High Reynolds Number Turbulent Flows Research Articles

A novel attention enhanced deep neural network for hypersonic spatiotemporal turbulence prediction

High Reynolds number turbulent flow of hypersonic vehicles exhibits multi-scale flow structures and non-equilibrium high-frequency characteristics, presenting a significant challenge for accurate prediction. A deep neural network integrated with attention mechanism as a reduced order model for hypersonic turbulent flow is proposed, which is capable of capturing spatiotemporal characteristics from high-dimensional numerical turbulent data directly. The network model leverages encoder–decoder architecture where the encoder captures high-level semantic information of input flow field, Convolutional Long Short-Term Memory network learns low-dimensional characteristic evolution, and the decoder generates pixel-level multi-channel flow field information. Additionally, skip connection structure is introduced at the decoding stage to enhance feature fusion while incorporating Dual-Attention-Block that automatically adjusts weights to capture spatial imbalances in turbulence distribution. Through evaluating the time generalization ability, the neural network effectively learns the evolution of multi-scale high-frequency turbulence characteristics. It enables rapid prediction of high Reynolds number turbulence evolution over time with reasonable accuracy while maintaining excellent computational efficiency.

Karhunen–Loéve decomposition of high Reynolds number turbulent pipe flows: a Voronoi analysis

We perform the Karhunen–Loéve decomposition of the data from direct numerical simulations pertaining to incompressible turbulent pipe flow at various Reynolds numbers, in order to identify large-scale coherent structures. A novel approach based on the Voronoi diagram is introduced to estimate the energy distribution along the radial direction as a function of the geometrical properties of the modes. In contrast to previous classifications, no user-defined criterion, threshold or ad-hoc separation of the eddies is required since the two most energetic branches are inherently present as the Reynolds number increases. Details about the Voronoi analysis are provided, together with a comprehensive validation and comparison with previous classifications at low Reynolds numbers. We discuss the results and potential of the presented approach at Reτ = 180 and 5200, commenting on the two classes of coherent structures with a varying and constant size in the radial direction appearing at Reτ = 5200.

Wall-modeled large eddy simulation in the immersed boundary-lattice Boltzmann method

This work presents the wall-modeled large eddy simulation (WMLES) in the immersed boundary-lattice Boltzmann method (IB-LBM). Here, the wall model with both diffusive- and sharp-interface immersed boundary methods (IBMs) is incorporated into the IB-LBM to handle the turbulent boundary layer in high Reynolds number turbulent flows. To maintain the numerical stability, two collision models, i.e., multiple-relaxation-time (MRT) and recursive regularized (RR), are implemented. The performance of these models in the WMLES is examined and compared in the simulation of internal and external flows by considering four benchmarks, i.e., turbulent flow in a channel, flow around a hull of submarine, flow around an Ahmed car model, and flow around a circular cylinder. It is found that a diffusive-interface IBM with wall model is capable to achieve excellent results for the simulation of external flows around bluff objects but fails in the simulation of internal flows of underestimating the wall shear stress due to its extra dissipation. The sharp-interface IBM with the wall model predicts the internal flow very well but fails in some simulations of external flow around bluff bodies due to the failure in the separation flow modeling. It is also found that the MRT-LBM is less dissipative than the RR-LBM, but it generates spurious nonphysical noise in the turbulent flows and tends to be unstable at high Reynolds numbers. Therefore, the diffusive-interface IBM with the wall model is more suitable for the external turbulent flow modeling, while its sharp-interface counterpart is more suitable for the internal turbulent flow modeling. The RR-LBM outperforms the MRT-LBM for the better stability and less nonphysical noise.

