Experimental investigation of turbulent entrainment in an annulus with moving sidewalls

The establishment of a turbulent mixed layer in a two-layer stratified shear flow, and the rate of entrainment into that layer were studied experimentally in a modified annulus. The modification of the conventional annulus was made by replacing the upper rotating screen with inner rotating sidewalls, extending over the upper half of the channel, so that the flow in the upper layer was nearly uniform and almost laminar, while the bottom layer was quiescent. Vertical density profile measurements were conducted using single electrode conductivity probes. The flow was visualized during the various stages of the experiment using the hydrogen bubble technique.After the start of the sidewalls rotation, the upper layer accelerates from rest, and consequently a transition process is taking place during which the initial density interface between the two layers is developed into a turbulent mixed layer. This turbulent layer is bounded by two sharp interfaces, each separating it from an outer non-turbulent zone. The generation of this five-layer structure seemed to be dominated by instabilities activated by the velocity difference between the upper and lower layer.Once a turbulent mixed layer is formed, entrainment of nonturbulent fluid into that layer is taking place causing its thickness to increase continuously. Depending on the overall Richardson number, based on the channel width, the slope of the entrainment law curve was found to have two different values, each indicating the dominance of a different source of turbulent energy production. For relatively low Richardson numbers, the slope is close to -1.8, implying that the velocity shear across each interface contributes significantly to the entrainment. On the other hand, for larger Richardson numbers the slope is about -1.25, in agreement with previous results of shear-free entrainment experiments.The measured velocity profiles indicate that as long as the mixed layer is not too thick, the radial inhomogeneities are small and the flow may be considered as nearly one-dimensional. It seems, therefore, that for the understanding of entrainment processes occurring in realistic stratified flows, the modified annulus is a more reliable tool than the conventional one.     

稳定分层流密度界面处湍流混合与分形结构

采用室内混合箱研究稳定分层流(上层淡水、下层盐水) 无剪切密度界面处的湍流混合与分形结构. 湍流通过浸没在盐水层中的振动格栅产生, 密度界面结构通过在盐水层中添加荧光剂或染料可视化, 共进行12 组实验. 实验观测并记录了:(1) 淡、盐水密度界面距混合箱底部的平均高程(h);(2) 淡、盐水层的密度(ρ₀,ρ), (3) 淡、盐水密度界面. 其中, 淡、盐水密度界面通过照片、录像进行记录. 观测结果用于计算:(1) 盐水层密度;(2) 卷挟速度, (3) 整体理查孙数(Ri_o), (4) 二维、三维密度界面, (5) 二维、三维密度界面的分形维度. 结果分析发现:(1) 湍流卷挟率随Rio 增大而减小, 并且满足Ri_o的-3=2 或-7=4 幂律;表明随着湍流强度的减弱, 混合的速度也越来越缓慢;(2) 二维密度界面分形维度大于1, 三维密度界面分形维度大于2;表明二维、三维密度界面存在分形结构;(3) 分形维度随Ri_o的增大而减小;表明随着湍流强度的减弱, 密度界面也越来越趋于光滑.      

Experiments on the spreading of shear-free turbulence under the influence of confinement and rotation

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Günther (Fluid Dyn Res 33:453–476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.     

Measurement of interfacial distortions at a stratified entrainment interface

A laser beam scanning technique was used to measure the rms amplitude of the largest wave (interfacial distortion) that is present at the entrainment interface of a stratified fluid. Both linearly-stratified and two-layer fluid systems, subjected to entrainment by oscillating-grid induced shear-free turbulence, are considered. The measurements were found to be in general agreement with a theory due to Long (1978), which predicts /D _e Ri ^–3/4 , where D _e is the mean thickness of the mixed layer and Ri is the appropriately defined bulk Richardson number at the interface.     

垂直上升气液环状流流动参数的数值计算

提出了一个新的气核-液膜耦合模型来求解垂直上升气液环状流在充分发展段的流动参数.本模型考虑了液膜、气核以及它们之间的相互影响和作用.模型中基本的气核区域和液膜区域的质量和动量方程由Fluent6.3.26进行求解,而液滴方程以及相界面上的夹带和沉积作用通过用户自定义接口函数UDF(User Defined Functi...     

