Comparison of length scale estimates for a sudden expansion flow estimated from spatial and auto correlation LDV measurements

Two-point velocity correlation measurements were made in the anisotropic flow field of an axisymmetric sudden expansion using two single component LDV systems. The integral length scales and Taylor microscales were estimated and compared with those obtained from auto correlation measurements in conjunction with Taylor's hypothesis. The agreement of the integral scales was within 20% and the values scale well with the flow geometry, while the agreement of the microscales was within 43%.     

A high-accuracy temporal–spatial pseudospectral method for time-periodic unsteady fluid flow and heat transfer problems

A temporal–spatial pseudospectral (TSP) method is proposed for the high-accuracy solutions of time-periodic unsteady fluid flow and heat transfer problems. In this method, both the spatial and temporal derivative terms in the governing equations are computed by pseudospectral method. The spatial derivatives are computed through Chebyshev and Lagrange polynomials while the time derivatives are computed by Fourier series. The TSP method is capable of directly finding out the periodic state solutions without the necessity to resolve the initial transient state solutions, hence holds high computational efficiency and high numerical accuracy properties for the time-periodic problems. This method is validated by three 2D benchmark problems: the time-periodic incompressible flow with exact solutions; the natural convection in enclosure with time-periodic temperature on one sidewall, and on both sidewalls. The TSP results fit well the exact solutions or the benchmark solutions and the TSP accuracy is much higher than the time marching spatial pseudospectral accuracy. Some time-dependent fluid flow and heat transfer characteristic parameters are analysed. The proposed TSP method could be further extended to more complex time-periodic unsteady fluid flow and heat transfer problems where high-accuracy results are required.     

An investigation of the spatial resolution requirements for two-point correlation measurements using LDV

The spatial resolution requirements for accurate two-point correlation measurements at small separations are investigated. Practical guidelines in terms of characteristic measuring volume sizes and estimated Kolmogorov length scales are given. Sample measurements of two-point one-component longitudinal correlations on the centerline of a turbulent jet are presented.Financial support from NUTEK, the Swedish National Board for Industrial and Technical Development, is acknowledged.     

High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume

 Two techniques are described for measuring the scalar structure of turbulent flows. A planar laser-induced fluorescence technique is used to make highly resolved measurements of scalar spatial structure, and a single-point laser-induced fluorescence probe is used to make highly resolved measurements of scalar temporal structure. The techniques are used to measure the spatial and temporal structure of an odor plume released from a low-momentum, bed-level source in a turbulent boundary layer. For the experimental setup used in this study, a spatial resolution of 150 μm and a temporal resolution of 1,000 Hz are obtained. The results show a wide range of turbulent structures in rich detail; the nature of the structure varies significantly in different regions of the plume. Received: 8 May 2000/Accepted: 15 November 2000     

A spectral-analysis method for nonstationary field measurements

A method for dealing with the problem of spectral analysis of nonstationary field measurements is presented. The method hypothesizes that the nonstationary signal consists of two stationary signals which belong to different populations (environment and working plus environment) which occur consecutively. The analysis method entails segmenting the time history and estimating the population of each segment. Two estimators are presented (average absolute value and energy in a frequency band) and their frequency characteristics are described. Discrete-Fourier transforms of zero-padded segments are used for estimating the spectral-density functions. This method is simply implemented and treats the problem of smoothing the spectral estimates. Moreover, it simplifies the use of different window functions by using convolution in the frequency domain. This paper describes the computational facilities used as well as some electronic circuits that were developed. It also discusses the results of the analysis of typical data which were recorded by LBF (West Germany) personnel for the strain of the front axle of a private car running on three test roads. The detailed computational procedure is given and the results are presented. These results show the power of the suggested estimators in estimating the population of the segments of data and the suitability of the spectral-estimation method in extracting meaningful spectral estimates. In addition, the results identify the properties of the typical signal used. This analysis method can be effectively used in the simulation of field data for the study of random fatigue. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

A method to recover water-wave profiles from pressure measurements

An operational formulation is proposed for reconstructing a time series of water surface displacement from waves using measurements of pressure. The approach is based on the fully nonlinear formulation for pressure below traveling-wave solutions of Euler’s equations developed by Oliveras, Vasan, Deconinck and Henderson. Its validity is tested using experiments in which both the pressure and the surface displacement are measured. The experiments include a wave system that is Galilean invariant – cnoidal waves, and wave systems that are not – reflected cnoidal waves and wave groups. We find that since the proposed formulation is nonlinear, it reproduces the amplitude spectrum of the measured surface displacements better than the hydrostatic model and better than the linear model that takes into account the pressure response factor due to small amplitude waves (the transfer function). Both the proposed formula and the transfer function reconstruct the surface reasonably well, with the proposed formula’s being about 5% more accurate.     

