Turbulent Channel Flow Research Articles

Transition route to elastic and elasto-inertial turbulence in polymer channel flows

Viscoelastic shear flows support additional chaotic states beyond simple Newtonian turbulence. In vanishing Reynolds number flows, the nonlinearity in the polymer evolution equation alone can sustain inertialess “elastic” turbulence (ET) while “elasto-inertial” turbulence (EIT) appears to rely on an interplay between elasticity and finite-Re effects. Despite their distinct phenomenology and industrial significance, transition routes and possible connections between these states are unknown. We identify here a common Ruelle-Takens transition scenario for both of these chaotic regimes in two-dimensional direct numerical simulations of FENE-P fluids in a straight channel. The primary bifurcation is caused by a recently discovered “polymer diffusive instability” associated with small but nonvanishing polymer stress diffusion which generates a finite-amplitude, small-scale traveling wave localized at the wall. This is found to be unstable to a large-scale secondary instability which grows to modify the whole flow before itself breaking down in a third bifurcation to either ET or EIT. The secondary large-scale instability waves resemble “center” and “wall” modes, respectively—instabilities which have been conjectured to play a role in viscoelastic chaotic dynamics but were previously only thought to exist far from relevant areas of the parameter space. Published by the American Physical Society 2024

Reference map technique for Lagrangian exploration of coherent structures

We explore the application of the reference map technique, originally developed for Eulerian simulation of solid mechanics, in Lagrangian kinematics of turbulent flows. Unlike traditional methods based on explicit particle tracking, the reference map facilitates the calculation of flow maps and gradients without the need for particles. This is achieved through an Eulerian update of the reference map, which records the take-off positions of fluid particles. This approach is found to be mathematically equivalent to the work of Leung (J. Comput. Phys., vol. 230, issue 9, 2011, pp. 3500–3524), who computed the flow map of simple two-dimensional flows using an Eulerian approach. We discuss important modifications necessary for its first application to complex three-dimensional turbulent flows, including the conservative, low-dissipation update of the flow map and the treatment of periodic boundary conditions. We first demonstrate the accuracy of finite-time Lyapunov exponent (FTLE) calculations based on the reference map against the standard particle-based approach in a two-dimensional Taylor–Green vortex. Then we apply it to turbulent channel flow at $Re_\tau =180$ , where Lagrangian coherent structures identified as ridges of the backward-time FTLE are found to bound vortical regions of flow, consistent with Eulerian coherent structures from the $Q$ -criterion. The reference map also proves suitable for material surface tracking despite not explicitly tracking particles. This capability can provide valuable insights into the Lagrangian landscape of turbulent momentum transport, complementing Eulerian velocity field analysis. The evolution of initially wall-normal material surfaces in the viscous sublayer, buffer layer and log layer sheds light on the Reynolds stress-generating events from a Lagrangian perspective.

Minimization Principle for Analytical Solution of Turbulent Flow in Channel

Abstract The analytical solution for turbulent flow in a channel, presented in Fedoseyev (2023), described the mean turbulent flow velocity as a superposition of the parabolic and superexponential solutions. In this study, the coefficients of superposition are obtained through the minimization principle, the principle of minimum viscous dissipation. The laminar flow showed a significantly larger dissipation rate. The obtained analytical solutions agreed well with turbulent flow experiments.

Analytical Solution for Transverse Velocity of Turbulent Flow in Channel

Abstract The analytical solution for the streamwise mean velocity of turbulent flow of incompressible fluid in a channel was presented in Fedoseyev (2023) paper. In this work, we present both the stationary and transient solutions for the transverse velocity component. The obtained transient solution is a product of a series of periodic functions in space and time, multiplied by a growing exponential function of time. This analytical solution reveals the instability and imminence of oscillations in the turbulent flow. The obtained solutions are compared with numerical simulation results and experimental data, demonstrating a close agreement or strong similarity.

