Evolution of passive scalar statistics in a spatially developing turbulence

Paul, Immanuvel; Papadakis, George; Vassilicos, J. C.

doi:10.1103/physrevfluids.3.014612

Cited by 4 publications

(3 citation statements)

References 60 publications

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“…The code is parallelised using the PETSc libraries (Balay et al 2014). Details of the solver have been reported in previous studies (Paul et al 2017;Paul 2017;Paul et al 2018), and are not repeated here.…”

Section: Methodsmentioning

confidence: 99%

Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence

2018

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The present direct numerical simulation (DNS) study, the first of its kind, explores the effect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to fine-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the grid-element, inside the production, peak and decay regions, respectively, are considered. The turbulent flow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous and fully turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11 %, while the peak location has the highest turbulence intensity of 15 %. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63 %, while in the decay region it is enhanced by only 28 %. This difference cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coefficient are found invalid for the production and peak locations, while they are satisfied in the decay region. It is established that the flow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the cylinder, and therefore the latter is very responsive to the impinging disturbances. The highest Nusselt number along the circumference of the cylinder is shifted 45 degrees from the front stagnation point. This shift is due to the turbulence-generating grid-element bars that result in the prevalence of intense events at the point of maximum Nusselt number compared to the stagnation point.

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Section: Methodsmentioning

confidence: 99%

Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence

2018

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“…Direct numerical simulation (DNS) development began with the pioneering work of the Stanford team with the investigation of the fully developed turbulent flow in a plane channel (Kim, Moin & Moser 1987) for the Reynolds number based on the friction velocity , half-channel width and dynamic viscosity , and is now a very valuable tool (Lee & Moser 2015; Paul, Papadakis & Vassilicos 2018) thanks to the rapid increase of super-computer power as well as the development of computational techniques including vectorization and parallelization (Schiestel & Chaouat 2022). Numerical simulations of turbulent flows are useful also in this framework of heat transfer for determining the thermal flow characteristics.…”

Section: Introductionmentioning

confidence: 99%

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

Chaouat

2023

J. Fluid Mech.

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We perform direct numerical simulations (DNS) of the fully developed turbulent channel flow with a passive scalar subjected to constant time-averaged scalar fluxes at the wall. The first case (case I) considers a constant time-averaged scalar flux $\left \langle q_w \right \rangle$ along with the specific condition of a non-fluctuating scalar $\theta _w$ imposed at the wall implying zero wall scalar fluctuation $\theta '_w=0$ and zero variance (isoscalar boundary condition) whereas the second case (case II) accounts for a constant instantaneous scalar flux $q_w$ in time and space leading to zero gradient of scalar fluctuation along the normal to the wall $(\partial \theta '/ \partial x_n)_w = 0$ (isoflux boundary condition) implying a non-zero variance. The friction Reynolds number takes on the value $R_\tau =395$ and the molecular Prandtl numbers considered are $P_r=0.01$ , 0.1, 1 and 10. The purpose is to investigate the effect of the wall scalar fluctuations on the scalar field. Emphasis is put on the mean passive scalar $\left \langle \theta \right \rangle$ , the half-scalar variance $k_\theta$ , the turbulent scalar fluxes $\tau _{i \theta }$ , the correlation coefficients $R_{i \theta }$ , the passive scalar to dynamic time-scale ratio $\mathcal {R}$ , the turbulent Prandtl number $Pr_t$ and higher-order scalar statistics. Systematic comparisons between these two scalar fields are undertaken. As a result of interest, it is found that the mean scalar remains almost the same whatever the type of the boundary layer condition but not the scalar variance. The budgets of transport equations for the half-scalar variance and turbulent fluxes reveal that some scalar quantities such as the dissipation-rate and the molecular diffusion terms are highly modified in the near-wall region but not really the production, diffusion and the scalar-pressure gradient correlation terms in a first approximation. Visualization of the instantaneous scalar fields indicates that the topology of the structures is strongly modified as the Prandtl number increases from $P_r=0.01$ up to $10$ . Finally, it is shown how to use this DNS database to devise and calibrate scalar flux equation models in the framework of both first and second moment closures. This study suggests that accounting for wall scalar fluctuations should be considered in the simulation of turbulent flows involving fluid and solid combinations at the interface and provides a useful high resolution DNS database.

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“…The difference between active vs passive scalar turbulence scaling has been explored by Celani et al (2002Celani et al ( , 2004. Moving to spatially developing turbulence, passive scalar statistics were measured by Paul, Papadakis & Vassilicos (2018). Applying self-similar scaling to RT turbulence, growth rates and scaling relations were found by Ristorcelli & Clark (2004).…”

Section: Introductionmentioning

confidence: 99%

Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock

Noble,

Ames,

McConnell

et al. 2023

J. Fluid Mech.

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The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths, vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn., vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids, vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. (Phys. Fluids, vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.

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Evolution of passive scalar statistics in a spatially developing turbulence

Cited by 4 publications

References 60 publications

Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence

Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock

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