A scanning PIV method for fine-scale turbulence measurements

A hybrid technique is presented that combines scanning PIV with tomographic reconstruction to make spatially and temporally resolved measurements of the fine-scale motions in turbulent flows. The technique uses one or two high-speed cameras to record particle images as a laser sheet is rapidly traversed across a measurement volume. This is combined with a fast method for tomographic reconstruction of the particle field for use in conjunction with PIV cross-correlation. The method was tested numerically using DNS data and with experiments in a large mixing tank that produces axisymmetric homogeneous turbulence at \(R_\lambda \simeq 219\) . A parametric investigation identifies the important parameters for a scanning PIV set-up and provides guidance to the interested experimentalist in achieving the best accuracy. Optimal sheet spacings and thicknesses are reported, and it was found that accurate results could be obtained at quite low scanning speeds. The two-camera method is the most robust to noise, permitting accurate measurements of the velocity gradients and direct determination of the dissipation rate.     

Evaluation of LDA temporal and spatial velocity structure functions in a low Reynolds number turbulent channel flow

 Measurements have been made using Laser Doppler Anemometry (LDA) in a fully developed turbulent channel flow with the aim of determining second-order and third-order temporal and spatial structure functions of the longitudinal velocity fluctuation. A reliable determination of these moments requires the data to be corrected for the effect of noise. Correction procedures are outlined, based on the behaviour of temporal or spatial correlation functions in the limit of small time intervals or small separations. No a priori assumptions about the nature of the noise are made so that the procedure should be quite general. The corrected LDA data indicate that, especially for spatial separations, the effect of noise can be felt even within the inertial range. The corrected structure functions should allow an unambiguous assessment to be made of Taylor’s hypothesis and of the extended self-similarity (ESS) method; examples are given in each case. Temporal structure functions obtained by hot wire anemometry (HWA) are much less affected by noise than the LDA data. Received: 8 April 1998/Accepted: 26 October 1998     

Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case

A multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials. The model developed is based on the higher-order homogenization theory with multiple spatial and temporal scales in one dimensional case. The amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non-Fourier heat conduction due to material heterogeneity and non-local effect of the homogenized solution. By separating the governing equations into various scales, the different orders of homogenized non-Fourier heat conduction equations are obtained. The reduced time dependence is thus eliminated and the fourth-order governing differential equations are derived. To avoid the necessity of C¹ continuous finite element implementation, a C⁰ continuous mixed finite element approximation scheme is put forward. Numerical results are shown to demonstrate the efficiency and validity of the proposed method.     

Time and spatial correlation measurements in the turbulent wake of a circular cylinder using Laser Doppler Anemometry

The present paper reports Laser Doppler Anemometry (LDA) measurements in the turbulent (R _d =1300) wake of a circular cylinder (d=2 mm). On several typical locations in the wake, at cross-section x/d=125, temporal and lateral space velocity correlations have been measured. Temporal autocorrelation functions were determined from the randomly sampled LDA data by means of the Slotting Technique. The autocorrelation functions which were obtained were too low, the discrepancy giving an indication of the influence of noise in the measurements. The influence of noise generated by the photomultiplier tubes, which appeared to be the most important noise source, could be reduced by a cross-correlation technique. A partly new LDA system for two-point velocity correlation measurements was developed, consisting of an elongated measuring volume and a two-point detection system including a semireflecting mirror to divide the scattered light. The results of this investigation clearly demonstrate that LDA is a powerful tool for measuring time and spatial correlations and related properties of turbulence.     

A general method for obtaining shear stress and normal stress functions from parallel disk rheometry data

The problems of converting the torque and normal force versus rim shear rate data generated by parallel disk rheometers into shear stress and normal stress difference as functions of shear rate are formulated as two independent integral equations of the first kind. Tikhonov regularization is used to obtain approximate solutions of these equations. This way of handling parallel disk rheometer data has the advantage that it is independent of the rheological constitutive equation and noise amplification is kept under control by the user-specified parameter in Tikhonov regularization. If the fluid under test exhibits a yield stress, Tikhonov regularization computation will simultaneously give an estimate of the yield stress. The performance of this method is demonstrated by applying it to a number of data sets taken from the published literature and to laboratory measurements conducted specifically for this investigation.     

周期性结构热动力时间-空间多尺度分析

研究一种时间-空间多尺度渐近均匀化分析方法，模拟不同的极端热和动力载荷下微尺度多 相周期性结构中热动力响应问题，并建立一个广义的波动函数场控制方程描述热动力响应. 通过引入一个放大空间尺度和两个缩小时间尺度，在不同时间尺度上获得由空间非均匀性引 起的波动效应和非局部效应. 根据高阶均匀化理论在空间和时间上进行均匀化，获得高阶非 局部函数场波动方程. 并进一步用C0连续修正了高阶非局部函数场波动方程的有限元近 似解，使问题的求解避免了对有限元离散的C1连续性要求. 并与经典的空间均匀化方法 相比较，指出了经典的空间均匀化方法的局限性，进一步以一维非傅立叶热传导和热动力问 题为例，讨论了各种情况下方法的正确性与有效性.     