On a symmetry-preserving unconditionally stable projection method on collocated unstructured grids for incompressible flows

This work establishes the conditions for having a symmetry-preserving unconditionally stable projection method for incompressible flows, such as PISO or Fractional Step Method (FSM), on collocated unstructured grids based on a compact stencil Poisson equation. Its formulation is based on preserving the underlying symmetries of the differential operators. In addition, a general theorem for these types of projection methods will be proven. To establish an unconditionally stable method, this theorem gives the mathematical requirements for the operators and the geometrical conditions a mesh must satisfy, even in cases where the mesh is highly distorted. This will be proven both theoretically and numerically. Conservation of (global) kinetic energy is also a key feature in simulations. Within this context, two canonical cases are tested, a turbulent channel flow at Reτ=395 to show the robustness of the method, and an air-filled differentially heated cavity at Ra=1010 (based on the cavity height), to show that the (artificial) kinetic energy error introduced by the pressure is negative and very small compared with the physical dissipation.

Ordinal pattern-based analysis of an opposition-controlled turbulent channel flow

We conduct a numerical study on the drag-reduction mechanism of an opposition- controlled turbulent channel flow from the viewpoint of a symbolic dynamics approach. The effect of the virtual wall formed by the opposition control is maximised at the location of the detection plane $y_d^+ \approx 10$ . At this wall-normal location, the local link strength of the self-loop of network nodes representing the negative correlation pattern between the streamwise and wall-normal velocity fluctuations is maximised in the uncontrolled flow. In the controlled case, the multiscale complexity–entropy causality plane and the spatial permutation entropy at $y_d^+ \approx 10$ indicate that the drag-reduction effect is attributed to the reduction of the region where streaks actively coalesce and separate and the suppression of the regeneration cycle in the region near the wall.

Localization of internal gravity waves in stratified channel flow

Localization of internal gravity waves in stratified channel flow

Grain-size distribution in suspension through open channel turbulent flow using space-fractional ADE

The main aim of the present study is to develop a mathematical formulation that can describe the grain-size distribution (GSD) of non-uniform sediments in suspension over erodible sediment beds in a wide open channel under non-equilibrium conditions. The two important characteristics of sediment particles, such as non-local mixing and the hiding-hindering effect during settling, has been considered in the current study. The traditional advection–diffusion equation (ADE) is taken in the modified form as fractional ADE which is capable of capturing non-local movement of particles unlike the traditional diffusion theory where particles jump within a restricted distance along the vertical direction over a small time interval. The equation is further modified for any kth class of non-uniform sediment and the effect of non-local movement is included in the expression of depth averaged sediment diffusivity also. The settling velocity of a particle is taken in a form that contains the effect of hiding and hindering due to the presence of non-uniform particles in the flow. The space-fractional derivative is taken in the Caputo sense where the order α of the fractional derivative varies from 1<α≤2. The non-local effect is considered in the bottom and top boundary conditions also and the governing equation with boundary and initial condition have been solved by Chebyshev collocation method along with Euler’s backward method. The temporal variation of concentration profiles for different size particles is studied by varying α and it is observed that the magnitude of concentration decreases for each size as α increases. Non-local effect on bottom concentration for different size particle is also studied and it is seen that overshooting of bottom concentration gradually decreases as α increases for a particular size. Sensitivity analysis of α on GSD at different heights also has been done. The model has been validated for GSD under equilibrium conditions with available experimental data and it is found that the model aligns well when the non-local mixing effect is taken into account. At the end, an error analysis has been conducted to confirm the accuracy of the presented model.

