Budget Of The Scalar Variance Equation In A Turbulent Patch Arising From Lee Wave Breaking

2015 ◽  
Vol 10 (4) ◽  
pp. 85-94
Author(s):  
Sergey Yakovenko
Keyword(s):  
Wave Breaking ◽  
Diffusion Processes ◽  
Transport Model ◽  
Spatial Behavior ◽  
Statistical Moments ◽  
Scalar Dissipation ◽  
Algebraic Expression ◽  
Lee Wave ◽  
Scalar Variance ◽  
Variance Equation

Based on averaged data of the direct numerical simulations, statistical moments are obtained in a turbulent patch arising after lee wave overturning in a flow with stable stratification and obstacle. Temporal evolution and spatial behavior of the scalar-variance transport equation budget have been studied. A priori estimations of algebraic approximations for scalar dissipation, scalar variance and turbulent-diffusion processes in the scalar-variance equation have been carried out. Such an analysis is helpful to explore the turbulent patch in terms of statistical moments, and to verify closure hypotheses in turbulence models. In the global balance of the scalar-variance equation, the compensation of production by dissipation and advection is shown, as for the turbulent kinetic energy equation. The ratio of turbulent time scales of the scalar and velocity fields varies from 0.2 to 2.2 within the wave breaking region, and the global value of this parameter is close to unity during the quasisteady period. The algebraic expression derived from the assumption of production and dissipation balance is incorrect leading to unphysical negative values, therefore the use of the full scalarvariance equation in the turbulent transport model is justified.

Budget of Equations for Reynolds Stresses in a Turbulent Patch Arising from Internal Wave Breaking

2012 ◽  
Vol 7 (4) ◽  
pp. 87-95
Author(s):  
Sergey Yakovenko
Keyword(s):  
Internal Wave ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Wave Breaking ◽  
Spatial Behavior ◽  
Statistical Moments ◽  
Mixing Efficiency ◽  
Reynolds Stresses ◽  
Local Isotropy ◽  
Reynolds Stress Tensor

Results of the direct numerical simulations are used to obtain statistical moments in a quasi-steady turbulent patch arising in a stably stratified flow above an obstacle after internal wave breaking. Temporal evolution and spatial behavior of the Reynolds-stress tensor components and budgets of the Reynolds-stress transport equations have been studied. Such an analysis is helpful to explore the turbulent patch and its energetic characteristics by means of statistical moments, to examine closure hypotheses in turbulence models, and to evaluate geophysically important quantites. In particular, the calculated global value of the mixing efficiency is about 0.2 as in oceanic applications. Moreover, simple algebraic relations are proposed between the turbulent kinetic energy and its dissipation rate. In the Reynolds stress tensor equation, the pressure-strain correlation term provides the redistribution of the normal stress components according to the linear returnto-isotropy approximation, whereas the dissipation tensor roughly follows the local-isotropy assumption

Modeling The Turbulent Scalar Fluxes In An Internal Wave Breaking Region In Stratified Flow With Obstacle

2017 ◽  
Vol 12 (1) ◽  
pp. 79-90
Author(s):  
Sergey Yakovenko
Keyword(s):  
Internal Wave ◽  
Reynolds Stress ◽  
Diffusion Processes ◽  
Local Equilibrium ◽  
Turbulence Models ◽  
Spatial Behavior ◽  
Statistical Moments ◽  
Scalar Flux ◽  
Flux Transport ◽  
Diffusion Type

Based on averaging of the direct numerical simulation data obtained earlier, statistical moments are calculated in a turbulent patch arising after internal wave overturning in a flow with obstacle and stable stratification. Temporal evolution and spatial behavior of the turbulent-scalar-flux transport equation budget have been studied. A priori estimations of approximations for the pressure-scalar-gradient correlation and turbulent-diffusion processes in this equation have been carried out. The performed analysis is helpful to explore the turbulent patch in terms of statistical moments, and to verify closure hypotheses in turbulence models. It is shown that, in the global balance of the turbulent-scalar-flux equation, the mean-shear and buoyancy productions and the pressure-scalargradient correlation are roughly balanced, as for the shear Reynolds stress equation, and in contrast to the scalar variance and normal Reynolds stress equations. The algebraic turbulent-scalar-flux relations of the gradient diffusion type, as well as those derived in local-equilibrium and nonequilibrium assumptions are incorrect; therefore the use of the full turbulent-scalar-flux equation is justified.

