Jet noise prediction using different turbulent scales

The turbulent energy dissipation rate time-scale and length-scale has been routinely used for the prediction of noise from turbulent flows, particularly jet streams. However, this is not the only possible choice. In general, scales evolving in a turbulent medium are threefold. First, those associated with the mean flow; second, those attributed to the turbulence and the mean flow interactions; and third, scales related to the turbulence-turbulence interactions. In this paper, special attention will be paid to further study of the underlying physics of aerodynamic noise by examining various time-scales. To do so, three time scales, namely, dissipation, production, and strain rate time scales, are defined and used in the source modelling to emphasis the effect of the turbulence structures at different jet regions on the jet noise production mechanism. The required mean value and turbulence parameters are obtained using a modified k − ∈ turbulence model, and Lighthill’s Acoustic Analogy is used for the prediction of the emanated noise. The text was submitted by the authors in English.     

A turbulence characteristic length scale for compressible flows

The current RANS models are generally established and calibrated under incompressible condition and these kinds of models could succeed in predicting many features of incompressible flows. However, these models extended to the high-speed, compressible flows are always less accurate. In the paper, a compressible von Kármán length scale is proposed for compressible flows considering the variable densities. It contains no empirical coefficients and is based on phenomenological theory. In the turbulent kinetic equation, the extra unclosed terms induced by non-constant densities are treated as dissipation terms and the equation is closed algebraically via the introduction of the von Kármán length scale. The original and the proposed von Kármán length scale lead to two different kinds of SAS (scale adaption simulation) models, KDO (turbulence kinetic energy dependent only) and CKDO (compressible KDO), respectively. Compressible mixing layer with significant compressibility is studied within standard k–?, k–ω, KDO turbulence models and their compressible versions. The compressibility effects such as the reduced mixing layer thickness, growth rate and turbulence intensity can be reproduced by CKDO. The new length scale can improve the performances of the model in predicting the mixing layer thickness, stream-wise velocity and Reynolds shear stresses when the convective Mach number is 0.8. Besides, the new length scale also leads to accurate computed growth rate when the convective Mach number ranges from 0.1 to 1.0.     

On the use of spires for generating inflow conditions with energetic coherent structures in large eddy simulation

While it has long been a practice to place spires near the inlet of a wind tunnel to quickly develop a turbulent boundary layer with similarities to an atmospheric boundary layer, this has not been the case for creating turbulent boundary layer inflow in large eddy simulations (LESs) of turbulent flows. We carry out LES with the curvilinear immersed boundary method to simulate the flow in a wind tunnel with a series of spires in order to investigate the feasibility of numerically developing inflow conditions from a precursory spire LES and assessing the similarities of the turbulence statistics to those of an atmospheric boundary layer. The simulated mean velocity field demonstrates that a turbulent boundary layer with height equal to the spire height develops very quickly, within five spire heights downstream. The major attribute of using spires for precursory simulations is the spatially evolving coherent structures that form downstream of the spires offering a range of length scales at both the vertical and streamwise directions allowing multiple turbulent inflow conditions to be extracted from a single simulation. While the distribution of length scales far from the spires resembles an atmospheric boundary layer, some turbulence statistics have some significant differences.     

横向粗糙元壁面槽道湍流的大涡模拟研究

采用大涡模拟和浸没边界法相结合对不同高度和不同间距横向粗糙元壁面槽道湍流进行了模拟,得到了光滑壁面和粗糙壁面湍流的流向平均速度分布,雷诺剪切应力,脉动速度均方根和近壁区拟序结构。结果发现横向粗糙元降低了流向平均速度,增大了流动阻力,粗糙壁面湍流的雷诺剪切应力大于光滑壁面。粗糙元降低了流向脉动速度,增强了展向和法向脉动速度。粗糙元高度越高,对湍流流动影响越大,而粗糙元间距对湍流统计特性的影响不大。粗糙壁面仍然存在着和光滑壁面类似的条带结构。     

Structure functions of quasi-two-dimensional turbulence in a laboratory experiment

The results of experiments for turbulent flows in a thin layer of conducting fluid above a solid surface generated by the Ampere force when passing a current and under the action of a spatially periodic magnetic field are considered. The statistical characteristics of the flows are shown to exhibit three-dimensional (3D) dynamics even on horizontal scales exceeding the layer thickness by an order of magnitude. In this case, the third-order longitudinal structure functions of the velocity field are approximately linear in spatial displacement and negative, as in 3D turbulence, due to the dominant contribution of energy dissipation when the boundary condition for adhesion on the lower surface is met. The dissipation and basic energy production terms are estimated for the energy balance equation.     

