shows that a three- dimensional characterisation of the modes is crucial to understand the mechanism, and that reconstructions based on 2D POD modes are incomplete.

physics.flu-dyn↗

arXiv2017

On the Strong Scaling of the Spectral Element Solver Nek5000 on Petascale Systems

The present work is targeted at performing a strong scaling study of the high-order spectral element fluid dynamics solver Nek5000. Prior studies indicated a recommendable metric for strong scalability from a theoretical viewpoint, which we test here extensively on three parallel machines with different performance characteristics and interconnect networks, namely Mira (IBM Blue Gene/Q), Beskow (Cray XC40) and Titan (Cray XK7). The test cases considered for the simulations correspond to a turbulent flow in a straight pipe at four different friction Reynolds numbers $Re_τ$ = 180, 360, 550 and 1000. Considering the linear model for parallel communication we quantify the machine characteristics in order to better assess the scaling behaviors of the code. Subsequently sampling and profiling tools are used to measure the computation and communication times over a large range of compute cores. We also study the effect of the two coarse grid solvers XXT and AMG on the computational time. Super-linear scaling due to a reduction in cache misses is observed on each computer. The strong scaling limit is attained for roughly 5000 - 10,000 degrees of freedom per core on Mira, 30,000 - 50,0000 on Beskow, with only a small impact of the problem size for both machines, and ranges between 10,000 and 220,000 depending on the problem size on Titan. This work aims at being a reference for Nek5000 users and also serves as a basis for potential issues to address as the community heads towards exascale supercomputers.

cs.DC↗

arXiv2016

Aspect ratio effect on particle transport in turbulent duct flows

The dynamics of dilute micron-sized spherical inertial particles in turbulent duct flows is studied by means of direct numerical simulations of the carrier phase turbulence with one-way coupled Lagrangian particles. The geometries are a square and a rectangular duct with width-to-height aspect ratio $AR$ of 3 operating at $Re_{τ,c}=360$ . The present study is designed to determine the effect of turbulence-driven secondary motion on the particle dynamics. Our results show that a weak cross-flow secondary motion significantly changes the cross-sectional map of the particle concentration, mean velocity and fluctuations. As the geometry of the duct is widened from $AR=1$ to 3, the secondary vortex on the horizontal wall significantly expands in the spanwise direction, and although the kinetic energy of the secondary flow increases close to the corner, it decays towards the duct centreplane in the $AR=3$ case so as the turbulent carrier phase approaches the behavior in spanwise-periodic channel flows, a fact that significantly affects the particle statistics. In the square duct the particle concentration in the viscous sublayer is maximum at the duct centreplane, whereas the maximum is found closer to the corner, at a distance of $|z/h|\approx1.25$ from the centreplane, in the $AR=3$ case. Interestingly the centreplane concentration in the rectangular duct is around 3 times lower than that in the square duct. Moreover, a second peak in the accumulation distribution is found right at the corners for both ducts. At this location the concentration increases with particle inertia. The secondary motion changes also the cross-stream map of the particle velocities significantly in comparison to the fluid flow statistics. These directly affect the particle velocity fluctuations such that multiple peaks appear near the duct walls for the particle streamwise and wall-normal velocity fluctuations.

physics.flu-dyn↗