Vibro-Acoustic Response of a Pipe Excited by a Turbulent Internal Flow

This article presents an experimental study of the vibro-acoustic response of a pipe excited by a fully-developed turbulent air flow. First, the wall pressure field acting on the internal pipe wall is investigated. The power spectral density of the wall pressure fluctuations is analyzed after cancellation of contaminating background noise. The convection velocity and correlation lengths are calculated from measured cross-spectra, and the cross-spectra are expressed in Corcos model form. Second, the vibro-acoustic response of the pipe is analyzed by referring to the structural modes of the pipe. This revised version was published online in July 2006 with corrections to the Cover Date.     

Direct Numerical Simulation of a Recirculating, Swirling Flow

A direct numerical simulation (DNS) of a recirculating, swirling flow is performed at a Reynolds number of 5000. Detailed one and two point statistics are presented in this paper. Flow visualization and frequency analysis are used to identify a precessing vortex core and to characterize its position, extent and influence on the flow field. The results are compared with laser Doppler velocimetry (LDV) measurements as well as large eddy simulation (LES) data reported in the literature. The present work constitutes a first step in setting up a DNS data base for complex flows.     

管内湍流旋流的数值计算

本文用有限差分法对直管内的湍流旋流进行了数值模拟。计算中采用Ｂｏｕｓｓｉｎｅｓｑ湍流涡粘性假设的基本思想和Ｋ－ε双方程模型来求解雷诺应力各分量。为了反映旋流中湍流转输的非均匀性和各向异性特征，对雷诺应力各分量及与之相主尖的各湍流粘性系数分别进行计算。计算结果表明该模型能较好地反映直管内湍流旋流的流动结构。     

Application of PDF Modeling to Swirling and Nonswirling Turbulent Jets

The turbulence modeling in probability density function (PDF) methods is studied through applications to turbulent swirling and nonswirling co-axial jets and to the temporal shear layer. The PDF models are formulated at the level of either the joint PDF of velocity and turbulent frequency or the joint PDF of velocity, wave vector, and turbulent frequency. The methodology of wave vector models (WVMs) is based on an exact representation of rapidly distorted homogeneous turbulence, and several models are constructed in a previous paper [1]. A revision to a previously presented conditional-mean turbulent frequency model [2] is constructed to improve the numerical implementation of the model for inhomogeneous turbulent flows. A pressure transport model is also implemented in conjunction with several velocity models. The complete model yields good comparisons with available experimental data for a low swirl case. The individual models are also assessed in terms of their significance to an accurate solution of the co-axial jets, and a comparison is made to a similar assessment for the temporal shear layer. The crucial factor in determining the quality of the co-axial jet simulations is demonstrated to be the proper specification of a parameter ratio in the modeled source of turbulent frequency. The parameter specification is also shown to be significant in the temporal shear layer.     

Invariant Analysis of Turbulent Pipe Flow

The anisotropy analysis of Lumley provides a useful tool to quantify the degree of anisotropy in turbulent flows. Also included in the analysis are relations which may be used to check if the flow is axisymmetric or two-dimensional. However, the method does not provide any scale information about the structures. The analysis has therefore been extended here to Fourier space, which allows scale information to be derived. The method was applied to fully developed pipe flow and it was shown that the large-scale motion is everywhere close to axisymmetric. The intermediate scales are strongly influenced by the restrictions posed by the pipe walls. At the centre line, the flow structure appears axisymmetric at all scales, but the measurement sindicate that true axisymmetry is lost very quickly away from the centre line. The structure of the smallest scales could not be determined reliably due to a singularity in the analysis which develops as the scales go to zero. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Decay of Swirling Flows in a Type of Cross-Section-Varying Pipes

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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.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

Effect of Interphase Heat Transfer on the Stability of a Turbulent Multicomponent Flow in a Vortex

The parameters of an axisymmetric turbulent two-phase swirling flow of a viscous heat-conducting gas containing a liquid dispersed phase in the presence of water vapor condensation on the particles are calculated. For the dispersed phase, a model taking into account the variation of the vapor concentration and the particle size due to condensation or evaporation is proposed. The distributions of the parameters of the basic unperturbed flow obtained numerically are used in the numerical solution of the linear problem of hydrodynamic stability within the time-dependent formulation. The parameters of small-amplitude harmonic perturbations propagating along the vortex axis are investigated in the linear formulation. A significant effect of heat release in the gas due to water vapor condensation on the parameters of the neutral perturbations and the neutral-stability curves is detected.     