On mean flow universality of turbulent wall flows. II. Asymptotic flow analysis

Understanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed.     

网格湍流对剪切层中预混火焰结构的影响

本文研究网格湍流对射流剪切层以及建立在其中的预混火焰的影响。利用热线风速仪测量射流的速度场,发现网格湍流使剪切层内湍流强度明显降低,抑制了低频速度脉动,同时增加了湍动能在小尺度脉动上的分配,使湍流更趋于各向同性,这表明网格湍流抑制了剪切层内的大涡和拟序结构。用细丝热电偶测量了火焰温度,结果显示网格湍流使火焰前峰的低频大幅摆动减少,小尺度皱褶增加,火焰区平均温度更高,说明网格湍流有利于剪切层中预混火焰的强化和稳定。     

Lagrangian Particle Approach to Large Eddy Simulations of Hydrodynamic Turbulence

The flux of energy from large to small scales in hydrodynamic turbulence controls the dissipation of energy at a given scale in the fluid. An accurate parametrization of this flux is a prerequisite in order to devise reliable methods to simulate turbulent flows without resolving all the scales of motion. This problem is discussed in the context of a particle method based on the Smooth Particles Hydrodynamics algorithm. Motivated by the von Karman–Howarth–Kolmogorov exact relation for the energy flux, and by Lagrangian dynamics considerations we postulate an energy transfer term which is quadratic in the velocity and formally time reversal invariant. The numerical simulation of the model however is observed to spontaneously break the time reversal symmetry, demonstrating that the proposed term acts on average as the desired eddy damping.     

Energy spectra stemming from interactions of Alfvén waves and turbulent eddies

We present a numerical analysis of an incompressible decaying magnetohydrodynamic turbulence run on a grid of 1536{3} points. The Taylor Reynolds number at the maximum of dissipation is approximately 1100, and the initial condition is a superposition of large-scale Arn'old-Beltrami-Childress flows and random noise at small scales, with no uniform magnetic field. The initial kinetic and magnetic energies are equal, with negligible correlation. The resulting energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectral law compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfvén waves; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k{perpendicular}{-2} spectrum, the perpendicular direction referring to the local quasiuniform magnetic field.     

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.     

Generation of magnetic field by combined action of turbulence and shear

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is lB proportional S(-1/2) and the growth rate is gamma proportional S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.     

Experimental measurement of wall shear stress in strongly disrupted flows

Mean and fluctuating wall shear stress is measured in strongly disrupted cases generated by various low-porosity wall-mounted single- and multi-scale fences. These grids generate a highly turbulent wake which interacts with the wall-bounded flow modifying the wall shear stress properties. Measurement methods are validated first against a naturally growing zero pressure gradient turbulent boundary layer showing accuracies of 1% and 4% for extrapolation and direct measurement of the mean shear stress respectively. Uncertainty associated with the root mean square level of the fluctuations is better than 2% making it possible to measure small variations originating from the different fences. Additionally, probability density functions and spectra are also measured providing further insight into the flow physics. Measurement of shear stress in the disrupted cases (grid+TBL) suggest that the flow characteristics and turbulence mechanisms remain unaltered far from the grid even in the most disrupted cases. However, a different root mean square level of the fluctuations is found for different grids. Study of the probability density functions seem to imply that there are different degrees of interaction between the inner and outer regions of the flow.     

Kolmogorov scaling of turbulent flow in the vicinity of the wall

How to scale even the simplest of turbulent flows continues to be a cause for considerable controversy. In the present research, a data base compiling results from channel flow direct numerical simulations and turbulent boundary layer experiments is employed to investigate the properties of shear and normal Reynolds stresses very close to the wall. Two types of scaling based on Kolmogorov length and velocity scales are analyzed. It is shown that it is highly likely that large length scales of the order of the channel half-width or the boundary layer thickness play an important role even in the innermost regions of wall-bounded turbulent flows, which hints at the persistence of Reynolds number effects in even high Reynolds number flows.     

Flow and mixing fields of turbulent bluff-body jets and flames

The mean structure of turbulent bluff-body jets and flames is presented. Measurements of the flow and mixing fields are compared with predictions made using standard turbulence models. It is found that two vortices exist in the recirculation zone; an outer vortex close to the air coflow and an inner vortex between the outer vortex and the jet. The inner vortex is found to shift downstream with increasing jet momentum flux relative to the coflow momentum flux and gradually loses its circulation pattern. The momentum flux ratio of the jet to the coflow in isothermal flows is found to be the only scaling parameter for the flow field structure. Three mixing layers are identified in the recirculation zone. Numerical simulations using the standard k-? and Reynolds stress turbulence models underpredict the length of the recirculation zone. A simple modification to the C₁ constant in the dissipation transport equation fixes this deficiency and gives better predictions of the flow and mixing fields. The mixed-is-burnt combustion model is found to be adequate for simulating the temperature and mixing field in the recirculation zone of the bluff-body flames.     

