A new method for probing the turbulence scalar spectrum by ultrasonic sonar scanning

 A new method is proposed to obtain a turbulent scalar spectrum and the energy dissipation rate in turbulent flow from ultrasonic frequency scanning data. A scanning sonar with frequency varying from 0.5 MHz to 5 MHz has been used to directly probe the energy dissipation rate ɛ and the three-dimensional scalar spectrum E _θ(k). Experiments were conducted in a laboratory open-channel flow in clear water with Reynolds numbers varying from 1.2×10⁵ to 6.9×10⁵. Good agreement is found between measured spectra and those predicted by the Batchelor theory. The energy dissipation rates compare favourably with those obtained from acoustic Doppler velocimeter measurements. Received: 20 March 1997/Accepted: 27 September 1997     

Measurements of wave-variance and velocity spectra in breaking waves

Displacements of mechanical waves superposed onto wind waves were measured with a laser displacement gauge in a wind-wave tank. The effects of wave breaking, especially the spilling breaking type, on the wave-variance spectra are investigated. In the absence of wave breaking, the quasi-equilibrium spectrum consists of an f ^–7/3 subrange in the capillary regime, and its spectral density increases with increasing wind speed. When intense spilling breaking occurs, the water surface is saturated with small-scale features that cause not only an increase in the spectral density but also a reduction in the slope of the spectrum at high frequencies. Velocity components under the water surface were measured with a laser Doppler velocimeter. The energy spectra of the vertical and longitudinal velocity components in breaking waves are practically identical in the frequency range near the dominant wave frequency. At higher frequencies, the spectra generally follow Kolmogorov's –5/3 law. In the intermediate frequency range, we observed a higher spectral density for the vertical velocity component than for its longitudinal counterpart. These results suggest that turbulence energy is transferred from the vertical component to the longitudinal component in breaking waves. The acceleration of the water motion becomes as large as gravitational acceleration when intense wave breaking takes place. The flow field in breaking waves is highly dissipative.     

Progress in subgrid-scale transport modelling for continuous hybrid non-zonal RANS/LES simulations

The partially integrated transport modelling (PITM) method can be viewed as a continuous approach for hybrid RANS/LES modelling allowing seamless coupling between the RANS and the LES regions. The subgrid turbulence quantities are thus calculated from spectral equations depending on the varying spectral cutoff location [Schiestel, R., Dejoan, A., 2005. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoretical and Computational Fluid Dynamics 18, 443–468; Chaouat, B., Schiestel, R., 2005. A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Physics of Fluids, 17 (6)] The PITM method can be applied to almost all statistical models to derive its hybrid LES counterpart. In the present work, the PITM version based on the transport equations for the turbulent Reynolds stresses together with the dissipation transport rate equation is now developed in a general formulation based on a new accurate energy spectrum function E(κ) valid in both large and small eddy ranges that allows to calibrate more precisely the c_sgs2 function involved in the subgrid dissipation rate _sgs transport equation. The model is also proposed here in an extended form which remains valid in low Reynolds number turbulent flows. This is achieved by considering a characteristic turbulence length-scale based on the total turbulent energy and the total dissipation rate taking into account the subgrid and resolved parts of the dissipation rate. These improvements allow to consider a large range of flows including various free flows as well as bounded flows. The present model is first tested on the decay of homogeneous isotropic turbulence by referring to the well known experiment of Comte-Bellot and Corrsin. Then, initial perturbed spectra E(κ) with a peak or a defect of energy are considered for analysing the model capabilities in strong non-equilibrium flow situations. The second test case is the classical fully turbulent channel flow that allows to assess the performance of the model in non-homogeneous flows characterised by important anisotropy effects. Different simulations are performed on coarse and refined meshes for checking the grid independence of solutions as well as the consistency of the subgrid-scale model when the filter width is changed. A special attention is devoted to the sharing out of the energy between the subgrid-scales and the resolved scales. Both the mean velocity and the turbulent stress computations are compared with data from direct numerical simulations.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate

We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate $ \left\langle \varepsilon \right\rangle $ in a variety of turbulent flows. The method relies on the validity of the first similarity hypothesis of Kolmogorov (C R (Doklady) Acad Sci R R SS, NS 30:301–305, 1941) (or K41) which implies that spectra of velocity fluctuations scale on the kinematic viscosity ν and $ \left\langle \varepsilon \right\rangle $ at large Reynolds numbers. However, the evidence, based on the DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a ?5/3 inertial subrange only when the Taylor microscale Reynods number R _λ is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30?≤?R _λ?≤?400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of $ \left\langle \varepsilon \right\rangle $ in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.     