scholarly journals Validation of an Eulerian Stochastic Fields Solver Coupled with Reaction–Diffusion Manifolds on LES of Methane/Air Non-premixed Flames

2020 ◽  
Author(s):  
Paola Breda ◽  
Chunkan Yu ◽  
Ulrich Maas ◽  
Michael Pfitzner
Keyword(s):  
Transport Model ◽  
Reaction Diffusion ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Combustion Model ◽  
Filtered Density Function ◽  
Detailed Chemistry ◽  
Stochastic Fields ◽  
Reduced Chemistry ◽  
Flame Behavior

AbstractThe Eulerian stochastic fields (ESF) combustion model can be used in LES in order to evaluate the filtered density function to describe the process of turbulence–chemistry interaction. The method is typically computationally expensive, especially if detailed chemistry mechanisms involving hydrocarbons are used. In this work, expensive computations are avoided by coupling the ESF solver with a reduced chemistry model. The reaction–diffusion manifold (REDIM) is chosen for this purpose, consisting of a passive scalar and a suitable reaction progress variable. The latter allows the use of a constant parametrization matrix when projecting the ESF equations onto the manifold. The piloted flames Sandia D–E were selected for validation using a 2D-REDIM. The results show that the combined solver is able to correctly capture the flame behavior in the investigated sections, although local extinction is underestimated by the ESF close to the injection plate. Hydrogen concentrations are strongly influenced by the transport model selected within the REDIM tabulation. A total solver performance increase by a factor of 81% is observed, compared to a full chemistry ESF simulation with 19 species. An accurate prediction of flame F instead required the extension of the REDIM table to a third variable, the scalar dissipation rate.

scholarly journals Seasonal dynamics modifies fate of oxygen, nitrate, and organic micropollutants during bank filtration — temperature-dependent reactive transport modeling of field data

2020 ◽  
Author(s):  
Isolde S. Barkow ◽  
Sascha E. Oswald ◽  
Hermann-Josef Lensing ◽  
Matthias Munz
Keyword(s):  
Surface Water ◽  
Reactive Transport ◽  
Oxygen Supply ◽  
Transport Model ◽  
Water Levels ◽  
Spatial Behavior ◽  
Seasonal Temperature ◽  
Bank Filtration ◽  
Organic Micropollutants ◽  
Degradation Rates

Abstract Bank filtration is considered to improve water quality through microbially mediated degradation of pollutants and is suitable for waterworks to increase their production. In particular, aquifer temperatures and oxygen supply have a great impact on many microbial processes. To investigate the temporal and spatial behavior of selected organic micropollutants during bank filtration in dependence of relevant biogeochemical conditions, we have set up a 2D reactive transport model using MODFLOW and PHT3D under the user interface ORTI3D. The considered 160-m-long transect ranges from the surface water to a groundwater extraction well of the adjacent waterworks. For this purpose, water levels, temperatures, and chemical parameters were regularly measured in the surface water and groundwater observation wells over one and a half years. To simulate the effect of seasonal temperature variations on microbial mediated degradation, we applied an empirical temperature factor, which yields a strong reduction of the degradation rate at groundwater temperatures below 11 °C. Except for acesulfame, the considered organic micropollutants are substantially degraded along their subsurface flow paths with maximum degradation rates in the range of 10−6 mol L−1 s−1. Preferential biodegradation of phenazone, diclofenac, and valsartan was found under oxic conditions, whereas carbamazepine and sulfamethoxazole were degraded under anoxic conditions. This study highlights the influence of seasonal variations in oxygen supply and temperature on the fate of organic micropollutants in surface water infiltrating into an aquifer.

