Wall-bounded Turbulent Flows Research Articles

Self-adaptive turbulence eddy simulation of a supersonic cavity-ramp flow

High Reynolds number supersonic wall-bounded turbulent flow is common in the aviation industry. However, accurately predicting this flow remains a long-standing challenge for turbulence modeling, particularly in separation cases. This study presents a numerical investigation of a Mach 2.92 turbulent cavity-ramp flow employing a new hybrid turbulence modeling approach, denoted as the self-adaptive turbulence eddy simulation (SATES) method. The results are compared with experimental data, as well as with outcomes from the conventional Reynolds-averaged Navier–Stokes (RANS) method and the previous delayed detached eddy simulation (DDES). The SATES model demonstrates a satisfactory prediction of time-averaged and fluctuating quantities in the free shear layer, redeveloping boundary layer, and ramp, showing better accuracy than the RANS results. Notably, the SATES results from the medium grid exhibit similarities to the DDES results from the extremely fine grid which is about 26 times compared with the SATES mesh. Furthermore, the significant features of the supersonic reattached flow, including turbulent properties, vortex structures, and unsteadiness characteristics, are analysed in detail, including the Reynolds stresses anisotropy invariant maps, transport process of vorticity, and frequency spectra. This work confirms that accurate numerical predictions of high Reynolds number supersonic separated and reattached flows are achievable using the SATES method with a relatively coarse mesh maintaining an affordable computational cost.

Deep Reinforcement Learning for the Management of the Wall Regeneration Cycle in Wall-Bounded Turbulent Flows

AbstractThe wall cycle in wall-bounded turbulent flows is a complex turbulence regeneration mechanism that remains not fully understood. This study explores the potential of deep reinforcement learning (DRL) for managing the wall regeneration cycle to achieve desired flow dynamics. To create a robust framework for DRL-based flow control, we have integrated the StableBaselines3 DRL libraries with the open-source direct numerical simulation (DNS) solver CaNS. The DRL agent interacts with the DNS environment, learning policies that modify wall boundary conditions to optimise objectives such as the reduction of the skin-friction coefficient or the enhancement of certain coherent structures’ features. The implementation makes use of the message-passing-interface (MPI) wrappers for efficient communication between the Python-based DRL agent and the DNS solver, ensuring scalability on high-performance computing architectures. Initial experiments demonstrate the capability of DRL to achieve drag reduction rates comparable with those achieved via traditional methods, although limited to short time intervals. We also propose a strategy to enhance the coherence of velocity streaks, assuming that maintaining straight streaks can inhibit instability and further reduce skin-friction. Our results highlight the promise of DRL in flow-control applications and underscore the need for more advanced control laws and objective functions. Future work will focus on optimising actuation intervals and exploring new computational architectures to extend the applicability and the efficiency of DRL in turbulent flow management.

Extension of the local domain-free discretization method to large eddy simulation of compressible flows

Most of the flow problems encountered in practical engineering are wall-bounded turbulent flows at high Reynolds numbers. Wall-modeled large eddy simulation (WMLES) is one of the most viable approaches for predicting these realistic flows. Immersed boundary (IB) approach is an efficient computational technique to solve flow problems involving complex and/or moving geometries. This work extends a sharp-interface IB method, named the local domain-free discretion (DFD), to WMLES of compressible flows at high Reynolds numbers. An equilibrium wall model based on solving the simplified compressible turbulent boundary layer equations is utilized to alleviate the requirement of high near-wall mesh resolution. In conjunction with the approximate boundary conditions prescribed by the modeled wall shear stress and wall heat flux, the tangential velocity and temperature at an exterior dependent node are evaluated. Then, the closure of the discrete form of governing equations at an interior node in the immediate vicinity of the immersed wall is accomplished. A simple non-equilibrium correction of the wall shear stress provided by the equilibrium wall model is introduced explicitly. The WMLES/DFD method is applied to a supersonic zero-pressure-gradient turbulent boundary layer flow, a shock wave/flat-plate boundary layer interaction, a supersonic compression ramp flow and high-speed turbulent Couette flows with various thermal boundary conditions. The influence of grid resolution is investigated in the simulation of zero-pressure-gradient turbulent boundary layer flow. By comparing the computed results with the referenced experimental data and/or numerical results, the accuracy and ability of the WMLES/DFD method to simulate compressible turbulent flows are verified.

