Large-Eddy Simulation of Dispersion from Line Sources in a Turbulent Channel Flow

Large-eddy simulations of the dispersion from scalar line sources at various locations within a fully developed turbulent channel flow at Re = uh/ν = 10,400 are presented. Both mean and fluctuating scalar quantities are compared with those from the single available set of experimental data (Lavertu and Mydlarski, J Fluid Mech 528:135–172, 2005) and differences are highlighted and discussed. The results are also discussed in the context of scalar dispersion in other kinds of turbulent flows, e.g. homogeneous shear-flow. Initial computations at a much lower Reynolds number are also reported and compared with the two available direct numerical simulation data sets.     

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10⁴ and 3.9 × 10⁴ (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10⁵) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10⁴ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10⁴ case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.     

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.     

Dynamics of hairpin vortices generated by a mixing tab in a channel flow

To better understand mixing by hairpin vortices, time-series particle image velocimetry (PIV) was applied to the wake of a trapezoidal-shaped passive mixing tab mounted at the bottom of a square turbulent channel (Re _h =2,080 based on the tab height). Instantaneous velocity/vorticity fields were obtained in sequences of 10 Hz in the tab wake in the center plane (x–y) and in a plane (x–z) parallel to the wall. Periodically-shed hairpin vortices were clearly identified and seen to rise as they advected downstream. Experimental evidence shows that the vortex-induced ejection of the near-wall viscous fluid to the immediate upstream is important to the dynamics of hairpin vortices. It can increase the strength of the hairpin vortices in the near tab region and cause generation of secondary hairpin vortices further downstream when the hairpin heads are farther away from the wall. Measurements also reveal the existence of a type of new secondary vortice with the opposite-sign spanwise vorticity. The distribution of vortex loci in the x–y plane shows that the hairpin vortices and the reverse vortices are spatially segregated in distinct layers. Turbulence statistics, including mean velocity profiles, Reynolds stresses, and turbulent kinetic energy dissipation rate distributions, were obtained from the PIV data. These statistical quantities clearly reveal imprints of the identified vortex structures and provide insight into mixing effectiveness. Received: 24 February 2000/Accepted: 24 October 2000     

Stabilization and evolution of parameters of a symmetric laminar flow in a plane channel with sudden expansion

A problem is formulated for computing the fields of parameters of a stationary laminar symmetric flow. A two-dimensional flow in a channel with a sudden change in the cross-sectional area is computed. The evolution of a three-dimensional perturbation inserted into the channel at the initial stage of computations is analyzed. It is demonstrated that the parameters of a two-dimensional flow in the channel at a Reynolds number Re = 50 become stabilized at a dimensionless time t > 20, whereas the steady state is reached under the same conditions at t ≈ 100. At a distance of approximately 10h (h is the channel width at the entrance), the flow becomes one-dimensional, but the streamwise component of the velocity vector remains a function of the streamwise coordinate owing to flow compressibility. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 35–42, January–February, 2007.     

Experiments on the effect of acceleration on the drag of tapwater bubbles

Three-dimensional (3D) trajectories of spherical air bubbles passing through a converging part of a rectangular channel have been measured. Bubble diameters, d _b, were less than 1 mm and the Reynolds numbers, Re _b, for stagnant tapwater and for mean liquid velocity vˉ _L=0.25 m/s were in about same range. Received: 15 January 2001 / Accepted: 12 June 2001     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

An experimental study of a two-dimensional plane turbulent wall jet

 Laser-Doppler measurements were conducted in a plane turbulent wall jet at a Reynolds number based on inlet velocity, Re ₀, of 9600. The initial development as well as the fully developed flow was studied. Special attention was given to the near-wall region, including the use of small measuring volumes and the application of specific near-wall data corrections, so that wall shear stresses were determined directly from the mean velocity gradient at the wall using only data below y ⁺=4. It was possible to resolve the inner peak in the streamwise turbulence intensity as well as the inner (negative) peak in the shear stress. Limiting values of (u′)⁺ and uv ⁺ were determined. Turbulence data from the outer region of the flow were compared to earlier hot wire measurements and large differences in the normal turbulence intensity and the shear stress were found. These differences can be attributed to high turbulence intensity effects on the hot-wires. Received: 17 October 1996 / Accepted: 8 December 1997     

Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers

 The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship at low Reynolds number, C _L =2γ, is obtained, the ratio C _L /γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140: C _L ≅0.45+(2γ−0.45) exp (−0.075γ^0.4 Re ^0.7) Received: 20 May 1996/Accepted: 9 November 1997     

Surge effect during the water exit of an axisymmetric body traveling normal to a plane interface: experiments and BEM simulation

 Experiments are presented on the surge effect induced by cylindrical bodies piercing a free surface at constant velocity. The study covers the following ranges: 0.1 < Froude² < 7.3, 0.7 < Weber < 89, 46 < Reynolds < 6000; with the Goucher number (Go) evolving between 1.8 and 4.5. Free-surface profiles are compared with those issued from a boundary element method (BEM) simulation based on potential theory and axisymmetric flow configuration. The free-surface deformation is accurately predicted by the BEM approach for Reynolds numbers (Re) higher than 500. However, for Re less than about 200, computed results underestimate the interface elevation, except on the axis of symmetry, where they remain accurate. Finally, the magnitudes of the interface deformation predicted by the numerical simulation are provided over a wide range of Goucher numbers (0.001 < Go < 50) both for hemispherical and conical tips. Implications of these results for phase detection probes are discussed. Received: 18 December 2000/Accepted: 25 January 2001     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

On near-wall hot-wire measurements

A specially constructed hot-wire probe was used to obtain very near-wall velocity measurements in both a fully developed turbulent channel flow and flat plate boundary layer flow. The near-wall hot-wire probe, having been calibrated in a specially constructed laminar flow calibration rig, was used to measure the mean streamwise velocity profile, distributions of streamwise and spanwise intensities of turbulence and turbulence kinetic energy k in the viscous sublayer and beyond; these distributions compare very favorably with available DNS results obtained for channel flow. While low Reynolds number effects were clearly evident for the channel flow, these effects are much less distinct for the boundary layer flow. By assuming the dissipating range of eddy sizes to be statistically isotropic and the validity of Taylor's hypothesis, the dissipation rate ɛ _iso in the very near-wall viscous sublayer region and beyond was determined for both the channel and boundary layer flows. It was found that if the convective velocity U _c in Taylor's hypothesis was assumed to be equal to the mean velocity Uˉ at the point of measurement, the value of (ɛ⁺ _iso)₁ thus obtained agrees well with that of (ɛ ⁺)_DNS for y ⁺ ≥ 80 for channel flow; this suggests the validity of assuming U _c=Uˉ and local isotropy for large values of y ⁺. However, if U _c was assumed to be 10.6u _τ , the value of (ɛ⁺ _iso)₂ thus obtained was found to compare reasonably well with the distribution of (ɛ⁺ _iso)_DNS for y ⁺≤ 15. Received: 31 May 1999/Accepted: 20 December 1999     

Breakdown of the Reynolds Analogy in a Stagnation Region Under Inflow Disturbances

A systematic analysis is performed for the Reynolds analogy breakdown at stagnation-region flow and heat transfer in the presence of inflow disturbances. The Reynolds analogy breakdown between momentum and energy transfers in a stagnation region is scrutinized by varying the Reynolds number (5000≤Re≤20000), the amplitude (0.00075≤A≤0.003) and the length scale (λ/δ=10.6). A spanwise sinusoidal variation is superimposed on the velocity component normal to the wall. Self-similarity solutions are obtained with trigonometric series expansions. The Reynolds analogy criterion demonstrates that the rate of change of skin friction is different from that of wall heat transfer. Different evolutions of the rates of skin friction and wall heat transfer are due to the difference between 〈s'v'〉 and 〈v'T'〉. An in-depth analysis on 〈s'v'〉 and 〈 v'T'〉 is performed by analysis using disturbance correlations based on the fluctuating velocity transport equations in vorticity form. It is found that the pressure fluctuations, the wall blocking and the Lamb vectors are responsible for the breakdown of the Reynolds analogy. A direct comparison is made between momentum and energy balances associated with the three responsible mechanisms. A common finding is that their profiles are changed significantly at a location where the evolution of the streamwise vortex is strong. Received 12 May 2000 and accepted 6 March 2001     

