On the analytical solution of transient friction in channel flows

The transient friction in channel mean flows is the sum of two contributions,i.e.,the underlying laminar flow(ULF)and the purely turbulent component(PTC),and the contributions are analyzed separately by theoretical experiments.It is found that,the transient friction may be higher or remarkably lower than that in equal-Reynolds number steady-state flows.The universal time constant for plane-parallel laminar flows is reported,and the role of the time constant in a turbulent mean flow is examined.It is shown that the time constant is related to the turbulence's frozen time.Finally,a study of the logarithmic layer during the transient flow is accomplished,which shows that the logarithmic layer is destroyed.

Experimental study on influence of boundary on location of maximum velocity in open channel flows

The velocity dip phenomenon may occur in a part of or in the whole flow field of open channel flows due to the secondary flow effect. Based on rectangular flume experiments and the laser Doppler velocimetry, the influence of the distance to the sidewall and the aspect ratio on the velocity dip is investigated. Through application of statistical methods to the experimental results, it is proposed that the flow field may be divided into two regions, the relatively strong sidewall region and the relatively weak sidewall region. In the former region, the distance to the sidewall greatly affects the location of maximum velocity, and, in the latter region, both the distance to the sidewall and the aspect ratio influence the location of the maximum velocity.

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.

SIDEWALL FLOW STABILITY IN THE MHD CHANNEL FLOWS

The velocity distribution between two sidewalls is; M-shaped for the MHD channel flows with rectangular cross section and thin conducting walls in a strong transverse magnetic field. Assume that the dimensionless numbers R(m) much less than 1, M, N much greater than 1, and sigma* much less than 1 and that the distance between two perpendicular walls is very long in comparison with the distance between two sidewalls. First, the equation for steady flow is established, and the solution of M-shaped velocity distribution is given. Then, an equation for stability of small disturbances is derived based on the velocity distribution obtained. Finally, it is proved that the stability equation for sidewall how can be transformed into the famous Orr-Sommerfeld equation, in addition, the following theorems are also proved, namely, the analogy theorem, the generalized Rayleigh's theorem, the generalized Fjortoft's theorem and the generalized Joseph's theorems.

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.

FIBER ORIENTATION DISTRIBUTIONS IN SLIT CHANNEL FLOWS WITH ABRUPT EXPANSION FOR FIBER SUSPENSIONS

The lattice Boltzmann method was used to investigate numerically the fiber orientation distributions in slit channel flows with abrupt expansion for fiber suspensions even in the concentrated regime. The channels have a thin slit geometry with 1：4 and 1：3 expansions. Both the interactions between fibers and that between fibers and channel walls were taken into consideration. Some of numerical results are qualitatively in agreement with the experiment data. It is found that most of fibers are aligned in the flow direction in all the suspensions in the entrance region of the expansion. Fiber orientation distributions, having different patterns in different regions of the flow, depend on the expansion ratio of the channel. The mechanical fiber-fiber interaction largely affects the fiber orientation in the downstream of the expansion and in the salient corner for the cases of concentrated suspensions. The hydrodynamic interaction plays an important role on the fiber orientation in the dilute suspension.

United friction resistance in open channel flows

It is now over half a century since Keulegan conducted his open channel flow experiments. Over the past decades, many empirical formulae were proposed based on his results, however, there is still not a combined expression to describe the effects of friction over all hydraulic regions in open channel flows. Therefore, in this letter, based on the analysis of the implicit model and the logarithmic matching method, the results of Keulegan （for authentic experiment data are no longer available, here we adopt the analytical solutions given by Dou） are rescaled into one monotone curve by combining the Reynolds number and the relative roughness of the river bed. A united expression that could cover the entire turbulence regions and be validated with Dou＇s analytical solutions is suggested to estimate the friction factor throughout the turbulent region in open channel flows, with higher accuracy than that of the previous formulas.

A numerical model for air concentration distribution in self-aerated open channel flows

The self-aeration in open channel flows, called white waters, is a phenomenon seen in spillways and steep chutes. The air distribution in the flow is always an important and fundamental issue. The present study develops a numerical model to predict the air concentration distribution in self-aerated open channel flows, by taking the air-water flow as consisting of a low flow region and an upper flow region. On the interface between the two regions, the air concentration is 0.5. In the low flow region where air concentration is lower than 0.5, air bubbles diffuse in the water flow by turbulent transport fluctuations, and in the upper region where air concentration is higher than 0.5, water droplets and free surface roughness diffuse in the air. The air concentration distributions obtained from the diffusion model are in good agreement with measured data both in the uniform equilibrium region and in the self-aerated developing region. It is demonstrated that the numerical model provides a reasonable description of the self-aeration region in open channel flows.

EVALUATION OF THE SHADING METHOD FOR REDUCING IMAGE BLOOMING IN THE PIV MEASUREMENT OF OPEN CHANNEL FLOWS

The shading method is a simple but effective way of reducing image blooming in the measurement of open channel flows with the Particle Image Velocimetry （PIV）.The current paper proposes a simplified analytical model for light attenuation using this method.The model is verified against experimental data,and the influence of several parameters is illustrated numerically.The possible adverse effect due to the light attenuation is shown to be limited when the parameters in the shading method are in an adequate range,as shown by processing standard images of Case B in PIV Challenge 03.A simple criterion for setting the shade in experiment is given for controlling the errors caused by the shading technique within an acceptable range.

