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.     

On the spectrum of magnetic field and scalar impurity fluctuations in acoustic turbulence

The fluctuations of a magnetic field in acoustic turbulence are examined. An equation is derived for the spectral tensor of homogeneous magnetic field fluctuations. In a certain limit case the spectrum of steady-state pulsations is obtained in the presence of an external source. It is shown that three kinds of spectra exist in an inertial subdomain, each of which corresponds to a definite domain in wave space. Analogous results have been obtained for the fluctuations of a homogeneous scalar impurity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 26–31, March–April 1971.In conclusion, the author grateful to R. Z. Sagdeev for discussing the results obtains at a seminar.     

A new method for the generation of representative time-domain turbulence excitations

In this paper we address the issue of generating, from the spectral and spatial parameters of turbulent flow excitations, time-domain random excitations suitable for performing representative nonlinear numerical simulations of the dynamical responses of flow-excited tubes with multiple clearance supports. The new method proposed in this work, which is anchored in a sound physical basis, can effectively deal with non-uniform turbulent flows, which display significant changes in their spatial excitation properties. Contrary to the classic technique developed by Shinozuka and coworkers, which generates a large set of correlated physical forces, the proposed method directly generates a set of correlated modal forces. Our approach is particularly effective leading to a much smaller number of generated time-histories than would be needed using physical forces to simulate the turbulence random field. In the case of strongly non-uniform flows, our approach allows for a suitable decomposition of the flow velocity profile, so that the spectral properties of the turbulence excitation are modeled in a consistent manner. The proposed method for simulating turbulence excitations is faster than Shinozuka׳s technique by two orders of magnitude. Also, in the framework of our modal computational approach, nonlinear computations are faster, because no modal projection of physical turbulent forces is needed. After presenting the theoretical background and the details of the proposed simulation method, we illustrate it with representative linear and nonlinear computations performed on a multi-supported tube.     

A new calibration and data reduction method for turbulence measurement by multihotwire probes

A new calibration technique has been developed for the simultaneous measurement of the instantaneous velocity components in a three dimensional turbulent flow field by miniature pyramidoidal four-wire probes. The method was tested in the boundary layer of a wind tunnel by comparison measurements with X-wire probes. The results are very satisfactory and in good agreement with other experiments known from the literature.     

A correction method for measuring turbulence kinetic energy dissipation rate by PIV

The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.     

A Petrov-Galerkin method for the numerical solution of the Bradshaw-Ferriss-Atwell turbulence model

The Bradshaw-Ferriss-Atwell model for 2D constant property turbulent boundary layers is shown to be ill-posed with respect to numerical solution. It is shown that a simple modification to the model equations results in a well-posed system which is hyperbolic in nature. For this modified system a numerical algorithm is constructed by discretizing in space using the Petrov-Galerkin technique (of which the standard Galerkin method is a special case) and stepping in the timelike direction with the trapezoidal (Crank-Nicolson) rule. The algorithm is applied to a selection of test problems. It is found that the solutions produced by the standard Galerkin method exhibit oscillations. It is further shown that these oscillations may be eliminated by employing the Petrov-Galerkin method with the free parameters set to simple functions of the eigenvalues of the modified system.     

A two-scale second-moment turbulence closure based on weighted spectrum integration

A two-scale second-moment turbulence closure has been derived based on the weighted integration of the dynamic equation for the covariance spectrum. The goal is to close the Reynolds stress equations with two additional scalar equations that provide separately the scales of the spectral energy transfer and of the turbulence energy dissipation rate. Such a model should provide better prediction of nonequilibrium turbulent flows. The derivation consists of analytical integration of the wave-number-weighted covariance spectrum using a model of the spectral equations with an assumed simple representation of the shape of the energy spectrum. The resulting closure consists of a set of three tensorial equations, one for the Reynolds stress and two for length scale tensors, the latter representing the energy containing- and dissipative eddies respectively. The trace of the two tensor-scale equations leads to a set of two scalar scale parameters. In the equilibrium limit, the model reduces to the standard second-moment single-scale closure. The approach makes it also possible to derive the scale equations in a more systematic manner as compared with the common single-scale and other multi-scale models. The performance of the model in capturing the scale dynamics is illustrated by predictions of several generic homogeneous and inhomogeneous unsteady flows, demonstrating the expected response of the two scale equations. PACS 03.50.De, 04.20-q, 42.65-k     

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     

Spectral element-FCT method for scalar hyperbolic conservation laws

A new algorithm based on spectral element discretizations and flux-corrected transport (FCT) ideas is developed for the solution of discontinuous hyperbolic problems. A conservative formulation is proposed, based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss–Chebyshev and Gauss–Lobatto–Chebyshev discretizations. In addition, high-order time-differencing schemes, a flux limiter and a general spectral filter are employed to improve the quality of the solution. It is demonstrated through model problems of linear advection and examples of one-dimensional shock formation that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy away from discontinuities. Typically, spectral or spectral element methods perform very poorly in the presence of even weak discontinuities, although they produce only exponentialy small errors for smooth solutions. Spectral element–FCT methods can provide spectral properties (i.e. minimum dispersion and diffusion errors) as well as great flexibility in the discretization, since a variable number of macroelements or collocation points per element can be employed to accommodate both accuracy and geometric requirements.     