Numerical investigation of a water flow in a rib-roughened channel by using Reynolds stress model

In this paper, water flow in a rib-roughened channel is investigated numerically by using Reynolds stress turbulence models (RSM) on a three-dimensional (3-D) domain. Computational results for mean streamwise velocity component and turbulent kinetic energy show good agreements with available experimental data. Five rib pitch-to-height ratios (p/h) of 1, 5, 10, 15 and 20 are analysed for six different Reynolds numbers (Re) of 3000, 7000, 12,000, 20,000, 40,000 and 65,000. Velocity vectors, streamlines and Reynolds stresses are showed for these ratios and Re numbers. Streamlines revealed that Reynolds numbers do not affect flowfield but play an important role in the Reynolds stresses.     

Comparison of turbulent channel and pipe flows with varying Reynolds number

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Re _τ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l ⁺ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l ⁺ = 22 and l/d >~200l/d \gtrsim 200, the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l ⁺ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l ⁺ and l/d were systematically varied reveal that l ⁺ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.     

Streamwise evolution of a high-Schmidt-number passive scalar in a turbulent plane wake

The concentration fluctuation c of diluted fluorescein dye, a high-Schmidt-number passive scalar (Sc=ν/D ≈ 2000, ν and D are the fluid momentum and dye diffusivities, respectively), is measured in the wake of a circular cylinder using a single-point laser-induced fluorescence (SPLIF) technique. The streamwise decay rate of the mean and rms values of c is slow in comparison to that of θ, the temperature fluctuation for which the molecular Prandtl number Pr=ν/κ is about 0.7 (κ is the thermal diffusivity). The comparison between mean and rms distributions of c and θ highlights the combined role the Reynolds and Schmidt numbers play in terms of dispersing the scalar. The streamwise evolution of the probability density functions (pdfs) of c and θ suggest that while p(θ) is approximately Gaussian in the intermediate wake (x/d ≈ 80), p(c) is strongly non-Gaussian, and depends on both x/d and Re. The skewness of c is larger than that of θ along the wake centreline. Arguably, the asymmetry of p(c) reflects the relatively strong organisation of the large-scale motion in the far-wake. Received: 27 July 2000/Accepted: 22 December 2000     

Experimental study of flow past a square cylinder at high Reynolds numbers

 Measurements of two-components of velocity in the wake of a square cylinder using a hot-wire anemometer are reported. Two Reynolds numbers, namely 8700 and 17,625, have been considered. The measurements were carried out in a low-speed, low-turbulence wind tunnel. Benchmark experiments at much lower Reynolds numbers show good agreement between the present experiments and published results. At higher Reynolds numbers, the experimental data reveal anticipated trends in terms of wake recovery and turbulence decay. Both velocity and velocity fluctuations show symmetry about the wake axis. The experimental data have been compared with the large eddy simulation (LES) calculation reported by Wang et al. [University of Illinois at Urbana – Champaign (1996) Report CFD 96-03] and LDV measurements of Lyn et al. [J Fluid Mech (1995) 304: 285–319]. The agreement among the three sets is generally acceptable in terms of the time-averaged velocity components, but not the velocity fluctuations. The turbulence fluctuations in the present experiments are seen to be lower than in the referred work. The differences have been traced to factors such as the aspect ratio, blockage ratio and upstream turbulence. Experiments with increased upstream turbulence did show a reduction in the discrepancy between the present experiments and the published data. An assessment of the experimental data in terms of physical mechanisms revealed that (a) streamwise normal stresses were correlated with the vortex centers, and (b) the turbulence kinetic energy profiles are similar to the turbulence shear stress. Spectral analysis of the velocity signals was carried out in the present work. Energy transfer from the mean flow to the streamwise velocity fluctuation was confirmed in the near wake. A redistribution of the kinetic energy between the streamwise and transverse components of velocity over a longer distance downstream was subsequently observed. Received: 17 May 1999/Accepted: 29 December 1999     

