Layered structure of turbulent plane wall jet

This paper investigates the layered structure of a turbulent plane wall jet at a distance from the nozzle exit. Based on the force balances in the mean momentum equation, the turbulent plane wall jet is divided into three regions: a boundary layer-like region (BLR) adjacent to the wall, a half free jet-like region (HJR) away from the wall, and a plug flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, as in a turbulent free jet, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall and a proper scale for the Reynolds shear stress is the product of the maximum mean streamwise velocity and the velocity scale for the mean wall-normal flow. The BLR region can be divided into four sub-layers, similar to those in a canonical pressure-driven turbulent channel flow or shear-driven turbulent boundary layer flow. Building on the log-law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee (1960) over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.     

Measurements in the near flow field of an isosceles triangular turbulent free jet

The near field mean flow and turbulence characteristics of a turbulent jet of air issuing from a sharp-edged isosceles triangular orifice into still air surroundings have been examined experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some measurements were made in an equilateral triangular free jet and in a round free air jet, both of which also issued from sharp-edged orifices. The Reynolds number, based on the orifice equivalent diameter, was 1.84×10⁵ in each jet. The three components of the mean velocity vector, the Reynolds normal and primary shear stresses, the one-dimensional energy spectra of the streamwise fluctuating velocity signals and the mean static pressure were measured. The mean streamwise vorticity, the half-velocity widths, the turbulence kinetic energy and the local shear in the mean streamwise velocity were obtained from the measured data. It was found that near field mixing in the equilateral triangular jet is faster than in the isosceles triangular and round jets. The mean streamwise vorticity field was found to be dominated by counter-rotating pairs of vortices, which influenced mixing and entrainment in the isosceles triangular jet. The one-dimensional energy spectra results indicated the presence of coherent structures in the near field of all three jets and that the equilateral triangular jet was more energetic than the isosceles triangular and round jets.     

Taylor and Lagrange correlations in a turbulent free shear layer

 The objective of this research was to study the effect of various Lagrange-tracking correlation methods in estimating the eddy lifetime for a two-stream, turbulent, planar free shear layer. Zeroth-, first- and second-order Lagrange correlation methods were applied to the time-evolving velocity field data collected from a cinematic particle image velocimetry technique. A time scale associated with the eddy lifetime was obtained based on a 2/e correlation of either vorticity or streamwise velocity fluctuations. When based on vorticity, this time scale significantly increased as expected when the tracking was computed with a second-order Lagrangian tracking technique as compared to a (zeroth-order) Taylor hypothesis approach. However when based on streamwise velocity fluctuations, this time scale did not increase significantly for the higher order projection methods. The latter result is attributed to occurrences of “reverse correlation” of the instantaneous streamwise velocity fluctuations caused by eddy rotation. Received: 2 April 1997/Accepted: 3 September 1997     

The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet

The flow at the outer boundary of a submerged self-similar turbulent jet at Re=2᎒³ is investigated experimentally by means of combined particle image velocimetry (PIV) laser-induced fluorescence (LIF) measurements. The jet fluid contains a fluorescent dye so that the LIF data can be used to discriminate between the jet fluid and the ambient fluid. The axial velocity, Reynolds stress, and vorticity are determined relative to the jet boundary. The results are compared against the conventional profiles, and the results of a direct numerical simulation of the turbulent far-wake behind a flat plate. The results show a sharp transition between rotational and irrotational fluid at the fluid interface, and the existence of a layer of irrotational velocity fluctuations outside the turbulent region.     

EXPERIMENTAL STUDY ON PROPERTIES OF TURBULENT/NON-TURBULENT INTERFACE OVER RIBLETS SURFACES AT LOW REYNOLDS NUMBERS1)

湍流/非湍流界面是流动中湍流和无旋流的边界,其相关研究在加深对湍流与无旋流之间的物质、动量和能量交换的理解有重要意义.本文采用时间解析的二维粒子图像测速技术,分别对零压梯度光滑、顺流向锯齿形沟槽表面平板在不同雷诺数下对湍流/非湍流界面的几何特征及动力学特性进行了实验研究.实验雷诺数为$Re_{\tau } =400\sim1000$.本文采用了湍动能准则对湍流/非湍流界面进行了识别,并分析界面高度分布、分形特征及界面附近的条件平均速度和涡量.结果表明在不同雷诺数下, 无论是光滑壁面还是沟槽壁面,界面平均高度在0.8 $\sim$ 0.9$\delta_{99} $附近. 对于沟槽壁面而言,减阻时对应的界面高度的概率密度分布与光滑壁面基本一致, 均遵循正态分布,而当阻力增大时, 界面高度分布偏离正态分布出现正的偏度. 在本实验情况下,界面分形维度、跨界面速度跳变均会随着雷诺数增大而增大. 此外,不同壁面情况下无量纲条件平均涡量在界面附近的分布相近,而界面附近无量纲速度梯度最大值近似为常数.     

