8 results
Structure of iso-scalar sets
- M. Gauding, F. Thiesset, E. Varea, L. Danaila
-
- Journal:
- Journal of Fluid Mechanics / Volume 942 / 10 July 2022
- Published online by Cambridge University Press:
- 17 May 2022, A14
-
- Article
- Export citation
-
An analytical framework is proposed to explore the structure and kinematics of iso-scalar fields. It is based on a two-point statistical analysis of the phase indicator field which is used to track a given iso-scalar volume. The displacement speed of the iso-surface, i.e. the interface velocity relative to the fluid velocity, is explicitly accounted for, thereby generalizing previous two-point equations dedicated to the phase indicator in two-phase flows. Although this framework applies to many transported quantities, we here focus on passive scalar mixing. Particular attention is paid to the effect of Reynolds (the Taylor based Reynolds number is varied from 88 to 530) and Schmidt numbers (in the range 0.1 to 1), together with the influence of flow and scalar forcing. It is first found that diffusion in the iso-surface tangential direction is predominant, emphasizing the primordial influence of curvature on the displacement speed. Second, the appropriate normalizing scales for the two-point statistics at either large, intermediate and small scales are revealed and appear to be related to the radius of gyration, the surface density and the standard deviation of mean curvature, respectively. Third, the onset of an intermediate ‘scaling range’ for the two-point statistics of the phase indicator at sufficiently large Reynolds numbers is observed. The scaling exponent complies with a fractal dimension of 8/3. A scaling range is also observed for the transfer of iso-scalar fields in scale space whose exponent can be estimated by simple scaling arguments and a recent closure of the Corrsin equation. Fourth, the effects of Reynolds and Schmidt numbers together with flow or scalar forcing on the different terms of the two-point budget are highlighted.
Space-scale-time dynamics of liquid–gas shear flow
- F. Thiesset, T. Ménard, C. Dumouchel
-
- Journal:
- Journal of Fluid Mechanics / Volume 912 / 10 April 2021
- Published online by Cambridge University Press:
- 15 February 2021, A39
-
- Article
- Export citation
-
Two-point statistical equations of the liquid-phase indicator function are used to appraise the physics of liquid–gas shear flows. The contribution of the different processes in the combined scale/physical space is quantified by means of direct numerical simulations of a temporally liquid–gas shear layer. Light is first shed onto the relationship between two-point statistics of the phase indicator and the geometrical properties of the liquid/gas interface, namely its surface density, mean and Gaussian curvatures. Then, the theory is shown to be adequate for highlighting the preferential direction of liquid transport in either scale or flow position space. A direct cascade process, i.e. from large to small scales, is observed for the total phase indicator field, while the opposite applies for the randomly fluctuating part, suggesting a transfer of ‘energy’ from the mean to the fluctuating component. In the space of positions within the flow, the flux tends to redistribute energy from the centreline to the edge of the shear layer. The influence of the mean shear rate and statistical inhomogeneities on the different scales of the liquid field are revealed.
The illusion of a Kolmogorov cascade
- F. Thiesset, L. Danaila
-
- Journal:
- Journal of Fluid Mechanics / Volume 902 / 10 November 2020
- Published online by Cambridge University Press:
- 03 September 2020, F1
-
- Article
-
- You have access Access
- HTML
- Export citation
-
The theory of Kolmogorov, enunciated for very large Reynolds numbers, has progressively been shown to be inoperative for characterizing flows of practical relevance. Yet, in a recent study by Alves Portela et al. (J. Fluid Mech., vol. 896, 2020, A16), the turbulence statistics in the very near wake of a square prism at modest Reynolds numbers, reveal a significant portion of scales complying with a cascade of Kolmogorov type. By resorting to a generalized version of the Kármán–Howarth–Kolmogorov equation, this intriguing observation is shown to be an illusion, hiding a measurable influence of coherent structures and statistical inhomogeneity. This striking conclusion highlights that a complete statistical theory of turbulence cannot dispense with the influence of large scales, possibly coherent, motions.
