Wavelet decomposition and coherent structures eduction of low Reλ turbulent hot wire signals

Hot wire signals obtained in grid-turbulence are processed through orthogonal wavelet transform. It is shown that using wavelet decomposition in combination with the form of scaling named Extended Self Similarity, some statistical properties of fully developed turbulence can be extended to very low Re_λ flows. Furthermore, based on the wavelet decomposition, a new technique for coherent structures identification is introduced. We present results obtained in grid turbulence data at low and very low Re_λ conditions.     

Statistical study of anisotropic anomalous behavior of a cylinder wake

 An experimental investigation of the statistical properties of the velocity difference in an anisotropic turbulent cylinder wake at moderate Re _λ is conducted by a triple hot-wire anemometer (HWA) probe. The energy spectra show a clear large scale anisotropy due to the presence of the Von Karman vortices. In spite of the low Re _λ and the large scale anisotropy, the extended-self-similarity (ESS) allows location of broad scaling ranges and the calculation of the scaling exponents of the three velocity structure function components in order to examine the intermittency anomalies. More intermittent behavior of the transverse velocity components with respect to the longitudinal one is found both by ESS and by comparison of the longitudinal and transverse velocity difference probability distribution functions (PDF). Received: 12 October 1997 / Accepted: 29 April 1998     

Turbulence in rough-wall boundary layers: universality issues

Wind tunnel measurements of turbulent boundary layers over three-dimensional rough surfaces have been carried out to determine the critical roughness height beyond which the roughness affects the turbulence characteristics of the entire boundary layer. Experiments were performed on three types of surfaces, consisting of an urban type surface with square random height elements, a diamond-pattern wire mesh and a sand-paper type grit. The measurements were carried out over a momentum thickness Reynolds number (Re _θ) range of 1,300–28,000 using two-component Laser Doppler anemometry (LDA) and hot-wire anemometry (HWA). A wide range of the ratio of roughness element height h to boundary layer thickness δ was covered (0.04 ￡ h/d ￡ 0.400.04 \leq h/\delta \leq 0.40). The results confirm that the mean profiles for all the surfaces collapse well in velocity defect form up to surprisingly large values of h/δ, perhaps as large as 0.2, but with a somewhat larger outer layer wake strength than for smooth-wall flows, as previously found. At lower h/δ, at least up to 0.15, the Reynolds stresses for all surfaces show good agreement throughout the boundary layer, collapsing with smooth-wall results outside the near-wall region. With increasing h/δ, however, the turbulence above the near-wall region is gradually modified until the entire flow is affected. Quadrant analysis confirms that changes in the rough-wall boundary layers certainly exist but are confined to the near-wall region at low h/δ; for h/δ beyond about 0.2 the quadrant events show that the structural changes extend throughout much of the boundary layer. Taken together, the data suggest that above h/δ ≈ 0.15, the details of the roughness have a weak effect on how quickly (with rising h/δ) the turbulence structure in the outer flow ceases to conform to the classical boundary layer behaviour. The present results provide support for Townsend’s wall similarity hypothesis at low h/δ and also suggest that a single critical roughness height beyond which it fails does not exist. For fully rough flows, the data also confirm that mean flow and turbulence quantities are essentially independent of Re _θ; all the Reynolds stresses match those of smooth-wall flows at very high Re _θ. Nonetheless, there is a noticeable increase in stress contributions from strong sweep events in the near-wall region, even at quite low h/δ.     

Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate

In this communication a generalized threedimensional steady flow of a viscous fluid between two infinite parallel plates is considered. The flow is generated due to uniform stretching of the lower plate in x- and y-directions. It is assumed that the upper plate is uniformly porous and is subjected to constant injection. The governing system is fully coupled and nonlinear in nature. A complete analytic solution which is uniformly valid for all values of the dimensionless parameters β, Re and λ is obtained by using a purely analytic technique, namely the homotopy analysis method. Also the effects of the parameters β, Re and λ on the velocity field are discussed through graphs.     

Creating homogeneous and isotropic turbulence without a mean flow

A novel method of creating homogeneous and isotropic turbulence with small mean flow has been developed. Eight synthetic jet actuators on the corners of a cubic chamber can create energetic turbulence with root-mean-square (rms) velocities as large as 0.87 m/s, corresponding to a Taylor microscale Reynolds number, Re , of 218. Stationary turbulence results show that the turbulence was isotropic, with the rms velocity ratio equal to 1.03, and also homogeneous within the region of interest. Natural decaying turbulence measurements confirmed the power-law decay of the turbulent kinetic energy, with the decay exponent n equal to 1.86 for an initial Re of 224.     