Continuous Eddy Simulation vs. Resolution-Imposing Simulation Methods for Turbulent Flows

The usual concept of simulation methods for turbulent flows is to impose a certain (partial) flow resolution. This concept becomes problematic away from limit regimes of no or an almost complete flow resolution: discrepancies between the imposed and actual flow resolution may imply an unreliable model behavior and high computational cost to compensate for simulation deficiencies. An exact mathematical approach based on variational analysis provides a solution to these problems. Minimal error continuous eddy simulation (CES) designed in this way enables simulations in which the model actively responds to variations in flow resolution by increasing or decreasing its contribution to the simulation as required. This paper presents the first application of CES methods to a moderately complex, relatively high Reynolds number turbulent flow simulation: the NASA wall-mounted hump flow. It is shown that CES performs equally well or better than almost resolving simulation methods at a little fraction of computational cost. Significant computational cost and performance advantages are reported in comparison to popular partially resolving simulation methods including detached eddy simulation and wall-modeled large eddy simulation. Characteristic features of the asymptotic flow structure are identified on the basis of CES simulations.

Control of flow separation over an aerofoil by external acoustic excitation at a high Reynolds number

The effectiveness of acoustic excitation as a means of flow control at high Reynolds number turbulent flows is investigated numerically by using improved delayed detached eddy simulations (IDDES). Previous studies on low Reynolds number laminar flows have shown that acoustic excitation can substantially suppress flow separation for specific effective frequency and amplitude ranges. However, the effect of acoustic excitation on higher Reynolds number turbulent flow separation has not yet been explored due to limitations on appropriate fidelity computational methods or experimental facility constraints. Therefore, this paper addresses this research gap. A NACA0015 airfoil profile at 1 × 106 Reynolds number based on the airfoil chord length is used for the investigations. Acoustic excitation is applied to the baseline flow field in the form of transient boundary conditions at the computational domain inlet. A parametric study revealed that the effective sound frequency range shows a Gaussian distribution around the frequency of the dominant disturbances in the baseline flow. A maximum of ∼43% increase in lift-to-drag ratio is observed for the most effective excitation frequency F+=1.0 at a constant excitation amplitude of Am=1.8%. The effect of excitation amplitude follows an asymptotic trend with a maximum effective excitation amplitude above which the gains are not significant. A fully reattached flow is observed for the highest excitation level considered (Am=10%) that results in ∼120% rise in airfoil lift-to-drag coefficient. Overall, the findings of the current work demonstrate the higher Reynolds number effectiveness of acoustic excitation on separated turbulent flows, thereby paving the way for application in realistic flow scenarios observed in aircraft and gas turbine engine flow fields.

Plastron restoration for underwater superhydrophobic surface by porous material and gas injection

Restoring and maintaining the gas layer (plastron) on underwater superhydrophobic surface (SHS) is critical for the real-world application of SHS, such as reducing friction drag in high-Reynolds number turbulent flows. In this work, we experimentally investigated the capability of a technology based on porous material and gas injection to restore the plastron on an underwater SHS from a fully wetted state. The SHS was created by sprayed coating a commercial superhydrophobic coating on a porous steel plate. In the experiments, the SHS was immersed in stationary liquid, the gas injection pressure and gas injection duration were independently controlled. The status of gas layer on SHS was examined by a high-speed camera. We found that the surface area being restored with a plastron increased with increasing gas injection pressure and gas injection duration, and that the plastron restoration process involved bubble formation, merging and detachment. A layer of gas was left on the surface after bubble detachment. The size of the detached bubble increased with time due to bubble merging, and became stable when there was no more bubble merging. Increasing gas injection pressure led to higher gas flow rates, larger detached bubble sizes and faster plastron restorations. A plastron restoration within 0.3 s was achieved at the highest pressure, faster than the in-situ gas generation methods. Furthermore, we found that the gas flow rate through the underwater SHS can be described by a modified Darcy’s law. Our results highlighted the potential of using porous material and gas injection to restore the plastron and made possible the real-world implementation of SHS.