Physics-informed data-driven reconstruction of turbulent wall-bounded flows from planar measurements

Obtaining accurate and dense three-dimensional estimates of turbulent wall-bounded flows is notoriously challenging, and this limitation negatively impacts geophysical and engineering applications, such as weather forecasting, climate predictions, air quality monitoring, and flow control. This study introduces a physics-informed variational autoencoder model that reconstructs realizable three-dimensional turbulent velocity fields from two-dimensional planar measurements thereof. Physics knowledge is introduced as soft and hard constraints in the loss term and network architecture, respectively, to enhance model robustness and leverage inductive biases alongside observational ones. The performance of the proposed framework is examined in a turbulent open-channel flow application at friction Reynolds number Reτ=250. The model excels in precisely reconstructing the dynamic flow patterns at any given time and location, including turbulent coherent structures, while also providing accurate time- and spatially-averaged flow statistics. The model outperforms state-of-the-art classical approaches for flow reconstruction such as the linear stochastic estimation method. Physical constraints provide a modest but discernible improvement in the prediction of small-scale flow structures and maintain better consistency with the fundamental equations governing the system when compared to a purely data-driven approach.

Direct calculation of the eddy viscosity operator in turbulent channel flow at Re τ = 180

This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method (Mani & Park, Phys. Rev. Fluids, 2021, 054607) to direct numerical simulation (DNS) of a turbulent channel flow at $Re_\tau =180$ using two different forcing strategies that are designed to separately assess the anisotropy and non-locality of momentum mixing. In the first strategy, the leading term of the Kramers–Moyal expansion of the eddy viscosity is quantified, revealing all 81 tensorial coefficients that essentially characterise the local-limit eddy viscosity. The results indicate the following: (1) the eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both the mean strain rate and mean rotation rate tensors associated with the momentum field and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity is quantified as an integration kernel revealing the non-local influence of the mean momentum gradient at each wall-normal coordinate on all nine components of the Reynolds stresses over the channel width. Our results indicate that while the shear component of the Reynolds stress is reasonably reproduced by the local mean gradients, other components of the Reynolds stress are highly non-local. These results provide an understanding of anisotropy and non-locality requirements for closure modelling of momentum transport in attached wall-bounded turbulent flows.

Fokker-Planck Central Moment Lattice Boltzmann Method for Effective Simulations of Fluid Dynamics

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory.

High-speed turbulent flows towards the exascale: STREAmS-2 porting and performance

Exascale High Performance Computing (HPC) represents a tremendous opportunity to push the boundaries of Computational Fluid Dynamics (CFD), but despite the consolidated trend towards the use of Graphics Processing Units (GPUs), programmability is still an issue. STREAmS-2 (Bernardini et al. Comput. Phys. Commun. 285 (2023) 108644) is a compressible solver for canonical wall-bounded turbulent flows capable of harvesting the potential of NVIDIA GPUs. Here we extend the already available CUDA Fortran backend with a novel HIP backend targeting AMD GPU architectures. The main implementation strategies are discussed along with a novel Python tool that can generate the HIP and CPU code versions allowing developers to focus their attention only on the CUDA Fortran backend. Single GPU performance is analyzed focusing on NVIDIA A100 and AMD MI250x cards which are currently at the core of several HPC clusters. The gap between peak GPU performance and STREAmS-2 performance is found to be generally smaller for NVIDIA cards. Roofline analysis allows tracing this behavior to unexpectedly different computational intensities of the same kernel using the two cards. Additional single-GPU comparisons are performed to assess the impact of grid size, number of parallelized loops, thread masking and thread divergence. Parallel performance is measured on the two largest EuroHPC pre-exascale systems, LUMI (AMD GPUs) and Leonardo (NVIDIA GPUs). Strong scalability reveals more than 80% efficiency up to 16 nodes for Leonardo and up to 32 for LUMI. Weak scalability shows an impressive efficiency of over 95% up to the maximum number of nodes tested (256 for LUMI and 512 for Leonardo). This analysis shows that STREAmS-2 is the perfect candidate to fully exploit the power of current pre-exascale HPC systems in Europe, allowing users to simulate flows with over a trillion mesh points, thus reducing the gap between the Reynolds numbers achievable in high-fidelity simulations and those of real engineering applications.

