Artificial neural network-based subgrid-scale models for LES of compressible turbulent channel flow

Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.

Mechanism of controlling turbulent channel flow with the effect of spanwise Lorentz force distribution

A direct numerical simulation（DNS） is performed to investigate the control effect and mechanism of turbulent channel flow with the distribution of spanwise Lorentz force. A sinusoidal distribution of constant spanwise Lorentz force is selected, of which the control effects, such as flow characters, mean Reynolds stress, and drag reductions, at different parameters of amplitude A and wave number k_x are discussed. The results indicate that the control effects vary with the parameter A and k_x. With the increase of A, the drag reduction rate D_r first increases and then decreases rapidly at low k_x,and slowly at high k_x. The low drag reduction（or even drag increase） is due to a weak suppression or even the enhancements of the random velocity fluctuation and mean Reynolds stress. The efficient drag reduction is due to the quasi-streamwise vortex structure induced by Lorentz force, which contributes to suppressing the random velocity fluctuation and mean Reynolds stress, and the negative vorticity improves the distribution of streamwise velocity. Therefore, the optimal control effect with a drag reduction of up to 58% can be obtained.

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.

On the capability of the curvilinear immersed boundary method in predicting near-wall turbulence of turbulent channel flows

The immersed boundary method has been widely used for simulating flows over complex geometries.However,its accuracy in predicting the statistics of near-wall turbulence has not been fully tested.In this work,we evaluate the capability of the curvilinear immersed boundary(CURVIB)method in predicting near-wall velocity and pressure fluctuations in turbulent channel flows.Simulation results show that quantities including the time-averaged streamwise velocity,the rms(root-mean-square)of velocity fluctuations,the rms of vorticity fluctuations,the shear stresses,and the correlation coefficients of u'and v"computed from the CURVIB simulations are in good agreement with those from the body-fitted simulations.More importantly,it is found that the time-averaged pressure,the rms and wavenumber-frequency spectra of pressure fluctuations computed using the CURVIB method agree well with the body-fitted results.

Error of large-eddy simulation in the wall pressure fluctuation of a turbulent channel flow

We analyze the error of large-eddy simulation(LES)in wall pressure fluctuation of a turbulent channel flow.To separate different sources of the error,we conduct both direct numerical simulations(DNS)and LES,and apply an explicit filter on DNS data to obtain filtered DNS(FDNS)data.The error of LES is consequently decomposed into two parts:The first part is the error of FDNS with respect to DNS,which quantifies the influence of the filter operation.The second part is the difference between LES and FDNS induced by the error of LES in velocity field.By comparing the root-mean-square value and the wavenumber-frequency spectrum of the wall pressure fluctuation,it is found that the inaccuracy of the velocity fluctuations is the dominant source that induces the error of LES in the wall pressure fluctuation.The present study provides a basis on future LES studies of the wall pressure fluctuation.

Independent component analysis of streamwise velocity fluctuations in turbulent channel flows

Independent component analysis(ICA)is used to study the multiscale localised modes of streamwise velocity fluctuations in turbulent channel flows.ICA aims to decompose signals into independent modes,which may induce spatially localised objects.The height and size are defined to quantify the spatial position and extension of these ICA modes,respectively.In contrast to spatially extended proper orthogonal decomposition(POD)modes,ICA modes are typically localised in space,and the energy of some modes is distributed across the near-wall region.The sizes of ICA modes are multiscale and are approximately proportional to their heights.ICA modes can also help to reconstruct the statistics of turbulence,particularly the third-order moment of velocity fluctuations,which is related to the strongest Reynolds shear-stressproducing events.The results reported in this paper indicate that the ICA method may connect statistical descriptions and structural descriptions of turbulence.

Transient response of enstrophy transport to opposition control in turbulent channel flow

The transient response of the turbulent enstrophy transport to opposition control in the turbulent channel flow is studied with the aid of direct numerical simulation. It is found that the streamwise enstrophy and the spanwise enstrophy are suppressed by the attenuation of the stretching terms at first, while the vertical enstrophy is reduced by inhibiting the tilt of the mean shear. In the initial period of the control, the streamwise enstrophy evolves much slower than the other two components. The vertical vorticity component exhibits a rapid monotonic decrease and also plays an important role in the attenuation of the other two components.

Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force

A formulation of the skin-friction drag related to the Reynolds shear stress in a turbulent channel flow is derived. A direct numerical simulation （DNS） of the turbulent control is performed by imposing the spatially oscillating spanwise Lorentz force. Under the action of the Lorentz force with several proper control parameters, only the periodi- cally well-organized streamwise vortices are finally observed in the near-wall region. The Reynolds shear stress decreases dramatically, especially in the near-wall area, resulting in a drag reduction.

