Experimental Determination of Lagrangian Velocity Statistics in Turbulent Pipe Flow

The calculation of Lagrangian statistics out of experimentally determined data from homogeneously seeded inhomogeneous turbulent flows is far from straightforward since statistical properties are position-dependent, necessitating local sampling. Two solutions for the preferential sampling of faster particles at a certain position in the flow are proposed. The performance of both methods was tested using DNS calculations for turbulent pipe flow. Both methods show a good performance for various statistical properties, thus providing two reliable ways to analyze experimental data from inhomogeneous turbulent flows.     

Turbulent Flow Produced by Piston Motion in a Spark-ignition Engine

Turbulence produced by the piston motion in spark-ignition engines is studied by 2D axisymmetric numerical simulations in the cylindrical geometry as in the theoretical and experimental work by Breuer et al. (Flow Turbul Combust 74:145, 2005). The simulations are based on the Navier–Stokes gas-dynamic equations including viscosity, thermal conduction and non-slip at the walls. Piston motion is taken into account as a boundary condition. The turbulent flow is investigated for a wide range of the engine speed, 1,000–4,000 rpm, assuming both zero and non-zero initial turbulence. The turbulent rms-velocity and the integral length scale are investigated in axial and radial directions. The rms-turbulent velocity is typically an order-of-magnitude smaller than the piston speed. In the case of zero initial turbulence, the flow at the top-dead-center may be described as a combination of two large-scale vortex rings of a size determined by the engine geometry. When initial turbulence is strong, then the integral turbulent length demonstrates self-similar properties in a large range of crank angles. The results obtained agree with the experimental observations of Breuer et al. (Flow Turbul Combust 74:145, 2005).     

Reynolds Number Dependence of Velocity Structure Functions in a Turbulent Pipe Flow

Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR _λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized second-order structure functions show a continuous evolution withR _λ. In particular, the scaling exponentζ _v , corresponding to the v structure function, continues to increase with R _λ in contrast to the nearly unchanged value of ζ _u . The Kolmogorov constant for δu shows a smaller rate of increase with R _λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR _λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the centreline of a fully developed channel flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Universal Velocity Defect Law for the Turbulent Boundary Layer

Turbulent plane boundary layer flows of an incompressible fluid are considered. A refinement of the known Coles wake law is proposed. This refinement makes it possible to ensure the smooth matching of the turbulent boundary layer velocity profile with the outer flow and to extend the range of validity of the law to the case of large positive pressure gradients. The accuracy of the analytical approximation obtained is verified by comparison with the known experimental equilibrium velocity profiles. Using the approximation proposed, a relation for calculating the cross-sectional distribution of the Reynolds stress in the equilibrium boundary layer is derived. The pressure distributions for which the equilibrium turbulent boundary layer flows are single- and two-valued are distinguished.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 89–101.Original Russian Text Copyright © 2005 by Mikhailov.     

Dynamic Response of Swirl Stabilized Turbulent Premixed Flames Based on the Helmholtz-Hodge Velocity Decomposition

The dynamic response of fully premixed flames stabilized in strongly swirled flows undergoing vortex breakdown is investigated with axisymmetric unsteady RANS simulations. The analysis relies on the well known Helmholtz-Hodge decomposition of the velocity field into its irrotational and rotational components. A novel methodology based on the linearization of the progress variable transport equation is developed to determine the separate contribution of these velocity components to the Flame Transfer Function (FTF). Due to the phase delay between the convected tangential velocity and instantaneously propagating axial velocity perturbations, a non-monotonic frequency dependence of the swirl number amplitude downstream the swirl generator is detected. In line with experimental observations, such non-monotonic frequency dependence is found also for the amplitude and phase of the FTF. This behaviour is associated here with rotational velocity perturbations generated by the Central Recirculation Zone (CRZ) generated by the phenomenon of vortex breakdown which, responding in a fashion totally similar to the swirl number perturbation, produces flame surface area fluctuations with the same distribution versus frequency.     

