Showing papers by "R. A. Antonia published in 2013"

Dynamical effect of the total strain induced by the coherent motion on local isotropy in a wake

Abstract: We assess the extent to which local isotropy (LI) holds in a wake flow for different initial conditions, which may be geometrical (the shape of the bluff body which creates the wake) and hydrodynamical (the Reynolds number), as a function of the dynamical effects of the large-scale forcing (the mean strain, $ \overline{S} $ , combined with the strain induced by the coherent motion, $\tilde {S} $ ). LI is appraised through either classical kinematic tests or phenomenological approaches. In this respect, we reanalyse existing LI criteria and formulate a new isotropy criterion based on the ratio between the turbulence strain intensity and the total strain ( $ \overline{S} + \tilde {S} $ ). These criteria involve either time-averaged or phase-averaged quantities, thus providing a deeper insight into the dynamical aspect of these flows. They are tested using hot wire data in the intermediate wake of five types of obstacles (a circular cylinder, a square cylinder, a screen cylinder, a normal plate and a screen strip). We show that in the presence of an organized motion, isotropy is not an adequate assumption for the large scales but may be satisfied over a range of scales extending from the smallest dissipative scale up to a scale which depends on the total strain rate that characterizes the flow. The local value of this scale depends on the particular nature of the wake and the phase of the coherent motion. The square cylinder wake is the closest to isotropy whereas the least locally isotropic flow is the screen strip wake. For locations away from the axis, the study is restricted to the circular cylinder only and reveals that LI holds at scales smaller than those that apply at the wake centreline. Arguments based on self-similarity show that in the far wake, the strength of the coherent motion decays at the same rate as that of the turbulent motion. This implies the persistence of the same degree of anisotropy far downstream, independently of the scale at which anisotropy is tested.

Invariants for slightly heated decaying grid turbulence

Abstract: The paper examines the validity of velocity and scalar invariants in slightly heated and approximately isotropic turbulence generated by passive conventional grids. By assuming that the variances is discussed in the context of published data for both passive and active grids.

Scale-by-scale turbulent energy budget in the intermediate wake of two-dimensional generators

Abstract: It is first established, on the basis of new X-wire measurements, that the equilibrium similarity of the terms in the scale-by-scale (s-b-s) budget of the turbulent energy q2¯ is reasonably well approximated on the axis of the intermediate wake of a circular cylinder. The similarity, which scales on the Taylor microscale λ and q2¯, is then used to determine s-b-s energy budgets from the data of Antonia, Zhou, and Romano [“Small-scale turbulence characteristics of two-dimensional bluff body wakes,” J. Fluid Mech. 459, 67–92 (2002)] for 5 different two-dimensional wake generators. In each case, the budget is reasonably well closed, using the locally isotropic value of the mean energy dissipation rate, except near separations comparable to the wavelength of the coherent motion (CM). The influence of the initial conditions is first felt at a separation Lc identified with the cross-over between the energy transfer and large scale terms of the s-b-s budget. When normalized by q2¯ and Lc, the mean energy dissipa...

Kármán-Howarth closure equation on the basis of a universal eddy viscosity.

Abstract: This Rapid Communication presents a simple closure for the two-point correlation transport equation in decaying isotropic turbulence. It relies essentially on an eddy viscosity ${\ensuremath{ u}}_{t}$ which exhibits some remarkable universal facets over an impressively wide range of scales. This allows us to model the third-order structure functions in different decaying flows covering a large extent of Reynolds numbers. The model is numerically time integrated to predict the decay of second-order structure functions and compared to experiments in grid turbulence. Agreement between predictions and measurements is satisfactory.