Temporal super-resolution using smart sensors for turbulent separated flows

Particle image velocimetry (PIV) data of high Reynolds number unsteady turbulent flows are often undersampled in time; this leads to aliasing of important spectral content. The present work proposes a novel data-driven estimation technique that uses oversampled sparsely placed surface-mounted pressure sensors and long short-term memory neural networks to resolve the aliased transient velocity dynamics from undersampled PIV data. The method leverages the time-resolved pressure dynamics to estimate the temporal evolution of a proper orthogonal decomposition-based low-dimensional subspace of the velocity field. The proposed approach is demonstrated on a PIV dataset of a high Reynolds number turbulent separated flow over a Gaussian speed-bump benchmark geometry ( $$\text{Re}_{H}=2.26\times 10^{5}$$ , where H is the Bump height). The 15 Hz PIV data is super-resolved to 2 kHz, and spectral analysis of the flowfields is conducted to educe the originally aliased unsteady dynamics of the turbulent separation bubble. The estimator is shown to accurately reconstruct the Reynolds shear stress from unseen sensor data, demonstrating its generalizability to resolve the coherent motions. The estimated velocity spectra show distributions consistent with those of other separated flows.

High-Order WENO-based Semi-Implicit Projection Method for Incompressible Turbulent Flows: Development, Accuracy, and Reynolds Number Effects

A novel high-order projection method is presented in this study for the simulation of incompressible turbulent flows, utilising weighted essentially non-oscillatory (WENO) schemes. Spatial discretization involves using WENO schemes for nonlinear convection and standard central differences (CD) for the viscous term. The approach combines various orders of WENO and central difference schemes (WENO3/CD2, WENO5/CD4, and WENO7/CD6) to achieve third, fifth, and seventh-order spatial accuracy for velocity fields, respectively. Validating this method involved a thorough examination using the 2D Taylor Green vortex problem in both space and time, along with simulations of 3D Taylor-Green vortex problems at increasing Reynolds numbers (Re) of 1, 600, 16, 000, and 160, 000. The outcomes encompassed analyses of kinetic energy, enstrophy, energy spectra, and vortex fields, indicating the method's effectiveness in accurately simulating high Reynolds number turbulent flows without additional sub-grid scale models.

Immersed boundary based near-wall modeling for large eddy simulation of turbulent wall-bounded flow

This paper describes the coupling of the immersed boundary method and the near-wall modeling of large eddy simulation for high Reynolds number turbulent flows over complex geometries on Cartesian grids. To overcome the spurious oscillation problem arising from the imposition of boundary conditions on the stair-case off-wall boundaries, several key ingredients have been employed, such as interpolating the friction velocity instead of the flow velocity from near-wall fluid interior points, evaluating the gradients by the weighted least square method and correcting the wall-normal gradient of the tangential velocity with the law of the wall at the off-wall boundaries. Furthermore, a hybrid RANS-LES approach has been applied to the near-wall eddy viscosity, either through an empirical blending function or the Reynolds stress balance constraint. We systematically discuss the effects of the hybrid eddy viscosity in a turbulent channel flow and a high lift three-element airfoil. Enforcing the Reynolds stress balance constraint turns out to be very robust in the considered cases. For the high lift three-element airfoil flow, the overall wall pressure and skin friction are predicted reasonably well and smoothly. The flow details are in a good agreement with the experimental data as well.

Numerical investigation of noise suppression and amplification in forced oscillations of single and tandem cylinders in high Reynolds number turbulent flows