Three-dimensional Turbulent Boundary Layer in a Shrouded Rotating System

A thre-dimensional direct numerical simulation is combined with a laboratory study to describe the turbulent flow in an enclosed annular rotor-stator cavity characterized by a large aspect ratio G = (b − a)/h = 18.32 and a small radius ratio a/b = 0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate Ω considered is equivalent to the rotational Reynolds number Re = Ωb ²/ν= 9 .5 × 10⁴ (ν the kinematic viscosity of water). This corresponds to a value at which experiment has revealed that the stator boundary layer is turbulent, whereas the rotor boundary layer is still laminar. Comparisons of the computed solution with velocity measurements have given good agreement for the mean and turbulent fields. The results enhance evidence of weak turbulence by comparing the turbulence properties with available data in the literature (Lygren and Andersson, J Fluid Mech 426:297–326, 2001). An approximately self-similar boundary layer behavior is observed along the stator. The wall-normal variations of the structural parameter and of characteristic angles confirm that this boundary layer is three-dimensional. A quadrant analysis (Kang et al., Phys Fluids 10:2315–2322, 1998) of conditionally averaged velocities shows that the asymmetries obtained are dominated by Reynolds stress-producing events in the stator boundary layer. Moreover, Case 1 vortices (with a positive wall induced velocity) are found to be the major source of generation of special strong events, in agreement with the conclusions of Lygren and Andersson (J Fluid Mech 426:297–326, 2001).     

Large eddy simulation of compressible channel flow

Astract The present study is a contribution to the analysis of wall-bounded compressible flows, including a special focus on wall modeling for compressible turbulent boundary layer in a plane channel. large eddy simulation (LES) of fully developed isothermal channel flows at Re = 3,000 and Re = 4,880 with a sufficient mesh refinement at the wall are carried out in the Mach number range 0.3 ≤ M ≤ 3 for two different source term formulations: first the classical extension of the incompressible configuration by Coleman et al. (J. Fluid Mech. 305:159–183, 1995), second a formulation presently derived to model both streamwise pressure drop and streamwise internal energy loss in a spatially developed compressible channel flow. It is shown that the second formulation is consistent with the spatial problem and yields a much stronger cooling effect at the wall than the classical formulation. Based on the present LES data bank, compressibility and low Reynolds number effects are analysed in terms of coherent structure and statistics. A study of the universality of the structure of the turbulence in non-hypersonic compressible boundary layers (M≤5) is performed in reference to Bradshaw (Annu. Rev. Fluid. Mech. 9:33–54, 1977). An improvement of the van Driest transformation is proposed; it accounts for both density and viscosity changes in the wall layer. Consistently, a new integral wall scaling (y ^c+) which accounts for strong temperature gradients at the wall is developed for the present non-adiabatic compressible flow. The modification of the strong Reynolds analogy proposed by Huang et al. (J. Fluid Mech. 305:185–218, 1995) to model the correlation between velocity and temperature for non-adiabatic wall layers is assessed on the basis of a Crocco–Busemann relation specific to channel flow. The key role of the mixing turbulent Prandtl number Pr _m is pointed out. Results show very good agreement for both source formulations although each of them involve a very different amount of energy transfer at the wall. The present work was performed within the framework of the French–German research initiative “large eddy simulation of complex flows’ (UR 507). The computing resources were provided by IDRIS-France. The authors gratefully acknowledge the financial support from the Centre National de la Recherche Scientifique (CNRS), the Centre d’été Mathématique de Recherche Avancée en Calcul Scientifique (CEMRACS) and the Direction Générale de l’Armement (DGA/D4S).     

Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence

The effects of coincidence window and measuring volume size on two-component laser velocimeter measurement of turbulence in an isothermal liquid flow through a concentric annular channel were studied. Three different coincidence windows (100–500 μs) and three different measuring volume sizes (diameter, 5–9 wall units; spanwise length, 24–91 wall units) were used in a flow of Reynolds number 31,500 and data density spanning the high end of intermediate to the low end of high (3–6). While no significant effects of the coincidence window and measuring volume size were found on the time-mean velocity and turbulence intensities, the streamwise Reynolds shear stress measured near a wall was found to be markedly affected by both. The smallest feasible measuring volume along with an appropriate coincidence window provides good measurement of the shear stress. Received: 8 September 1999/Accepted: 11 July 2000