Response of a Thin Cylindrical Shell Excited by a Turbulent Internal Flow

This paper presents results obtained within the scope of a collaboration between the “Laboratoire de Mécanique et d'Acoustique” (Marseille, France), the “Laboratoire de Mécanique des Fluides et d'Acoustique” of the Ecole Centrale (Lyon, France) and the “Laboratoire de Vibrations et d'Acoustique” of the Institut National des Sciences Appliquées (Lyon, France). The main aspect of this collaboration is to establish a comparison between a measured and a model vibro-acoustics response of a thin cylindrical pipe excited by a turbulent internal flow. After a brief review of the literature, a model of the response of the shell, based on a matched asymptotic expansion, is given. Some numerical results are also given. The spectral density of the acceleration of the shell is compared with experimental results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe

In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow. Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz (K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales.     

Prediction of Pressure Oscillations in a Premixed Swirl Combustor Flow and Comparison to Measurements

The most common and reliable technique used for flame stabilization of industrial combustors with high thermal loads is the application of strongly swirling flows. In addition to stabilization, swirl flames offer the possibility to influence emission characteristics by simply changing the swirl intensity or the type of swirl generation. Despite of these major advantages, swirling flows tend to evolve flow instabilities, that considerably constitute a significant source of noise. In general, noise generation is substantially enhanced, when such a swirling flow is employed for flames. Thus, the minimization of the resulting noise emissions under conservation of the benefit of high ignition stability is one major design challenge for the development of modern swirl stabilized combustion devices. The present investigation makes an attempt to determine mechanisms and processes to influence the noise generation of flames with underlying swirling flows. Therefore, a new burner has been designed, that offers the possibility to vary geometrical parameters as well as the type of swirl generation, typically applied in industrial devices. Experimental data has been acquired for the isothermal flow as well as swirl flames by means of 3-D-LDV-diagnostics comprising the components of long-time averaged mean and rms-velocities as well as spectrally resolved velocity fluctuations for all components. The noise emission data was acquired with microphone probes resulting in sound pressure levels outside the zone of the perceptible fluid flow. Along to the experiments, numerical simulations using RANS and LES have been carried out for isothermal cases with different burner outlet geometries. The results of the measurements show a distinct rise of the sound pressure level, obtained by changing both the test setup from the isothermal into the flame configuration as well as the geometrical parameters. This is also resembled by the LES simulation results. Furthermore, a physical model has been developed from experiments and verified by the LES simulation, that explains the formation of coherent flow structures and allows to separate their contribution to the overall noise emission from ordinary turbulent noise sources.     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Velocity Measurements of a Free-Surface Turbulent Flow Penetrating a Porous Medium Composed of Uniform-Size Spheres

We present a laboratory experimental investigation of the interaction between the turbulent flow in an open channel and the turbulent flow within its very permeable bed. The bed was composed of uniform-size spheres packed in a cubic pattern. Fluid velocities were measured by Particle Image Velocimetry (PIV), which allowed us to investigate the spatial distribution of the time-averaged flow properties in the zone where they are strongly affected by the geometry of the rough bed. We investigate the effect of bed porosity on these flow properties by comparing the results of two experimental configurations: one with an impermeable bed composed of a single layer of spheres and another with a permeable bed composed of five layers. For the latter case, PIV measurements of velocities were also carried out inside two pores adjacent to the bed surface. This data provides an insight into the mechanisms of momentum transfer between the turbulent open channel flow and the turbulent flow within its very permeable bed.     

Measurements in the vaneless diffuser of a radial flow compressor

Results from an experimental study of flow behaviour at the inlet of a vaneless diffuser of a centrifugal compressor are presented. Measurements from a crossed hot-wire probe are given for operating points having inlet flow coefficients ranging from 0.006 to 0.019 at different Reynolds numbers. Instantaneous, time-averaged, and phase-averaged absolute velocity and flow angle at the diffuser inlet are deduced from the hot-wire signals after correction for mean density variations. These results show how flow behaviour varies in stable, rotating stall and surge regimes of compressor operation     

Start-up Flow of a Bingham Fluid in a Pipe

We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian.     

