Corrections for velocity and temperature derivatives in turbulent flows

Spectral corrections, which are based on local isotropy, are presented for all the spatial derivatives of velocity and temperature fluctuations which feature in the average dissipations of turbulent energy and temperature. The corrections, which compensate for the spectral attenuation due to the separation between sensors, depend only weakly on the choice of the three-dimensional energy (or temperature) spectrum and therefore on the turbulence Reynolds number. Corrections are also obtained for the variances of velocity and temperature derivatives. The diagonal velocity derivatives require smaller corrections than either the off-diagonal velocity derivatives or the temperature derivatives. Corrections of comparable magnitude are required for the average dissipations of turbulent energy and temperature.     

Laser Doppler velocity bias in separated turbulent flows

Velocity bias effects on data obtained with a coincident two channel laser Doppler velocimeter in a highly turbulent separated supersonic flow are presented. Probability distributions of the fluctuating velocities were distorted by velocity bias in a manner consistent with theory and a two-dimensional velocity inverse weighting function bias correction produced reasonable appearing velocity probability distributions. The addition of an approximate correction term to account for the effects of the unmeasured third velocity component improved these results but had little effect on the velocity statistics. Experimental factors that could partially compensate or falsely add to the velocity bias, conditions for the bias to occur, and conditions for which the bias may also be observed and corrected for are discussed.     

On predicting particle-laden turbulent flows

The paper provides an overview of the challenges and progress associated with the task of numerically predicting particle-laden turbulent flows. The review covers the mathematical methods based on turbulence closure models as well as direct numerical simulation (DNS). In addition, the statistical (pdf) approach in deriving the dispersed-phase transport equations is discussed. The review is restricted to incompressible, isothermal flows without phase change or particle-particle collision. Suggestions are made for improving closure modelling of some important correlations.Lecture presented at a workshop on turbulence in particulate multiphase flow, Fluid Dynamics Laboratory, Battelle Pacific Northwest Laboratory, Richland, WA, March 22–23, 1993.     

Kinds of local self-similarity of the velocity field of prewall turbulent flows

An analysis of dimensionalities and an approach used by Millikan [1] in analysis of mean motion are applied to investigation of the pulsational motion of three types of prewall flows of an incompressible liquid, i.e., in a boundary layer with longitudinal flow around a plate, in a round tube, and in a flat channel. It is shown that with sufficiently large Reynolds numbers there exists an interval of distances from the wall x₂, within which the integral one-point correlations and the narrow-band one-point correlations _jk do not depend on x₂. In frequency space, there exists a hyperbolic interval in which _jk=A_jku ²f^-1. Here A_jk=const; u is the dynamic velocity; and f is the frequency. It is also shown that, from the point of view of the mean motion, a distinction must be made between Kármán turbulent flow with rather large Reynolds numbers and non-Kármán flow with small, but turbulent Reynolds numbers. In the latter case, the coefficients in the logarithmic profiles of the velocity and in the law of the resistance depend on the Reynolds number. The article gives an evaluation of the Reynolds number, which can be assumed to be rather large.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–42, November–December, 1976.The author considers it his pleasant duty to express his indebtedness to M. A. Kashina for furnishing experimental data.     

On the motion of particles in turbulent duct flows

Existing knowledge on particle deposition rates on walls from turbulent pipe and channel flows is summarized and it is shown that discrepancies exist between experimental and theoretical findings. To contribute to the existing experimental information, laser Doppler measurements are reported of the flow field of a glass particle-air two-phase flow. The results reveal certain seemingly peculiar behaviors of the particles which obviously defy the predictions of the conventional analyses of turbulent two-phase suspension flows.In an accompanying approximate, yet pragmatic theoretical approach, an attempt is made to find a rational basis for the explanation of these experimentally observed particle behaviors. It is shown for the particles in the present study, there exists a limiting size above which their response to the agitation of the fluctuating motion of the surrounding fluid could be treated as if the flow were laminar. On this rational basis, these experimentally observed particle behaviors can then be qualitatively explained by the existing theory of particle excursion in a laminar shear flow field.Reported also is a suggestion to extend the present analysis to a dispersion of particles of multiple sizes.     

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.     