The noise generated by a three-dimensional turbulent wake behind an oscillating single or tandem cylinder(s) is studied using detached eddy simulation and the Ffowcs Williams-Hawkings (FW-H) method. This hybrid methodology is validated using some experimental data of a turbulent flow past a single or tandem stationary cylinder(s) and some numerical data (obtained from a direct numerical simulation) of a laminar flow past tandem oscillating cylinders. For an oscillating cylinder at a fixed Reynolds number Re=120,000, the sound energy is suppressed compared to that of a stationary cylinder provided the value of oscillation frequency approaches 57% of the original vortex-shedding frequency of the stationary cylinder. This noise reduction arises from the structural oscillations suppressing the noise generated by the vortex shedding from the stationary cylinder—the additional source of noise stemming from the structural oscillations is too small to compensate for the mechanism responsible for the noise suppression. The noise generated by the cylinder motion includes contributions from the loading and thickness noise, whereas the noise generated by vortex shedding from the stationary cylinder only includes the loading noise. The flow past tandem stationary cylinders exhibits a larger number of spectral peaks in the sound pressure power spectrum and the peaks occur at a lower frequency compared to the flow past a single cylinder. The drag force fluctuations result in the propagation of the sound pressure in the in-line direction, whereas the lift force fluctuations result in the propagation of the sound pressure in the transverse direction. Five different scenarios of stationary and/or oscillating tandem cylinders are studied. The second and third invariants of the velocity gradient tensor are used to visualize the distinct vortex structures in the wake for the five different scenarios of tandem cylinders. A single cylinder oscillating in the transverse direction exhibits a larger sound pressure level (SPL) than the streamwise oscillation of the same cylinder. In contrast, the streamwise (in-line) oscillation of one or the other cylinder in a tandem array results in a larger SPL than the transverse oscillation of one or the other cylinder. Finally, the SPL is more sensitive to the oscillations of the rear (downstream) cylinder than the front (upstream) cylinder.

Wall model‐based diffuse‐interface immersed boundary method for simulation of incompressible turbulent flows

AbstractIn this work, a method is proposed to simulate the high Reynolds number turbulent flows by combining the diffuse‐interface immersed boundary method (IBM) with different wall models. In this method, two auxiliary layers (a series of Lagrangian points) are set outside the wall: the reference layer and the enforced layer. The wall model is applied at the reference layer to calculate the wall shear stress and the boundary condition is implemented at the enforced layer. When implementing the boundary condition, the implicit velocity correction‐based IBM is used. This process requires the velocity at the enforced layer. To calculate the velocity at the enforced layer, the momentum equation is integrated along the normal direction of the wall to link the tangential component of the velocity to the wall shear stress predicted by the wall models, and the normal component of the velocity is approximately reconstructed by the parabolic distribution. In addition, the Reichardt's law combined with Spalding's formula is utilized to determine the integral length. Numerical experiments for the turbulent flows around the flat plate, the NACA0012 airfoil and the NACA23012 airfoil are carried out to verify the feasibility of this method.

Eruption of ultralow-viscosity basanite magma at Cumbre Vieja, La Palma, Canary Islands

The viscosity of magma exerts control on all aspects of its migration through the crust to eruption. This was particularly true for the 2021 eruption of Cumbre Vieja (La Palma), which produced exceptionally fast and fluid lava at high discharge rates. We have performed concentric cylinder experiments to determine the effective viscosities of the Cumbre Vieja magma, while accounting for its chemistry, crystallinity, and temperature. Here we show that this event produced a nepheline-normative basanite with the lowest viscosity of historical basaltic eruptions, exhibiting values of less than 10 to about 160 Pa s within eruption temperatures of ~1200 to ~1150 °C. The magma’s low viscosity was responsible for many eruptive phenomena that lead to particularly impactful events, including high-Reynolds number turbulent flow and supercritical states. Increases in viscosity due to crystallization-induced melt differentiation were subdued in this eruption, due in part to subtle degrees of silica enrichment in alkaline magma.

Hydrodynamic characteristics of flow past a circular cylinder with four attached flexible plates in a high Reynolds number turbulent flow

In this study, the model is employed to evaluate the effects of flexible plates on the hydrodynamic forces acting on a circular cylinder in turbulent flows. In this regard, four flexible plates are attached to the circular cylinder. Besides, the finite volume method and finite element method have been utilized to discretize the governing equations of the fluid flow and the flexible plates, respectively. The Reynolds number based on the cylinder diameter is kept constant at . The effects of fin angle and the flexural rigidity on the wake structure, displacement amplitude, Strouhal number as well as lift and drag coefficients are investigated. The results showed that the flexural rigidity of plates had a significant influence on the hydrodynamic coefficients. Indeed, an increase in the non-dimensional flexural rigidity enhanced the drag coefficient, and then it approximately remained constant. For the averaged drag coefficient is approximately constant and equal to 6.1. As the increases, the drag coefficient increases rapidly and reaches the value of 14.37 for In the second configuration , values of the drag coefficient for low and high values of flexural rigidity are equal to 7.81 and 8.79, respectively.