低雷诺数沟槽表面湍流/非湍流界面特性的实验研究

湍流/非湍流界面是流动中湍流和无旋流的边界,其相关研究在加深对湍流与无旋流之间的物质、动量和能量交换的理解有重要意义.本文采用时间解析的二维粒子图像测速技术,分别对零压梯度光滑、顺流向锯齿形沟槽表面平板在不同雷诺数下对湍流/非湍流界面的几何特征及动力学特性进行了实验研究.实验雷诺数为$Re_{\tau } =400\sim1000$.本文采用了湍动能准则对湍流/非湍流界面进行了识别,并分析界面高度分布、分形特征及界面附近的条件平均速度和涡量.结果表明在不同雷诺数下, 无论是光滑壁面还是沟槽壁面,界面平均高度在0.8 $\sim$ 0.9$\delta_{99} $附近. 对于沟槽壁面而言,减阻时对应的界面高度的概率密度分布与光滑壁面基本一致, 均遵循正态分布,而当阻力增大时, 界面高度分布偏离正态分布出现正的偏度. 在本实验情况下,界面分形维度、跨界面速度跳变均会随着雷诺数增大而增大. 此外,不同壁面情况下无量纲条件平均涡量在界面附近的分布相近,而界面附近无量纲速度梯度最大值近似为常数.      

Generalized detection of a turbulent front generated by an oscillating grid

This report presents experimental results on the propagation of a turbulent front induced by an oscillating grid starting from rest. The purpose of this preliminary investigation is to implement and validate detection methods of the turbulent/non-turbulent interface, which are based on flow measurements (velocity and vorticity) and scalar intensity, for oscillating grid turbulence. This is done using particle image velocimetry (PIV) and fluorescent dye visualization, separately. The results of both techniques describe the spreading of the turbulent front, confirming the known dependency of the front location, H, on time, t. It is demonstrated, that the level-based detection of a turbulent front can be applied to an unsteady flow, such as grid turbulence advancing into a fluid at rest.     

On the capability of the curvilinear immersed boundary method in predicting near-wall turbulence of turbulent channel flows

The immersed boundary method has been widely used for simulating flows over complex geometries.However, its accuracy in predicting the statistics of near-wall turbulence has not been fully tested. In this work, we evaluate the capability of the curvilinear immersed boundary(CURVIB) method in predicting near-wall velocity and pressure fluctuations in turbulent channel flows. Simulation results show that quantities including the time-averaged streamwise velocity, the rms(root-mean-square) of velocity fluctuations, the rms of vorticity fluctuations, the shear stresses, and the correlation coefficients of u and v computed from the CURVIB simulations are in good agreement with those from the body-fitted simulations. More importantly, it is found that the time-averaged pressure, the rms and wavenumber-frequency spectra of pressure fluctuations computed using the CURVIB method agree well with the body-fitted results.     

Optimal transient growth in turbulent pipe flow

The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the subspace spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth amplification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n=1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δ_v are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.     

Three-component LDA measurements in a turbulent boundary layer

An experimental study of a three-dimensional, pressuredriven, attached turbulent boundary-layer flow was made at Mach 0.4. Both the mean velocities and the full Reynolds stress tensor were measured simultaneously by a three-component LDA system. Value of the resultant shear stress to turbulent kinetic energy ratio varied between 0.1 and 0.2 and did not remain constant across the boundary-layer. Slopes of the streamwise and azimuthal mixing length distributions in the wall region were around 0.4 and 1.2, respectively. Skew angle of the turbulent shear stress was larger than skew angle of the velocity gradient.     

