Simulation Of Turbulent Channel Flow Research Articles

Direct numerical simulations of the drag degradation mechanism in channel flow over trapezoidal riblets

Direct numerical simulations of turbulent channel flows with trapezoidal riblets were conducted to analyze the characteristics of the near-wall flow structures in the drag reduction, drag neutral, and drag increase regimes. The trapezoidal riblets possess a tip angle of α =15°and a height–to-width ratio of k/s = 0.335 for cross-section-area based sizes lg+=Ag+= 11.7, 17, 23.2, and 29 at a friction Reynolds number of Reτ=395. The Reynolds stresses are compared with the smooth wall case, and it is observed that the intensity of the turbulent activities in the boundary layer is diminished for drag reduction riblet and enhanced for drag increase riblets. The roughness sublayer indicates that riblet only directly affect the near-wall region of the flow. By applying the Fukagata, Iwamoto, and Kasagi (FIK) identity in Phys. Fluids, vol. 14, 2002, L73, it is found that the modification of the overall drag is mainly due to the turbulent shear stress. The variation of the dispersive stress is only evident within the roughness sublayer for the drag increasing riblets. The enhanced mean wall-shear stress in the valley is responsible for the drag increase for oversized riblets. The production and convection terms of the turbulent stress reveal that although the total drag contribution is trivial, the convection inside the riblet valleys caused by secondary flow is crucial for the redistribution of the turbulent stress and drag increase of oversized riblets.

Sessile super-droplets as quasi-static wall deformations in direct numerical simulation of turbulent channel flow

Condensation is an important aspect of many flow applications due to the ubiquitous presence of humidity in the air at ambient conditions. For direct numerical simulations of such flows, simulating the gas phase as a mixture characterized by temperature and humidity coupled by the latent heat release and absorption has been shown to yield results consistent with multiphase direct numerical simulations at reduced cost. In the case of surface condensation, the deposition of condensate droplets represents an additional mechanism for flow modification. Extending the single-phase approach by tracking the mean deposition rates and consolidating the condensate mass into static super-droplets reintroduces the effects of surface droplets on the flow while retaining the computational advantages of simulating only the gas phase. Results of simulations of turbulent flow through a cooled, vertical channel with and without such droplets illustrate the additional effects captured compared to the original approach. In the immediate vicinity of a super-droplet, turbulent heat and vapor transport towards the cooled wall is enhanced. Direct impingement and deflection of the flow on the super-droplet cause a qualitative change in the distribution of the condensation rates, increasing on the surface of the super-droplets and decreasing in the surrounding regions. This modification of the near-wall transport leads to increased global cooling and drying efficiency compared to a smooth channel.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Effect of Stokes number and particle-to-fluid density ratio on turbulence modification in channel flows

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$ , and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$ . It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$ . The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles’ extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles’ back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows.

Reynolds Number Dependency of Wall-Bounded Turbulence Over a Surface Partially Covered by Barnacle Clusters

The settlement of barnacles on a ship hull is a common form of marine biofouling. In this study, the Reynolds number dependency of turbulent flow over a surface partially covered by barnacle clusters is investigated using direct numerical simulations of turbulent channel flow at friction Reynolds numbers ranging from 180 to 720. Mean flow, Reynolds and dispersive stress statistics are evaluated and compared to the corresponding results for a generic irregular rough surface with a Gaussian height distribution. For the barnacle surface, distinctive features emerge in the velocity statistics due to the interplay between the barnacle clusters and the large, connected smooth-wall sections surrounding them. This aspect is further investigated by applying a rough-smooth decomposition to the local time-averaged flow statistics for the barnacle surface. Using this decomposition, the partial recovery of smooth-wall behaviour over the smooth sections of the barnacle surface can be observed in the Reynolds stress statistics with the streamwise Reynolds stresses exhibiting a similar behaviour as previously found for boundary layers over surfaces with a rough to smooth transition.

