3 results
The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface
- Markus Gampert, Jonas Boschung, Fabian Hennig, Michael Gauding, Norbert Peters
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- Journal:
- Journal of Fluid Mechanics / Volume 750 / 10 July 2014
- Published online by Cambridge University Press:
- 10 June 2014, pp. 578-596
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Based on a direct numerical simulation (DNS) of a temporally evolving mixing layer, we present a detailed study of the turbulent/non-turbulent (T/NT) interface that is defined using the two most common procedures in the literature, namely either a vorticity or a scalar criterion. The different detection approaches are examined qualitatively and quantitatively in terms of the interface position, conditional statistics and orientation of streamlines and vortex lines at the interface. Computing the probability density function (p.d.f.) of the mean location of the T/NT interface from vorticity and scalar allows a detailed comparison of the two methods, where we observe a very good agreement. Furthermore, conditional mean profiles of various quantities are evaluated. In particular, the position p.d.f.s for both criteria coincide and are found to follow a Gaussian distribution. The terms of the governing equations for vorticity and passive scalar are conditioned on the distance to the interface and analysed. At the interface, vortex stretching is negligible and the displacement of the vorticity interface is found to be determined by diffusion, analogous to the scalar interface. In addition, the orientation of vortex lines at the vorticity and the scalar based T/NT interface are analyzed. For both interfaces, vorticity lines are perpendicular to the normal vector of the interface, i.e. parallel to the interface isosurface.
Conditional statistics of the turbulent/non-turbulent interface in a jet flow
- Markus Gampert, Venkat Narayanaswamy, Philip Schaefer, Norbert Peters
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- Journal:
- Journal of Fluid Mechanics / Volume 731 / 25 September 2013
- Published online by Cambridge University Press:
- 29 August 2013, pp. 615-638
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Using two-dimensional high-speed measurements of the mixture fraction $Z$ in a turbulent round jet with nozzle-based Reynolds numbers $R{e}_{0} $ between 3000 and 18 440, we investigate the scalar turbulent/non-turbulent (T/NT) interface of the flow. The mixture fraction steeply changes from $Z= 0$ to a final value which is typically larger than 0.1. Since combustion occurs in the vicinity of the stoichiometric mixture fraction, which is around $Z= 0. 06$ for typical fuel/air mixtures, it is expected to take place largely within the turbulent/non-turbulent interface. Therefore, deep understanding of this part of the flow is essential for an accurate modelling of turbulent non-premixed combustion. To this end, we use a composite model developed by Effelsberg & Peters (Combust. Flame, vol. 50, 1983, pp. 351–360) for the probability density function (p.d.f.) $P(Z)$ which takes into account the different contributions from the fully turbulent as well as the turbulent/non-turbulent interface part of the flow. A very good agreement between the measurements and the model is observed over a wide range of axial and radial locations as well as at varying intermittency factor $\gamma $ and shear. Furthermore, we observe a constant mean mixture fraction value in the fully turbulent region. The p.d.f. of this region is thus of non-marching character, which is attributed physically to the meandering nature of the fully turbulent core of the jet flow. Finally, the location and in particular the scaling of the thickness $\delta $ of the scalar turbulent/non-turbulent interface are investigated. We provide the first experimental results for the thickness of the interface over the above-mentioned Reynolds number range and observe $\delta / L\sim R{ e}_{\lambda }^{- 1} $, where $L$ is an integral length scale and $R{e}_{\lambda } $ the local Reynolds number based on the Taylor scale $\lambda $, meaning that $\delta \sim \lambda $. This result also supports the assumption often made in modelling of the stoichiometric scalar dissipation rate ${\chi }_{st} $ being a Reynolds-number-independent quantity.
Experimental investigation of dissipation-element statistics in scalar fields of a jet flow
- Markus Gampert, Philip Schaefer, Norbert Peters
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- Journal:
- Journal of Fluid Mechanics / Volume 724 / 10 June 2013
- Published online by Cambridge University Press:
- 29 April 2013, pp. 337-366
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We present a detailed experimental investigation of conditional statistics obtained from dissipation elements based on the passive scalar field $\theta $ and its instantaneous scalar dissipation rate $\chi $. Using high-frequency planar Rayleigh scattering measurements of propane discharging as a round turbulent jet into coflowing carbon dioxide, we acquire with Taylor’s hypothesis a highly resolved three-dimensional field of the propane mass fraction $\theta $. The Reynolds number (based on nozzle diameter and jet exit velocity) varies between 3000 and 8600. The experimental results for the joint probability density of the scalar difference $ \mathrm{\Delta} \theta $ and the length $l$ of dissipation elements resembles those previously obtained from direct numerical simulations of Wang & Peters (J. Fluid Mech., vol. 554, 2006, pp. 457–475). In addition, the normalized marginal probability density function $\tilde {P} (\tilde {l} )$ of the length of dissipation elements follows closely the theoretical model derived by Wang & Peters (J. Fluid Mech., vol. 608, 2008, pp. 113–138). We also find that the mean linear distance ${l}_{m} $ between two extreme points of an element is of the order of the scalar Taylor microscale ${\lambda }_{u} $. Furthermore, the conditional mean $\langle \mathrm{\Delta} \theta \vert l\rangle $ scales with Kolmogorov’s $1/ 3$ power law. The investigation of the orientation of long dissipation elements in the jet flow reveals a preferential alignment, perpendicular to the streamwise direction for long elements, while the orientation of short elements is close to isotropic. Following an approach proposed by Kholmyansky & Tsinober (Phys. Lett. A, vol. 373, 2009, pp. 2364–2367), we finally investigate the probability density function of the scalar increment $\delta \theta $ in the streamwise direction, when strong dissipative events are either retained in or excluded from the measurement volume. In the present study, however, these events are related to maximum points of the scalar dissipation rate $\chi $ together with their local extent. When these regions are excluded from the scalar field, we observe a tendency of the probability density function $P(\delta \theta (r))$ towards a Gaussian bell-shaped curve.