高雷诺数壁湍流的研究进展及挑战

高雷诺数壁湍流(high Reynolds number wall-bounded turbulence,HRNWT)是目前湍流科学研究的一个热点也是一个难点,对其现象、规律及机制的认知不足,理论体系远未建立而且研究手段受到各种限制.本文基于对HRNWT主要研究手段的介绍,针对HRNWT中的湍流统计量、超大尺度结构(very large scale motions,VLSMs)的尺度和形态以及起源和影响及其与颗粒的相互作用,总结了HRNWT的研究现状和最新进展,特别梳理了近年来本文作者团队在HRNWT特别是高雷诺数颗粒两相壁湍流方面的研究成果,并对HRNWT的进一步研究给出了建议及展望.      

Assessment of two‐equation turbulence modelling for high Reynolds number hydrofoil flows

This paper presents an evaluation of the capability of turbulence models available in the commercial CFD code FLUENT 6.0 for their application to hydrofoil turbulent boundary layer separation flow at high Reynolds numbers. Four widely applied two‐equation RANS turbulence models were assessed through comparison with experimental data at Reynolds numbers of 8.284×106 and 1.657×107. They were the standard k–εmodel, the realizable k–εmodel, the standard k–ωmodel and the shear‐stress‐transport (SST) k–ωmodel. It has found that the realizable k–εturbulence model used with enhanced wall functions and near‐wall modelling techniques, consistently provides superior performance in predicting the flow characteristics around the hydrofoil. Copyright © 2004 John Wiley & Sons, Ltd.     

The effect of Reynolds number on boundary layer turbulence

A new facility for studying high Reynolds number incompressible turbulent boundary layer flows has been constructed. It consists of a moderately sized wind tunnel, completely enclosed by a pressure vessel, which can raise the ambient air pressure in and around the wind tunnel to 8 atmospheres. This results in a Reynolds number range of about 20:1, while maintaining incompressible flow. Results are presented for the zero pressure gradient flat plate boundary layer over a momentum thickness Reynolds number range 1500–15?000. Scaling issues for high Reynolds number non-equilibrium boundary layers are discussed, with data comparing the three-dimensional turbulent boundary layer flow over a swept bump at Reynolds numbers of 3800 and 8600. It is found that successful prediction of these types of flows must include length scales which do not scale on Reynolds number, but are inherent to the geometry of the flow.     

Some experimental support at a high Reynolds number to a new hypothesis for turbulence modeling

A new dynamical subgrid model of 2D turbulence has been recently derived from the rapid distortion theory. This model is based on an hypothesis of nonlocality of the interaction of the scales of turbulence. The validity of this hypothesis was demonstrated by numerical simulation in 2D turbulence. It is supported here for real 3D turbulence at high Reynolds number by a spectral analysis of hot wire measurements in a turbulent boundary layer.     

Constant Reynolds number turbulence downstream of an orificed perforated plate

Quasi-isotropic turbulence was experimentally produced in a wind tunnel via an orificed, perforated plate (OPP) at 10.5 m/s. The OPP consists of a lattice arrangement of 38.1 mm holes occupying 57% of the plate area. The OPP turbulence was found to be homogeneous over the cross section normal to the mean flow with Gaussian-like turbulence fluctuation. The isotropy of the turbulence field as portrayed by the streamwise/lateral turbulence intensity ratio was found to be approximately 1.1. The OPP turbulence is essentially self-preserving wherein the Taylor microscale Reynolds number remains nearly constant and the lateral velocity correlations collapse into a single curve.     

Effective eddy viscosities in implicit modeling of decaying high Reynolds number turbulence with and without rotation

We assess the applicability of the numerical dissipation as an implicit turbulence model. The nonoscillatory finite volume numerical scheme MPDATA developed for simulations of geophysical flows is employed as an example of a scheme with an implicit turbulence model. A series of low resolution simulations of decaying homogeneous turbulence with and without Coriolis forces in the limit of zero molecular viscosity are performed. To assess the implicit model the long-time evolution of turbulence in the simulations is investigated and the numerical velocity fields are analyzed to determine the effective spectral eddy viscosity that is attributed to the numerical discretization. The detailed qualitative and quantitative comparisons are made between the numerical eddy viscosity and the theoretical results as well as the intrinsic eddy viscosity computed exactly from the velocity fields by introducing an artificial wave number cutoff. We find that the numerical dissipation depends on the time step and exhibits contradictory dependence on rotation: it is overestimated for rapid rotation cases and is underestimated for nonrotating cases. These results indicate that the numerical dissipation may fail to represent the effects of the physical subgrid scale processes unless the parameters of a numerical scheme are carefully chosen.     

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier-Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k-ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results - at a reduced CPU time - as compared to the Dynamic Smagorinsky model.     

Reynolds number dependence of gas-phase turbulence in gas–particle flows

A downward flow of glass bead particles in a vertical pipe is investigated using a two-component LDV/PDPA for a range of Re (6400 < Re < 24,000) and a constant particle loading (m = 0.7). Two particle sizes of 70 and 200 μm are considered in the present work. For the 70 μm particles, the presence of the particles dampens the gas-phase turbulence intensity at the lowest value of Re investigated (8300) compared with the single-phase flow at the same Re. As Re increases, the gas turbulence increases, and for Re > 13,800 the gas turbulence is enhanced compared with the single-phase flow at the same Re. For the 200 μm particles, the intensity also increases with Re and is enhanced for all values of Re investigated, except at the lowest value of Re investigated (6400). At this value, the gas turbulence is equal to that of single-phase flow at the same Re. The observed trend in the gas-phase turbulence modulation with Re is proposed to be due to the change in the segregation patterns and in the average volume fractions of the particles with increasing Re. More importantly, the present experimental results suggest that, consideration of either the gas and particle characteristic length scales or the particle Reynolds number solely is insufficient to predict gas-phase turbulence modulation in gas–particle flows.     