Development of an Interpolated RANS-LES solver for wall-bounded turbulent fluid flows

Scale-resolving hybrid RANS-LES models are being increasingly used to numerically simulate wall-bounded turbulent flows since they are computationally efficient compared to LES (Large Eddy Simulation) while also being more accurate compared to RANS (Reynolds-Averaged Navier–Stokes) models. Existing hybrid RANS-LES models typically either suffer from modeled stress depletion or they can introduce a sharp jump in the mean Reynolds stress across the RANS-LES zone. We present a novel interpolated RANS-LES (IRL) solver implemented in OpenFOAM, in which the RANS equations (for eddy-viscosity) and LES equations (for filtered velocity) are evolved simultaneously on the same computational grid. Based on the distance from the no-slip wall, the flow domain is demarcated into a near-wall, free-stream, and a “hybrid” region, sandwiched between the near-wall and free-stream regions. Spalart Allmaras (S-A) model has been used to evolve the RANS eddy viscosity, while the Wall Adapting Local Eddy Viscosity (WALE) model is used for evolving the filtered LES velocity. Using a novel scheme based on solving a partial differential equation, the turbulent eddy-viscosity is interpolated between the RANS eddy viscosity in the near wall region and the effective eddy viscosity from the resolved LES fluctuations in the free-stream region. The mean subgrid stress in the LES momentum equation is then corrected in the near-wall and hybrid regions using the interpolated turbulent eddy-viscosity. IRL’s grid resolution requirements are the same as DES’s (Detached Eddy Simulation). Grid convergence and sensitivity studies have been carried out for two canonical flow geometries. For turbulent channel flow simulations, the IRL solver does not display the typical mean stress depletion observed in DES while also predicting resolved Reynolds stresses accurately in the free-stream region. For simulations of flow over backward facing step, the IRL solver can predict the friction factor and coefficient of pressure better than that DES, especially after the reattachment point.

Large-eddy simulation of turbulent channel flows with antifouling-featured bionic microstructures

The large-eddy simulation of a shark skin surface at Reynolds numbers of Reτ=1200, 2400, and 4500 is carried out in a fully turbulent flow channel to investigate the antifouling mechanism of shark skin from the perspective of hydrodynamics. The antifouling properties are validated through the confocal laser scanning microscopy of microorganism settlement and a measurement of the reduction in pollutant mass. A large-eddy simulation database is then analyzed, focusing on mean and turbulent statistics, to explain the flow characteristics of time-varying fields of the flow that surrounds and skims over the shark skin. A phenomenological scenario based on instantaneous visualizations of vortical events using the Q-criterion is put forward to identify the spatiotemporal evolution of turbulent coherent structures in the outer region. Subsequently, the proposed scenario is accessed by analyzing two-point correlation coefficients, the conditional averaging of vortical events, the wall friction coefficient distribution, and the spatiotemporal evolution of vortices. The flow patterns are predominantly driven by the periodic emission of hairpin-type vortices, which form a strong shear layer and exacerbate shear stress and momentum exchange. Furthermore, these vortices are associated with the generation of a bicyclical system involving an unsteady propagation of turbulent fluids, which develops separately near the front and back of each shark scale. These modes elaborate the antifouling mechanism of shark skin. Analysis of the probability density function and the spatiotemporal map reveals that these strong events have high levels of intermittency in time and space, which vitally contributes to the antifouling properties manifested in the evolution of periodic shear friction over different surfaces.

Influence of Ridge Spacing, Ridge Width, and Reynolds Number on Secondary Currents in Turbulent Channel Flow Over Triangular Ridges

Most studies of secondary currents (SCs) over streamwise aligned ridges have been performed for rectangular ridge cross-sections. In this study, secondary currents above triangular ridges are systematically studied using direct numerical simulations of turbulent channel flow. The influence of ridge spacing on flow topology, mean flow, and turbulence statistics is investigated at two friction Reynolds numbers, 550 and 1000. In addition, the effects of ridge width on SCs, which have not previously been considered for this ridge shape, are explored. The influence of SCs on shear stress statistics increases with increased ridge spacing until SCs fill the entire channel. One of the primary findings is that, for ridge configurations with pronounced secondary currents, shear stress statistics exhibit clear Reynolds number sensitivity with a significant growth of dispersive shear stress levels with Reynolds number. In contrast to rectangular ridges, no above-ridge tertiary flows are observed for the tested range of ridge widths. Flow visualisations of SCs reveal the existence of corner vortices that form at the intersection of the lateral ridge sides and the smooth-wall sections. These are found to gradually disappear as ridges increase in width. Premultiplied spectra of streamwise velocity fluctuations show strong dependency on the spanwise sampling location. Whereas spanwise averaged spectra show no strong modifications by SCs, a significant increase of energy levels emerges at higher wavelengths for spectra sampled at the spanwise locations that correspond to the centres of the secondary currents.

