Efficient estimation of power spectral density from laser Doppler anemometer data

 A non-biased estimator of power spectral density (PSD) is introduced for data obtained from a zeroth order interpolated laser Doppler anemometer (LDA) data set. The systematic error, sometimes referred to as the “particle-rate filter” effect, is removed using an FIR filter parameterized using the mean particle rate. Independent from this, a procedure for estimating the measurement system noise is introduced and applied to the estimated spectra. The spectral estimation is performed in the domain of the autocorrelation function and assumes no further process parameters. The new technique is illustrated using simulated and measured data, in the latter case with direct comparison to simultaneously acquired hot-wire data. Received: 9 June 1997/Accepted: 14 October 1997     

Generation of artificial earthquakes via the wavelet transform

A wavelet-based procedure is presented to generate an accelerogram whose response spectrum is compatible with a target spectrum. The acceleration time history of a recorded ground motion is decomposed into a number of component time histories. Next, each of the time histories is appropriately scaled so that its response spectrum matches a specified design spectrum at selected periods. The modified components are used to reconstruct an updated accelerogram, its spectrum is compared with the target spectrum and the process is repeated until a reasonable match is obtained. To achieve this goal, a new wavelet, based on the impulse response function of an underdamped oscillator is proposed. The proposed procedure is illustrated by modifying five recorded accelerograms with different characteristics so that their spectra match a seismic design spectrum prescribed in the 1997 Uniform Building Code for a seismic zone 3 and soil type S_B (rock).     

Linearization as a method for determining parameters of relaxation spectra

A new method for determining parameters of a relaxation spectrum of visco-elastic bodies is proposed. The basic idea of the method consists of presenting measured frequency dependencies of the dynamic modules components by the power series. The coefficients of these series are found by comparing varying values with experimental data by linear functional of errors. The parameters of a spectrum are then calculated from the coefficients of the series. This procedure allows us to overcome the main problem of finding relaxation times, i.e. to pass from non-linear to linear functional of errors. It gives us the unique possibility of unambiguously estimating weights (partial moduli) of lines in a discrete relaxation spectrum and relaxation times because there is only a single minimum in the functional of errors. Received: 8 December 1999/Accepted: 10 December 1999     

A new method for probing the turbulence scalar spectrum by ultrasonic sonar scanning

 A new method is proposed to obtain a turbulent scalar spectrum and the energy dissipation rate in turbulent flow from ultrasonic frequency scanning data. A scanning sonar with frequency varying from 0.5 MHz to 5 MHz has been used to directly probe the energy dissipation rate ɛ and the three-dimensional scalar spectrum E _θ(k). Experiments were conducted in a laboratory open-channel flow in clear water with Reynolds numbers varying from 1.2×10⁵ to 6.9×10⁵. Good agreement is found between measured spectra and those predicted by the Batchelor theory. The energy dissipation rates compare favourably with those obtained from acoustic Doppler velocimeter measurements. Received: 20 March 1997/Accepted: 27 September 1997     

A computer method for simulating service loads

A recently presented study addressed the problem of analyzing field data that are best characterized as nonstationary stochastic signais. The analysis method hypothesizes that the nonstationary signal consists of two stationary signals, which belong to different populations, occurring consecutively according to a suitable probabilistic model. The analysis procedure involves the following: segmenting the time history, estimating the population of each segment, estimating the power spectrum of each segment, averaging the power spectra which belong to each population, presenting the power spectra via parameters of digital filters (which shape white noise sequences into sequences with the measured power spectra), and measuring the parameters of the probabilistic model. In this paper a simulation method is presented that uses the results of the analysis method mentioned above to create a sequence that simulates the statistical characteristics of the nonstationary field data. This simulation method is designed to be efficiently implemented on a general-purpose computer of any size, including micros. First, a review of the stochastic model is given. Then the steps of simulation are presented: generating a white sequence on the digital computer, generating the probabilistic model, and developing an algorithm for using digital filters in shaping the power spectra. Sample results are shown to reflect the soundness of the procedure. This simulation method can prove useful in computer studies of the fatigue of mechanical components under field loading. Since it is exactly reproducible in different laboratories, this method can also serve in comparison studies of fatigue-life prediction procedures. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

Relaxation time spectra of star polymers

 The linear viscoelastic data for model star polymer melts with varying functionality and arm molecular weight were represented by means of a modified Baumgaertel-Schausberger-Winter (BSW) relaxation time spectrum, based on data analysis with the parsimonius model of Baumgaertel et al., reported in 1990. In the case of high arm functionality, the second slow terminal relaxation observed by Vlassopoulos et al. in 1997, was captured with a straightforward extension of the BSW model using broad cut-off functions. This study represents a potentially promising attempt to extend the applicability of this representation of viscoelastic data to more complex architectures, beyond simple linear chains which are characterized by self-similarity. The casting of linear viscoelastic data into spectra allows the exploration of star polymer behavior. It is a necessary step in preparation for large scale complex flow calculations in conjunction with constitutive models and for material databases. Received: 18 November 1998/Accepted: 12 August 1999     