Lagrangian time scales and its relationship to Eulerian equivalents in turbulent channel flow

Lagrangian and Eulerian time scales were obtained from the direct numerical simulation of turbulent channel flow at two Reynolds numbers based on the friction velocity and channel half-height, Rer= 80, 100. The Lagrangian integral time scales and time microscales were compared to their Eulerian equivalents. It is found that the ratio of Lagrangian to TL Eulerian integral time scales is given by TE/TiE= 1 ＋ 0.1y＋ for y＋ ≤ 10, and that the ratios between the Lagrangian to theEulerian time microscales are almost the same irrespective of the components. Those increase with y＋ are approximated by ≈ 2.75 - 1.75 exp （-v＋/a） . These results also show that these expressions are independent of the Reynolds number.

Formation of Gel-Like Shear-Induced Structure with Dosing of Dilute Surfactant Solution and Its Effect on Turbulent Channel Flow

A shear-induced structure (SIS) is formed under appropriate concentration and shear conditions in a surfactant micellar solution. In this study, we performed experiments of surfactant solution dosing in a fully developed two-dimensional turbulent channel flow from a sintered metallic wire mesh plate attached to a side wall. We investigated the behavior of the solution under the elongation during its passing through the wire mesh and under the strong shear due to the channel flow. It was confirmed that the dosed solution containing a laser dye was visualized by a laser sheet, and the accumulated gel from the wire mesh formed a layer and developed with time. Consequently, on dosing the dilute surfactant solution from the wire mesh, a gel-like SIS layer was formed, which majorly covered the wire mesh plate. The gel-like SIS layer on the wire mesh plate acted as a sticky solid and restricted the flow in the channel. This layer continued to grow while dosing, owing to which the pressure drop of the channel flow significantly increased. The gel-like SIS layer grew rapidly even in the turbulent flow and reached the equilibrium thickness. After the termination of the dosing, the gel layer collapsed gradually. In addition, the thickness of the gel-like SIS layer (indicating the strength indirectly) strongly depended on the surfactant concentration and the elongation rate in the wire mesh.

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

Considering the demanding of grid requirements for high-Reynolds-number wall-bounded flow,the wall-modeled large-eddy simulation(WMLES)is an attractive method to deal with near wall turbulence.However,the effect of subgrid-scale(SGS)models for wall-bounded turbulent flow in combination with wall stress models is still unclear.In this paper,turbulent channel flow at Reτ=1000 are numerically simulated by WMLES in conjunction with four different SGS models,i.e.,the wall-adapting local eddy-viscosity model,the dynamic Smagorinsky model,the dynamic SGS kinetic energy model and the dynamic Lagrangian model.The mean velocity profiles are compared with the law of the wall,and the velocity fluctuations are compared with direct numerical simulation data.The energy spectrum of velocity and wall pressure fluctuations are presented and the role of SGS models on predicting turbulent channel flow with WMLES is discussed.

LARGE EDDY SIMULATION OF THERMALLY-STRATIFIED TURBULENT CHANNEL FLOW WITH TEMPERATURE OSCILLATION ON THE BOTTOM WALL

Thermally-stratified shear turbulent channel flow with temperatureoscillation on the bottom wall of the channel was investigated with the Large Eddy Simulation (LES)approach coupled with dynamic Sub-Grid-Scale (SGS) models. The effect of temperature oscillation onthe turbulent channel flow behavior was examined. The phase-averaged velocities and temperature, andflow structures at different Richardson numbers and periods of the oscillation was analyzed.

LARGE EDDY SIMULATION OF PARTICLE TRANSPORT IN FULLY DEVELOPED VERTICAL TURBULENT CHANNEL FLOW

Fully developed vertical turbulent channel flow with particle transport wasinvestigated by use of Large Eddy Simulation (LES) approach coupled with dynamic the Sub-Grid Scale(SGS) model. It was assumed that the motion of each particle is followed in a Lagrangian frame ofreference driven by the forces exerted by fluid motion and gravity under the condition of one-waycoupling. The goal of this study is to investigate the effectiveness of the LES technique forpredicting particle transport in turbulent flow and the behavior of particle-laden turbulent channelflow for three kinds of particles at different Stokes numbers. To depict the behavior ofparticle-laden turbulent channel flow, statistical quantities including particle fluctuation andfluid-particle velocity correlation, and visualization of the particle number density field wereanalyzed.

SIMULATION OF LAGRANGIAN DISPERSION USING A LAGRANGIAN STOCHASTIC MODEL AND DNS IN A TURBULENT CHANNEL FLOW

The mean square displacements of fluid particles in a turbulent channel flow at Reτ = 100 are investigated using a modified Langevin equation, and are compared with DNS results. Both the Lagrangian integral time scales directly obtained from DNS and the predicted values using an empirical relation between the Eulerian and the Lagrangian integral time scales are used in the modified Langevin equation to test the effects of integral time scales on the dispersion of particles. The results show that the slight variation of the Lagrangian integral time scale has little influence on the dispersion. The agreement between results of the model equation and those of DNS is satisfactory except the streamwise dispersion for intermediate times （ 20 〈 t^＋ 〈 300 ）, where the results of the model equation are slightly overestimated compared to those of DNS. The cause of such discrepancy is discussed.