The effect of air-water interface on the vortex shedding from a vertical circular cylinder

The flow past an interface piercing circular cylinder at the Reynolds number Re=2.7×10⁴ and the Froude numbers Fr=0.2 and 0.8 is investigated using large-eddy simulation. A Lagrangian dynamic subgrid-scale model and a level set based sharp interface method are used for the spatially filtered turbulence closure and the air-water interface treatment, respectively. The mean interface elevation and the rms of interface fluctuations from the simulation are in excellent agreement with the available experimental data. The organized periodic vortex shedding observed in the deep flow is attenuated and replaced by small-scale vortices at the interface. The streamwise vorticity and the outward transverse velocity generated near the edge of the separated region, which enforces the separated shear layers to deviate from each other and restrains their interaction, are primarily responsible for the devitalization of the periodic vortex shedding at the interface. The lateral gradient of the difference between the vertical and transverse Reynolds normal stresses, increasing with the Froude number, is the main source of the streamwise vorticity and the outward transverse velocity at the interface.     

Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity

High Reynolds number, low Mach number, turbulent shear flow past a rectangular, shallow cavity has been experimentally investigated with the use of dual-camera cinematographic particle image velocimetry (CPIV). The CPIV had a 3 kHz sampling rate, which was sufficient to monitor the time evolution of large-scale vortices as they formed, evolved downstream and impinged on the downstream cavity wall. The time-averaged flow properties (velocity and vorticity fields, streamwise velocity profiles and momentum and vorticity thickness) were in agreement with previous cavity flow studies under similar operating conditions. The time-resolved results show that the separated shear layer quickly rolled-up and formed eddies immediately downstream of the separation point. The vortices convect downstream at approximately half the free-stream speed. Vorticity strength intermittency as the structures approach the downstream edge suggests an increase in the three-dimensionality of the flow. Time-resolved correlations reveal that the in-plane coherence of the vortices decays within 2–3 structure diameters, and quasi-periodic flow features are present with a vortex passage frequency of ~1 kHz. The power spectra of the vertical velocity fluctuations within the shear layer revealed a peak at a non-dimensional frequency corresponding to that predicted using linear, inviscid instability theory.     

Direct Numerical Simulation of a Gaussian acoustic wave interaction with a turbulent premixed flame

The interaction of a Gaussian negative pulse with a H₂/O₂/N₂ turbulent premixed flame is examined using Direct Numerical Simulation (DNS). Transport properties and chemical kinetics are described in a very detailed manner. An extended nonlinear local Rayleigh's criterion, for laminar as well as turbulent, premixed or nonpremixed flames, is proposed. Situations in which amplification or attenuation occur are listed. Calculations of a turbulent flame are then carried out with and without an acoustic wave and results are recorded at the same time. The influence of acoustic wave/turbulent flame interaction is obtained by a simple difference. It is shown that longitudinal and transverse velocity components are perturbed by the turbulent flame. Moreover, the vorticity induced by the acoustic wave is observed to be weak. Finally, Rayleigh's criterion shows that wave amplification occurs punctually. To cite this article: A. Laverdant, D. Thévenin, C. R. Mecanique 333 (2005).     

An experimental study of a turbulent wing-body junction and wake flow

Extensive measurements were conducted in an incompressible turbulent flow around the wing-body junction formed by a 3∶2 semi-elliptic nose/NACA 0020 tail section and a flat plate. Mean and fluctuating velocity measurements were performed adjacent to the wing and up to 11.56 chord lengths downstream. The appendage far wake region was subjected to an adverse pressure gradient. The authors' results show that the characteristic horseshoe vortex flow structure is elliptically shaped, with ? (W)/?Y forming the primary component of the streamwise vorticity. The streamwise development of the flow distortions and vorticity distributions is highly dependent on the geometry-induced pressure gradients and resulting flow skewing directions. The primary goal of this research was to determine the effects of the approach boundary layer characteristics on the junction flow. To accomplish this goal, the authors' results were compared to several other junction flow data sets obtained using the same body shape. The trailing vortex leg flow structure was found to scale on T. A parameter known as the momentum deficit factor (MDF = (Re _T)² (θ/T)) was found to correlate the observed trends in mean flow distortion magnitudes and vorticity distribution. Changes in δ/T were seen to affect the distribution of u′, with lower ratios producing well defined local turbulence maxima. Increased thinning of the boundary layer near the appendage was also observed for small values of δ/T.     