A method for reconstruction of residual stress fields from measurements made in an incompatible region

A method is introduced by which the complete state of residual stress in an elastic body may be inferred from a limited set of experimental measurements. Two techniques for carrying out this reconstruction using finite element analysis are compared and it is shown that for exact reconstruction of the stress field via this method, the stress field must be measured over all eigenstrain-containing regions of the object. The effects of error and incompleteness in the measured part of the stress field on the subsequent analysis are investigated in a series of numerical experiments using synthetic measurement data based on the NeT TG1 round-robin weld specimen. It is hence shown that accurate residual stress field reconstruction is possible using measurement data of a quality achievable using current experimental techniques.     

New framework for Bayesian statistical analysis and interpolation of residual stress measurements

In the present study, different residual stress and strain data measured from various techniques are analyzed using a Bayesian statistical approach and finally interpolated utilizing modified Shepard method. This research is carried out to compare the capability, simplicity and accuracy of Bayesian approach with different probability density functions. Three different probability density functions: Gaussian, Cauchy and Sivia's distribution are studied and compared here. Finally the modified Shepard method is utilized with new interpolant and weight functions, to interpolate the scattered measured data. The proposed framework is then applied to two sets of measured residual data obtained from various experimental techniques.     

A model-free noise removal for the interpolation method of correlation and spectral estimation from laser Doppler data

A procedure to estimate and remove the contribution of data noise to the correlation function and the power spectral density calculated from laser Doppler data with the interpolation method is introduced. In comparison with earlier approaches, the new procedure is model free and, therefore, more objective. The new procedure is proven based on experimental data taken with a laser Doppler system, where the power spectral density obtained with the interpolation method is compared directly to data from a hot-wire reference measurement.     

A method for separating shock wave motion and turbulence in LDV measurements

 Two-component laser Doppler velocimetry (LDV) measurements were made in a planar, two-dimensional flow containing an unsteady oblique shock wave formed by the convergence of two supersonic streams past a thick plate. High-speed wall pressure measurements locate the shock wave and, consequently, allow separation of the effects of shock wave motion from the turbulence fluctuations in the LDV measurements of the shock-separated free shear layer. In the current flow isolating the large-scale changes in the position of the shock from the turbulence primarily reduces the experimental scatter rather than significantly changing the shapes or magnitudes of the turbulent stress profiles. Changes in the direction of shock motion do not significantly affect the mean velocity, but do affect the turbulent stresses. Received: 11 August 1997/Accepted: 30 September 1998     

A method to provide statistical measures of large-scale instantaneous particle clusters from planar images

Particle clusters are preferential accumulations of a solid, secondary phase that can be caused by turbulence. It is well known that particle clusters can influence the performance of systems employing suspension flows, such as pulverised fuel combustion systems. However, statistical analysis of clusters is limited by available methods to quantify them. In the current study, a method to identify planar slices of large-scale particle clusters from planar images of instantaneous particle distributions is presented. The method employs smoothing of instantaneous particle scatter images by a length scale, L _S , to produce pseudo-scalar fields of particle distributions. The scalar fields are compared with mean (not smoothed) images to produce cluster masks that are then multiplied by the original instantaneous image to produce a map of the locations of cluster slices. The sensitivity to the smoothing length scale is assessed parametrically for its influence on the statistical measures of the following parameters characterising slices of large-scale clusters in four representative flows: the physical locations of the cluster slice centroids; the area of the cluster slice; and the number of cluster slices per image. While the results are influenced by the selected value of smoothing length scale, L _S , the sensitivity is low in a physically reasonable range and the method performs well in this range for the four different flow cases. The method could be extended to provide volumetric measurements with suitable volumetric imaging systems.     

A sensitivity analysis of the point reference global correlation (PRGC) technique for spatio-temporal correlations in turbulent flows

The point reference global correlation (PRGC) technique which combines single and global measurements as proposed by Chatellier and Fitzpatrick (Exp Fluids 38(5):563–757, 2005) is of significant interest for the analysis of the turbulent statistics for noise source modeling in jet flows as it allows the 2D spatio-temporal correlation functions to be obtained over a region of the flow. This enables the statistical characteristics including inhomogeneous and anisotropic features to be determined. The sensitivity of the technique is examined in some detail for the specific case of laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Simulated data are used to enable a parametric study of the accuracy of the PRGC technique to be determined as a function of the various measurement parameters. The sample frequencies and the number of samples of both the LDV and PIV signals are shown to be critical to errors associated with the estimated spatio-temporal correlations and that low data rates can lead to significant errors in the estimates. Measurements performed in single stream and co-axial jet flows at Mach 0.24 using PIV and LDV systems are reported and the 2D space–time correlation functions for these flows are determined using the PRGC technique. The results are discussed in the context of noise source modeling for jet flows.