Effects of laminar burning velocity to friction velocity ratio on turbulent premixed flame-wall interaction within turbulent boundary layers

Direct numerical simulation of flame-wall interaction (FWI) for two flame configurations under different laminar burning velocity to nonreacting wall friction velocity ratio, SL/uτNR, have been performed. The first configuration considered is a V-flame in a turbulent channel flow with isothermal inert walls and represents oblique wall interaction. The second configuration is representative of head-on interaction (HOI) of a planar flame interacting with a wall in a fully developed turbulent boundary layer. In the case of the V-flame with SL/uτNR=0.4, a smaller flame angle is obtained when compared with that of the V-flame with SL/uτNR=0.7. This is a consequence of the differences in the turbulent burning velocities between the two V-flame cases, where the case with SL/uτNR=0.4 has a lower turbulent burning velocity when compared with that of the case with SL/uτNR=0.7. By contrast, the ratio of turbulent to laminar burning velocity is higher for the SL/uτNR=0.4 HOI case when compared to the corresponding HOI case with SL/uτNR=0.7. The flame orientations with respect to the streamwise component of velocity and wall-normal direction in addition to the SL/uτNR values have been found to have a significant impact on the variations of wall heat flux, wall shear stress, and wall friction velocity in premixed FWI within turbulent boundary layers. The behaviors of nondimensional streamwise velocity, u+, and nondimensional temperature using wall units, T+, have also been investigated for different SL/uτNR ratios and it is found that the standard log-law profiles in the case of u+ and T+ are not valid for the two configurations and the two SL/uτNR ratios considered. Published by the American Physical Society 2024

Wall temperature effects in high-enthalpy supersonic turbulent channel flows considering air dissociation

Direct numerical simulations of temporally evolving high-enthalpy supersonic turbulent channel flows are performed at a Mach number of 3.0 and Reynolds number of 4880. The high-enthalpy air is assumed to behave as a chemical and thermal equilibrium of five-species mixture. The wall temperatures in the range of 1733.2 K to 4100.0 K to study the influence of wall temperature on the chemical activity, turbulent statistics and aerodynamic characteristics. The results show that the chemical activity is remarkable because the air is relatively sufficient dissociated. When the wall temperature higher than 2300 K, an extreme value can be observed in the distributions of mean and fluctuating mass fraction of atomic nitrogen close to the wall. Many of the influence of wall temperature on the turbulent statistics which hold for low-enthalpy conditions also hold for high-enthalpy conditions, including mean and fluctuating velocity, recovery enthalpy, and strong Reynolds analogy. As the wall temperature increases, the turbulent momentum flux and turbulent heat flux decrease, the turbulent mass flux mainly depends on species mass fractions fluctuations. The integral formulas of decomposing the aerodynamic characteristics are proposed, and the predicted heat flux and skin friction are all in good agreement with those direct estimation. The wall temperature does not change the primarily contributions of aerodynamic characteristics. Although the turbulent heat flux term is approximately 6%, its part of turbulent transport of enthalpy significantly increases with increasing wall temperature. The turbulent Schmidt number is insensitive to wall temperature.

Impact of spanwise rotation on flow separation and recovery behind a bulge in channel flows

Direct numerical simulations of spanwise-rotating turbulent channel flow with a parabolic bump on the bottom wall are employed to investigate the effects of rotation on flow separation. Four rotation rates, $Ro_b := 2\varOmega H/U_b = \pm 0.42$ , $\pm$ 1.0, are compared with the non-rotating scenario. The mild adverse pressure gradient induced by the lee side of the bump allows for a variable pressure-induced separation. The separation region is reduced (increased) when the bump is on the anti-cyclonic (cyclonic) side of the channel, compared with the non-rotating separation. The total drag is reduced in all rotating cases. Through several mechanisms, rotation alters the onset of separation, reattachment and wake recovery. The mean momentum deficit is found to be the key. A physical interpretation of the ratio between the system rotation and mean shear vorticity, $S:=\varOmega /\varOmega _s$ , provides the mechanisms regarding stability thresholds $S=-0.5$ and $-$ 1. The rotation effects are explained accordingly, with reference to the dynamics of several flow structures. For anti-cyclonic separation, particularly, the interaction between the Taylor–Görtler vortices and hairpin vortices of wall-bounded turbulence is proven to be responsible for the breakdown of the separating shear layer. A generalized argument is made regarding the essential role of near-wall deceleration and resultant ejection of enhanced hairpin vortices in destabilizing an anti-cyclonic flow. This mechanism is anticipated to have broad impacts on other applications in analogy to rotating shear flows, such as thermal convection and boundary layers over concave walls.