Acoustic Lagrangian velocity measurement in a turbulent air jet

Measuring Lagrangian velocities in a turbulent flow is of a great interest for turbulence modeling. We report measurements made in an axisymmetric turbulent air jet at Reynolds number R _λ ≃ 320, using acoustical Doppler scattering. Helium-filled soap bubbles are used as Lagrangian tracers. We describe an experimental setup which allows the simultaneous measurement of the full three-component Lagrangian velocity and the longitudinal Eulerian one. Lagrangian velocity probability density functions (PDF) are found Gaussian, close to Eulerian ones. Velocity correlations are analysed as well as the statistical dependence between components.     

Spatial correlation measurement in turbulent flows using pulsed wire anemometry

Details of a new technique in pulsed wire anemometry, developed to allow measurement of two-point spatial velocity correlations in highly turbulent flows, are described. An outline of the interface devices necessary for linking two anemometers to a microcomputer is given and examples of the use of the technique are presented. Firstly, measurements of spatial correlations with and without time delay in the near wake of a nominally two-dimensional cylinder normal to a uniform stream confirmed the viability of the technique. Secondly, measurements in the highly turbulent, separated region behind a normal flat plate fitted with a downstream splitter plate are presented as a demonstration of the effectiveness of the technique in such difficult flows. We believe that these are the first direct measurement of spatial correlation functions within a separated flow.     

Corrections for spatial velocity derivatives in a turbulent shear flow

Possible corrections for measured spatial velocity derivatives have been inferred from a direct numerical simulation database for a fully developed turbulent channel flow. The magnitude of the correction depends much less on the distance from the wall for derivatives in the spanwise direction than for those in the wall-normal direction. Corrections based on local isotropy are better approximations for spanwise derivatives than for wall-normal derivatives.The support of the Australian Research Council is gratefully ackowledged.     

Simultaneous measurement of velocity and temperature in high-temperature turbulent flows: a combination of LDV and a three-wire temperature probe

This paper deals with a simple and reliable technique for simultaneous measurement of velocity and temperature in high-temperature turbulent flows, including combustion. The technique is based on the combination of laser Doppler velocimetry and a digitally compensated fine-wire thermocouple. For temperature measurement, a two-thermocouple probe with a fine cold wire [Tagawa et al. (1998) Rev Sci Instrum 69: 3370–3378] is used, which enables in situ measurement of thermocouple time constants and accurate compensation of the thermocouple response. When tested in a turbulent wake behind a heated cylinder, the technique proves to be highly reliable and effective for investigating heat transport processes in various non-isothermal turbulent flows. Received: 24 June 1999/Accepted: 10 March 2000     

On the nature of the organized structures in turbulent near-wall flows

A physical mechanism of onset of large-scale organized structures in turbulent flows along a plane wall which are the cause of intensification of turbulent fluctuations is formulated. The structures take the form of high-speed and low-speed streaks caused by streamwise vortices, i.e., motions in the plane of the transverse cross-section. The streamwise vortices are excited as a result of instability under the action of the anisotropy of the normal components of the Reynolds stress tensor. A model for describing these vortices that gives characteristics in qualitative and quantitative agreement with the experimental data is proposed. In particular, the most probable and mean distances between neighboring vortices are correctly reproduced. The theory makes it possible to explain certain methods of turbulent flow control for the purpose of drag reduction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–30, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00602).     

Effect of the measurement volume in turbulent pipe flow measurement by the ultrasonic velocity profile method (mean velocity profile and Reynolds stress measurement)

 The ultrasonic velocity profile measurement method has some favorable advantages over the conventional flow measurement methods, such as measurement of the instantaneous velocity profile over the measuring line and its applicability to opaque liquids. The method has another advantage of being non-intrusive. Hence, it is applicable to various flow conditions, although it requires a relatively large measurement volume. In this paper, the effects of the measurement volume on the mean velocity profile and the Reynolds stress measurement have been investigated for fully developed turbulent flows in a vertical pipe. The results were then compared with data obtained by direct numerical simulation. Received: 9 March 2000 / Accepted: 27 March 2001 Published online: 29 November 2001     

4D Magnetic resonance velocimetry for mean velocity measurements in complex turbulent flows