Analysis of Streamwise Velocity Fluctuations in Turbulent Pipe Flow with the Use of an Ultrasonic Doppler Flowmeter

Data collected from several studies of experimental and numerical nature in wall-bounded turbulent flows and in particular in internal flows (channel and pipe flows, Mochizuki and Nieuwstadt [1]) at different Reynolds numbers R ⁺(Ru _*/ν), indicate that: (i) the peak of the rms-value (normalized by u _*) of the streamwise velocity fluctuations (σ _u ⁺|_peak) is essentially independent of the Reynolds number, (ii) the position of the rms peak value (y ⁺|_peak) is weakly dependent of the Reynolds number, (iii) the skewness of the streamwise velocity fluctuations (S _u ) is close to zero at the position in which the variance has its peak. A series of measurements of streamwise velocity fluctuations has been performed in turbulent pipe flow with the use of an Ultrasonic Doppler Velocimeter and our results support those reported in [1]. This revised version was published online in July 2006 with corrections to the Cover Date.     

蜗壳内紊流流场的有限元法计算

用有限元法计算径流式叶轮机械蜗壳的紊流时均流场.有关紊流模型采用K-ε两方程模型,用关于压力p的罚函数方法求解.所得结果可供分析蜗壳流场用.文中方法也可用于计算其他形状的二维通道流动.     

Simulations of Turbulent Flow in a Plane Asymmetric Diffuser

Large-eddy simulations (LES) of a planar, asymmetric diffuser flow have been performed. The diverging angle of the inclined wall of the diffuser is chosen as 8.5°, a case for which recent experimental data are available. Reasonable agreement between the LES and the experiments is obtained. The numerical method is further validated for diffuser flow with the diffuser wall inclined at a diverging angle of 10°, which has served as a test case for a number of experimental as well as numerical studies in the literature (LES, RANS). For the present results, the subgrid-scale stresses have been closed using the dynamic Smagorinsky model. A resolution study has been performed, highlighting the disparity of the relevant temporal and spatial scales and thus the sensitivity of the simulation results to the specific numerical grids used. The effect of different Reynolds numbers of the inflowing, fully turbulent channel flow has been studied, in particular, Re _b  = 4,500, Re _b  = 9,000 and Re _b  = 20,000 with Re _b being the Reynolds number based on the bulk velocity and channel half width. The results consistently show that by increasing the Reynolds number a clear trend towards a larger separated region is evident; at least for the studied, comparably low Reynolds-number regime. It is further shown that the small separated region occurring at the diffuser throat shows the opposite behaviour as the main separation region, i.e. the flow is separating less with higher Re _b . Moreover, the influence of the Reynolds number on the internal layer occurring at the non-inclined wall described in a recent study has also been assessed. It can be concluded that this region close to the upper, straight wall, is more distinct for larger Re _b . Additionally, the influence of temporal correlations arising from the commonly used periodic turbulent channel flow as inflow condition (similar to a precursor simulation) for the diffuser is assessed.     

Flow of a shear-thinning liquid in a cylindrical container with a rotating end wall

The flow patterns produced by rotating one end wall of a circular cylinder completely filled with a strongly shear-thinning viscoelastic liquid have been investigated using the laser-induced fluorescence flow visualization technique. An intense toroidal vortex is produced in the vicinity of the rotating end wall with outward spiraling flow over the end wall itself. This vortex drives a second countercirculating vortex of low intensity in the region of the stationary end wall. Under some circumstances an axial jet of fluid is observed moving away from the rotating end wall. This jet showed evidence of instability, whereas all flows were otherwise completely steady. The double-vortex structure is different from those recently observed in either a Newtonian or slightly shear-thinning liquid or in the low Reynolds number flow of an elastic liquid. There are, however, similarities with older work for a viscoelastic liquid at relatively high Reynolds numbers. The observations highlight the suitability of the cylinder/rotating end wall configuration as a sensitive test case for computational work.