Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.     

Flow structure and distribution effects in gas-liquid mixture flows

Air-water mixtures which are assumed to flow homogeneously in a pipe are usually described by a one-dimensional momentum balance. This allows definition of a friction factor in a manner similar to single phase flows. By defining a momentum flux distribution parameter, the momentum balance has been modified to correctly include the etfects of phase and velocity distributions and the effect of these on calculated friction factors has been investigated. Resistivity probes were used to measure void fraction and gas phase velocity distributions for selected vertical and horizontal flow conditions, and these were combined with static pressure measurements to calculate friction factors. For bubbly flows, the inclusion of these distribution effects did not substantially alter friction factor estimates which are approximately 10% above single phase values (for Reynolds numbers based on liquid viscosity).

Friction factor values are shown to be related to flow development with higher values associated with deveioping flows. In particular, high friction factors are associated with the need to break-up bubbles to an “equilibrium” size. In order to experimentally simulate fully developed vertical flows, the highly turbulent nozzle mixer is most suitable while the less turbulent wall-injection type seems appropriate for horizontal flows.     

Similarity solutions of vertical plane wall plume based on finite analytic method

The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.     

Numerical study of effects of pulsatile amplitude for transitional turbulent pulsatile flow in pipes with ring‐type constrictions

The effects of pulsatile amplitude on sinusoidal transitional turbulent flows through a rigid pipe in the vicinity of a sharp‐edged mechanical ring‐type constriction have been studied numerically. Pulsatile flows were studied for transitional turbulent flow with Reynolds number (Re) of the order of 10⁴, Womersley number (Nw) of the order of 50 with a corresponding Strouhal number (St) of the order of 0.04. The pulsatile flow considered is a sinusoidal flow with dimensionless amplitudes varying from 0.0 to 1.0. Transitional laminar and turbulent flow characteristics in an alternative manner within the pulsatile flow fields were observed and studied numerically. The flow characteristics were studied through the pulsatile contours of streamlines, vorticity, shear stress and isobars. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity, turbulent shear stress are smaller during the acceleration phase when compared with those during deceleration period. Various parametric equations within a pulsatile cycle have also been formulated through numerical experimentations with different pulsatile amplitudes. In the vicinity of constrictions, the empirical relationships were obtained for the instantaneous flow rate (Q), the pressure gradient (dp/dz), the pressure loss (P_loss), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max). Elliptic relation was observed between flow rate and pressure gradient. Quadratic relations were observed between flow rate and the pressure loss, the maximum values of shear stress, wall shear stress, turbulent kinematic energy and the turbulent viscosity. Linear relationships exist between the instantaneous flow rate and the maximum values of vorticity, wall vorticity and velocity. The time‐average axial pressure gradient and the time average pressure loss across the constriction were observed to increase linearly with the pulsatile amplitude. Copyright © 1999 John Wiley & Sons, Ltd.     

Investigation of particle-laden turbulent pipe flow at high-Reynolds-number using particle image/tracking velocimetry (PIV/PTV)

An experimental investigation of a high Reynolds number flow (Re = 320 000) of a dilute liquid-solid mixture (<1% by volume) was conducted. The turbulent motion of both the liquid phase (water) and particles (0.5, 1, and 2 mm glass beads) was evaluated in an upward pipe flow using a particle image/tracking velocimetry (PIV/PTV) technique. Results show that the Eulerian mean axial velocity of the glass beads is lower than that of the liquid phase in the central region but higher in the near-wall region. Moreover, the presence of the coarse particles has a negligible effect on the turbulence intensity of the liquid phase. Particles show higher streamwise and radial fluctuations than the liquid-phase at the tested conditions. The profiles of particle concentration across the pipe radius show almost constant concentration in the core of the pipe with a decrease towards the near wall region for 0.5 and 1 mm particles. For the 2 mm particles, a nearly linear concentration gradient from centre to the pipe wall is observed. The results presented here provide new information concerning the effect of a dispersed particulate phase on the turbulence modulation of the liquid carrier phase, especially at high Reynolds numbers. The present study also demonstrates how correlations developed to determine if particles cause turbulence attenuation/augmentation are not applicable for solid-liquid flows at high Reynolds numbers. Finally, the importance of particle-fluid slip velocity on fluid phase turbulence modulation is illustrated.     

Comparison between three static mixers for emulsification in turbulent flow

This paper deals with comparing performances of three different static mixers in terms of pressure drop generated by both single-phase flow and liquid–liquid flow in turbulent flow regime and in terms of emulsification performances. The three motionless mixers compared are the well-known SMX™ and SMV™ and the new version of the SMX called SMXPlus™. This experimental study aims at highlighting the influence of the dispersed phase concentration and some of the geometrical parameters such as number of elements and design of the motionless mixer on droplets size distributions characteristics. Finally, experimental results are correlated in terms of Sauter mean diameter as a function of hydrodynamic dimensionless numbers.     