An experimental research on the instability of natural convection boundary layer around a vertical heated flat plate

Experimental results on the instability of the isothermal naturalconvection boundary layer around a vertical heated flat plate are presented. It is demonstrated that the characteristics of the instability wave in the outer layer is consistent with the calculation of Brewster & Gebhart. After an initial growth of its low frequency components at the downstream side of the turning point of the neutral curve (Gr≈120) its comparatively higher frequency components develop and become turbulent subsequently with a buoyancy subrange in its power spectra. Simultaneously, in the measurement at the inner layer near the wall a viscous instability signal the same as the Tollmien-Schlichting waves in ordinary boundary layer and its subharmonics in a much higher frequency domain is discovered and an inertial subrange can be observed in the spectra atGr≈378.6. The project supported by the National Natural Science Foundation of China (19572004)     

Response of mean turbulent energy dissipation rate and spectra to concentrated wall suction

The response of mean turbulent energy dissipation rate and spectra to concentrated suction applied through a porous wall strip has been quantified. Both suction and no suction data of the spectra collapsed reasonably well for Kolmogorov normalised wavenumber k ₁^* > 0.2. Similar results were also observed for second-order structure functions (not shown) for Kolmogorov normalised radius r* < 10. Although, the quality of collapsed is poorer for transverse component, the result highlights that Kolmogorov similarity hypothesis is reasonably well satisfied. However, the suction results shows a significant departure from the no suction case of the Kolmogorov normalised spectra and second-order structure functions for k ₁^* < 0.2 and r* > 20, respectively. The departure at the larger scales with collapse at the small scales suggests that suction induce a change in the small-scale motion. This is also reflected in the alteration of mean turbulent energy dissipation rate and Taylor microscale Reynolds number. This change is a result of the weakening of the large-scale structures. The effect is increased as the suction rate is increased.     

Turbulent Energy Scale-Budget Equations for nearly Homogeneous Sheared Turbulence

For moderate Reynolds numbers, the isotropic relation between second-order and third-order moments for velocity increments (Kolmogorov's equation) is not respected, reflecting a non-negligible correlation between the scales responsible for the injection, transfer and dissipation of the turbulent energy. For (shearless) grid turbulence, there is only one dominant large-scale phenomenon, which is the non-stationarity of statistical moments resulting from the decay of energy downstream of the grid. In this case, the extension of Kolmogorov's analysis, as carried out by Danaila, Anselmet, Zhou and Antonia, J. Fluid Mech. 391, 1999 359-369) is quite straightforward. For shear flows, several large-scale phenomena generally coexist with similar amplitudes. This is particularly the case for wall-bounded flows, where turbulent diffusion and shear effects can present comparable amplitudes. The objective of this work is to quantify, in a fully developed turbulent channel flow and far from the wall, the influence of these two effects on the scale-by-scale energy budget equation. A generalized Kolmogorov equation is derived. Relatively good agreement between the new equation and hot-wire measurements is obtained in the outer region (40 < x ⁺ ₃ < 150) of the channel flow, for which the turbulent Reynolds number is R _λ≈ 36.     