Direct numerical simulation of fully-developed supersonic turbulent channel flows with dense vapors

This work aims to investigate the impact of the molecule-complexity effect and the non-ideal effect on wall-bounded turbulent flows by applying direct numerical simulation (DNS) to fully-developed channel flows of two typical organic vapors: R1233zd(E) and octamethyltrisiloxane (MDM). For each vapor, three thermodynamic states are analyzed: one in the dilute-gas region, one near the saturation line, and one in the supercritical region. For mean flow fields, it is found that, due to smaller Prandtl and Eckert numbers, both the molecule-complexity effect and the non-ideal effect reduce the mean temperature rise from the cold wall to the channel center. Meanwhile, the molecule-complexity effect weakens the mean density drop, while the non-ideal effect strengthens the drop. Furthermore, once the density and viscosity variations are considered, the mean streamwise velocity profiles of dense vapors are practically the same as the ideal gas. For turbulent fluctuations, it is found that the correlations between T′, p′, and ρ′ in dense vapors are more complicated than the ideal gas: for the ideal gas, fluctuations are dominated by “vorticity mode”; hence, ρ′ and T′ are strongly related to u′ but independent of p′; however, for dense vapors, “acoustic mode” can also play an important role. A newly derived equation illustrates that, through the “acoustic mode,” the molecule-complexity effect obviously enhances the positive correlation between ρ′ and p′, while the non-ideal effect can enhance the positive correlation between T′ and p′. Further analysis of instantaneous flow fields shows that p′ is isotropic. The isotropic character affects fluctuation magnitudes but has limited effect on the specified wall-direction turbulent transport. Consequently, Walz's equation and Reynolds analogy in terms of enthalpy are still valid. Finally, a comparison between the DNS energy budget and k equation of Reynolds-averaged Navier–Stokes (RANS) model has been carried out. Results show that obvious deviation happens on the production term in spite of the careful selection of eddy viscosity model.

Turbulent Micropolar Open-Channel Flow

The present paper focuses on the investigation of the turbulent characteristics of an open-channel flow by employing the micropolar model. The underlying model has already been proven to correctly describe the secondary phase of turbulent wall-bounded flows. The open-channel case comprises an ideal candidate to further test the micropolar model as many environmental flows carry a secondary phase, the behavior of which is of great interest for applications such as sedimentation transport and debris flow. Direct Numerical Simulations (DNSs) have been carried out on an open channel for Reb = 11,200 based on mean crossectional velocity, channel height, and the fluid kinematic viscosity. The simulated results are compared against previous experimental as well as Langrangian DNS data of similar flows, with excellent agreement. The micropolar model is capable of describing the same problem but in an Eulerian frame, thus significantly simplifying the computational cost and complexity.

Strategies for Enhancing One-Equation Turbulence Model Predictions Using Gene-Expression Programming

This paper introduces innovative approaches to enhance and develop one-equation RANS models using gene-expression programming. Two distinct strategies are explored: overcoming the limitations of the Boussinesq hypothesis and formulating a novel one-equation turbulence model that can accurately predict a wide range of turbulent wall-bounded flows. A comparative analysis of these strategies highlights their potential for advancing RANS modeling capabilities. The study employs a single-case CFD-driven machine learning framework, demonstrating that machine-informed models significantly improve predictive accuracy, especially when baseline RANS predictions diverge from established benchmarks. Using existing training data, symbolic regression provides valuable insights into the underlying physics by eliminating ineffective strategies. This highlights the broader significance of machine learning beyond developing turbulence closures for specific cases.

Wall Modeling of Turbulent Flows with Varying Pressure Gradients Using Multi-Agent Reinforcement Learning

We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents receive off-wall environmental states, including pressure gradient and turbulence strain rate, ensuring adaptability to a wide range of flows characterized by pressure-gradient effects and separations. Based on these states, the agents determine an action to adjust the wall eddy viscosity and, consequently, the wall-shear stress. The model training is in situ with wall-modeled large-eddy simulation grid resolutions and does not rely on the instantaneous velocity fields from high-fidelity simulations. Throughout the training, the agents compute rewards from the relative error in the estimated wall-shear stress, which allows them to refine an optimal control policy that minimizes prediction errors. Employing this framework, wall models are trained for two distinct subgrid-scale models using low-Reynolds-number flow over periodic hills. These models are validated through simulations of flows over periodic hills at higher Reynolds numbers and flows over the Boeing Gaussian bump. The developed wall models successfully capture the acceleration and deceleration of wall-bounded turbulent flows under pressure gradients and outperform the equilibrium wall model in predicting skin friction.