Relationship between temporal and spatial averages in grid turbulence

Abstract: A long-time direct numerical simulation (DNS) based on the lattice Boltzmann method is carried out for grid turbulence with the view to compare spatially averaged statistical properties in planes perpendicular to the mean flow with their temporal counterparts. The results show that the two averages become equal a short distance downstream of the grid. This equality indicates that the flow has become homogeneous in a plane perpendicular to the mean flow. This is an important result, since it confirms that hot-wire measurements are appropriate for testing theoretical results based on spatially averaged statistics. It is equally important in the context of DNS of grid turbulence, since it justifies the use of spatial averaging along a lateral direction and over several realizations for determining various statistical properties. Finally, the very good agreement between temporal and spatial averages validates the comparison between temporal (experiments) and spatial (DNS) statistical properties. The results are also interesting because, since the flow is stationary in time and spatially homogeneous along lateral directions, the equality between the two types of averaging provides strong support for the ergodic hypothesis in grid turbulence in planes perpendicular to the mean flow.

Restricted scaling range models for turbulent velocity and scalar energy transfers in decaying turbulence

Abstract: The effect of finite Reynolds numbers and/or internal intermittency on the total kinetic energy and scalar energy transfers is examined in detail. For this purpose, two distinct models for velocity and scalar energy transfer are proposed in the specific context of freely decaying isotropic turbulence. The first one extends the already existing dynamical models (hereafter DYM, i.e. based on transport equations originated in Navier–Stokes and advection-diffusion transport equations). The second one relies on the characteristic time of the strain at a specific scale (hereafter SBM). Both models account for the Reynolds number dependence of the scaling exponent of the second-order structure functions, over a range of scales where such exponents may be defined, i.e. a restricted scaling range (RSR). Therefore, the models developed aim at reproducing the energy transfer over the RSR. The predicted energy transfer is very sensible to variations of the scaling exponent, especially at low Reynolds numbers. The app...

Effect of mesh grids on the turbulent mixing layer of an axisymmetric jet

Abstract: This article focuses on the effect that two different mesh grids have on the structure of the mixing layer of an axisymmetric jet. Detailed measurements of mean velocity and turbulent velocity fluctuations are made with an X hot-wire probe in the range 0.5 ≤ x/d ≤ 10, where x is the longitudinal distance from the nozzle exit plane and d is the nozzle diameter. The grids are introduced at two locations—one location just downstream of the nozzle exit plane and the other location upstream of the nozzle exit plane in order to perturb the nozzle exit boundary layer. One mesh completely covers the nozzle (full mesh or FM) and the other mesh covers the central, high-speed zone (disk mesh or DM). With reference to the undisturbed jet, FM yields a significant reduction in the turbulence intensity and width of the shear layer, whereas DM enhances the turbulence intensity and increases the width of the shear layer. Both grids suppress the formation of the Kelvin–Helmholtz instability in the mixing layer. Results are...