Surface roughness effects in turbulent boundary layers

The effects of surface roughness on a turbulent boundary layer are investigated by comparing measurements over two rough walls with measurements from a smooth wall boundary layer. The two rough surfaces have very different surface geometries although designed to produce the same roughness function, i.e. to have nominally the same effect on the mean velocity profile. Different turbulent transport characteristics are observed for the rough surfaces. Substantial effects on the stresses occur throughout the layer showing that the roughness effects are not confined to the wall region. The turbulent energy production and the turbulent diffusion are significantly different between the two rough surfaces, the diffusion having opposite sign in the region γ/δ < 0.5. Although velocity spectra exhibit differences between the three surfaces, the mean energy dissipation rate does not appear to be significantly affected by the roughness. Received: 19 August 1998/Accepted: 16 February 1999     

On the correlation between enstrophy and energy dissipation rate in a turbulent wake

All three components of the vorticity fluctuation have been measured simultaneously in a turbulent wake using a new eight-sensor vorticity probe. The vorticity fluctuation spectra agree reasonably well with those from a direct numerical simulation of a turbulent channel flow at high wavenumbers. The similarity between the instantaneous energy dissipation rate ε and the instantaneous enstrophy ω² is examined using spectra and probability density functions. The correlation between ω² and ε is evaluated in some detail. The homogeneous value of ε is strongly correlated with ω². The full value of ε and, more especially its isotropic value, are less well correlated with the enstrophy. Conditional averaging indicates that high enstrophy regions are associated with high energy dissipation rate regions.     

Transport equations for the mean energy and temperature dissipation rates in grid turbulence

 Simultaneous measurements of velocity and temperature fluctuations were made in the turbulent flow downstream of a grid-heated screen combination. The magnitudes of n and m, the power-law exponents for the decay of turbulent energy and temperature variances, are nearly equal. This approximate equality is in conformity with the locations of the peaks in the three-dimensional turbulent energy and temperature spectra. The values of n and m are consistent with the isotropic forms of the transport equations for the mean turbulent energy and temperature variance. They are also consistent, allowing for the measurement accuracy, with the isotropic forms of the equations for the mean turbulent energy and temperature dissipation rates. Received: 20 October 1998 / Accepted: 26 March 1999     

Large Eddy Simulations: How to evaluate resolution

The present paper gives an analysis of fully developed channel flow at Reynolds number of Re=u_τδ/ν=4000 based on the friction velocity, u_τ, and half the channel height, δ. Since the Reynolds number is high, the LES is coupled to a URANS model near the wall (hybrid LES–RANS) which acts as a wall model. It it found that the energy spectra is not a good measure of LES resolution; neither is the ratio of the resolved turbulent kinetic energy to the total one (i.e. resolved plus modelled turbulent kinetic energy). It is suggested that two-point correlations are the best measures for estimating LES resolution. It is commonly assumed that SGS dissipation takes place at high wavenumbers. Energy spectra of the fluctuating velocity gradients show that this is not true; the major part of the SGS dissipation takes place at low to midrange wavenumbers. Furthermore, the energy spectra of the fluctuating velocity gradients reveals that the accuracy of the predicted velocity gradients at the highest resolved wavenumbers is very poor.     

Generation and direct viscous dissipation of turbulent energy

Existing information about the generation and viscous dissipation of turbulent energy is based, as a rule, on the Laufer test data obtained for fluid flow in circular tubes at two Reynolds numbers (5 · 10⁵ and 5 · 10⁴). Computational dependences are presented herein for the generation and viscous dissipation of turbulent energy, common over the whole stream section and for the whole range of variation of the Reynolds number. The equation of the average energy balance during fluid flow in a circular tube and a flat channel is solved taking account of the equation of motion and the turbulent friction profile obtained by the author [1]. The computational dependences satisfy all the evident boundary conditions, agree with the Laufer test results [2] and yield a well-founded passage to the limit modes of average turbulent motion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 30–36, November–December, 1973.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

An investigation of the scales in transitional boundary layers under high free-stream turbulence conditions