Interaction of von Karman vortices and intersecting main streams in staggered tube bundles

 Flow visualization, heat transfer and pressure drop characteristics in flow through staggered tube bundles have been regarded as classical, with results well-documented. However, the mechanism of producing such results has been left untouched. Applications of staggered tube bundles are abundant in industry, for example as heat exchange devices like the shell-and-tube type and fuel bundles in nuclear reactor cores. An experimental study is recorded in the present paper which investigates the interaction of von Karman vortices and intersecting main streams in staggered tube bundles. Flow visualization by means of the particle tracing method, laser Doppler velocimetry (LDV) and pressure drop measurements using a piezometer are conducted. A modified Reynolds number appropriate to flow through a staggered tube arrangement is defined together with a pressure drop coefficient. Auto-correlation and power spectrum analyses of signals obtained from LDV measurements yield an optimum spectrum frequency which is correlated against the Reynolds number. It is concluded that flow characteristics in staggered tube bundles are determined by the interaction between the von Karman vortex street and X-shaped interacting main streams. Received: 4 August 1997 / Accepted: 3 October 1998     

Light scattering experiments and extended thermodynamics

Light in a gas is scattered on density fluctuations and the spectrum of the scattered light is influenced by the constitutive properties of the gas. The Navier-Stokes-Fourier theory does not always describe the spectrum of the scattered light in gases satisfactorily; it fails for small densities. Extended thermodynamics of many moments however may be used to predict the scattering spectra of dilute gases correctly. In this paper we compare the results of extended thermodynamics with measurements. Received: January 2, 1997     

Power requirement for the mixing of thixotropic liquids

A procedure has recently been proposed by Godfrey et al. [1] for the calculation of the variation of power consumption with time when a thixotropic liquid is agitated from rest using an impeller which rotates at constant speed. This procedure requires a knowledge of the power requirement for Newtonian and time-independent non-Newtonian liquids together with viscometric data for the thixotropic liquid obtained under constant shear rate conditions.Experimental work to test the procedure has been carried out in a 0.126-m-diameter cylindrical vessel with anchor, helical ribbon and helical screw impellers. Power consumption data were obtained for a range of Newtonian and time-independent non-Newtonian liquids and this was then used to make predictions of the measured power input to the thixotropic liquids: salad cream, tomato ketchup, yoghurt, paint and Laponite solutions.The agreement between experiment and theory was usually better than 10%. However, for the case of the helical screws rotating in Laponite it was observed that regions existed close to the vessel wall where there was no fluid circulation. In such cases, the predicted power input was greatly in excess of the measured value. This is not a serious limitation of the predictive procedure since efficient industrial mixers would keep the entire fluid in circulation.     

Taylor length scale measurement by laser Doppler velocimetry

 A new method for making direct measurements of the spatial velocity correlation coefficient, based on two-point laser Doppler velocimetry (LDV), has been developed. In this paper, the effects of control parameters on the correlation coefficient are being investigated. The main sources of experimental error have been identified and analysed. It appears that the probe volume length has a key effect on the accuracy of Taylor micro-scale measurement. A data processing procedure has been established and validated for the determination of this scale. The procedure shows that the portion of the correlation curve used to determine Taylor scale is a function of the integral scale to Taylor micro-scale ratio. Received: 7 June 1995/Accepted: 8 December 1997     

A hardware-oriented method for simulating service loads

This is the third paper in a series which includes A Computer Method for Simulating Service Loads' (pp. 42–46) and ‘A Spectral-Analysis Method for Nonstationary Field Measurements’ (pp. 47–55). This paper presents a hardware method to digitally simulate nonstationary stochastic signals which are analyzed using the procedures outlined in the first paper. The method of analysis hypothesizes that the nonstationary signal consists of two stationary signals which belong to different populations occurring consecutively according to a suitable probabilistic model. The analysis procedure involves the following steps: segmenting the time history, estimating the population of each segment, estimating the power spectrum of each segment, averaging the power spectra which belong to each population, presenting the power spectra via parameters of digital filters which shape white-noise sequences into sequences with the measured power spectra, and measuring the parameters of the probabilistic method. This paper presents a simulation method that uses the results of the analysis method above to create a sequence that simulates the statistical characteristics of nonstationary field data. This simulation method is designed to be efficiently generated via a simple digital-electronic circuit and to be available at a high sampling rate. First a review of the stochastic model is given. The simulation method is then illustrated by means of a block diagram. The main steps of the simulation method include generation of a white sequence, generation of the probabilistic model, and digital filtering. The circuits used for these three-functions are illustrated, and sample results of the use of this hardware are presented. This simulation method can provide a fast reproducible sequence for running mechanical testing mechines. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

HIGH-ORDER SCHEMES IN BOUNDARY ELEMENT METHODS FOR TRANSIENT NON-LINEAR FREE SURFACE PROBLEMS

In this paper the boundary element method is applied to solve transient non-linear free surface flow problems formulated from potential theory. For the temporal evolution a high-order time-stepping procedure based on a truncated forward-time Taylor series expansion is compared with the classical Runge–Kutta technique. The numerical code for both two-dimensional and axisymmetric configurations has been successfully implemented. Emphasis in the paper is placed on describing the analytical development achieved by the use of Maple software. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids, 24: 1049–1072, 1997.     