The turbulent/non-turbulent interface in an adverse pressure gradient turbulent boundary layer

The turbulent/non-turbulent interface (TNTI) in an adverse pressure gradient (APG, β = 1.45) turbulent boundary layer (TBL) is explored here by using direct numerical simulation (DNS) data; β is the Clauser pressure gradient parameter. For comparison, the DNS data for a zero pressure gradient (ZPG) TBL is included. The interface is extracted with an approach based on enstrophy criteria. Depending on the enstrophy, the outer boundary layer flow can be classified into the free stream, boundary layer wake, and intermittent flow regimes. The fractal dimension of the interface is obtained by using the box-counting algorithm, and was found to be constant over a long range of box sizes. The TNTI shows a monofractal behavior. The geometric complexity of a TNTI can be determined in terms of the genus, which is defined as the number of handles in a geometric object. We examine the volume and projection area of the genus of the TNTI to analyze the entrainment process. The geometric complexity of the APG TBL interface and the local entrainment are greater than those of the ZPG TBL, as is evident in the increases in the genus near the interface. The local entrainment velocity is dominantly affected by the viscous diffusion at the interface.     

The flow structure in the front of a moving surface layer

Summary Behind the frontal wedge of a moving surface layer there is a zone of entrainment in which the flow is turbulent due to the onset of a Kelvin-Helmholtz instability. The entrainment coefficient is inversely proportional to the Richardson number. In the turbulent region the gradient Richardson number approached a constant value less than 1/4. The layer thickness and the mean velocity depend on the salt concentration of the underlying fluid. Finally the turbulence decayed leaving a stable interface and the layer behaved much like a free homogeneous flow over a solid boundary.

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Übersicht Hinter der keilförmigen Front einer fließenden Schicht gibt es eine Mischungszone, in der die Strömung turbulent ist. Die Turbulenz entsteht durch eine Kelvin-Helmholtz Instabilität. Der Ansaugbeiwert der turbulenten Strömung verhält sich umgekehrt zur Richardsonschen Zahl. In der turbulenten Strömung nähert sich die Richardsonsche Zahl einer konstanten Zahl kleiner als 1/4. Die Dicke und die mittlere Geschwindigkeit der Schicht hängt sehr von der Dichte der unteren Flüssigkeit ab. Schließlich stirbt die turbulente Strömung ab, und die Schicht fließt wie eine homogene Strömung längs einer ebenen Platte.

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The work described herein was carried out as part of a research programme of the Hydraulics Research Station, and the paper is published by permission of the Director of Hydraulics Research. The author wishes also to express his thanks to Mr. J. A. Weller for his help in measurement, and to a referee for his helpful comments.     

Turbulent separated reattached flow in a two-dimensional curved-wall diffuser

A turbulent separation-reattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter. The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel. At the inlet of the diffuser, Reynolds number based on the diffuser height is 1.2×10⁵ and the velocity is 25.2m/s. The results of experiments are presented and analyzed in new defined streamline-aligned coordinates. The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress. A scale is formed using the maximum Reynolds shear stresses. It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law exists in the forward shear flow. Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model. The length scale is taken from that developed by Schofield and Perry. The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield-Perry velocity scale as well as the edge velocity of the boundary layer. The results of these experiments are presented in this paper.     

Experimental study of turbulence in isothermal and stably stratified homogeneous shear flows: Mean flow measurements

The evolution of freestream turbulence under the combined action of linear shear and stable linear temperature profile is investigated. The experiment is carried out in a small, open circuit, low-speed test cell that uses air as working fluid. The temperature gradient formed at the entrance to the test section by means of an array of 24 horizontal, differentially heated elements is varied to get a maximum Brunt-Vaisala frequency N_o[=({g/T_m}{∂T/∂y})^1/2] of 3.1⁻¹. Linear velocity profiles are produced using screens of variable mesh size. The Reynolds number Re_M based on centre-line velocity and mesh size is varied from 80 to 175. Isothermal studies are carried out in four different experiments with varying velocity gradients. The effect of inlet turbulence level on growth of turbulence is studied in these flows by keeping the shear parameter Sh (=(x/u)(∂u/∂y)) constant. The range of shear parameters considered is 2.5–7.0. Shear and stratification combined produce a maximum gradient Richardson number Ri_g (= N_o²/(∂u/∂y)²) of 0.0145. Results have been presented in terms of evolution of variance of velocity fluctuations, Reynolds shear stress and temperature fluctuations. Measurements show the following: In isothermal flows the growth rate of turbulence quantities depends on both shear parameter and inlet turbulence level. There are distinct stages in the evolution of the flow and that can be identified by the power-law exponent of growth of turbulence. Shear is seen to promote the growth of turbulence and accelerate it towards a fully developed equilibrium state. Stratification initially suppresses the growth of turbulence and, hence, enhances the degree of underdevelopment. Under these conditions shear becomes active and subsequently enhances the growth rate of turbulence quantities.     

