LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation （DNS） and large-eddy simulation （LES） of turbulent channel flows. It is found from the comparisons that the LES with an eddy-viscosity subgrid scale （SGS） model over-predicts the space-time corre- lations than the DNS. The overpredictions are further quantified by the integral scales of directional correlations and convection velocities. A physical argument for the overpre- diction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions. This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows. It suggests that enstrophy is crucial to the LES prediction of spacetime correlations. The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.

AN EXPLORATION TO THE MODELLING OF TWO-DIMENSIONAL COMPLEX TURBULENT SHEAR FLOWS

The regions with shear stress and mean velocity gradient of opposite sign often exist in complex turbulent shear flows.In these cases,the eddy viscosity hypothesis breaks down.Hinze regards the,departure from eddy viscosity hypothesis as a result from transportation of mean momentum over distance by the large structures and arrives at a shear stress expression including the second order derivatives of the mean velocity.However,his expression greatly overestimates the shear stress.This implies that the flow particles are unlikely to have enough memory of the mean momentum over distance.By assuming the departure from eddy viscosity hypothesis as a result from transportation of the shear stress contained in smaller eddies over distance by the large structures,the present author has arrived at a new shear stress expression.The shear stress estimated so far is in good agreement with the experiments.

EFFECTS OF WALL ROUGHNESS ON COHERENT STRUCTURE IN TURBULENT SHEAR FLOWS

There are many examples that fluid flows on rough wall, such as channel flow in nature, pipe flow, etc. In order to know the flow structure of real fluids, it is important to study the effects of wall roughness on coherent structure in turbulent shear flows. The experiments were carried out in a square glass channel, which is 600cm long, with the cross section of 30×25cm^2. The flow velocity was varied from 2 to 40 cm/s. Uniform sands whose diameters were 0.0012cm, 0.2gcm, 0.385cm, 0.594cm and 0.896cm respectively were glued to the floor of the channel. The rough Reynolds number Re_Δ= U_*Δ/ν=0.04～73, where U_*is the shear velocity, Δ is the diame- ter of uniform sand, v is the kinematic viscosity coefficient. Hydrogen bubble technique for flow visualization and HWL-II hot-film anemometer for velocity mea- surement were used in the experiments.

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.

A numerical method for spherical particle motion in turbulent flow with large Reynolds number

A new mathematical model, fluctuation spectrum random trajectory model (FSRTM) for the particle motion in environmental fluid was developed using Lagrangian method, in which the time mean velocity of the fluid was calculated by a time mean velocity formula for two dimensional homogeneous shear turbulent flows in open channel, the velocity fluctuation of the fluid was determined by Fourier expansion and fluctuation spectrum, and the particle motion equation was solved using Ronge Kutta method. For comparison, the spherical cation exchange resins with a density of 1 44 g/cm\+3 and diameters ranging from 0 50—0 60 mm, 0 60—0 70 mm and 0 80—0 90 mm were selected as the experimental solid particles, and their moving velocities and trajectories in shear turbulent flows with the flow Reynolds number of 4710, 10240, 11900 and 20760 were investigated. The comparing analyses of the modeled results with the measured results have shown that the model developed in this paper can describe the motions of the particles in shear turbulent flow.

Direct and noisy transitions in a model shear flow

The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.

THE EXPERIMENTAL RESULTS OF 2-D FREE SHEAR TURBULENT FLOWS AND THE COMPARISON WITH THE THEORETICAL COMPUTATION

An extensive set of measurements in 2-D turbulent mixing layer, wake and jet flow by the hot-wire technique and data sampling are presented. The measured quantities, i. e. the mean velocity, the turbulence intensity, the Reynolds stress and higher-order correlations of the fluctuating velocity in the self-preserving region of the above free shear flows are compared with the computational results based on Zhou's theory for the shear turbulence of in- compressible fluid. The experimental and computational results are in good agreement.

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations（DNSs） of purely elastic turbulence in rectilinear shear flows in a three-dimensional（3D） parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures＇ behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures＇ elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.