Numerical simulation on compressible turbulence by spectral method

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.     

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     

Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum

Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines is developed and compressibility of this mapping appears as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. In the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k ^?3 at large k, which appear to take the same form as the Kraichnan spectrum for the enstrophy cascade. For turbulence with weak anisotropy the k dependence of the spectrum due to the sharp gradients coincides with the Saffman spectrum: E(k) ~ k ^?4. Numerical investigations of decaying turbulence reveal exponential growth of di-vorticity with a spatial distributed along straight lines. Thus, indicating strong anisotropy and accordingly the spectrum is close to the k ^?3-spectrum.     

A direct method for laboratory spectrum crack growth testing

In linear elastic fracture mechanics (LEFM), the fatigue crack growth rates are related to the elastic stress intensity factor range and the load ratio. However, this relationship is difficult to derive when the loading condition is of variable amplitude (spectrum loading). Attention is paid to the most encountered case of cracks growing in their own plane under mode I loading. A testing procedure is presented to directly evaluate the fatigue life of real cracks under spectrum loading. The direct method intrinsically has wide applicability. A separate communication will present an application of the method.     

A new interferometric method for vibration measurement by electronic holography

Electronic holography is a well-established technique used in real-time, non-contact, whole-field displacement measurements. When using the real-time, time-averaged method for vibration measurments, the quantitative interpretation of dense fringe patterns is difficult because of speckle noise. Even when speckle-reducing procedures are used, such as multiple-frame averaging or rotation of the illumination beam, the remaining speckles and decreasing visibility of higher-order Bessel fringes are serious limitations. The primary objective of this paper is to present a new realtime, interferometric method for mechanical vibration measurements and the associated quantitative interpretation. The fringe pattern obtained by this method is quasi-binary and half as dense as in the time-averaged method. The method greatly improves the overall visibility (contrast, resolution) of vibration fringe patterns without any sacrifice in the real-time capabilities. Quantitative fringe interpretation is straightforward and based on binary fringe tracking. It allows quantitative measurements in situations where the time-averaged fringe processing fails.     

Velocity profile measurement by ultrasonic doppler method

The ultrasonic velocity profile measuring method has been developed at PSI for application in fluid mechanics and fluid flow measurement. It uses pulsed ultrasonic echography together with the detection of the instantaneous Doppler shift frequency. This method has the following advantages over the conventional techniques: (1) an efficient flow mapping process, (2) applicability to opaque liquids, and (3) a record of the spatiotemporal velocity field. After a brief introduction of its principle, the characteristics and specifications of the present system are given. Then examples in fluid engineering for oscillating pipe flow, T-branching flow of mercury, and recirculating flow in a square cavity are described that confirm the method's advantages. Several other works under way by other investigators are introduced. A potential for in-depth study of fluid dynamics is demonstrated by several examples from an investigation of modulated wavy flows in a rotating Couette system. The position-averaged power spectrum and the time-averaged energy spectral density were used to study the dynamic characteristics of the flow, and subsequently the velocity field was decomposed into its intrinsic wave structure based on two-dimensional Fourier analysis.     

Burst event detection in wall turbulence by WVITA method

Wavelet Variable Interval Time Average (WVITA) is introduced as a method incorporating burst event detection in wall turbulence. Wavelet transform is performed to unfold the longitudinal fluctuating velocity time series measured in the near wall region of a turbulent boundary layer using hot-film anemometer. This unfolding is both in time and in space simultaneously. The splitted kinetic of the longitudinal fluctuating velocity time series among different scales is obtained by integrating the square of wavelet coefficient modulus over temporal space. The time scale that related to burst events in wall turbulence passing through the fixed probe is ascertained by maximum criterion of the kinetic energy evolution across scales. Wavelet transformed localized variance of the fluctuating velocity time series at the maximum kinetic scale is put forward instead of localized short time average variance in Variable Interval Time Average (VITA) scheme. The burst event detection result shows that WVITA scheme can avoid erroneous judgement and solve the grouping problem more effectively which is caused by VITA scheme itself and can not be avoided by adjusting the threshold level or changing the short time average interval. The project supported by the National Natural Science Foundation of China (19732005) and the National Climbing Project of China     

The possibility of measuring turbulence by a correlation method

In [1] a correlation method for measuring the velocity pulsations in stationary plasma flows was described. The magnitude of the pulsations was determined from the value of the frequency deviation in the spectrum of the cross-correlation functions of optical fluctuations at two closely arranged points along the flow.In the present work, an attempt is made to justify such a method for measuring the characteristics of turbulence both in plasma and in any low-temperature gas flows.