Flow characterization of diffusion flame oscillations using particle image velocimetry

Particle image velocimetry (PIV) was used to measure velocity fields inside and around oscillating methane-air diffusion flames with a slot fuel orifice. PIV provided velocity and directional information of the flow field comprised of both the flame and air. From this, information on flow paths of entrained air into the flame were obtained and visualized. These show that at low fuel flow rates for which the oscillations were strongest, the responsible mechanism for the oscillating flow appeared to be the repetitive occurrence of flame quenching. PIV findings indicated that quenching appears to be associated primarily with air entrainment. Velocity was found to be considerably larger in regions where quenching occurred. The shedding of vortices in the shear layer occurs immediately outside the boundary of the flame envelope and was speculated to be the primary driving force for air entrainment.     

Laboratory observations of interactions of forced plumes with stratified shear layers

Plumes of fluid are often observed in nature to interact with stratified shear layers. Examples of this include chimney plumes hitting inversion-layer ceilings; sewage plumes impinging on unmixed fresh/saltwater interfaces; descending plumes of cold water formed at ice-leads interacting with the oceanic thermocline; and volcano plumes interacting with atmospheric interfaces. Controlled laboratory studies of these phenomena have not previously been described in the literature, and as a result there is a lack of understanding regarding their morphology and dynamics. Thus, a novel set of experiments is described here in which the behaviour of a turbulent plume is observed in the presence of a two-layer ambient. The lower layer, into which the plume initially emerges, is quiescent and at a relatively high density. The upper layer is forced to flow uniformly across the top of the lower layer, and has a lower density. The flow of the resulting plume is characterised by (a) its vertical and lateral spreading in the lower layer; (b) the nature of its extension upstream and downstream at the interface; and (c) the extent to which it penetrates into the upper layer. The behaviour is found to be governed by three non-dimensional parameters: the initial gradient Richardson number of the interface Ri_G, the ratio of the upper layer crossflow speed to the speed of the plume when it first impinges on the interface U_F/U_PI, and the ratio of the plume Monin–Obukhov lengthscale to the lower layer depth L_MO/H_L. Regime diagrams are presented showing the effects of changing these parameters on the plume flow, quantitative relationships are determined, and practical applications of the results are considered.     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel

By method of the Laplace transform, this article presents semi-analytical solutions for transient electroosmotic and pressure-driven flows (EOF/PDF) of two-layer fluids between microparallel plates. The linearized Poisson-Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio ε , density ratio ρ , pressure ratio p, viscosity ratio μ of layer II to layer I, interface zeta potential difference △ψ, interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity α , and the normalized pressure gradient B on transient velocity amplitude are presented.We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The velocity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF velocity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers (h1 and h2 ) and pressure gradient on the velocity are also investigated.     

Laboratory experiments of a jet impinging on a stratified interface

 The entrainment rates of vertical and inclined jets impinging on a stratified interface are measured in water tank experiments. At moderate Richardson number, the entrainment rate of the vertical jet is proportional to Ri ^-1/2, independent of Reynolds number. The inclined jets are tilted at 15° from the vertical. In one case, the jet nozzle is rotated about a vertical axis, so that the inclined jet precesses, while in the other, it is stationary. The inclined jets entrain at a rate proportional to Ri ^-3/2, whether precessing or not. This behavior is consistent with a new model of stratified entrainment which accounts for vortex persistence. Received: 15 October 1996/Accepted: 19 December 1996     

