On the spatial resolution of velocity and velocity gradient-based turbulence statistics measured with multi-sensor hot-wire probes

A highly resolved turbulent channel flow direct numerical simulation with Re _τ = 200 has been used to investigate the ability of 12-sensor hot-wire probes to accurately measure velocity and velocity gradient based turbulence statistics. Various virtual sensor separations have been tested in order to study the effects of spatial resolution on the measurements. First, the effective cooling velocity has been determined for each sensor for (1) an idealized probe where the influence of the velocity component tangential to the sensors and flow blockage by the presence of the prongs and the finite lengths of and thermal cross-talk between the sensors are neglected and, (2) for a real probe, the characteristics of which have been determined experimentally. Then, simulating the response of the virtual probes for these two cases to obtain the effective velocities cooling the sensors, velocity and vorticity component statistics have been calculated by assuming the velocity gradients to be constant over the probe sensing area.     

A hot-wire probe configuration and data reduction method to minimize velocity gradient errors for simultaneous measurement of three velocity components in turbulent flows

A highly resolved turbulent channel flow direct numerical simulation (DNS) with Re _?? ?=?200 has been used to investigate the influence of the velocity gradients on the measurement accuracy of a hot-wire probe capable of measuring all three velocity components simultaneously. A new proposed sensor arrangement has been tested. First, the effective cooling velocity was determined for each sensor of the idealized probe, where the influence of the velocity component tangential to the sensors and flow blockage by the presence of the probe are neglected. Then, velocity component statistics were calculated, neglecting the velocity gradients over the probe sensing area, and they were compared to the DNS database values. It has been shown that the influence of the velocity gradients on the new proposed arrangement is minimized. Its accuracy was compared to existing three- and four-sensor configurations as well as to two-sensor X- and V-array probes.     

The accuracy of turbulent velocity component measurements by multi-sensor hot-wire probes: a new approach to an old problem

The measurement accuracy of different hot-wire probes possessing between two and 12 sensors is analyzed. Experimental data were sampled in a round free jet and in a zero-pressure-gradient turbulent boundary layer by a 12-sensor hot-wire probe. Testing of the various hot-wire configurations is enabled by selectively considering different combinations of the 12 available anemometer output voltages. The influence on the measurement accuracy of neglecting the velocity gradients as well as neglecting one velocity component is analyzed. Two approaches were applied. One is based on expressions that relate the instantaneous velocity components and velocity gradients, and the other is based on a simple least-squares regression method. It is found that neglecting the instantaneous fluctuations of the velocity gradients for the measurement of the cross-stream velocity component, V, has a crucial influence and results in large errors. It is also shown that this influence is less significant or even negligible for the measurement accuracy of the other two velocity components, U and W.     

Measurement of velocity vectors with orthogonal and non-orthogonal triple-sensor probes

A new method of interpreting the signals from triple-sensor thermal anemometer probes has been developed based on fast solution for all the roots of the non-linear Jorgensen (1971) equations describing the directional response of each cylindrical sensor. The sensors can be oriented at arbitrary angles to each other, but always within a range of probe geometries that keep prong interference and thermal wake interference below acceptable levels. The properties of a class of non-orthogonal symmetric tetrahedral probe geometries are studied in relation to the range of flow vector angles that can be measured, the sensitivity of the probe with respect to changes in flow angle, and the sensitivity of the computed velocity components due to angular errors associated with the construction of the probe. The solutions of Jorgensen's equations are inherently multiple-valued, but if the velocity vector is restricted to be within a cone of angles, they are unique. It is shown that measurements with non-orthogonal triple sensor signals are sensitive to angular deviations of a few degrees of the sensor angles from the nominally orthogonal probe geometry, indicating the need of a non-orthogonal algorithm. The mean, rms, Reynolds stress, and power spectrum of the velocity in fully developed turbulent pipe flow were measured using a specially designed triple sensor probe and the proposed algorithm.Presently with the Dept. of Mechanical Engineering at The University of Iowa     

In situ calibration of hot wire probes in turbulent flows

A method for in situ calibration of hot-wires in a turbulent flow is presented. The method is particularly convenient (even necessary) for calibrating large probe arrays, like the 143-wire boundary layer rake of the WALLTURB experiment. It is based on polynomial expansion of the velocity statistics in terms of voltage statistics as originally described by George et al. [Exp Ther Fluid Sci 2(2):230–235, 1989]. Application of the method requires knowing reference mean velocity and higher order central moments (with the array in place) of the turbulent velocity at the probe location at only one freestream velocity. These were obtained in our experiment by a stereo PIV plane just upstream of the probe array. Both the procedure for implementing the method and sample results are presented in the article.     

Free-surface fluctuations in hydraulic jumps: Experimental observations

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air–water “free-surface” detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar (F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps.     

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.     

Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.     