Interface Splitting Algorithm: A Parallel Solution to Diagonally Dominant Tridiagonal Systems

We present an interface-splitting algorithm (ITS) for solving diagonally dominant tridiagonal systems in parallel. The construction of the ITS algorithm profits from bidirectional links in modern networks, and it only needs one synchronization step to solve the system. The algorithm trades some necessary accuracy for better parallel performance. The accuracy and the performance of the ITS algorithm are evaluated on four different parallel machines of up to 2048 processors. The proposed algorithm scales very well, and it is significantly faster than the algorithm used in ScaLAPACK. The applicability of the algorithm is demonstrated in the three-dimensional simulations of turbulent channel flow at Reynolds number 41,430.

Large-eddy simulation of free-surface turbulent channel flow over square bars

The results of large-eddy simulations of free-surface turbulent channel flow over spanwise-aligned square bars are used to investigate the effects of bed roughness and water surface deformations on the root-mean-squared velocity fluctuations, dispersive shear stress, double-averaged Reynolds shear stress, wake kinetic energy and double-averaged turbulent kinetic energy. Two bar spacings, corresponding to transitional and k-type roughness, at similar Reynolds and Froude numbers are considered. The main peak of all statistical quantities occurs at the bar crest height. The effects of a standing wave at the water surface in flow over k-type roughness is marked by a local peak under the water surface for all statistical quantities considered here except wall-normal and spanwise velocity fluctuations. Quadrant analysis shows that sweeps and ejections are the strongest events contributing to both dispersive and double-averaged Reynolds shear stress but their contributions are different for the two bar spacings. Examining the budgets of dispersive and double-averaged Reynolds shear stress reveals that the dominant terms of these stresses are pressure–strain correlation and pressure transport and the contribution of wake production is similar for both of these stresses but with opposite sign. In addition to the main role of the bars in consuming or producing wake kinetic energy through production and transport and convection, the standing wave at the water surface in flow over k-type roughness induces large convection in the bulk flow too. The dominant terms in the double-averaged turbulent kinetic energy budget are similarly production, transport and convection. Large shear production renders large temporal fluctuations than spatial fluctuations of flow variables. The interaction of bars, bed and water surface is seen in the convection term in flow over k-type roughness.

Models of interphase drag force from direct numerical simulations of upward turbulent particle-laden channel flows

Data from the interfaced-resolved direct numerical simulations (IR-DNSs) of upward turbulent channel flow laden with finite-size heavy particles at particle concentration ranging from 0.84% to 2.36% are used to develop improved drag correlations which account for the effect of turbulence on drag enhancement. First, the contribution of drag nonlinearity to drag enhancement for the turbulent flow over a fixed sphere is analyzed with the consideration of velocity fluctuation anisotropy. The nonlinear drag enhancement is generally smaller than the actual drag enhancement in our numerical simulations. Second, several models for turbulence correction are presented with different choice of model parameters, and it is found that the turbulent intensity normalized by the mean slip velocity and the particle size normalized by the Kolmogorov scale are most important for modeling the effect of turbulence on particle drag, while the anisotropy of fluctuating velocity and the particle Reynolds number are less important.

Drag-reduction effect of staggered superhydrophobic surfaces in a turbulent channel flow

In this study, direct numerical simulations of turbulent channel flow with superhydrophobic surfaces (SHS) were performed. The staggered SHS pattern alternating the free-shear and no-slip regions was designed to be robust to variations in the main flow direction. A constant-pressure gradient condition was imposed, and the Reynolds number was set to Reτ=180 and 395. The bulk mean velocity in the SHS case increased compared with the no-slip case, and the effect was enhanced by increasing the size of the free-shear region lb+. The main reason for the increase in bulk mean velocity was the increase in slip velocity (or slip length). If the size of the free-shear region was small, the drag-reduction rate was found to be proportional to the slip velocity. However, the turbulent contribution to the bulk mean velocity remained almost unchanged in the no-slip case owing to the negative coherent component of the Reynolds shear stress.

Assessment of subgrid-scale models in wall-modeled large-eddy simulations of turbulent channel flows

Assessment of subgrid-scale models in wall-modeled large-eddy simulations of turbulent channel flows

Wall-modeled large-eddy simulation integrated with synthetic turbulence generator for multiple-relaxation-time lattice Boltzmann method

The synthetic turbulence generator (STG) lies at the interface of the Reynolds averaged Navier–Stokes (RANS) simulation and large-eddy simulation (LES). This paper presents an STG for the multiple-relaxation-time lattice Boltzmann method (LBM) framework at high friction Reynolds numbers, with consideration of near-wall modeling. The Reichardt wall law, in combination with a force-based method, is used to model the near-wall field. The STG wall-modeled LES results are compared with turbulent channel flow simulations at Reτ=1000,2000,5200 at different resolutions. The results demonstrate good agreement with direct numerical simulation, with the adaptation length of 6–8 boundary layer thickness. This method has a wide range of potentials for hybrid RANS/LES-LBM related applications at high friction Reynolds numbers.