Suppression of turbulence by self-generated and imposed mean flows

The first direct experimental evidence of the suppression of quasi-two-dimensional turbulence by mean flows is presented. The flow either is induced externally or appears in the process of spectral condensation due to an inverse cascade in bounded turbulence. The observed suppression of large scales is consistent with an expected reduction in the correlation time of turbulent eddies due to shearing. At high flow velocities, sweeping of the forcing-scale vortices reduces the energy input, leading to a reduction in the turbulence level.     

Simultaneous Droplet Size and Gas-Phase Turbulence Measurements in a Spray Flow using Phase-Doppler Interferometry

A recently developed method to increase the sensitivity of a phase-Doppler interferometer (PDI) has been applied to an annular air flow interacting with a spray under isothermal conditions in order to demonstrate the applicability of the method to obtaining velocity and turbulence characteristics of the gas-phase in a two-phase flow. A conventional PDI system operated in the first order refraction mode cannot be configured to efficiently detect small seed particles in the presence of large droplets due to the limited dynamic range of the photodetectors. It is therefore difficult or impossible to obtain seed particle detection rates sufficient for turbulence measurements. Doping the spray with a very small quantity of dye preferentially attenuates the light intensity scattered by large droplets, thus allowing the PDI system to detect small seed particles without damaging the photodetectors when large particles are present in the flow. Application of this method to a two-phase flow produced by a pressure-swirl atomizer coaxially located within an annular air jet has resulted in profiles of axial mean and fluctuating velocities and shear stresses as well as integral time scales and turbulent energy spectra.     

Generalised scale-by-scale energy-budget equations and large-eddy simulations of anisotropic scalar turbulence at various Schmidt numbers

A necessary condition for the accurate prediction of turbulent flows using large-eddy simulation (LES) is the correct representation of energy transfer between the different scales of turbulence in the LES. For scalar turbulence, transfer of energy between turbulent length scales is described by a transport equation for the second moment of the scalar increment. For homogeneous isotropic turbulence, the underlying equation is the well-known Yaglom equation. In the present work, we study the turbulent mixing of a passive scalar with an imposed mean gradient by homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and LES are performed for this configuration at various Schmidt numbers, ranging from 0.11 to 5.56. As the assumptions made in the derivation of the Yaglom equation are violated for the case considered here, a generalised Yaglom equation accounting for anisotropic effects, induced by the mean gradient, is derived in this work. This equation can be interpreted as a scale-by-scale energy-budget equation, as it relates at a certain scale r terms representing the production, turbulent transport, diffusive transport and dissipation of scalar energy. The equation is evaluated for the conducted DNS, followed by a discussion of physical effects present at different scales for various Schmidt numbers. For an analysis of the energy transfer in LES, a generalised Yaglom equation for the second moment of the filtered scalar increment is derived. In this equation, new terms appear due to the interaction between resolved and unresolved scales. In an a-priori test, this filtered energy-budget equation is evaluated by means of explicitly filtered DNS data. In addition, LES calculations of the same configuration are performed, and the energy budget as well as the different terms are thereby analysed in an a-posteriori test. It is shown that LES using an eddy viscosity model is able to fulfil the generalised filtered Yaglom equation for the present configuration. Further, the dependence of the terms appearing in the filtered energy-budget equation on varying Schmidt numbers is discussed.     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

Direct numerical simulations of second-order Stokes wave driven smooth-walled oscillatory channel: investigation of net current formation

In wall-bounded time-periodic flows, nonlinearity, associated with higher harmonic term(s) in velocity and/or acceleration outside the boundary layer, can significantly change the wall turbulence compared with that in the linear Stokes Boundary Layer. A significant feature of a nonlinear wall-bounded turbulent time-periodic flow is the formation of a net current which has not yet been mechanistically explained. This study investigates the effects of asymmetric velocity outside the boundary layer on wall turbulence and net current formation through Direct Numerical Simulations of a smooth-walled planar channel driven by the Second-order Stokes Wave. Simulation results suggest that net current characteristics depend on whether developed turbulence is present. When turbulence is developed, asymmetric viscous length scale is found to be the primary reason of the net current whereby a vertical offset between negative and positive Reynolds shear stress profiles, associated with forward and reverse flows, respectively, is created in a cycle. After averaging over a cycle, residual Reynolds shear stress, which drives the net current, is observed to be within the offset layer.