On the streamwise velocity variance in the near-wall region of turbulent flows

We study the behaviour of the streamwise velocity variance in turbulent wall-bounded flows using a direct numerical simulation (DNS) database of pipe flow up to friction Reynolds number${{Re}}_{\tau } \approx 12000$. The analysis of the spanwise spectra in the viscous near-wall region strongly hints to the presence of an overlap layer between the inner- and the outer-scaled spectral ranges, featuring a$k_{\theta }^{-1+\alpha }$decay (with$k_{\theta }$the wavenumber in the azimuthal direction, and$\alpha \approx 0.18$), hence shallower than suggested by the classical formulation of the attached-eddy model. The key implication is that the contribution to the streamwise velocity variance$(\langle{u}^2\rangle)$from the largest scales of motion (superstructures) slowly declines as${{Re}}_{\tau }^{-\alpha }$, and the integrated inner-scaled variance follows a defect power law of the type$\langle u^2 \rangle ^+ = A - B \, {{Re}}_{\tau }^{-\alpha }$, with constants$A$and$B$depending on$y^+$. The DNS data very well support this behaviour, which implies that strict wall scaling is restored in the infinite-Reynolds-number limit. The extrapolated limit distribution of the streamwise velocity variance features a buffer-layer peak value of$\langle u^2 \rangle ^+ \approx 12.1$, and an additional outer peak with larger magnitude. The analysis of the velocity spectra also suggests a similar behaviour of the dissipation rate of the streamwise velocity variance at the wall, which is expected to attain a limiting value of approximately$0.28$, hence slightly exceeding the value$0.25$which was assumed in previous analyses (Chen & Sreenivasan,J. Fluid Mech., vol. 908, 2021, R3). We have found evidence suggesting that the reduced near-wall influence of wall-attached eddies is likely linked to the formation of underlying turbulent Stokes layers.

Coherent structures in stably stratified wall-bounded turbulent flows

Coherent structures in stably stratified wall-bounded turbulent flows

Large-eddy simulation of wall-bounded incompressible turbulent flows based on multi-moment finite volume formulation

The multi-moment based numerical model is proposed for performing large-eddy simulation (LES) of wall-bounded incompressible turbulent flows on the unstructured grids. In this model, velocity is defined as volume integral average (VIA) and point values (PVs) which are updated as prognostic variables simultaneously in time. Using VIA and PV in each cell, this method constructs higher-order polynomial on a compact stencil and more importantly, provides a new approach to design subgrid-scale (SGS) models for LES. Various SGS models are developed in this framework where the eddy-viscosity is computed separately at both VIA and PVs using the least-square method on different interpolation stencils. Compared with conventional finite volume schemes, the proposed method effectively reduces numerical dissipation and largely suppresses the sensitivity of numerical solution on SGS models and resolves more elaborated flow structures on the same mesh resolution. It also reduces solution dependence on the shape and quality of grid elements, as demonstrated by comparing numerical results on the different types of grids. The proposed method can attain high-fidelity simulation without loss of numerical efficiency and robustness, which is highly appealing for complex turbulent problems with high Reynolds numbers and complicated geometries.

Enhanced transport of flexible fibers by pole vaulting in turbulent wall-bounded flow

Enhanced transport of flexible fibers by pole vaulting in turbulent wall-bounded flow

Characteristics of turbulent core–annular flow with water-lubricated high viscosity oil in a horizontal pipe

Direct numerical simulations are performed to investigate the characteristics of a turbulent core–annular flow with water-lubricated high viscosity oil in a horizontal pipe. Six different superficial velocity ratios ( $\,j_w/j_o = 0.057\unicode{x2013}0.41$ ) are examined by changing the water superficial velocity $j_w$ for a fixed oil superficial velocity $j_o$ . The pressure drops in the pipe and the shapes of the phase interface agree well with those from previous experiments. The oil core flow is almost a plug flow, and the gaps between the phase interface and pipe wall are narrow and wide near the upper and lower surfaces of the pipe, respectively, due to the buoyancy. Within a narrow gap, water is confined mostly in a valley region of the wavy phase interface and hardly goes through its crest. On the other hand, water near the phase interface at a wide gap convects downstream almost at the core speed and the flow near the wall is similar to that of single-phase wall-bounded turbulent flow. The annular flow is characterized by three different regimes depending on the clearance Reynolds number ( $Re_c$ ) based on the core velocity and local gap size: laminar Couette flow driven by the core for $Re_c \le 600$ , transitional flow for $600 < Re_c < 2500$ and turbulent flow for $Re_c \ge 2500$ . The minimum pressure drop occurs at $j_w/j_o = 0.11$ in the early transition regime. For all $j_w/j_o$ considered, the negative lift force acting on the core comes from the pressure force which balances the buoyancy.