Effects of mean shear on the vortex identification and the orientation statistics

This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows. It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold. Regarding the vortex orientation, the inclination angle remains similar. However, as the wall-normal distance increases, a more and more obvious distinction is noticed for its orientation with respect to the spanwise (z) direction. It is mainly due to their intrinsic differences and attendant contrasting preference for the vortex identification, i.e., vortices rotating in the −z direction for the total velocity field and in the z direction for the fluctuating one. These observations function as a reasonable explanation for various remarks in previous studies.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

Wavelet-based adaptive large-eddy simulation of supersonic channel flow with different thermal boundary conditions

This work investigates the effect of different thermal wall boundary conditions on the wavelet-based adaptive large-eddy simulation of supersonic turbulent channel flow. The compressible flow governing equations are expressed in terms of wavelet-based Favre-filtered variables and are supplied with the anisotropic minimum dissipation closure model. Various computations are performed, where the resolved temperature field is constrained by either Dirichlet (isothermal) or Neumann (adiabatic) boundary conditions at the walls. The turbulence diagnostics include mean flow features and turbulent fluctuations statistics. The successful comparison with reference direct numerical simulations demonstrates the validity and the efficiency of the wavelet-based adaptive approach for wall-bounded turbulent compressible flow, regardless of the thermal boundary conditions that are imposed.

Uniform momentum and temperature zones in unstably stratified turbulent flows

Wall-bounded turbulent flows exhibit a zonal arrangement, in which streamwise velocity organizes into uniform momentum zones (UMZs), separated by thin layers of elevated interfacial shear. While significant research efforts have focused on these structural features in neutrally stratified flows, the effects of unstable thermal stratification on UMZs and on analogous uniform temperature zones (UTZs) have not been considered previously. In this article, statistical properties of UMZs and UTZs are investigated using a suite of large eddy simulations of unstably stratified turbulent channel flow spanning weakly to highly convective conditions. When normalized by the friction velocity and stability-dependent mixing length, the mean velocity gradient based on UMZ interfacial velocity jumps and the vorticity thickness exhibits good collapse for all stabilities, establishing a link between UMZ properties and scaling predictions from Monin–Obukhov similarity theory. A similar relationship is found between UTZ properties and surface-layer scaling of the mean temperature gradient. In the mixed layer, mean UMZ depth is quasi-constant with wall-normal distance, while the deepest UTZs are found in the centre of the boundary layer. These instantaneous structures are found to be linked to the well-mixed velocity and temperature profiles in the convective mixed layer. Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. These results demonstrate a tangible connection between instantaneous structural features, mean properties and scaling laws in unstably stratified flows.

A wall stress model to predict high-Reynolds number flow over rough walls

Wall-modeled large eddy simulation of turbulent channel flow with rough walls was performed for Reynolds numbers of Reτr=615–2080. The eddy viscosity parameter in a wall stress model was modified to include the effects of wall roughness. Symmetric and asymmetric channel flows were studied for transitionally and fully rough states with ks+=62 and 112, respectively. The wall shear stress was estimated based on the velocity field within the wall layer using the total shear stress term. For the wall layer, the matching point was located well above the height of the virtual roughness elements. The numerical predictions for the mean velocity profile and Reynolds stresses compared well with the experimental data. The prediction for the mean velocity shift due to roughness agreed with the experimental measurements and empirical correlations. For the asymmetric channel flows with roughness on only one wall, the numerical simulations correctly reproduced the displacement of the mean flow away from the rough wall. Overall, the proposed wall-model allows for the prediction of the effects of wall roughness without resolving the geometry of the roughness elements on the wall. This is consistent with the goal of performing large eddy simulations of wall-bounded flows at high-Reynolds numbers with minimal resolution of the wall region, which results in a much reduced computational cost.

Turbulence control for drag reduction through deep reinforcement learning

Deep reinforcement learning was applied to turbulence control for drag reduction in direct numerical simulation of turbulent channel flow. The learning determines the optimal distribution of wall blowing and suction based on the wall shear stress information. From an investigation of the optimal actuation fields, two distinct drag reduction mechanisms were identified. One of them, which had not previously been recognized, attempts to cancel the near-wall sweep and ejection events.