Liquid transport in scale space
- F. Thiesset, B. Duret, T. Ménard, C. Dumouchel, J. Reveillon, F. X. Demoulin
-
- Journal:
- Journal of Fluid Mechanics / Volume 886 / 10 March 2020
- Published online by Cambridge University Press:
- 08 January 2020, A4
-
- Article
- Export citation
-
When a liquid stream is injected into a gaseous atmosphere, it destabilizes and continuously passes through different states characterized by different morphologies. Throughout this process, the flow dynamics may be different depending on the region of the flow and the scales of the involved liquid structures. Exploring this multi-scale, multi-dimensional phenomenon requires some new theoretical tools, some of which need yet to be elaborated. Here, a new analytical framework is proposed on the basis of two-point statistical equations of the liquid volume fraction. This tool, which originates from single phase turbulence, allows us notably to decompose the fluxes of liquid in flow–position space and scale space. Direct numerical simulations of liquid–gas turbulence decaying in a triply periodic domain are then used to characterize the time and scale evolution of the liquid volume fraction. It is emphasized that two-point statistics of the liquid volume fraction depend explicitly on the geometrical properties of the liquid–gas interface and in particular its surface density. The stretch rate of the liquid–gas interface is further shown to be the equivalent for the liquid volume fraction (a non-diffusive scalar) of the scalar dissipation rate. Finally, a decomposition of the transport of liquid in scale space highlights that non-local interactions between non-adjacent scales play a significant role.
Isolating strain and curvature effects in premixed flame/vortex interactions
- F. Thiesset, F. Halter, C. Bariki, C. Lapeyre, C. Chauveau, I. Gökalp, L. Selle, T. Poinsot
-
- Journal:
- Journal of Fluid Mechanics / Volume 831 / 25 November 2017
- Published online by Cambridge University Press:
- 13 October 2017, pp. 618-654
-
- Article
- Export citation
-
This study focuses on the response of premixed flames to a transient hydrodynamic perturbation in an intermediate situation between laminar stretched flames and turbulent flames: an axisymmetric vortex interacting with a flame. The reasons motivating this choice are discussed in the framework of turbulent combustion models and flame response to the stretch rate. We experimentally quantify the dependence of the flame kinematic properties (displacement and consumption speeds) to geometrical scalars (stretch rate and curvature) in flames characterized by different effective Lewis numbers. Whilst the displacement speed can be readily measured using particle image velocimetry and tomographic diagnostics, providing a reliable estimate of the consumption speed from experiments remains particularly challenging. In the present work, a method based on a budget of fuel on a well chosen domain is proposed and validated both experimentally and numerically using two-dimensional direct numerical simulations of flame/vortex interactions. It is demonstrated that the Lewis number impact neither the geometrical nor the kinematic features of the flames, these quantities being much more influenced by the vortex intensity. While interacting with the vortex, the flame displacement (at an isotherm close to the leading edge) and consumption speeds are found to increase almost independently of the type of fuel. We show that the total stretch rate is not the only scalar quantity impacting the flame displacement and consumption speeds and that curvature has a significant influence. Experimental data are interpreted in the light of asymptotic theories revealing the existence of two distinct Markstein numbers, one characterizing the dependence of flame speed to curvature, the other to the total stretch rate. This theory appears to be well suited for representing the evolution of the displacement speed with respect to either the total stretch rate, curvature or strain rate. It also explains the limited dependence of the flame displacement speed to Lewis number and the strong correlation with curvature observed in the experiments. An explicit relationship between displacement and consumption speeds is also given, indicating that the fuel consumption rate is likely to be altered by both the total stretch rate and curvature.