Turbulence measurements in pipe flow using a nano-scale thermal anemometry probe

A new nano-scale thermal anemometry probe (NSTAP) has been developed using a novel procedure based on deep reactive ion etching. The performance of the new probe is shown to be superior to that of the previous design by Bailey (J Fluid Mech 663:160–179, 2010). It is then used to measure the streamwise velocity component of fully developed turbulent pipe flow, and the results are compared with data obtained using conventional hot-wire probes. The NSTAP agrees well with the hot-wire at low Reynolds numbers, but it is shown that it has better spatial resolution and frequency response. The data demonstrate that significant spatial filtering effects can be seen in the hot-wire data for probes as small as 7 viscous units in length.     

The velocity field of the turbulent very near wake of a circular cylinder

Hot-wire measurements were conducted in the very near wake (x/d10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re _d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.This study has been funded by the NASA-Ames University Consortium Cooperative Agreement, NCC2-5003. We wish to thank Patrick Beaudan for providing us with the LES results for comparison and Parviz Moin for his interest in and encouragement of this experiment to provide validation data for the LES. We also wish to thank loseph Murray for his help with the look-up-table data reduction program.     

How to estimate the low wavenumber turbulence frequency spectrum

 An estimate of the low wavenumber component of surface turbulence shear stress as a function of frequency has been obtained through measurements of the correlations of the longitudinal component of turbulence velocity made close to the surface at y ⁺=7. The data were acquired in a fully-developed turbulent pipe flow at a Reynolds number (based on centreline velocity and pipe diameter) of 268000, using two single hot-wire anemometer probes. A novel data analysis procedure has been introduced to establish the accuracy limits of the low wavenumber turbulence energy estimate for frequencies in the similarity regime of wall turbulence and the results are compared with other measurement techniques. Received: 18 November 1993/Accepted: 21 April 1997     

Simultaneous measurement of velocity and pressure in a plane jet

A new technique was developed for the simultaneous measurement of velocity and pressure in turbulent flows. To accomplish this objective, a new probe (hereafter called the combined probe) that consists of an X-type hot-wire probe and a newly devised pressure probe was developed. The pressure probe was miniaturized by the MEMS fabrication process and by using a 0.1-in. microphone as a pressure sensor for improving the spatial resolution. This pressure probe was placed between two hot-wire sensors of which the X-type hot-wire probe was composed. The pressure probe was given a hemispherical tip, like that of a pitot tube, because an earlier pressure probe with a conical tip suffered from a reduction in spatial resolution. The spatial arrangement of the pressure probe and the hot-wire probe for the combined probe was carefully determined, because there was a risk that the measurement accuracy of one probe will be influenced by disturbances caused by the other probe when the two probes were placed very close to each other. Therefore, the combined probe was arranged to engender no noticeable interference between the velocity data and the pressure data measured by their respective probes. As one application of this combined probe, simultaneous measurements of pressure and two components of instantaneous velocity were performed in a plane jet. The turbulent energy budget and the cross-correlation coefficient of velocity and pressure in the intermittent region of the plane jet were estimated. The results show that the mean streamwise velocity, velocity fluctuation, and pressure fluctuation profiles were consistent with those measured individually using the X-type hot-wire probe or pressure probe. Moreover, it was shown that the integral value of the diffusion term (which should theoretically be equal to zero) in the turbulent energy transport equation was closer to zero than previous reports (Bradbury in J Fluid Mech 23(Part 1):31–64, 1965). In addition, the time variation of the cross-correlation coefficient in the intermittent region supports the vortex structure model predicted in previous studies (Browne et?al. in J Fluid Mech 149:355–373, 1984; Tanaka et?al. JSME Int J Ser B 49(4):899–905, 2006; Sakai et?al. J Fluid Sci Technol 2(3):611–622, 2007).     

Flow distortion in flux measurements with IMST/SA-CNRS Lyman-alpha hygrometer

A Lyman-alpha hygrometer with a reduced sampling volume has been developed in order to measure small-scale, fast fluctuations of humidity in laboratory. It is combined with an X-wire anemometer probe to measure the local value of the turbulent flux or with a resistant wire temperature probe to measure humidity-temperature mixed statistics. In order to determine the influence of the flow distortion by the probe itself on these measurements, the structure of the flow is investigated experimentally both inside the hygrometer sampling volume and at the location of the velocity or temperature probe. This investigation includes flow visualizations, measurements with a single hot wire in a calibration tunnel and measurements with a X-wire probe and a temperature resistance wire probe in a large turbulent boundary layer.     

Silicon based flow sensors used for mean velocity and turbulence measurements

Small and directional sensitive silicon based sensors for velocity measurements have been designed and fabricated using microelectronic technology. Single-chip as well as double-chip sensors for the determination of mean velocity and turbulent stresses have been developed. To determine the performance of these silicon sensors, comparisons with conventional hot-wire sensors were done in a well-defined two-dimensional turbulent flat plate boundary layer at a constant Reynolds number of 4.2 · 10⁶. All the silicon sensors were found to have a spatial and frequency resolution that makes them suitable for turbulence measurements. In the studied flow field the measured profiles of mean velocities and Reynolds stresses of all silicon sensors show the same accuracy as corresponding hot-wire measurements. The silicon sensors are also shown to operate with good resolution even when the temperature of the heated part of the chip is reduced considerably.     