Investigation of Different Condensation Regimes in Isobaric Turbulent Air-Steam Jets

Condensation in axisymmetric turbulent air-steam jets is studied theoretically and experimentally under bench experiment conditions in which a hot mist jet is injected from a nozzle into air. On the basis of the physico-mathematical model developed, four problems are considered: homogeneous condensation in the jet at a fairly low ambient air temperature, heterogeneous condensation on particles introduced into the jet at the nozzle outlet, heterogeneous condensation on particles ejected into the jet from the surrounding space, and condensation on ions entering the jet from a corona point on the flow axis. The local characteristics of the dispersed phase (mean particle size, standard deviation of the particle size, particle number and volume concentrations) and its integral characteristics (coefficient of vapor conversion into condensed phase and the optical thickness of the jet in different sections) are determined. The calculation results are compared with experimental data. As an application of the model developed, the characteristics of heterogeneous condensation in the jets of certain modern aircraft engines (IL-96-300, Tu-204, MiG-29, Boeing-707) are found on the assumption that the condensation occurs on particles entering the jet at the nozzle outlet and the particle growth rate in all stages (including the initial stage of particle irrigation) coincides with the growth rate of liquid drops.     

Large-Scale Flows in a Turbulent Convective Layer with an Immersed Moving Thermal Insulator

Large-scale motions developing against the background of developed convective turbulence in a rectangular vessel heated from below, in which a horizontal disk floats freely at a fixed depth, are studied experimentally. It is found that regular or chaotic oscillations may develop in the vessel. Transitional regimes characterized by interruptions of the motion or frequency variations are also possible. A regime map in the Rayleigh number — relative disk depth plane is constructed. It is shown that in the regular-oscillation regime the oscillation frequency is a linear function of the Rayleigh number.     

Similarity Laws for the Velocity Distribution and the Reynolds Tensor Components in the Wall Region of a Turbulent Boundary Layer with Injection and Suction

Similarity laws of the distributions of the average velocity, tangential stress, and mean-square transverse velocity fluctuation are established in an intermediate zone of a turbulent boundary layer with injection and suction. This zone is located in the neighborhood of the wall outside the viscous sublayer. The similarity relationship for the velocity profile is a generalization of the well-known logarithmic law to include the case of the presence of a mass flow at the wall.     

Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach is derived from the Reynolds averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k– model are not consistent with most of the new turbulent scaling laws.     

Modeling Turbulent Droplet Motion in Vaporizing Sprays

The present article is concerned with the influence of turbulent gas-velocity fluctuations on both droplet dispersion and droplet-gas slip velocity in the context of spray simulation. The role of turbulence in generating slip and thus enhancing interphase heat and mass transfer has so far received little attention and is investigated in this work. A model for turbulent gas-velocity fluctuations along droplet trajectories is presented and is first tuned to reproduce elementary dispersion phenomena. It is then shown to give good results for more general dispersion problems as well as for slip velocities. As a fundamental source of information and for the purpose of model validation and comparison, direct numerical simulation (DNS) of droplet motion in homogeneous isotropic steady turbulence (HIST) is used. Dispersion of “injected” droplets (i.e. droplets under the influence of drift due to high injection velocity) as well as slip velocities for linear and nonlinear droplet drag are studied, and reasonable agreement is found with the model. The distributions of the slip velocity are found to be very similar for linear and highly nonlinear drag law. The present model is also used to investigate the influence of turbulence on droplet penetration. Comparison is made with an eddy-interaction model (the KIVA-2 model), which reveals various weaknesses of this model, in particular the underprediction of average slip velocity. The influence of slip due to turbulence on vaporization is shown for a fuel spray injected into a premix gas-turbine combustor. The classical eddy-interaction model is seen to underestimate the rate of vaporization due to the underprediction of slip. This revised version was published online in July 2006 with corrections to the Cover Date.     

气固两相流场的湍流颗粒浓度理论模型

本文进行了气固两相流动颗粒湍流扩散现象的理论分析，提出了颗粒湍流扩散系数和气流弥散效应二个颗粒湍流模化新概念，在此基础上建立了气固两相流场湍流颗粒浓度模型。理论模型包括离心力和其它外加力场作用下颗粒运动和浓度分布的计算方法。运用湍流颗粒浓度模型，对直管气固两相流动、受限射流气固两相流动和９０°弯管气固两相流动等三种流动做了数值模拟，计算获得颗粒速度、颗粒浓度等主要流动参数。讨论了湍流颗粒浓度模型的适用性。     