Wavelet-based resolvent analysis of non-stationary flows

This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. Under this formulation, resolvent analysis may extend to turbulent flows with non-stationary mean states. The optimal resolvent modes are augmented with a temporal dimension and are able to encode the time-transient trajectories that are most amplified by the linearised Navier–Stokes equations. We first show that the wavelet- and Fourier-based resolvent analyses give equivalent results for statistically stationary flow by applying them to turbulent channel flow. We then use wavelet-based resolvent analysis to study the transient growth mechanism in the near-wall region of a turbulent channel flow by windowing the resolvent operator in time and frequency. The computed principal resolvent response mode, i.e. the velocity field optimally amplified by the linearised dynamics of the flow, exhibits characteristics of the Orr mechanism, which supports the claim that this mechanism is key to linear transient energy growth. We also apply this method to non-stationary parallel shear flows such as an oscillating boundary layer, and three-dimensional channel flow in which a sudden spanwise pressure gradient perturbs a fully developed turbulent channel flow. In both cases, wavelet-based resolvent analysis yields modes that are sensitive to the changing mean profile of the flow. For the oscillating boundary layer, wavelet-based resolvent analysis produces oscillating principal forcing and response modes that peak at times and wall-normal locations associated with high turbulent activity. For the turbulent channel flow under a sudden spanwise pressure gradient, the resolvent modes gradually realign themselves with the mean flow as the latter deviates. Wavelet-based resolvent analysis thus captures the changes in the transient linear growth mechanisms caused by a time-varying turbulent mean profile.

Influence of particle density on turbulence characteristics over a rough surface

The objective of the study is to use a 3D Acoustic Doppler Velocimeter (ADV) to gauge the typical flow and turbulence characteristics within a non-uniform open channel. The findings of experimental examinations of the subcritical flow along the channel are presented in this work. The behavior of sand grains in turbulent open channel flow across porous and rough bed surfaces was examined in laboratory research, and the results were obtained. The properties of turbulent flow, i.e., turbulence intensity, turbulent kinetic energy, and Reynolds shear stresses, are determined from ADV data. The continuity equation and the Reynolds equation of open-channel flow have been used to build theoretical formulations for the velocity distribution and Reynolds stress distribution in the vertical direction. Measured profiles of vertical velocity and Reynolds stress are compared to the derived expressions. The impact of the size of particles on the distribution of mean flow characteristics is discussed. This work provides a novel origin for the profile and analyzes the behavior of the vertical velocity distribution in the region where fully formed turbulence is dominating in open channels using the Navier–Stokes equations. In comparison to other sand roughness, Chopan sand bed (with greater density) exhibits the strongest turbulence intensities in both vertical and streamwise direction just next to the bed when away from the channel boundary. In contrast to flow across a rough surface, the variance ranges between 150 and 250% concerning the channel bed’s roughness type, impacting the velocity triple products that signifies transfer of turbulent kinetic energy.

A time-relaxation reduced order model for the turbulent channel flow

Regularized reduced order models (Reg-ROMs) are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical Galerkin ROM (G-ROM) in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and the evolve-filter-relax ROM (EFR-ROM) and one eddy viscosity model, the mixing-length model, in the numerical simulation of the turbulent channel flow at Reτ=180 and Reτ=395 in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) the higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance with respect to the ROM dimension, N, and the filter order. We also perform sensitivity studies of the three Reg-ROMs with respect to the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM. (ii) All three Reg-ROMs are more accurate than the ROM projection in terms of Reynolds stresses. (iii) With the optimal parameter values, the new TR-ROM yields more accurate results than the L-ROM and the EFR-ROM in all tests. (iv) The new TR-ROM is more accurate than the mixing-length ROM. (v) For most N values, DF yields the most accurate results for all three Reg-ROMs. (vi) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most N values, demonstrating the Reg-ROM predictive capabilities. (vii) All three Reg-ROMs are sensitive to the filter order and the filter radius, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (viii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two Reτ values.