Comparative analyses of phase-detective intrusive probes in high-velocity air–water flows

A comparative analysis of a wide range of air–water flow properties was conducted for two types of phase-detection intrusive probes including fiber-optical and conductivity probes. Experiments were conducted on a stepped spillway model for a skimming flow discharge q = 0.478 m²/s and for Re = 4.7 10⁵ in a flow region just downstream of the inception point of free-surface aeration and in the fully developed flow region. The comparison of a large number of key air–water flow properties showed a very close agreement for the two sensor types including void fraction, interfacial velocity and equivalent clear water flow depth enabling a direct comparison of past and future data collected with either phase-detection probe type. Minor differences were observed in terms of chord sizes, clustered properties and interparticle arrival times linked with the slightly smaller sensor size of the fiber-optical probe. The in-line positioning of the leading and trailing tips of the fiber-optical probe affected the trailing tip properties resulting in elevated turbulence intensities. An optimum dual-tip phase-detection probe design should consist of small probe tips positioned side-by-side.     

Advanced pneumatic method for gradient flow analysis

Pneumatic 5-hole probes are widely known reliable sensors for the analysis of three-dimensional flow fields. Since the accuracy of such measurements depends strongly on the volume of the probe and the gradients in the flow, a miniature spherical five-hole-probe with an improved analysis method was developed. With the new method, the complete physically reasonable angle measurement range can be used now by introducing modified calibration functions. A dimensionless examination of the flow around spheres shows the independence of the calibration functions within a wide range of flow velocities. Misrepresentations in flows with high gradients caused by the volume of the probe are estimated by a geometry based correction method. The quality of the method is analysed by an extensive error calculation. Results of measurements in a three-dimensional model combustor are discussed.     

Reynolds stress, mean velocity, and dynamic static pressure measurement by a four-hole pressure probe

An improved version of the four-hole directional pressure probe, or Cobra probe, is described, in which the frequency response has been extended to 1.5 kHz. The probe measures all three orthogonal mean and turbulent velocity components at a point in the flow field. The probe also resolves the local mean and turbulent components of static pressure, allowing moments between the fluctuating velocity components and pressure to be determined. The techniques developed to allow the improved frequency response and the use of the probe in turbulent, developed pipe flow (a calibration flow) are described. Also given are the turbulent pressure-velocity correlations, which show a high degree of anticorrelation for one velocity component.     

Quadruple hot-wire probes in a simulated wall flow

A method for calibration and measurement with a fourwire probe is described. The method does not require any assumption about the response of the wires and it is not necessary to know the exact probe geometry. Measurements in a two-dimensional turbulent boundary layer showed large errors in the shear stress, although the probe had a wire arrangement practically insensitive to mean velocity gradients normal to the wall. The problem seems to be caused by the strong instantaneous spanwise velocity gradients, as suggested by the computed response of a simple probe model inserted into a numerical flow obtained by direct simulation.     

Highly spatially resolved velocity measurements of a turbulent channel flow by a fiber-optic heterodyne laser-Doppler velocity-profile sensor

Velocity measurements with a high spatial resolution are important in turbulent flow research. In this paper, we report on the development of a new fiber-optic laser-Doppler velocity-profile sensor exhibiting a spatial resolution of up to 5 μm and its application to turbulent boundary layers. The sensor developed in the present work employs a frequency-division-multiplexing technique in order to separate two measurement signals from the two fringe systems. Velocity measurements close to zero at the solid wall were realized using heterodyne technique. The use of fiber optics improved a robustness of the sensor. The measurement accuracy of the sensor was experimentally investigated with respect to the spatial resolution and velocity. Universal velocity profile of a turbulent flow was obtained in a fully developed channel flow. Mean and fluctuating velocity are presented with a high spatial resolution.     

A model for tracking inertial particles in a lattice Boltzmann turbulent flow simulation

A computationally inexpensive model for tracking inertial particles through a turbulent flow is presented and applied to the turbulent flow through a square duct having a friction Reynolds number of Re_τ = 300. Prior to introducing particles into the model, the flow is simulated using a lattice Boltzmann computation, which is allowed to evolve until a steady state turbulent flow is achieved. A snapshot of the flow is then stored, and the trajectories of particles are computed through the flow domain under the influence of this static probability field. Although the flow is not computationally evolving during the particle tracking simulation, the local velocity is obtained stochastically from the local probability function, thus allowing the dynamics of the turbulent flow to be resolved from the point of view of the suspended particles. Particle inertia is modeled by using a relaxation parameter based on the particle Stokes number that allows for a particle velocity history to be incorporated during each time step. Wall deposition rates and deposition patterns are obtained and exhibit a high level of agreement with previously obtained DNS computational results and experimental results for a wide range of particle inertia. These results suggest that accurate particle tracking through complex turbulent flows may be feasible given a suitable probability field, such as one obtained from a lattice Boltzmann simulation. This in turn presents a new paradigm for the rapid acquisition of particle transport statistics without the need for concurrent computations of fluid flow evolution.