Organizational Modes of Large-Scale Vortices in an Axisymmetric Turbulent Jet

Large vortices occurring in the axial plane of a self-similar axisymmetric turbulent jet are educed by spatially filtering PIV data. First, the instantaneous PIV frame is convolved with a Gaussian kernel to obtain a smooth (low-pass) field. Next, the low-pass field is Galilean transformed to expose the large vortices residing near the edges of the jet. Large vortices tend to organize themselves in preferred modes; evidence of ring and helical modes is revealed by Galilean transformation of the low-pass filtered field. Both modes seem to occur prominently in jets, with the helical mode being the more frequent. The overall diameter of both ring and helical modes is comparable with the local jet width. The low-pass field occasionally exhibits arrowhead shaped structures with large entrainment at their downstream tips. Stochastic estimates computed from the Galilean-transformed low-pass filtered field indicate that jet meander and a sweep-in of ambient fluid are sufficient to reconstruct large vortices. The frequency of occurrence of modes agrees with previously quoted results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulation and Modelling of Turbulent Trailing-Edge Flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–ε) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Kármán vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Particle Clustering in Isotropic Turbulent Flow

A kinetic statistical model for describing the dispersion and clustering of heavy particles in homogeneous isotropic turbulence is presented. The model developed is used for calculating the relative velocities and the radial distribution function of a pair of particles in a steady suspension. The results obtained are compared with the known data obtained by direct numerical simulation.     

Effect of the Turbulent Energy Gradient and the Presence of a Wall on the Turbulent Process of Momentum Transport

A mathematical model of turbulent transport processes is modified to make allowance for the turbulent energy gradient and the presence of walls. The modification consists in making the variance tensor in the Gaussian probability density distribution for the initial mole velocities anisotropic for nonzero turbulent energy gradient and a ratio of the turbulence scale to the distance from the wall of the order of unity. Formulas for the variance tensor components are derived and the empirical coefficients of these formulas are determined. The expression for the dimensionless turbulent friction stress is compared with experimental data for three boundary-layer-type flows, namely, in the wake of a cylinder, in the boundary layer on a flat plate, and in a channel with parallel walls.     

Electric Charging of Soot Particles in Aircraft Engine Exhaust Plumes

A physico-mathematical model is developed and the variation of the charge on soot particles interacting with positive and negative ions in the exhaust of modern subsonic aircraft is simulated numerically. The calculations are based the gas dynamic system of equations for an axisymmetric turbulent isobaric jet. The system is supplemented with the thermodynamic relations, kinetic equations, and equations for the turbulent viscosity. Ion and neutral and charged soot particle concentration distributions over the exhaust jet on the ground and under cruising flight conditions are obtained.     

Simulation and Modelling of a Skewed Turbulent Channel Flow

A time-dependent three-dimensionally skewed flow is investigated using direct numerical simulations of the incompressible Navier-Stokes equations. The effect on the instantaneous and mean turbulent field is investigated. Instantaneous flowfields reveal that the skewing has the effect of initially reducing the strength and height of quasi-streamwise vortices of both signs of rotation with respect to the skewing. A mechanism for this process is put forward. The mean flowfields show drops in turbulence quantities such as turbulence kinetic energy. In addition to this, two-equation turbulence modelling of the flow is carried out. This highlights a deficiency, in that the standard turbulence models are unable to capture the drop in turbulence intensity due to the skewing. A modification based on the exact dissipation equation is found to significantly improve the model behaviour for this flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

壁湍流边界层奇异标度律的实验研究

采用热线风速仪对平板湍流边界层的流向速度进行测量,用速度结构函数研究不同尺度结构标度律的变化规律,结果显示小尺度区的概率密度曲线尾部明显偏离高斯型,说明高幅值间歇性事件占的份额较多;惯性子区的曲线向高斯型靠近,间歇性事件所占份额减少;大尺度结构的曲线趋于高斯型,间歇性事件所占份额最小。在耗散区、惯性子区和较大的尺度结构区存在大小不同的绝对标度指数,越靠近壁面这些区域的标度指数均越偏离p/3而逐渐变小。绝对标度指数与边界层位置有关,在缓冲层各阶标度指数与线性标度律偏差很大,显示较强的奇异性,当过渡到对数层及外区,标度指数逐渐增大,接近均匀各向同性湍流的状态。缓冲层、对数层及外区具有各异的绝对标度指数增长率,与各层的不同湍流结构特征和运动形式有关。     

Turbulent Structure of a Gas-Liquid Impinging Jet

The turbulent structure of a submerged axisymmetric impinging jet containing small gas bubbles is studied experimentally under conditions of periodic external excitation. On the basis of measuring the surface-friction pulsatory component in the jet impinging on an obstacle, the effect of the suppression of large-scale eddies at large gas volume fractions is registered. The conditions of resonant growth of coherent structures and the suppression of wide-band turbulence are determined for both the single-phase and the two-phase impinging jet. An analysis of the development of different pulsatory friction components in the impinging-jet gradient region is presented.