An Immersed Boundary Method Based on Parallel Adaptive Cartesian Grids for High Reynolds Number Turbulent Flow

In this paper, a set of parallelised adaptive hierarchical Cartesian-based immersed boundary methodology is developed for high Reynolds number compressible flow. First, a robust and efficient grid generation method based on the separation axis theorem for arbitrary geometry is presented for automatic Cartesian grid generation. Second, an immersed boundary method (IBM) is presented coupling with wall model for high Reynolds number flow. Third, a parallel strategy is implemented and special treatment is proposed to guarantee large-scale computing. Finally, cell-based adaptive mesh refinement (AMR) technology is used to capture fluid phenomena under different regimes including but not limited to shock waves and vortices. The overall performance of the methodology is tested through a wide range of regimes including transonic and supersonic flow with high Reynolds number in both two and three dimensions. Results are in good agreement with reference data and indicate the capability and robustness of the present methodology.

A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Large-eddy simulations (LES) are widely used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired coarsening approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for both physical understanding and modelling even in that simple case. For example, an alternative to the Germano identity is introduced and used to define a dynamic procedure without the need for a test filter. Non-uniform resolution can be represented in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. Potential extensions of the theory to more complex physics such as multiphase flows are briefly discussed.

Comment on “Mathematical constraints on the scaling exponents in the inertial range of fluid turbulence” [Phys. Fluids 33(3), 031703 (2021)

The paper [Djenidi et al., Phys. Fluids 33(3), 031703 (2021)] considers a classical issue of an anomalous scaling of velocity structure functions in a high-Reynolds number turbulent flow. The paper offers a mathematical proof of the ground-breaking result: the intermittency is an artifact of the Reynolds number finiteness. However, the proof contains a technical error that makes this conclusion ungrounded.

A robust and accurate finite element framework for cavitating flows with moving fluid-structure interfaces

In the current work, we present a variational mechanics framework for the coupled numerical prediction of cavitating turbulent flow and structural motion via a stabilized finite element formulation. To model the finite mass transfer rate in cavitation phenomena, we employ the homogenous mixture-based approach via phenomenological scalar transport differential equations given by the linear and nonlinear mass transfer functions. Stable linearizations of the finite mass transfer terms for the mass continuity equation and the reaction term of the scalar transport equations are derived for the robust and accurate implementation. The linearized matrices for the cavitation equation are imparted a positivity-preserving property to address numerical oscillations arising from high-density gradients typical of two-phase cavitating flows. The proposed formulation is strongly coupled in a partitioned manner with an incompressible 3D Navier-Stokes finite element solver, and the unsteady problem is advanced in time using a fully-implicit generalized-α time integration scheme. We first verify the implementation on the benchmark case of the Rayleigh bubble collapse. We demonstrate the accuracy and convergence of the cavitation solver by comparing the numerical solutions with the analytical solutions of the Rayleigh-Plesset equation for bubble dynamics. We find our solver to be robust for large time steps and the absence of spurious oscillations/spikes in the pressure field. The cavitating flow solver is coupled with a hybrid URANS-LES turbulence model. We validate the coupled solver for a very high Reynolds number turbulent cavitating flow over a NACA0012 hydrofoil section. Finally, the proposed method is applied in an Arbitrary Lagrangian-Eulerian framework to study turbulent cavitating flow over a pitching hydrofoil section and the characteristic features of cavitating flows such as re-entrant jet and periodic cavity shedding are discussed.