An improved sample-and-hold reconstruction procedure for estimation of power spectra from LDA data

Techniques for deriving the auto or power spectrum (PSD) of turbulence from laser Doppler anemometry (LDA) measurements are reviewed briefly. The low pass filter and step noise errors associated with the sample-and-hold process are considered and a discrete version of the low pass filter for the resampled signal is derived. This is then used to develop a procedure by which the PSD estimates obtained from sample and hold measurements can be corrected. The application of the procedures is examined using simulated data and the results show that the frequency range of the analysis can be extended beyond the Nyquist frequency based on the mean sample rate. The results are shown to be comparable to those obtained using the method of Nobach et al. (1998) but the new procedures are more straightforward to implement. The technique is then used to determine the PSD of real LDA data and the results are compared with those from a hot wire anemometer.     

Generating arbitrarily sized interrogation windows for correlation-based analysis of particle image velocimetry recordings

 We describe a technique that allows an arbitrary size of the interrogation window when using the traditional FFT algorithm in analysing PIV recordings by either cross- or auto-correlation methods. The length and width of the effective interrogation window are no longer required to be composed of a number of pixels making a power of 2 (16, 32, 64 etc). This gives a higher flexibility in selecting the appropriate window size. Received: 28 January 1997/Accepted: 11 August 1997     

The effects of propeller tip vane on flow-field behavior

 This paper investigates the effects of attaching a tip vane to a propeller blade on the development and propagation of a tip vortex. The study employed a two-bladed propeller operating with and without a tip vane. Evaluation of the tip vortex was studied by using both smoke-wire flow visualization, hot wire anemometer, and strain gauge load-cell techniques. The mean velocity distributions and the velocity unsteadiness data as well as thrust, input power and efficiencies were obtained. Experiments were repeated at various rotating speeds ranging from 2000 to 5000 rpm. Received: 26 November 1995/Accepted: 11 April 1997     

Iterative multigrid approach in PIV image processing with discrete window offset

 The features of an improved algorithm for the interrogation of (digital) particle image velocimetry (PIV) pictures are described. The method is based on cross-correlation. It makes use of a translation of the interrogation areas. Such a displacement is predicted and corrected by means of an iterative procedure. In addition, while iterating, the method allows a refinement of the size of the interrogation areas. The quality of the measured vectors is controlled with data validation criteria applied at each intermediate step of the iteration process. A brief section explains the expected improvements in terms of dynamic range and resolution. The accuracy is assessed analysing images with imposed displacement fields. The improved cross-correlation algorithm has been applied to the measurement of the turbulent flow past a backward facing step (BFS). A systematic comparison is presented with Direct Numerical Simulation (DNS) data available on the subject. Received: 7 October 1997/Accepted: 11 August 1998     

On pipe diameter effects in surfactant drag-reducing pipe flows

Remarkable power saving in a fluid transport system is possible if the surfactant drag reduction technology is used. Application of surfactant drag reduction to district heating and cooling systems has been investigated in the past. The establishment of the scale-up law in drag-reducing pipe flows is one of the most important problems in this application. Main purpose of this study is aimed to develop a reliable scale-up law in surfactant drag-reducing flows. As the basic data of surfactant solutions, both non-Newtonian viscosity and viscoelasticity were experimentally determined. A turbulent eddy diffusivity model based on the Maxwell model was employed to estimate the drag reduction of surfactant solutions. The predictions by the turbulence model developed in this study with proper rheological characteristics of surfactant solutions has resulted in a reliable estimation of the pipe diameter effect in surfactant drag-reducing flows over the pipe diameter range from 11 to 150mm. Received: 30 June 1997 Accepted: 29 December 1997     

根据散斑统计性质测量运动速度的一种新方法

本文提出了一种根据散斑统计性质测量物体运动速度的新方法.在夫朗和费衍射区一点记录运动物体的漫射散斑场随时间的变化,并将记录时城信号作快速付氏变换,转换到频率域上,从功率谱宽度或其所覆面积可推算出物体运动速度.本文从理论上作了分析,推导出物体的运动速度和记录信号功率谱函数的简单关系.实验验证与理论分析吻合一致.该法可作实时测量.     

Scalar concentration measurements in liquid-phase flows with pulsed lasers

The suitability of pulsed lasers for laser-induced-fluorescence (LIF) measurements of the local concentration of scalars in liquid-phase flows is investigated. Experiments were performed to measure the fluorescence intensity of aqueous solutions of rhodamine-6G chloride excited by a Q-switched, frequency-doubled, Nd:YAG laser. The fluorescence intensity is found to be linear with dye concentration, but not with illumination power density. The fluorescence intensity saturates at laser power densities easily exceeded by short-pulse-duration lasers. A procedure for calibrating and normalizing the raw image data is discussed which relies only on weak absorption and the linearity of fluorescence intensity with concentration. This procedure enables quantitative concentration measurement with pulsed-laser-induced fluorescence.