Breakdown of Kolmogorov’s scaling in grid turbulence

Abstract: A direct numerical simulation (DNS) based on the lattice Boltzmann method is carried out for decaying grid turbulence at low Reynolds numbers with the view to investigating possible departures from Kolmogorov scaling. 1D and 3D spectra show that the Kolmogorov scaling is no longer valid when the Reynolds number falls below a certain value. The results are in agreement with the low Reynolds number DNS in a 3D periodic box by Mansour and Wray [1]. We are now investigating possible departures from local isotropy when the Kolmogorov scaling breaks down. Introduction and Numerical Set Up The first similarity hypothesis of Kolmogorov (or K41) implies that spectra of velocity fluctuations scale on the kinematic viscosity ν and the turbulent kinetic energy dissipation rate < ε > at large Reynolds numbers. However, evidence, based on both DNS data and measurements, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. Recently, Djenidi and Antonia [2] exploited this to develop a spectral method for estimating <ε > in various turbulent flows. One can however expect that this scaling will break down when the Reynolds number becomes relatively small. Mansour and Wray [1] showed that for 3D periodic box turbulence, the energy power spectrum scaled on Kolmogorov variables deviates for the “universal Kolmogorov spectrum” at high wave numbers, suggesting indeed that this breakdown has occurred. The present work aims at extending Mansour and Wray’s work to grid turbulence. We will investigate how the Kolmogorov-scaled power spectrum evolves as the Reynolds number continues to decrease, with the view of determining the critical Reynolds number below which the Kolmogorov scaling breaks down. A second aim is to determine whether local isotropy is still valid and how the structure functions behave when the Kolmogorov scaling has broken down. The direct numerical simulation (DNS) is based on the lattice Boltzmann method (LBM). Rather than solving the governing fluid equations (Navier-Stokes equations), the LBM solves the Boltzmann equation on a lattice [3]. The method was successfully used to simulate turbulent flows [e.g. 4, 5, 6]. The computational uniform Cartesian mesh consists of 1600 x 240 x 240 mesh points with Δx = Δy = Δz (x is the longitudinal direction and y and z the lateral directions). The turbulence-generating grid (placed at the x-node of 180) is made up of 6 by 6 floating flat square elements in an aligned arrangement (see [4]). Each element is represented by 1 x 20 x 20 mesh points and the mesh spacing (M) between the centre of two elements is 40 mesh points (i.e. 2D), yielding a grid solidity of 0.25. The downstream distance extends to x/D = 70 (equivalently x/M = 35), where the origin of x is the grid plane and D = 20 mesh points is the block side length. Periodic conditions are applied in the y and z directions. At the inlet, a uniform velocity (U0 = 0.05, and V0 = W0 = 0) is imposed, and a convective boundary condition is applied at the outlet. A no-slip condition at the grid elements is implemented with a bounce-back scheme [7]. The Reynolds number, RM, is varied between 1600 and 3200. Results and Discussion Figure 1 compares the 1D and 3D spectra for the present simulation with those of existing DNS [1, 8] and measurements [9]. The present 3D spectra follow reasonably well those of Mansour and Wray [1] at similar Reynolds numbers. There is a clear deviation from the spectrum of Comte-Bellot and Corrsin [9] which was measured at Rλ = 60.7. The same deviation is also observed in the 1D spectra between the present ones and those of Comte-Bellot and Corrsin [9] (Rλ = 60.7) and Abe et al. [8] at Rλ = 66 obtained at the centerline of a turbulent channel flow. Notice the flattening of the low Reynolds spectra in both the present and those of Mansour and Wray relative to those of Comtebellot and Corrsin [9] and Abe et al. [8]. Interestingly, Mansour and Wray [1] observed that the nonlinear terms remain active at low Rλ, despite the clear absence of an inertial range in the spectra. It should be recalled that Kerr [10] has observed a similar spectral deviation and flattening when Rλ = 18.4 in his DNS of 3D periodic box turbulence. Figure 1 indicates that the deviation increases as Rλ decreases, thus corroborating Mansour and Wray’s [1] conclusion that “the shape of the spectra at the Kolmogorov length scales is Reynolds number dependent” at low Reynolds numbers. It thus appears that the Kolmogorov scaling breaks down when Rλ ≤ 20. Note however that the critical value Rλ,c at which the spectral deviation begins may be higher than 20. Figure 1 suggests that this value is likely to be less than 60; Mansour and Wray [1] proposed a value of 50. Clearly, further measurements and/of DNS are required to determine the actual value of Rλ,c. We are currently carrying out tests on local isotropy at low Reynolds numbers using second and third-order structure functions. The results will be presented at the conference.

Behaviours of Energy Spectrum at Low Reynolds Numbers in Grid Turbulence

Abstract: Abstract—This paper reports an experimental investigation of the energy spectrum of turbulent velocity fields at low Reynolds numbers (Rλ) in grid turbulence. Hot wire measurements are carried out in grid turbulence with subjected to a 1.36:1 contraction of the wind tunnel. Three different grids are used: (i) large square perforated grid (mesh size 43.75 mm), (ii) small square perforated grid (mesh size 14. and (iii) woven mesh grid (mesh size 5mm). The results indicate that the energy spectrum at small Rλ does not follow Kolmogorov’s universal scaling. It is further found that the critical Reynolds number, Rλ,c below which the scaling breaks down, is around 25.