Performance of a three-component vorticity probe in a turbulent far-wake

  A new four X-wire vorticity probe has been developed to measure all three components of the vorticity fluctuation vector simultaneously. The performance of this probe is tested in a turbulent far-wake. The measured Reynolds stresses agree with those obtained previously from simpler hot wire configurations. The variances of the lateral vorticity components agree within ±15% with those measured with a one-component vorticity probe. The variances of the streamwise vorticity component are also in reasonable agreement with those inferred from two X-wires. At high wavenumbers, the measured vorticity spectra agree with those obtained by direct numerical simulation (DNS) in the central region of a turbulent channel flow. The comparison of measured high-order moments of vorticity on the wake centerline with local isotropy also suggests the probe performs satisfactorily. Received: 31 December 1997/Accepted: 6 January 1999     

A vorticity stretching diagnostic for turbulent and transitional flows

Vorticity stretching in wall-bounded turbulent and transitional flows has been investigated by means of a new diagnostic measure, denoted by Γ, designed to pick up regions with large amounts of vorticity stretching. It is based on the maximum vorticity stretching component in every spatial point, thus yielding a three-dimensional scalar field. The measure was applied in four different flows with increasing complexity: (a) the near-wall cycle in an asymptotic suction boundary layer (ASBL), (b) K-type transition in a plane channel flow, (c) fully turbulent channel flow at Re _τ = 180 and (d) a complex turbulent three-dimensional separated flow. Instantaneous data show that the coherent structures associated with intense vorticity stretching in all four cases have the shape of flat ‘pancake’ structures in the vicinity of high-speed streaks, here denoted ‘h-type’ events. The other event found is of ‘l-type’, present on top of an unstable low-speed streak. These events (l-type) are further thought to be associated with the exponential growth of streamwise vorticity in the turbulent near-wall cycle. It was found that the largest occurrence of vorticity stretching in the fully turbulent wall-bounded flows is present at a wall-normal distance of y ⁺?=?6.5, i.e. in the transition between the viscous sublayer and buffer layer. The associated structures have a streamwise length of ~200–300 wall units. In K-type transition, the Γ-measure accurately locates the regions of interest, in particular the formation of high-speed streaks near the wall (h-type) and the appearance of the hairpin vortex (l-type). In the turbulent separated flow, the structures containing large amounts of vorticity stretching increase in size and magnitude in the shear layer upstream of the separation bubble but vanish in the backflow region itself. Overall, the measure proved to be useful in showing growing instabilities before they develop into structures, highlighting the mechanisms creating high shear region on a wall and showing turbulence creation associated with instantaneous separations.     

A turbulent near-wall model on convective heat transfer from an abrupt expansion tube

Turbulent heat transfer from a sudden expansion pipe subjected to an externally convective boundary condition is studied numerically using the proposed modified turbulence model. Both HYBRID and QUICK schemes are employed for comparison purposes. The calculated velocity distribution and turbulent kinetic energy show a significant improvement over the existing model solutions. The present results of center-line velocity, temperature distribution and Nusselt number under a limiting condition compare well with the available experimental data.     

Mean Flow and Turbulence Measurements in a Turbulent Free Cruciform Jet

The results of measurements of all three components of the mean velocity vector, the Reynolds normal and primary shear stresses and the mean static pressure in a turbulent free jet, issuing from a sharp-edged cruciform orifice, are presented in this paper. The measurements were made with an x-array hot-wire probe and a pitot-static tube in the near flow field of the jet. The Reynolds number, based upon the equivalent diameter of the orifice, was 1.70 × 10⁵. In addition to the quantities measured directly, the mean streamwise centreline velocity decay, the jet half-velocity widths, the jet spreading rate, the mean streamwise vorticity, the mass entrainment rate, the integral momentum flux and the one-dimensional energy spectra have been derived from the measured data. The results show that the mean streamwise centreline velocity decay rate of the cruciform jet is higher than that of a round jet issuing from an orifice with the same exit area as that of the cruciform orifice. The mean streamwise velocity field changed shape continuously from a cruciform close to the orifice exit plane to circular at 12 and half equivalent diameters downstream. The mean streamwise vorticity field, up to about three equivalent diameters downstream of the orifice exit plane, consists of four pairs of counter-rotating cells, which are aligned with the four edges in the centre of the cruciform orifice.     

Performance of a transverse vorticity probe in a turbulent channel flow

 The performance of a four hot-wire transverse vorticity probe is tested by comparing measurements in a fully developed turbulent channel flow with corresponding data obtained from direct numerical simulations (DNS) of the same flow. In the inner region, the probe performs poorly, the rms vorticities being consistently smaller than the DNS values. In the outer region of the flow, there is reasonable agreement between measured and DNS vorticity statistics, especially after correcting the measurements for the effect of spatial resolution. In this region, the imbalance indicated by the vorticity form of the streamwise momentum equation is approximately constant. The magnitude of the imbalance can be reduced to an acceptable level of accuracy by considering sources of error which affect the velocity–vorticity correlations. Received: 17 March 1997/Accepted: 17 November 1997