Large Eddy Simulation of Turbulent Channel Flows over Rough Walls with Stochastic Roughness Height Distributions

This paper studies the 3-D turbulent channel flows over rough walls with stochastic roughness height distributions by using the large eddy simulation and the immersed boundary method. The obtained mean and fluctuating velocity profiles for the smooth and rough channel flows agree well with the available numerical and experimental results. The stochastic surface roughness is found to have a more significant influence than the uniform surface roughness on the turbulent velocity statistics and the coherent structures, with the same average roughness height. With a greater variation in the roughness height, the mean velocity and the streamwise fluctuating velocity is decreased and the spanwise velocity and the wall-normal fluctuating velocity are increased. In addition, one observes larger and more profuse quasi-streamwise vortices, hairpin vortices and elongated structures above the crest plane of the roughness array in cases of highly stochastic rough walls. However, the low-speed streaky structures are broken up locally and the ejection and sweep events are depressed by the stochastic roughness below the average roughness height. The results of this study support Townsend’s wall-similarity hypothesis for both stochastic and uniform rough wall turbulences, demonstrating that in both cases the effects of the surface roughness on the turbulent flow are limited to the rough sub-layer.

Large-eddy simulation of suspended sediment transport in turbulent channel flow

The numerical simulation of the non-cohesive sediment transport in a turbulent channel flow with a high concentration is a challenging but practical task. A modified coherent dynamic eddy model of the Large Eddy Simulation （LES） with a pick-up function is used in the present study to simulate the sediment erosion and the deposition in a turbulent channel flow. The rough wall model is used instead of the LES with the near-wall resolution to obtain the reasonable turbulent flow characteristics while avoiding the high costs in the computation. Good results are obtained, and are used to analyze the sediment transport properties. The results show that the streamwise vortices play an important role in the riverbed erosion and the sediment pick-up, which may serve as guidelines for the sediment management and the water environment protection engineering.

HIGH ORDER LAGRANGIAN VELOCITY STATISTICS IN A TURBULENT CHANNEL FLOW WITH Re_τ=80

The scaling properties of high-order Lagrangian velocity structure functions are investigated numerically for a turbulent flow with a friction-velocity based Reynolds number Re_τ=80.The Lagrangian particles are released from locations of different distances to the wall.The relative scaling exponents of the longitudinal velocity component are found to increase with the released distance to the wall and to approach asymptotically to theoretical predictions.However,the scaling exponents of the transverse velocity component are smaller than ,indicating a more intermittent nature.Specifically for the release locations in the center region,the relative scaling exponents agree very well with theoretical predictions.

Exact mathematical formulas for wall-heat flux in compressible turbulent channel flows

In this paper,several exact expressions for the mean heat flux at the wall(qw)for the compressible turbulent channel flows are derived by using the internal energy equation or the total energy equation.Two different routes,including the FIK method and the RD method,can be applied.The direct numerical simulation data of compressible channel flows at different Reynolds and Mach numbers verify the correctness of the derived formulas.Discussions related to the different energy equations,and different routes are carried out,and we may arrive at the conclusion that most of the formulas derived in the present work are just mathematical ones and that they generally are lacking in clear physical interpretation in our opinion.They can be used to estimate qw,but might not be suitable for exploring the underlying physics.

Numerical implementation and evaluation of resolvent-based estimation for space-time energy spectra in turbulent channel flows

Resolvent operator has been increasingly used to investigate turbulent flows and develop control strategies.Recently,Towne et al.(J Fluid Mech 883:A17,2020)proposed a resolvent-based estimation(RBE)method for predicting turbulent statistics in a channel flow.In this paper,we utilize the RBE method to predict the root-mean-square(RMS)and space-time energy spectra of streamwise velocity fluctuation,where the input is the space-time energy spectra at a reference horizontal plane located in the logarithmic layer and the output is the space-time energy spectra in the buffer layer.The explicit formulas for the RBE method are given in detail for numerical implementation.The results show the capability of the RBE method in the prediction of the convection velocity and bandwidth of the space-time energy spectra.Furthermore,we make a systematic evaluation of the performance of the RBE method by varying the input configurations,including the wall-normal location of the reference plane,the inclusion or exclusion of the pressure as an input variable,the implementation approach of the pressure boundary condition,and the choice of the window function.It is found that the results of both RMS velocity and space-time energy spectra obtained from the RBE method are sensitive to the location of the reference plane.However,the pressure boundary conditions and inclusion of pressure as an input do not cause significant change in the RMS velocity and space-time energy spectra.Although it does not influence the prediction of the RMS velocity,a window function is found crucial in the RBE method for the prediction of the space-time energy spectra.

Numerical Research on the Fiber Suspensions in a Turbulent T-shaped Branching Channel Flow

The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investi-gated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho-mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.