Passive-scalar wake behind a line source in grid turbulence

2000 ◽  
Vol 416 ◽  
pp. 117-149 ◽  
Author(s):  
D. LIVESCU ◽  
F. A. JABERI ◽  
C. K. MADNIA
Keyword(s):  
Line Source ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Transport Equations ◽  
Source Size ◽  
Scalar Dissipation ◽  
Grid Turbulence ◽  
Scalar Flux ◽  
Convective Regime ◽  
Scalar Variance

The structure and development of the scalar wake produced by a single line source are studied in decaying isotropic turbulence. The incompressible Navier–Stokes and the passive-scalar transport equations are solved via direct numerical simulations (DNS). The velocity and the scalar fields are generated by simulating Warhaft's (1984) experiment. The results for mean and r.m.s. scalar statistics are in good agreement with those obtained from the experiment. The structure of the scalar wake is examined first. At initial times, most of the contribution to the scalar variance is due to the flapping of the wake around the centreline. Near the end of the turbulent convective regime, the wake develops internal structure and the contribution of the flapping component to the scalar variance becomes negligible. The influence of the source size on the development of the scalar wake has been examined for source sizes ranging from the Kolmogorov microscale to the integral scale. After an initial development time, the half-widths of mean and scalar r.m.s. wakes grow at rates independent of the source size. The mixing in the scalar wake is studied by analysing the evolution of the terms in the transport equations for mean, scalar flux, variance, and scalar dissipation. The DNS results are used to test two types of closures for the mean and the scalar variance equations. For the time range simulated, the gradient diffusion model for the scalar flux and the commonly used scalar dissipation model are not supported by the DNS data. On the other hand, the model based on the unconditional probability density function (PDF) method predicts the scalar flux reasonably well near the end of the turbulent convective regime for the highest Reynolds number examined. The scalar source size does not significantly influence the models' predictions, although it appears that the time-scale ratio of mechanical dissipation to scalar dissipation approaches an asymptotic value earlier for larger source sizes.

Statistical Moments Transport Model for the prediction of slug flow properties

2019 ◽  
Vol 120 ◽  
pp. 103086 ◽  
Author(s):  
J.R. Fagundes Netto ◽  
G.F.N. Gonçalves ◽  
A.P. Silva Freire
Keyword(s):  
Slug Flow ◽  
Transport Model ◽  
Statistical Moments ◽  
Flow Properties

scholarly journals Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

2012 ◽  
Vol 24 (5) ◽  
pp. 055103 ◽  
Author(s):  
E. Knudsen ◽  
E. S. Richardson ◽  
E. M. Doran ◽  
H. Pitsch ◽  
J. H. Chen
Keyword(s):  
Large Eddy Simulation ◽  
Transport Equation ◽  
Scalar Dissipation ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Scalar Variance

Comparison between passive scalar and velocity fields in a turbulent cylinder wake

2017 ◽  
Vol 813 ◽  
pp. 667-694 ◽  
Author(s):  
J. G. Chen ◽  
T. M. Zhou ◽  
R. A. Antonia ◽  
Y. Zhou
Keyword(s):  
Velocity Fluctuation ◽  
Passive Scalar ◽  
Velocity Fields ◽  
Temperature Fields ◽  
Scalar Dissipation ◽  
Stream Velocity ◽  
Cylinder Wake ◽  
Lateral Velocity ◽  
Cylinder Diameter ◽  
Scalar Variance

This work compares the enstrophy with the scalar dissipation rate, as well as the passive scalar variance with the turbulent kinetic energy, in the presence of coherent Kármán vortices in the intermediate wake of a circular cylinder. Measurements are made at$x/d=10$, 20 and 40, where$x$is the streamwise distance from the cylinder axis and$d$is the cylinder diameter, with a Reynolds number of$2.5\times 10^{3}$based on the cylinder diameter and the free-stream velocity. A probe consisting of eight hot wires (four X-wires) and four cold wires is used to measure simultaneously the three components of the fluctuating velocity and vorticity vectors, as well as the fluctuating temperature gradient vector at nominally the same point in the plane of the mean shear. It is found that the enstrophy and scalar dissipation spectra collapse approximately at all wavenumbers except around the Kármán vortex street wavenumber for$x/d\geqslant 20$. The spectral similarity between the streamwise velocity fluctuation$u$and the passive scalar$\unicode[STIX]{x1D703}$is better than that between the velocity fluctuation vector$\boldsymbol{q}$and$\unicode[STIX]{x1D703}$. This is closely related to the highly organized lateral velocity fluctuation$v$in this flow. The present observations are fully consistent with the expectation that small scales of the velocity and temperature fields are more likely to exhibit a close relationship than scales associated with the bulk of the turbulent energy or scalar variance. The variation across the wake of the time scale ratio between scalar and velocity fields is significantly smaller than that of the turbulent Prandtl number.

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