Turbulent stratified open channel flow with solar heating up to Pr=7 using Direct Numerical Simulation

This paper investigates the turbulent structure of stratified open-channel flow subjected to a radiative volumetric heat source modelled by the Beer–Lambert law, for Prandtl numbers (Pr) varying from 0.07 to Pr=7. Direct Numerical Simulation (DNS) was employed to model the open-channel flow. To overcome the increased computational resources required to resolve the thermal fields when Pr>1, a multi-resolution method using quadratic interpolation was employed to resolve the temperature and momentum fields on different spatial and temporal resolutions. This scheme was implemented in an in-house computational fluid dynamics (CFD) code. To further reduce the computation cost, the DNS of Pr=2.2 and 7 fluids were initialised using the outputs of minimal channel simulations. The simulations were conducted for Pr=0.07, 0.22, 0.71, 2.2, and 7 under neutral (λ=0), near-neutral (λ=0.1), and stable (λ=0.5) thermal stratification. The results demonstrate that Pr significantly affects the flow structure and turbulence characteristics of stratified flows, particularly near the free surface. This includes higher velocity, temperature gradient, and buoyancy effects for Pr=7 compared to lower Pr values. For stratified Pr=7 flow, examination of the Reynolds stresses and turbulent heat flux reveals significant damping of turbulence near the surface, with flow displaying near-laminar behaviour.

Direct numerical simulation of turbulent flow and heat transfer in a particle-laden turbulent channel flow

Direct numerical simulation (DNS) is conducted to investigate the impact of solid particles on heat transfer in a plane channel flow. For comparison, two corresponding DNSs of unladen channel flow are also performed. The numerical simulation of the particle-laden case employs a two-way coupled Eulerian–Lagrangian computational model, which allows for the consideration of momentum transfer between the two phases: discrete particles and the continuous fluid phase. The presence of particles results in an increase in the mean temperature, the root mean square (rms) of temperature fluctuations, and the streamwise turbulent heat flux within the core region. Furthermore, particles exert a more significant influence on these characteristics at higher solid volume fractions. Additionally, the correlation between velocity and temperature is affected by the presence of particles. When comparing heat transfer in particle-laden channel flow to that in the corresponding unladen channel flow, it is observed that the difference in heat flux arises from changes in the rms of the wall-normal velocity and temperature fluctuations. The impact of particles on turbulent heat flux transport is significant in the vicinity of the wall, while their influence within the core region is relatively small.

Defiltering turbulent flow fields for Lagrangian particle tracking using machine learning techniques

We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical applications require an affordable grid size due to the limitation of computational resources; for instance, a large-eddy simulation reduces the number of grid points with a filtering operator. However, low resolution flow fields usually underestimate the fluctuations of particle velocity. We thus present a novel approach to defilter the fluid velocity to improve the particle motion in coarse-grid (i.e., filtered) fields. The proposed method, which is based on the machine learning techniques, intends to reconstruct the fluid velocity at a particle location. We assess this method in a priori manner using a turbulent channel flow at the friction Reynolds number Reτ=180. The investigation is conducted for the filter size, nfilter, of 4, 8, and 16. In the case of nfilter=4, the proposed method can perfectly reconstruct the fluid velocity fluctuations. The results of nfilter=8 and 16 also exhibit substantial improvements in the fluctuation statistics although with some underestimations. Subsequently, the particle motion computed using the present method is analyzed. The trajectories, the velocity fluctuations, and the deposition velocity of particles are reconstructed accurately. Moreover, the generalizability of the present method is also demonstrated using the fields whose computational domain is larger than that used for the training. The present findings suggest that machine learning-based velocity reconstruction will enable us precise particle tracking in coarse-grid flow fields.