Dynamical interactions between the coherent motion and small scales in a cylinder wake
- F. Thiesset, L. Danaila, R. A. Antonia
-
- Journal:
- Journal of Fluid Mechanics / Volume 749 / 25 June 2014
- Published online by Cambridge University Press:
- 15 May 2014, pp. 201-226
-
- Article
- Export citation
-
Most turbulent flows are characterized by coherent motion (CM), whose dynamics reflect the initial and boundary conditions of the flow and are more predictable than that of the random motion (RM). The major question we address here is the dynamical interaction between the CM and the RM, at a given scale, in a flow where the CM exhibits a strong periodicity and can therefore be readily distinguished from the RM. The question is relevant at any Reynolds number, but is of capital importance at finite Reynolds numbers, for which a clear separation between the largest and the smallest scales may not exist. Both analytical and experimental tools are used to address this issue. First, phase-averaged structure functions are defined and further used to condition the RM kinetic energy at a scale $r$ on the phase $\phi $ of the CM. This tool allows the dependence of the RM to be followed as a function of the CM dynamics. Scale-by-scale energy budget equations are established on the basis of phase-averaged structure functions. They reveal that energy transfer at a scale $r$ is sensitive to an additional forcing mechanism due to the CM. Second, these concepts are tested using hot-wire measurements in a cylinder wake, in which the CM is characterized by a well-defined periodicity. Because the interaction between large and small scales is most likely enhanced at moderate/low Reynolds numbers, and is also likely to depend on the amplitude of the CM, we choose to test our findings against experimental data at $R_{\lambda } \sim 10^2$ and for downstream distances in the range $10 \leq x/D \leq 40$. The effects of an increasing Reynolds number are also discussed. It is shown that: (i) a simple analytical expression describes the second-order structure functions of the purely CM. The energy of the CM is not associated with any single scale; instead, its energy is distributed over a range of scales. (ii) Close to the obstacle, the influence of the CM is perceptible even at the smallest scales, the energy of which is enhanced when the coherent strain is maximum. Further downstream from the cylinder, the CM clearly affects the largest scales, but the smallest scales are not likely to depend explicitly on the CM. (iii) The isotropic formulation of the RM energy budget compares favourably with experimental results.
Consequences of self-preservation on the axis of a turbulent round jet
- F. Thiesset, R. A. Antonia, L. Djenidi
-
- Journal:
- Journal of Fluid Mechanics / Volume 748 / 10 June 2014
- Published online by Cambridge University Press:
- 08 May 2014, R2
-
- Article
- Export citation
-
On the basis of a two-point similarity analysis, the well-known power-law variations for the mean kinetic energy dissipation rate $\overline{\epsilon }$ and the longitudinal velocity variance $\overline{u^2}$ on the axis of a round jet are derived. In particular, the prefactor for $\overline{\epsilon } \propto (x-x_0)^{-4}$, where $x_0$ is a virtual origin, follows immediately from the variation of the mean velocity, the constancy of the local turbulent intensity and the ratio between the axial and transverse velocity variance. Second, the limit at small separations of the two-point budget equation yields an exact relation illustrating the equilibrium between the skewness of the longitudinal velocity derivative $S$ and the destruction coefficient $G$ of enstrophy. By comparing the latter relation with that for homogeneous isotropic decaying turbulence, it is shown that the approach towards the asymptotic state at infinite Reynolds number of $S+2G/R_{\lambda }$ in the jet differs from that in purely decaying turbulence, although $S+2G/R_{\lambda } \propto R_{\lambda }^{-1}$ in each case. This suggests that, at finite Reynolds numbers, the transport equation for $\overline{\epsilon }$ imposes a fundamental constraint on the balance between $S$ and $G$ that depends on the type of large-scale forcing and may thus differ from flow to flow. This questions the conjecture that $S$ and $G$ follow a universal evolution with $R_{\lambda }$; instead, $S$ and $G$ must be tested separately in each flow. The implication for the constant $C_{\epsilon 2}$ in the $k-\overline{\epsilon }$ model is also discussed.
Dynamical effect of the total strain induced by the coherent motion on local isotropy in a wake
- F. Thiesset, L. Danaila, R. A. Antonia
-
- Journal:
- Journal of Fluid Mechanics / Volume 720 / 10 April 2013
- Published online by Cambridge University Press:
- 27 February 2013, pp. 393-423
-
- Article
- Export citation
-
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.