The structure of fine-scale scalar mixing in gas-phase planar turbulent jets

Su, Lester K.; Clemens, Noel T.

doi:10.1017/s002211200300466x

Cited by 129 publications

(100 citation statements)

References 37 publications

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“…Our data show that the scale l max follows now the same dependence with Reynolds number as the Kolmogorov scale, i.e. l max ∼ R −3/2 λ This result is similar to finding in [10,11] for Sc ∼ 1 and does not change for Sc ≫ 1.…”

Section: Fig 1: (Color Online)supporting

confidence: 89%

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Geometry of Intensive Scalar Dissipation Events in Turbulence

2006

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Maxima of the scalar dissipation rate in turbulence appear in form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross-section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analysed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales take always values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow. When a scalar concentration field θ(x, t) is transported in a turbulent flow very large scalar gradients are generated which can be associated with potentially intensive mixing [1]. Frequently, such large-amplitude gradient regions exist across scales that are finer than the smallest turbulent eddies, a case which is known as the Batchelor regime of scalar mixing [2]. Their cross-section is usually estimated by a single mean diffusion scale, the Batchelor scale η B , that equilibrates advection by flow and scalar diffusion. However, scalar gradients are known to fluctuate strongly in turbulent mixing. These fluctuations are caused by the fluctuating scalar amplitudes and by the varying spatial sections across which the scalar differences are built up. Both aspects will cause the strong spatial variability of potentially intensive mixing regions. Thus, a whole range of local diffusion scales l d , which quantifies exactly this variability, will exist around the mean diffusion scale η B . Their distribution is interesting for several reasons. It can enter mixing efficiency measures [3]. The scales prescribe the extension of chemically reactive layers in which the combustion of fuel takes place [4] or the variations of the fluorescence signal as used for the measurement of zooplankton patchiness in the ocean [5].In this Letter, we want to calculate this local diffusion scale distribution p(l d ). It arises from the competition of two dynamic processes. On one hand, the scale distribution will be affected by molecular diffusion that causes a diminishing of existing steep gradients as well as the completion of their formation by reconnection [6,7]. On the other hand, the scales will be determined by the statistics of the local advection flow patterns that pile up scalar differences. While the strongest scalar gradients were related to instantaneous velocity gradients in Ref.[8], we will go one step further in the second part of the Letter and relate the local diffusion scale distribution to the distribution of Lagrangian contraction rates of the flow, as given by the smallest of the three finite-time Lyapunov exponents along Lagrangian trajectories. The Lagrangian approach incorporates the temporal evolution of the persistent flow patterns that eventually generate the strongest scalar gradients or the finest local dissipation...

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Section: Fig 1: (Color Online)supporting

confidence: 89%

“…Experimental studies on the geometry of scalar dissipation fields are very challenging since gradients have to be measured and only a few exist [10,11]. Figure 1 shows a two-dimensional (2D) slice cut through a DNS snapshot of ǫ θ (x, t).…”

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confidence: 99%

Geometry of Intensive Scalar Dissipation Events in Turbulence

2006

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“…Su & Clemens 2003). Scalar dissipation measurements have been used to probe fine-scale mixing in canonical turbulent flows (Buch & Dahm 1996, 1998, constrain combustion models with turbulent jets (Su & Clemens 2003), and understand passive-scalar mixing in isotropic turbulence (Eswaran & Pope 1988;Girimaji 1992). We compute χ from the scalar fields using the numerical approach described in Buch & Dahm (1996).…”

Section: Scalar Dissipation Rate Fields and Mechanisms Of Mixingmentioning

confidence: 99%

“…In both regimes it was found that strained, laminar, sheet-like diffusion layers comprised much of the scalar dissipation rate fields. Scalar concentration measurements were obtained by Su & Clemens (2003) in turbulent jets using two parallel laser sheets with Rayleigh scattering and laser-induced fluorescence. Here the spatial derivative of the scalar field was computed in all three directions, permitting more accurate estimation of the scalar dissipation rate field.…”

Section: Introductionmentioning

confidence: 99%

An experimental investigation of mixing mechanisms in shock-accelerated flow

et al. 2008

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An experimental investigation of mixing mechanisms in a shock-induced instability flow is described. We obtain quantitative two-dimensional maps of the heavy-gas (SF 6 ) concentration using planar laser-induced fluorescence for the case of a shockaccelerated cylinder of heavy gas in air. The instantaneous scalar dissipation rate, or mixing rate, χ, is estimated experimentally for the first time in this type of flow, and used to identify the regions of most intense post-shock mixing and examine the underlying mechanisms. We observe instability growth in certain regions of the flow beginning at intermediate times. The mixing rate results show that while these unstable regions play a significant role in the mixing process, a large amount of mixing also occurs by mechanisms directly associated with the primary instability, including gradient intensification via the large-scale strain field in a particular non-turbulent region of the flow.

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“…The pdf of the (conditional) scalar dissipation rate has been largely assumed to follow a lognormal distribution, whose mean and variance enter in models of turbulent combustion. However, many measured pdf ( χ) show a difference to the lognormal distribution at both low and high values of χ in isothermal 17,[30][31][32] and reacting flows. 24,[27][28][29] The pdf typically has longer tails for low dissipation rate values and falls-off faster at high dissipation rate values, compared to the lognormal distribution.…”

Section: Introductionmentioning

confidence: 95%

Mixing and scalar dissipation rate statistics in a starting gas jet

2015

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We quantify the temporal development of the mixing field of a starting jet by measuring the mixture fraction and the scalar dissipation rate and their statistics in an isothermal, impulsively started, gaseous jet. The scalar measurements are performed using planar laser induced fluorescence and, with appropriate processing of the resulting images, allow scalar dissipation rate measurements within 20%. The probability density functions of the mixture fraction, measured within a region of the order of 3 times the Batchelor length scale of the flow, are bimodal and skewed around a well-mixed radial location, which depends on the downstream distance and the time after the start of injection. The instantaneous distributions of the scalar dissipation rate reveal regions of high mixing at the jet periphery and at the developing vortex ring. The normalised probability density function (pdf) of the scalar dissipation rate at various flow positions and times after the start of injection has the same characteristic shape but differs from the usually suggested lognormal distribution at both low and high dissipation values; the same, also, holds true for the pdf conditioned on different values of the mixture fraction. The mean of the scalar dissipation rate conditional on mixture fraction shows a variation across the mixture fraction range, which differs between flow locations and times after the start of injection; however, at later times and for larger downstream distances the conditional mean between flow locations has similar distributions. Implications of the measurements for the auto-ignition of gaseous jets are examined and demonstrate that near the nozzle exit or at earlier times conditions are un-favourable for auto-ignition.

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The structure of fine-scale scalar mixing in gas-phase planar turbulent jets

Cited by 129 publications

References 37 publications

Geometry of Intensive Scalar Dissipation Events in Turbulence

Geometry of Intensive Scalar Dissipation Events in Turbulence

An experimental investigation of mixing mechanisms in shock-accelerated flow

Mixing and scalar dissipation rate statistics in a starting gas jet

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