Numerical investigation of turbulent flow over a randomly packed sediment bed using a variable porosity continuum model

A large eddy simulation (LES) is performed for a turbulent open channel flow over a porous sediment bed at permeability Reynolds number of ReK∼2.56 (Reτ = 270) representative of aquatic systems. A continuum approach based on the upscaled, volume-averaged Navier−Stokes (VaNS) equations is used by defining smoothly varying porosity across the sediment water interface (SWI) and modeling the drag force in the porous bed using a modified Ergun equation with Forchheimer corrections for inertial terms. The results from the continuum approach are compared with a pore-resolved direct numerical simulation (PR-DNS) in which turbulent flow over a randomly packed sediment bed of monodispersed particles is investigated [Karra et al.,J. Fluid Mech. 971, A23 (2023)] A spatially varying porosity profile generated from the pore-resolved DNS is used in the continuum approach. Mean flow, Reynolds stress statistics, and net momentum exchange between the freestream and the porous bed are compared between the two studies, showing reasonably good agreement. Small deviations within the transitional region between the sediment bed and the freestream as compared to the PR-DNS results are attributed to the local protrusions of particles in a randomly packed bed that are absent in the continuum approach but are present in the PR-DNS. A better representation of the effective permeability in the top transition layer that accounts for roughness effect of exposed particles is necessary. The continuum approach significantly reduces the computational cost, thereby making it suitable to study hyporheic exchange of mass and momentum in large scale aquatic domains with combined influence of bedform and bed roughness.

JAX-Fluids 2.0: Towards HPC for differentiable CFD of compressible two-phase flows

In our effort to facilitate machine learning-assisted computational fluid dynamics (CFD), we introduce the second iteration of JAX-Fluids. JAX-Fluids is a Python-based fully-differentiable CFD solver designed for compressible single- and two-phase flows. In this work, the first version is extended to incorporate high-performance computing (HPC) capabilities. We introduce a parallelization strategy utilizing JAX primitive operations that scales efficiently on GPU (up to 512 NVIDIA A100 graphics cards) and TPU (up to 1024 TPU v3 cores) HPC systems. We further demonstrate stable parallel computation of automatic differentiation gradients across extended integration trajectories. The new code version offers enhanced two-phase flow modeling capabilities. In particular, a five-equation diffuse-interface model is incorporated which complements the level-set sharp-interface model. Additional algorithmic improvements include positivity-preserving limiters for increased robustness, support for stretched Cartesian meshes, refactored I/O handling, comprehensive post-processing routines, and an updated list of state-of-the-art high-order numerical discretization schemes. We verify newly added numerical models by showcasing simulation results for single- and two-phase flows, including turbulent boundary layer and channel flows, air-helium shock bubble interactions, and air-water shock drop interactions.

Sediment transport on rippled beds

We conduct an Euler-Lagrange, direct numerical simulation of a turbulent channel flow at a shear Reynolds number of Reτ=180 over an erodible particle bed. The particle bed consists of approximately 1.3 × 106 monodisperse particles, resulting in a bed thickness of around 12–13 particles. The particle density and size are chosen to achieve a ratio of 4 for the Shields stress to the critical Shields stress necessary for incipient motion such that particle transport occurs primarily as bedload. The simulation is run long enough for ripples to form. We track the temporal evolution of the particle flux and excess Shields stress for the entire bed as well as for the four regions of a ripple, namely, the crest, trough, lee side, and stoss side. We find that the particle flux and excess Shields stress closely match the Wong and Parker correlation when the particle bed is featureless at early time but diverge from the correlation when ripples form. This deviation primarily arises from particle transport in the trough and lee side regions. Conversely, particle transport in the crest and stoss side regions remains largely consistent with the Wong and Parker correlation. A root mean square-based correction for the bed is proposed to be used in conjunction with the Wong and Parker correlation. Additionally, ripples attain a self-similar profile in the shape and near-bed shear stress when they are sufficiently distant from their upstream neighbor. Any departure from self-similarity occurs when the upstream neighbor gets within close proximity.