The scales in a transitional boundary layer subject to high (initially 8%) free-stream turbulence and strong acceleration (K as high as 9×10^–6) were investigated using wavelet spectral analysis and conditional sampling of experimental data. The boundary layer shows considerable evolution through transition, with a general shift from the lower frequencies induced by the free-stream unsteadiness to higher frequencies associated with near-wall-generated turbulence. Within the non-turbulent zone of the intermittent flow, there is considerable self-similarity in the spectra from the beginning of transition to the end, with the dominant frequencies in the boundary layer remaining constant at about the dominant frequency of the free-stream. The frequencies of the energy-containing scales in the turbulent zone change with streamwise location and are significantly higher than in the non-turbulent zone. When normalized on the local viscous length scale and velocity, however, the turbulent zone spectra also show good self-similarity throughout transition. Turbulence dissipation occurs almost exclusively in the turbulent zone. The velocity fluctuations associated with dissipation are isotropic, and their normalized spectra at upstream and downstream stations are nearly identical. The distinct differences between the turbulent and non-turbulent zones suggest the potential utility of intermittency based transition models in which these zones are treated separately. The self-similarity noted in both energy containing and dissipation scales in both zones suggests possibilities for simplifying the modeling for each zone.

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Development of a HS-LIF-system for Lagrangian correlation measurement

Within the presented work, a key assumption for a combustion noise model is validated. Heat release fluctuations are the main reason for the noise emission of turbulent premixed flames. Within the combustion noise model of Hirsch et al. [31st Symposium (Int.) on Combustion, pp 1435–1441, 2006], the heat release is computed in the wavenumber domain and transferred into the frequency domain, subsequently. The transformation of the spectra requires a power law dependence of the scalar spectra upon the wavenumber proportional to and upon the frequency proportional to f ⁻² in the inertial subrange. The validation of the latter assumption requires a measurement system, which allows time dependent recording of fluid properties, e.g. the progress variable. These are provided by a HS-LIF-system, which supports a repetition rate of 1 kHz with sufficient energy to detect OH-radicals. From the high speed video data, the motion of the flame front is reconstructed. The presented study shows the set up of the HS-LIF-system as well as the various image post processing steps, including data binarization, flame front tracking and finally, computation of the lagrangian correlation for the progress variable. It can be shown that the spectral distribution of the progress variable in the Lagrangian frame is as assumed by the above mentioned combustion noise model.     

竖直平板间自然对流的湍流频谱特性

根据直接数值模拟的计算结果，对竖直平板间湍流自然对流的脉动动能、速度及温度等物理量的时间序列进行频谱分析．结果表明，流动达到充分发展状态后，小尺度到大尺度的能谱很宽，计算的分辨率足够．从能谱分布可以观察到含能区、惯性子区和耗散区的存在，文中对各区的特性进行分析．由于该流动的强各向异性，惯性子区很窄．并讨论了法向位置对脉动动能的影响以及大尺度结构的特性．     

Thin Shear Layer Structures in High Reynolds Number Turbulence

Three-dimensional tomographic time dependent PIV measurements of high Reynolds number (Re) laboratory turbulence are presented which show the existence of long-lived, highly sheared thin layer eddy structures with thickness of the order of the Taylor microscale and internal fluctuations. Highly sheared layer structures are also observed in direct numerical simulations of homogeneous turbulence at higher values of Re (Ishihara et al., Annu Rev Fluid Mech 41:165–180, 2009). But in the latter simulation, where the fluctuations are more intense, the layer thickness is greater. A rapid distortion model describes the structure and spectra for the velocity fluctuations outside and within ‘significant’ layers; their spectra are similar to the Kolmogorov (C R Acad Sci URSS 30:299–303, 1941) and Obukhov (Dokl Akad Nauk SSSR 32:22–24, 1941) statistical model (KO) for the whole flow. As larger-scale eddy motions are blocked by the shear layers, they distort smaller-scale eddies leading to local zones of down-scale and up-scale transfer of energy. Thence the energy spectrum for high wave number k is $E_X (k)\sim Bk^{-2p}$ . The exponent p depends on the forms of the large eddies. The non-linear interactions between the distorted inhomogeneous eddies produce a steady local structure, which implies that 2p?=?5/3 and a flux of energy into the thin-layers balancing the intense dissipation, which is much greater than the mean $\left<\epsilon\right>$ . Thence $B\sim\left<\epsilon\right>^{2/3}$ as in KO. Within the thin layers the inward flux energises extended vortices whose thickness and spacing are comparable with the viscous microscale. Although peak values of vorticity and velocity of these vortices greatly exceed those based on the KO scaling, the form of the viscous range spectrum is consistent with their model.