Effect of initial conditions on decaying grid turbulence at low R λ

The transport equations for the second-order velocity structure functions 〈(δu)²〉 and 〈(δq)²〉 are used as a scale-by-scale budget to quantify the effect of initial conditions at low Reynolds numbers, typical of grid turbulence. The validity of these equations is first investigated via hot-wire measurements of velocity and transverse vorticity fluctuations. The transport equation for 〈(δq)²〉 is shown to be balanced at all scales, while anisotropy of the large scales leads to a significant imbalance in the equation for 〈(δu)²〉. The effect of using similarity to evaluate the transport equation is rigorously tested. This approach has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous term of the transport equation. The similarity form of the 〈(δq)²〉 equation produces nearly identical results as those obtained without the similarity assumption. In the case of the 〈(δu)²〉 equation, the similarity method forces a balance at large separation, although the imbalance due to large scale anisotropy remains. The initial conditions of the turbulence at constant R _M ≃ 10,400 (28≤ R _λ≤ 55) are changed by using three grids of different geometries. Initial conditions affect the shape and magnitude of the second- and third-order structure functions, as well as the anisotropy of the large scales. The effect of initial conditions on the scale-by-scale budget is restricted to the inhomogeneous term of the transport equations, while the dissipation term remains unaffected despite the low R _λ. Scales as small as λ are affected by the changes in initial conditions.     

Improvement of cold-wire response for measurement of temperature dissipation

This work aimed at improving fine-scale measurements using cold-wire anemometry. The dissipation ɛ _θ of the temperature variance was measured on the axis of a heated turbulent round jet. The measurements were performed with a constant current anemometer (CCA) operating fine Pt–10%Rh wires at very low overheat. The CCA developed for this purpose allowed the use of the current injection method in order to estimate the time constant of the wire. In the first part of the paper, it is shown that the time constants obtained for two wire diameters −d=1.2 and d=0.58 μm – compare well with those measured at the same time using two other methods (laser excitation and pulsed wire). Moreover, for these two wires, the estimated time constants were in good agreement with those obtained from a semi-empirical relation. In the second part of the paper, a compensation procedure – post-processing filtering – was developed in order to improved the frequency response of the cold-wire probes. The measurements carried out on the axis of the jet (Re _D =16 500, Re _λ  ≃ 167) showed that the frequency response of the 1.2 μm wire was significantly improved. In fact, the spectral characteristics of the compensated signal obtained with the 1.2 μm wire compared fairly well with those from the 0.58 μm wire. Moreover, the results indicated that the compensation procedure must be applied when the cut-off frequency of the cold-wire f _c is lower than two times the Kolmogorov frequency f _K. In the case where f _c ≃ 0.6f _K, the compensation procedure can reduce the error in the estimate of ɛ _θ by more than 20%. When f _c ≃ 2f _K, the effect of the compensation is reduced to about 5%. Received: 3 November 2000/Accepted: 23 March 2001     

Turbulent flow in a circular separationless diffuser at Reynolds numbers smaller than 2000

The results of experimental and numerical investigation of flow in a circular conical diffuser with a small conicity angle ensuring separationless flow are presented. The measurements are carried out in an air flow with the Reynolds number Re₂ in the diffuser exit section ranging from 600 to 3000. A considerable effect of the channel expansion on the flow pattern is found to exist. It is shown that, as distinct from a tube, in which only laminar flow can be realized as steady for Re < 2000, in the exit section of a diffuser with the generator slope of 0.3° and a length equal to 70 entry diameters a developed turbulent flow is formed for Re₂ > 1000. For Re₂ > 1300 this flow is steady, that is, almost independent of the turbulence level at the entry, and is determined by the Reynolds number Re₂ in the exit section. For Re₂ ≈ 1000 the turbulent flow continuously goes over into a laminar flow. The flow parameters measured at the diffuser exit correspond to calculations in accordance with the threeequation turbulence model.     

A tomographic PIV resolution study based on homogeneous isotropic turbulence DNS data

In order to accurately assess measurement resolution and measurement uncertainty in DPIV and TPIV measurements, a series of simulations were conducted based on the flow field from a homogeneous isotropic turbulence data set (Re _λ = 141). The effect of noise and spatial resolution was quantified by examining the local and global errors in the velocity, vorticity and dissipation fields in addition to other properties of interest such as the flow divergence, topological invariants and energy spectra. In order to accurately capture the instantaneous gradient fields and calculate sensitive quantities such as the dissipation rate, a minimum resolution of x/η = 3 is required, with smoothing recommended for the TPIV results to control the inherently higher noise levels. Comparing these results with experimental data showed that while the attenuation of velocity and gradient quantities was predicted well, higher noise levels in the experimental data led increased divergence.     

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Re _λ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.