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 investigation of compressibility effects in turbulent channel flows using large eddy simulation

The large eddy simulation (LES) of compressible turbulent channel flows at three different Mach numbers is performed in the present work,by extending the dynamic mixed subgrid-scale (SGS) model to compressible flows.The turbulent statistics agree well with those from the existing direct numerical simulation (DNS) results,indicating that the LES method established in the present work is reliable.The analysis of the turbulent fluctuations computed by the present LES reveals that the flows considered in this work follow the Morkovin's hypothesis.Thus,the compressibility effects are dominated by the mean field properties,and the relevant statistical ratios are invariant to the variation of Mach number.The near-wall streamwise streaks are more coherent and the spacing between streaks is wider as the Mach number increases.This can be regarded as a direct feature characterized by the compressibility effects.The restrained influences of compressibility effects on the production and dissipation of the turbulence kinetic energy are also identified based on the present LES results.

AN INVESTIGATION OF TURBULENT HEAT TRANSFER IN CHANNEL FLOWS BY LARGE EDDY SIMULATION

Large Eddy Simulation (LES) of fully developed turbulent channel flow with heat transfer was performed to investigate the effects of the Reynolds number on the turbulence behavior. In the present study, the bottom wall of the channel was cooled and the top wall was heated. The Reynolds numbers, based on the central mean-velocity and the half-width of the channel, were chosen as 4000, 6000, 10 4 and 2×10 4, and the Prandtl number as 1.0. To validate our calculations, the present results were compared with available data obtained by Direct Numerical Simulation (DNS), which proves to be in good agreement with each other. To reveal the effects of the Reynolds number, some typical quantities, including the velocity fluctuations, temperature fluctuation, heat fluxes and turbulent Prandtl number, were studied.

Geomorphic Characteristics of Hillslope and Channelized Debris Flows: A Case Study in the Shitou Area of Central Taiwan

The data on the hillslope and channelized debris flows in the Shitou area of central Taiwan occurred during Typhoons Toraji and Nali in 2001 were applied in this paper. The geomorphic parameters, including the flow length, gully gradient, drainage area and form factor of the debris flows were determined by spatial analysis using a Geographic Information System (GIS) based on the data derived from field investigation, aerial photographs, and topographical maps. According to such determined geomorphic parameters, the threshold conditions and empirical equations, such as the relationship between the gully gradient and drainage area and that between gully length and drainage area and topographic parameter, are presented and used to distinguish the geomorphic characteristics between the channelized and hillslope debris flows.

Analysis of the spanwise vortex of open channel flows based on the Omega-Liutex vortex identification method

In this paper, a particle imaging velocimetry (PIV) system of high-temporal-spatial resolution is used to investigate the spanwise vortex distribution of fully developed turbulent flows in an open channel and its relationship with the turbulence. The distributions of the time-averaged velocity, the turbulence intensity and the Reynolds stress are obtained in the longitudinal profile. The third-generation vortex identification method (based on the Omega-Liutex vector) is applied to accurately identify and analyze the vortex in the spanwise direction. The results suggest that the vortex density increases with the Reynolds number at a given aspect ratio (B / H) of the flow. The distribution trend of the spanwise vortex density in the vertical direction remains unchanged for different discharges. Specifically, the vortex density increases along the vertical direction and reaches the peak at y / H = 0.15, then decreases and reaches the bottoms at the flow surface.

NUMERICAL MODELING OF COMPOUND CHANNEL FLOWS

A numerical model capable of predicting flow characteristics in a compound channel was established with the 3-D steady continuity and momentum equations along with the transport equations for turbulence kinetic energy and dissipation rate. Closure was achieved with the aid of algebraic relations for turbulent shear stresses. The above equations were discretized with implicit difference approach and solved with a step method along the flow direction. The computational results showing the lateral distribution of vertical average velocities and the latio of total flow in the compound channel agree well with the available experimental data.

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.

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.

Characteristics of a Drainage Channel with Staggered Indented Sills for Controlling Debris Flows

The characteristics of a new type of drainage channel with staggered indented sills for controlling debris flows were studied. The intermediate fluid in the non-viscous debris flow exhibited a helical movement, whereas the fluid near the sidewall had a stop-start movement pattern; the viscous debris flow exhibited a stable structure between the indented sills. The experimental results indicate that the mean velocity of the debris flow increased with increasing channel gradients, and the debris flow velocity was slightly affected by the angle of the sills. The average velocity of the non-viscous debris flow increased in the range of(0.5–1.5) interval between the indented sills, whereas the average velocity of the viscous debris flow increased initially and then decreased in the range of(0.75–1.25) interval between the indented sills. The depth of the non-viscous debris flow tended to gradually increase as the channel gradients increased, whereas the depth of the viscous debris flow gradually decreased as the channel gradients increased. When the discharge of the debris flow was constant, the angle and the interval between the indented sills had a slight effect on the depth of the viscous debris flow, whereas the depth of the non-viscous debris flow exhibited a different trend, as the sill angles and intervals were varied.

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.

Constrained large-eddy simulation of laminar-turbulent transition in compressible channel flows

An improved approach for constrained large-eddy simulations(CLES)of wall-bounded compressible transitional flows is proposed by introducing an intermittency factor.The improved model is tested and validated with compressible channel flows at various Mach numbers and Reynolds numbers that are transitioning from laminar to turbulent states.The improved model is compared against traditional dynamic Smagorinsky model(DSM)and Direct Numerical Simulations(DNS),where the improved model is in better agreement with DNS results than traditional DSM model,in terms of mean velocity profiles,total Reynolds stress and total heat flux.Therefore,the proposed method can be used to accurately predict the temporal laminar-turbulent transition process of compressible wall-bounded flows.