Gas-particle two-phase turbulent flow in a vertical duct

Two-phase gas-phase turbulent flows at various loadings between the two vertical parallel plates are analyzed. A thermodynamically consistent turbulent two-phase flow model that accounts for the phase fluctuation energy transport and interaction is used. The governing equation of the gas-phase is upgraded to a two-equation low Reynolds number turbulence closure model that can be integrated directly to the wall. A no-slip boundary condition for the gas-phase and slip-boundary condition for the particulate phase are used. The computational model is first applied to dilute gas-particle turbulent flow between two parallel vertical walls. The predicted mean velocity and turbulence intensity profiles are compared with the experimental data of Tsuji et al. (1984) for vertical pipe flows, and good agreement is observed. Examples of additional flow properties such as the phasic fluctuation energy, phasic fluctuation energy production and dissipation, as well as interaction momentum and energy supply terms are also presented and discussed.

Applications to the relatively dense gas-particle turbulent flows in a vertical channel are also studied. The model predictions are compared with the experimental data of Miller & Gidaspow and reasonable agreement is observed. It is shown that flow behavior is strongly affected by the phasic fluctuation energy, and the momentum and energy transfer between the particulate and the fluid constituents.     

DNS and Modelling of Passive Scalar Transport in Turbulent Channel Flow with a Focus on Scalar Dissipation Rate Modelling

A direct numerical simulation of turbulent channel flow with an imposed mean scalar gradient is analyzed with a focus on passive scalar flux modelling and in particular the treatment of the passive scalar dissipation equation. The Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half width is 265. Budgets are presented for the passive scalar variance and its dissipation rate, as well as for the individual scalar flux components. These form a basis for a discussion of modelling issues related to explicit algebraic scalar flux modelling. This revised version was published online in July 2006 with corrections to the Cover Date.     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun     

Analytical series solution for the fully developed forced convection duct flow with frictional heating and variable viscosity

Laminar forced convection flow of a liquid in the fully developed region of a circular duct with isothermal wall is analyzed. The effects of viscous dissipation as well as of temperature dependent viscosity are taken into account. The coupled momentum and energy equations are solved analytically by means of a power series method. Then, reference is made to the Poiseuille model for the temperature change of viscosity. For a fixed value of the axial pressure gradient along the duct, dual solutions are found for the velocity and temperature fields. Although dual solutions correspond to the same value of the axial pressure gradient, they lead in general to different values of the average fluid velocity, of the average fluid temperature and of the wall heat flux. It is shown that, for a given fluid and for a fixed duct radius, the absolute value of the axial pressure gradient has an upper bound above which no steady laminar solution can exist.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

绕壁面小障碍物的湍流边界层研究

采用RNGK－ε模型，对统平板壁面上的条柱、方柱等多种不同形状二维小障碍物的固壁剪切湍流进行数值研究，获得了小障碍物下游回流区及其发展区的时均速度场、回流分离点长度和湍流边界层厚度，计算结果与实验比较吻合良好．结果表明，小障碍物在壁面上的设置，明显地改变了平板壁面边界层的湍流形态和结构．     

NUMERICAL STUDIES OF TRANSITIONAL TURBULENT PULSATILE FLOW IN PIPES WITH RING–TYPE CONSTRICTIONS

Pulsatile flows in the vicinity of mechanical ring-type constrictions in pipes were studied for transitional turbulent flow with a Reynolds number (Re) of the order of 10⁴. The Womersley number (Nw) is in the range 30–50, with a corresponding Strouhal number (St) range of 0·0143–0·0398. The pulsatile flows considered are a pure sinusoidal flow, a physiological flow and an experimental pulsatile flow profile for mechanical aortic valve flow simulations. Transitional laminar and turbulent flow characteristics in an alternating manner within the pulsatile flow fields were studied numerically. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity and turbulent shear stress are smaller during the acceleration phase than during the deceleration period. Various parametric equations have been formulated through numerical experimentation to better describe the relationships between the instantaneous flow rate (Q), the pressure loss (ΔP), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max) for turbulent pulsatile flow in the vicinity of constrictions in the vascular tube. An elliptic relationship has been found to exist between the instantaneous flow rate and the instantaneous pressure gradient. Other linear and quadratic relations between various flow parameters were also obtained.     

Turbulent Couette–Poiseuille flow with zero wall shear

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (u_τ,S) and half the channel height (h) is Re_τ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Re_τ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.     