Turbulent Skin Friction Reduction through the Application of Superhydrophobic Coatings to a Towed Submerged SUBOFF Body

Abstract In the present study, the drag-reducing effect of sprayed superhydrophobic surfaces (SHSs) is determined for two external turbulent boundary layer (TBL) flows. We infer the modification of skin friction created beneath TBLs using near-wall laser Doppler velocity measurements for a series of tailored SHSs. Measurements of the near-wall Reynolds stresses were used to infer reduction in skin friction between 8%and 36%in the channel flow. The best candidate SHS was then selected for application on a towed submersible body with a SUBOFF profile. The SHS was applied to roughly 60% of the model surface over the parallel midbody of the model. The measurements of the towed resistance showed an average decrease in the overall resistance from 2% to 12% depending on the speed and depth of the towed model, which suggests a SHS friction drag reduction of 4–24% with the application of the SHS on the model. The towed model results are consistent with the expected drag reduction inferred from the measurements of a near-zero pressure gradient TBL channel flow. Introduction Nature has provided a plethora of materials to be studied and mimicked for everyday applications (Jung & Bhushan 2010). One material pertinent for use in the marine environment is the lotus leaf, which is known for its self-cleansing properties and resistance to wetting (Neinhuis & Barthlott 1997). More specifically, lotus-inspired superhydrophobic surfaces (SHSs) have been biomimetically developed for skin friction reduction in various flow applications (Bhushan et al. 2009; Samaha et al. 2012). Being exhaustively studied in small-scale laminar flows (see Rothstein [2010] for a review of SHS drag reduction and slip on SHSs), advances in the design and fabrication of SHSs have permitted application of these materials in more naval-relevant flows. Previously, it has been shown that in laminar flow, SHSs can reduce drag (Watanabe et al. 1999; Ou et al. 2004; Ou & Rothstein 2005; Zhao et al. 2007; Daniello et al. 2009; Woolford et al. 2009), and in low–Reynolds number turbulent flows, SHS drag reduction has been observed using small-scale, structured surfaces and large air–water interfaces (Henoch et al. 2006; Daniello et al. 2009; Park et al. 2014). However, these surfaces, in higher turbulence flows, can be unstable or become wetted. If the SHS possesses roughness features with small scales compared with the viscous length scale of the flow, researchers have demonstrated SHS friction drag reduction for wall-bounded, high–Reynolds number turbulent flows (Zhao et al. 2007; Aljallis et al. 2013; Bidkar et al. 2014; Golovin et al. 2016; Ling et al. 2016b; Gose et al. 2018a).

Direct numerical simulation of compressible turbulence in a counter-flow channel configuration

We introduce a counter-flow turbulent channel configuration, amenable to simulation and modeling. It has periodic streamwise and spanwise boundaries and isothermal no-slip walls. A tangent hyperbolic forcing function drives the flow in opposite directions on the upper and lower halves of the channel, forming an antisymmetric mean shear velocity profile. Compared to conventional channel flows, the mean flow is inflectional and the maximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The counter-flow channel can sustain high turbulent Mach numbers which is useful for studying high Reynolds and Mach number turbulent flows.

Static pressure measurement error for wall taps with high Reynolds number turbulent pipe flow

An experimental study on a static pressure measurement errors in wall taps was conducted using a high Reynolds number actual flow facility (Hi-Reff). The bulk Reynolds number ReD examined was up to 1.3 × 107 and tap Reynolds number Ret was up to 8.5 × 104. The behavior of the static pressure measurement error at high Reynolds numbers was clarified experimentally. The static pressure measurement error normalized by wall shear stress increases with Reynolds number and reaches an asymptotic value. Its maximum value is 7.1 at Ret = 8470. The asymptotic value increases with the size of the tap diameter up to 6 mm and then becomes constant for tap diameters exceeding 6 mm. The universal curve reported in previous studies is observed for only a limited range of tap Reynolds numbers of below 700 and of tap diameters below 4 mm.