Simultaneous entrainment of oil and water droplets in high Reynolds number gas turbulence in horizontal pipe flow

We develop a 1D cross sectional concentration profile model for oil and water droplets that coexist in the turbulent gas phase (of Re ∼ 10⁶) in near horizontal stratified pipe flows. Entrainment of the oil and water mixture from a liquid film near the bottom of the pipe into the gas is modeled based on earlier single-fluid entrainment correlations. A Gamma distribution for the droplet sizes based on the breakup of liquid filaments, is adopted. An explicit algebraic–exponential formula for the total concentration profile for either phase can then be derived.     

Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD

The flow past a circular cylinder at high Reynolds number is studied by means of PIV, 3C-PIV and Time-Resolved PIV techniques. One of the goals of this study was to allow comparisons with numerical simulations on a domain identical to that of the experiment. For this reason, the cylinder was placed in a confined environment, with a high blockage and a low aspect ratio, thereby allowing computations on a mesh of reasonable size, and avoiding “infinite conditions”. This paper deals with the decomposition of the flow in a coherent and random parts. To this aim, phase averaged quantities were first obtained using the wall pressure signal on the cylinder as a trigger signal. This was achieved using both conditional sampling and LSE with similar results. This decomposition is then analysed using the Time Resolved PIV measurements, as well as by comparison of the contributions of the organised and turbulent fluctuations to the time-independent Reynolds stress tensor with those estimated from velocity spectra by interpolation and integration of the continuous part. In agreement with other studies, it is found that the contribution of the turbulent motion is overestimated as a result of the occurence of phase jitter between the trigger and velocity signal. A POD analysis was then performed to extract the coherent motion and to compare this decomposition with that obtained by phase averaging. Similarly to the phase averaging, the POD allows the decomposition of the time-independent stress tensor as the sum of two contributions corresponding to the first N modes, and the rest of the modes. This decomposition is then analysed by comparing these contributions to those obtained from the velocity spectra, according to the value N chosen. It is found that these contributions are strongly dependent on N, and the contribution of the first modes greatly overestimate the coherent motion if N is too large. In order to obtain a good decomposition of the flow in coherent and random parts, the difficulty in this case lies in the choice of the modes. Finally, the POD coefficients of the first two modes are used instead of the pressure signal to determine the phase of the vortex shedding, and the phase averaging is reconsidered. It is found that the phase averaged vortices are less smeared by the averaging process, the turbulent stresses better follow the evolution of the vortices, and the contributions of both coherent and turbulent fluctuations are found to agree well with those evaluated from the velocity spectra. This enhancement is obtained because the phase angle is determined directly from the velocity fields to be averaged, thereby reducing the phase-jitter effect. A comparison with a detached eddy simulation is also briefly shown and demonstrates the high level of agreement obtainable between simulation and experiment, as well as confirming the enhancement of the phase averaging using this procedure.     

Numerical continuation of high Reynolds number external flows

A numerical continuation method for the compressible Reynolds‐Averaged Navier–Stokes equation with the Spalart–Allmaras turbulence model is presented and applied to the flow around a 2D airfoil. Using continuation methods it is possible to study the steady flow states of a system as a parameter such as angle of attack is varied. This approach allows unstable solutions to be calculated, which are important for understanding the nonlinear dynamics of the system. Furthermore, this method can be used to find any multivalued solutions that exist at a single parameter value. The eigenvalues of the system are calculated using the Cayley transform to precondition the eigenvalue solver ARPACK. The eigenvalues are important as they show the stability of the solutions as well as accurately detect parameter values at which bifurcations take place. Copyright © 2010 John Wiley & Sons, Ltd.     

随机湍流工况低雷诺数风力机翼型优化研究

为改善小型风力机随机湍流工况适应性,以NACA0012翼型为研究对象,采用非嵌入式概率配置点法,获得随机湍流工况下小型风力机叶片翼型运行攻角分布规律;在气动优化中耦合层流分离预测,基于Transition SST模型、拉丁超立方试验设计、Kriging模型和带精英策略非支配排序遗传算法NSGA-II进行高湍流低雷诺数风力机翼型气动优化。结果表明,优化翼型叶片平均风能捕获效率分别提高3.01%和4.76%,标准差分别降低4.76%和14.93%,优化翼型湍流适应性增强。该方法将翼型设计与湍流风况相匹配,为湍流工况低雷诺数翼型及小型风力机设计提供参考。     

Nonlinear aspects of high Reynolds number channel flows

This paper considers the flow in a two-dimensional channel at high Reynolds number, with wall deformations which can lead to flow separation. An asymptotic model is proposed by using the successive complementary expansion method with generalized asymptotic expansions. In particular, the model emphasizes the asymmetry of the channel geometry by introducing a change of variables. It is shown that the model is more general than the models developed with the method of matched asymptotic expansions. Comparisons with Navier–Stokes solutions show that the model is well founded and enables us to treat original problems.     

Phase-averaged measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by 2C-PIV and 3C-PIV

The near wake of a circular cylinder at high Reynolds number is investigated by means of 2D-PIV and stereoscopic PIV. Phase-averaged measurements of the instantaneous fields have been performed. The linear stochastic estimation (LSE) has been adapted to estimate the phase-averaged quantities. This avoids the long time acquisition and the large storage needed for phase averaging. A good comparison is achieved between the results of the conditional sampling and those of LSE. Therefore, the estimation has been applied to the three-component datas and allowed evaluation of the whole phase-averaged turbulent stress tensor.     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.