Influence of flow path modification on oscillation of cavity shear layer

This study investigates the influence on the oscillating characteristics of a cavity shear layer by introducing either a sloped bottom or a flow path modifier at the bottom of the cavity. All the experiments are performed in a recirculating water channel. The laser Doppler velocimetry system and the laser sheet technique are employed to perform the quantitative velocity measurements and the qualitative flow visualization, respectively. The Reynolds number, based on the momentum thickness at the upstream edge of the cavity, is kept at about Re _{θ 0}=194 ± 3.4. It is found that, in addition to the feedback effect, the upstream moving part of the recirculating flow inside the cavity also plays an important role in changing the oscillating characteristics of the unstable shear layer. As the bottom of the cavity is either negatively or positively sloped, the oscillating characteristics of the cavity shear layer are modified to different extents. Significant reduction of the oscillating amplitude within the cavity is found while the bottom slope increases up to d/L=± 2/5. As the bottom slope further increases up to d/L=± 1/2, the self-excited oscillation is completely suppressed. In addition, the ability to suppress the self-excited oscillation by the negative bottom slopes is superior to that in the case of a positive bottom slope. Depending upon the fence locations, the upstream moving part of the recirculating flow will perturb the unstable shear layer at different x/L locations, leading to different oscillating amplitudes. The ability to promote the enlarged oscillating amplitude of the unstable shear layer is better for a fence inclined at a positive angle than for one at a negative angle. Received: 31 May 2000/Accepted: 11 January 2001     

DNS of a Laminar Separation Bubble in the Presence of Oscillating External Flow

A three-dimensional Direct Numerical Simulation (DNS) of a laminar separation bubble in the presence of oscillating flow is performed. The oscillating flow induces a streamwise pressure gradient varying in time. The special shape of the upper boundary of the computational domain, together with the oscillating pressure gradient causes the boundary layer flow to alternately separate and re-attach. When the inflow decelerates, the shear layer starts to separate and rolls up. Simultaneously the flow becomes 3D. After a transient period, the phase-averaged reverse flow inside the separation bubble reaches speeds ranging from 20 up to 150% of the free-stream velocity. During these phases, the flow is absolutely unstable and self-sustained turbulence can exist. When the inflow starts to accelerate, a spanwise roll of turbulent flow is shed from the shear layer. Shortly after this, the remainder of the separation bubble moves downstream and rejoins with the shed turbulent roll. During the flow-acceleration phase, a patch of laminar boundary layer flow is obtained. Along the flat plate, a series of turbulent patches of flow travelling downstream, separated by laminar flow can be observed, reminiscent of boundary layer flow in a turbine cascade with periodically appearing free-stream disturbances.     

Large eddy simulation of boundary layer flow under cnoidal waves

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers.Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before.Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.     

Experimental study of thermal mixing layer using variable temperature hot-wire anemometry

The buoyancy effects on the development of the thermal mixing layer downstream from a horizontal separating plate were studied by comparing stable and unstable counter-gradient configurations. In this study, the novel experimental technique called parameterizable constant temperature anemometer, proposed by Ndoye et al. (Meas Sci Technol 21(7):075401, 2010), was improved to make possible the simultaneous measurement of temperature and two velocity components with an x-wire probe. The buoyancy effects on the flow are discussed through the transport equations of turbulent kinetic energy and temperature variance. In view of the low Richardson numbers at stake (Ri _f < 0.03), the buoyancy forces appeared logically to be quantitatively negligible compared to the main driving forces, but such a low-energy forcing mechanism was in fact sufficient in unstable configurations to increase the shear stress and the expansion rate of the mixing layer significantly, both phenomena being associated with enhanced production of turbulence.     

Non-oscillating/Oscillating Shear Layer over a Large Deep Cavity at Low-Subsonic Speeds

The flow over a deep cavity at low subsonic velocity is considered in the present paper. The cavity length-to-depth aspect ratio is L/H = 0.2. Single hot-wire measurements characterized the incident turbulent boundary layer and show the influence of the cavity on the streamwise statistic components just downstream from the cavity. The streamwise mean and fluctuating velocity profiles are affected by the cavity. PIV measurements reveal the presence for ejection-like events responsible of local perturbations of the skewness and the flatness coefficients. Time-resolved PIV technic is also used to characterize phase properties of shear layer oscillating cycle. It is shown that for deep cavity with first Rossiter mode, only one vortical structure is formed at the cavity leading edge. Then, it grows while convecting downstream along the shear layer. A well-defined ejection process begins after the vortex impact near the cavity downstream corner. A cylinder device placed spanwisely near the cavity leading edge eliminates the resonance and highly modifies the behavior of the shear layer flow. In fact, the shear layer could be divided into upper and lower parts with different structure aspects.     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i