Turbulent drag reduction using dolphin-inspired near-wall ultrasonic microvibrations

The skin-friction drag generated by wall-bounded turbulent flows can potentially be reduced by a wall-parallel oscillatory motion. Inspired by microvibrations and the high sensitivity of dolphin skin, we examine whether wall-normal undulating motion actuated by longitudinal micro-ultrasonic waves (LMUWs) with ultrasonic-frequency oscillations and micro-size amplitudes significantly alters the multi-eddy motion on the surface, thereby reducing skin-friction drag. Simulations of the LMUW-induced turbulent flows are performed in an open channel at a Reynolds number of 1.24 × 106 for three motion modes, i.e., two traveling waves (downstream and upstream) in the streamwise direction and a standing wave. It is verified that the wall-normal turbulent fluctuations are remarkedly altered within the viscous sublayer of the turbulent boundary layer, resulting in a reduced velocity gradient. This leads to lower or even extinguished friction drag, which is strongly associated with the LMUW-excitation mode. Informed and validated by numerical results, we further derived a theoretical model for the dynamic boundary layer. This model is based on Fourier series expressions of the velocities and is used to elucidate the underlying mechanisms in association with the LMUW-excited turbulent flow and active friction drag reduction. The results indicate that upstream traveling waves enable 100% friction drag reduction, while downstream traveling waves are capable of overcoming the trade-off between friction and pressure drag, accomplishing 100% total drag reduction. This study thus provides a novel active and controllable method for turbulent drag reduction.

Interplay of scales during the spatial evolution of energy-containing motions in wall-bounded turbulent flows

This article extends the previous investigation of the spatial evolution of energy-containing motions in wall-bounded turbulent flows (Kannadasan et al., J. Fluid Mech., vol. 955, 2023, R1) by examining their scale-interactions through spectral analysis based on the spanwise scale decomposition of turbulent kinetic energy and the Reynolds stress transport equation. The energy-containing motions located at the inflow of a turbulent channel flow are artificially removed and the interscale transport mechanisms involved in their spatial evolution are studied. This scale interaction analysis reveals the presence of a significant inverse transfer of streamwise Reynolds stress from the near-wall streaks to larger scales in the spatial evolution of energy-containing motions. This transfer is due to the spanwise variation of streamwise velocity fluctuations, represented by $\partial u'/\partial z$ , which is the primary mechanism of streak instability. The analysis presented in this study also shows that the inverse cascade of spanwise energy may correspond to the regeneration of streamwise vortices in the process of reactivating the self-sustaining mechanism in the spatial evolution of energy-containing motions.

Investigating the use of 3-component-2-dimensional particle image velocimetry fields as inflow boundary condition for the direct numerical simulation of turbulent channel flow

Direct numerical simulation (DNS) of turbulent wall-bounded flows requires long streamwise computational domains to establish the correct spatial evolution of large-scale structures with high fidelity. In contrast, experimental measurements can relatively easily capture large-scale structures but struggle to resolve the dissipative flow scales with high fidelity. One methodology to overcome the shortcomings of each approach is by incorporating experimental velocity field measurements into DNS as an inflow boundary condition. This hybrid approach combines the strengths of DNS and experimental measurements, allowing for a reduction in the streamwise computational domain and accelerated development of large-scale structures in turbulent wall-bounded flows. To this end, this paper reports the results of an investigation to establish the impact of limited spatial resolution and limited near-wall experimental inflow data on the DNS of a wall-bounded turbulent shear flow. Specifically, this study investigates the spatial extent required for the DNS of a turbulent channel flow to recover the turbulent velocity fluctuations and energy when experimental inflow data is typically unable to capture fluctuations down to the viscous sub-layer or the smallest viscous scales (i.e. the Kolmogorov scale or their surrogate viscous scale in wall-bounded turbulent shear slows) is used as the inflow to a DNS. A time-resolved numerically generated experimental field is constructed from a periodic channel flow DNS (PCH-DNS) at Reτ=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_{\ au } =$$\\end{document} 550 and 2300, which is subsequently used as the inflow velocity field for an inflow–outflow boundary conditions DNS. The time-resolved experimental inflow field is generated by appropriately filtering the small scales from the PCH-DNS velocity by integrating over a spatial domain that is representative of a particle image velocimetry interrogation window. This study shows that the recovery of small scales requires a longer domain as the spatial resolution at the inflow decreases with all flow scales recovered and their correct scale-dependent energy is re-established once the flow has developed for 3 channel heights.

On the difficulty of determining Kármán “constants” from direct numerical simulations

The difficulty of determining the slope of the famed logarithmic law in the mean velocity profile of wall-bounded turbulent flows, the inverse of the Kármán “constant” κ, from direct numerical simulations (DNS) is discussed for channel flow. Unusual approaches as well as the analysis of the standard log-indicator function are considered and analyzed, including the identification of the higher order linear overlap term. This leads to the conclusion that a definitive determination of the channel flow κ from DNS with an uncertainty of, say, 2%–3% will require the residue of the mean streamwise momentum equation in the simulations to be reduced by at least an order of magnitude.