A note on local isotropy criteria in shear flows with coherent motion

Abstract: Whilst Local Isotropy (LI) is widely used, it is also necessary to test its validity, especially in shear flows, characterized by large-scale anisotropy. Important questions are whether the small scales are isotropic and how their properties depend on large-scale parameters (mean shear, the shear induced by a coherent motion, the Reynolds number etc.). We focus on two families of LI tests: i) classical, kinematic tests, in which time-averages are compared to their isotropic values. The large-scale parameters do not appear explicitly. We only use here one example of such tests. ii) Phenomenological tests, which explicitly account for the large-scale strain, as well as its associated dynamics. In flows populated by coherent motions in which phaseaverages are pertinent for describing the flow dynamics, we propose a Local Isotropy (LI) criterion based on the intensity of the turbulent strain rate at a given scale~r and a particular phase φ , sφ (~r,φ). The formulation is the following: ”If LI were to be valid at a vectorial scale~r and a phase φ , then the intensity of the turbulent strain rate sφ (~r,φ) should prevail over the combined effect of the mean shear S and of the shear S̃ associated with the coherent motion”. The mathematical expression of sφ (~r,φ) depends on the Laplacian of the total kinetic energy second-order structure function. Therefore, the proposed expression allows the eventual anisotropy to be taken into account. The new LI criterion is used together with data taken in the intermediate wake behind a circular cylinder. It is highlighted that (i) when S+ S̃ is important, LI only holds for scales smaller than the Taylor microscale (ii) when S+ S̃ is small, the domain in which LI is valid extends up to the largest scales. INTRODUCTION Local isotropy (LI) is seemingly one of the most important hypotheses on small-scale statistics. LI was first enunciated by Kolmogorov (1941), and further utilized and sometimes tested, in most of the laboratory flows. From the analytical viewpoint, LI leads to simplified expressions of e.g. the total kinetic energy, the dissipation rate of kinetic energy or scalar variance, structure functions at a given scale. Simple expressions of statistics are useful for the experimentalists, because of the limited possibilities to measure all the velocity components, as well as their spatial distribution. Although LI is extensively used, it is nonetheless necessary to test its validity, especially in shear flows, characterized by large-scale anisotropy. Important questions are whether the small scales are isotropic and if there is a clear dependence of their statistics on large-scale parameters (mean shear S, the shear induced by a coherent motion S̃, the Reynolds number etc.). Using a compilation of experimental and numerical data, Schumacher et al. (2003) showed that LI prevails for small values of the ratio S/Rλ (Rλ is the Taylor microscale Reynolds number). One should expect that the magnitude of the shear will play some role in determining how high an Rλ is required for LI to prevail. Whereas the conclusion of Schumacher et al. (2003) is optimistic quid the restoration of LI, the analytical study of Durbin & Speziale (1991) demonstrated that small scales cannot be isotropic in shear flows, independently of the values of Rλ and S. From a general viewpoint, the assessment of LI can only be done through specific criteria and a definitive conclusion about the validity of LI is unlikely to be realistic. The aim of this study is to understand how, in the context of shear flows, the anisotropy propagates across the scales from the largest to the smallest, how it evolves down the scales and finally, what the degree of anisotropy is at any given scale. To this end, we propose a phenomenological LI criterion based on the intensity of the turbulent strain rate at a given scale r. As a first step in answering the question of what the isotropy level is at any particular scale, we consider flows populated by a single-scale, persistent coherent motion (hereafter, CM). A good candidate is the cylinder wake flow, and this study focuses entirely on this flow. The other advantage of investigating the wake flow is that it allows to invoke phase averages. The latter operation results in a dependence of any statistical quantities on the phase φ characterizing the temporal dynamics of the CM. We focus on two families of LI tests: i) classical, kinematic tests, in which time-averages are compared to their isotropic values. The large-scale parameters (shear) does not appear explicitly. We only use here one example of such tests. ii) Phenomenological tests, which explicitly account for the