An adaptation of a medical magnetic resonance imaging system to the noninvasive measurement of three-component mean velocity fields in complex turbulent engineering flows is described. The aim of this paper is to evaluate the capabilities of the technique with respect to its accuracy, time efficiency and applicability as a design tool for complex turbulent internal geometries. The technique, called 4D magnetic resonance velocimetry (4D-MRV), is used to measure the mean flow in fully developed low-Reynolds number turbulent pipe flow, Re=6400 based on bulk mean velocity and diameter, and in a model of a gas turbine blade internal cooling geometry with four serpentine passages, Re=10,000 and 15,000 based on bulk mean velocity and hydraulic diameter. 4D-MRV is capable of completing full-field measurements in three-dimensional volumes with sizes on the order of the magnet bore diameter in less than one hour. Such measurements can include over 2 million independent mean velocity vectors. Velocities measured in round pipe flow agreed with previous experimental results to within 10%. In the turbulent cooling passage flow, the average flow rates calculated from the 4D-MRV velocity profiles agreed with ultrasonic flowmeter measurements to within 7%. The measurements lend excellent qualitative insight into flow structures even in the highly complex 180° bends. Accurate quantitative measurements were obtained throughout the Re=10,000 flow and in the Re=15,000 flow except in the most complex regions, areas just downstream of high-speed bends, where velocities and velocity fluctuations exceeded MRV capabilities for the chosen set of scan parameters. General guidelines for choosing scanning parameters and suggestions for future development are presented.     

On the directional dependence of turbulence properties in anisotropic turbulent flows

 An examination is made of the consequences of a zero correlation between fluctuations in velocity level and flow direction in a stationary anisotropic turbulent flow. This zero correlation results from the fact that in a stationary turbulent flow fluctuations in both velocity level and flow direction are entirely random processes. In this paper this is considered to be an inherent property of stationary flow and utilised to simplify both the computation and the measurement of anisotropic turbulence. This new method shows several advantages compared to earlier methods. First, the spatial distribution of the flow turbulence has been shown to be a trigonometric function of the spatial parameter. Second, the relationship between Reynolds normal and shear stresses has been established. Third, when a two-dimensional flow field is concerned, two measurements using a one-component LDA system are sufficient to identify the turbulence. Until now it has been considered that three such measurements were necessary. The feasibility of the method, known as zero correlation method, has been analysed and demonstrated by experiment. Received: 29 January 1997/Accepted: 30 July 1997     

On the eddy viscosity model of periodic turbulent shear flows

Physical argument shows that eddy viscosity is essentially different from molecular viscosity. By direct numerical simulation, it was shown that for periodic turbulent flows, there is phase difference between Reynolds stress and rate of strain. This finding posed great challenge to turbulence modeling, because most turbulence modeling, which use the idea of eddy viscosity, do not take this effect into account. The project supported by the National Natural Science Foundation of China (19732005) and Liu Hui Center for Applied Mathematics of Nankai & Tianjin University     

On the accuracy of simultaneously measuring velocity component statistics in turbulent wall flows with arrays of three or four hot-wire sensors

A highly resolved turbulent channel flow direct numerical simulation (DNS) with Re _τ = 200 has been used to investigate the ability of probes made up of arrays of three or four hot-wire sensors to simultaneously and accurately measure statistics of all three velocity components in turbulent wall flows. Various virtual sensor arrangements have been tested in order to study the effects of position, number of sensors and spatial resolution on the measurements. First, the effective cooling velocity was determined for each sensor of an 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, simulating the response of the virtual probes to obtain the effective velocities cooling the sensors, velocity component statistics have been calculated neglecting the velocity gradients over the probe sensing area. A strong influence of both mean and fluctuation velocity gradients on measurement accuracy was found. A new three-sensor array configuration designed to minimize the influence of the velocity gradients is proposed, and its accuracy is compared to two-sensor X- and V-array configurations.     

Assessment of a quintuple hotwire measurement technique for highly turbulent flows

A five-wire calibration and measurement technique is presented, which is an extension of the four-wire method developed by Döbbeling et al. (1990a, b). From numerical simulations of the uniqueness domain and the angular resolution it is concluded that the uniqueness domain of the quintuple technique can be expanded to a hemisphere as opposed to the four-wire techniques which are restricted to a conical domain of about 40° half angle. Measurements of the mean velocities and Reynolds stresses in a low-turbulence jet and in grid turbulence confirm and complement the results of the numerical simulations. It is thus shown that the quintuple method achieves increased accuracy in an expanded measurement range.The work of D. Hölzer, student of engineering at the University of Karlsruhe, and the support of W. Paulat and W. Pfeffinger in writing the data aquisition software, and H. Klette who manufactured the probe, is gratefully acknowledged. This work was supported by the Deutsche Forschungsgemeinschaft within the framework of the Sonderforschungsbereich 167, Hochbelastete Brennräume- Stationäre Gleichdruckverbrennung, Teilprojekt A10.