Application of the method of near-wall boundary conditions to an investigation of turbulent flows with longitudinal pressure gradients

The dynamic and thermal characteristics of steady near-wall boundary layers in flow deceleration regions are studied on the basis of differential turbulencemodels. The method of transferring the boundary conditions from the wall into the flow is tested for flows with variable longitudinal pressure gradients. Using differential turbulence models in the transition and low-Reynolds-number regions near surfaces the effect of the parameters of highly turbulent free stream on the development of dynamic processes in the developed turbulent boundary layer in the flow deceleration region is studied. The calculated profiles of the velocity, the kinetic energy of turbulence, the friction and thermal conductivity coefficients, and the temperature factor are compared with the experimental data in the cases in which the boundary conditions are preassigned both on the wall and in the flow. The effect of an intermediate boundary condition on the results of the calculations is analyzed.     

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.     

波浪与新型双排开孔圆筒防波堤相互作用三维数值模拟

双排开孔圆筒防波堤是基于圆筒、板式结构的一种复合式新型结构型式;基于不可压缩两相流模型建立三维数值波浪水槽,通过RNG k-ε湍流模型进行湍流封闭,并采用TruVOF方法捕捉自由液面,开展波浪与双排开孔圆筒防波堤相互作用数值模拟,探究相对排间距、开孔率对新型双排开孔圆筒防波堤消浪性能的影响,分析了后排开孔圆筒防波堤附近的复杂水动力现象和流动特性.结果表明,在本文研究工况范围内,沿程平均波高随相对排间距的增大先增大后减小,随开孔率的增大而增大,周期对沿程平均波高的影响没有明显规律;当B/D=9, e=23.11%时,新型双排开孔圆筒防波堤消浪效果最优,反射系数在0.4～0.46之间,透射系数在0.3～0.35之间,耗散系数在0.8～0.85之间;自由液面破碎、水气掺混、环状涡运动演化是新型双排开孔圆筒防波堤紊动耗能消波的主要原因;相对排间距会引起后排防波堤附近涡量分布以及剪切层形态的变化,从而导致不同的紊动特性,影响双排开孔圆筒防波堤消浪特性.研究结果可以为新型双排开孔圆筒防波堤工程设计与消浪机理研究提供理论支撑.     

Turbulence Budgets in Buoyancy-affected Vertical Backward-facing Step Flow at Low Prandtl Number

The paper investigates buoyancy impact on the vertical flow over a backward-facing step at low Prandtl number by Direct Numerical Simulation. In particular, the very low Prandtl number of liquid sodium, 0.0088, is considered in the regime of mixed convection, i.e. for Richardson numbers below unity. The effects of buoyancy on mean flow, heat transfer and turbulence are assessed. Buoyancy is found to attenuate recirculation and, consequently, increase heat transfer. Turbulence is decreased in the attached boundary layer for moderate buoyancy impact but surpasses the levels found in forced convection at the largest Richardson number investigated. Beyond the mean flow and second moments, the budgets of turbulent kinetic energy, Reynolds shear stress, temperature variance, and turbulent heat flux components are studied and related to the alterations in the mean field quantities. Due to scale separation, production and dissipation nearly balance for temperature variance while this is not the case for turbulent kinetic energy. Similar findings for the turbulent heat fluxes show that the correlation between temperature and pressure gradient is the most important contribution to the budget aside from production and dissipation. In addition to the physical insight into this flow, the data presented may be used for the validation and improvement of turbulence models for liquid metal flows.     

Towards the numerical simulation of the horizontal slug front

Steps towards the numerical simulation of the flow behind the slug front in horizontal slug flow performed with a streamfunction-vorticity representation of the mean flow and an energy dissipation model for the turbulence are discussed. The flow field consists of two vortices, one saddle point and four stagnation regions. Attention is focused on the following boundary conditions: moving wall jet, moving wall, free jet velocity discontinuity and vertical liquid-gas open surface. A dissipation flux boundary condition is suggested to simulate the interaction of the turbulent eddies with the open surface. A method to assess the necessity to use a transport model equation for the dissipation rather than a geometric specification of a length is suggested. Three different ways to characterize the mixing zone length are proposed.     

A Direct Numerical Study of Transport and Anisotropy in a Stably Stratified Turbulent Flow with Uniform Horizontal Shear

Direct numerical simulations of homogeneous turbulence in stably stratified shear flow have been performed to aid the understanding of turbulence and turbulent mixing in geophysical flow. Two cases are compared. In the first case, which has been studied in the past, the mean velocity has vertical shear and the mean density is vertically stably stratified. In the second case, which has not been studied systematically before, the mean velocity has horizontal shear and the mean density is again vertically stably stratified. The critical value of the gradient Richardson number, for which a constant turbulence level is obtained, is found to be an order of magnitude larger in the horizontal shear case. The turbulent transport coefficients of momentum and vertical mass transfer are also an order of magnitude larger in the horizontal shear case. The anisotropy of the turbulence intensities are found to be in the range expected of flows with mean shear with no major qualitative change in the range of Richardson numbers studied here. However, the anisotropy of the turbulent dissipation rate is strongly affected by stratification with the vertical component dominating the others. This revised version was published online in July 2006 with corrections to the Cover Date.