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.

Analogy between velocity and scalar fields in a turbulent channel flow

2009 ◽  
Vol 628 ◽  
pp. 241-268 ◽  
Author(s):  
ROBERT ANTHONY ANTONIA ◽  
HIROYUKI ABE ◽  
HIROSHI KAWAMURA
Keyword(s):  
Kinetic Energy ◽  
Prandtl Number ◽  
Channel Flow ◽  
Longitudinal Velocity ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Turbulent Heat ◽  
Scalar Variance

The relationship between the fluctuating velocity vector and the temperature fluctuation has been examined using direct numerical simulation databases of a turbulent channel flow with passive scalar transport using a constant time-averaged heat flux at each wall for h+ = 180, 395, 640 and 1020 (where h is the channel half-width with the superscript denoting normalization by wall variables) at Prandtl number Pr=0.71. The analogy between spectra corresponding to the kinetic energy and scalar variance is reasonable in both inner and outer regions irrespective of whether the spectra are plotted in terms of kx or kz, the wavenumbers in the streamwise and spanwise directions respectively. Whereas all three velocity fluctuations contribute to the energy spectrum when kx is used, the longitudinal velocity fluctuation is the major contributor when kz is used. The quality of the analogy in the spectral domain is confirmed by visualizations in physical space and reflects differences between spatial organizations in the velocity and scalar fields. The similarity between the spectra corresponding to the enstrophy and scalar dissipation rate is not as good as that between the kinetic energy and scalar variance, emphasizing the prominence of the scalar sheets as the centre of the channel is approached. The ratio R between the characteristic time scales of the velocity and scalar fluctuations is approximately constant over a major part of the channel and independent of h+, when the latter is sufficiently large. This constancy, which is not observed in quantities such as the turbulent Prandtl number, follows from the spectral similarities discussed in this paper and has implications for turbulent heat transport models.

The interference of thermal fields from line sources in grid turbulence

1984 ◽  
Vol 144 ◽  
pp. 363-387 ◽  
Author(s):  
Z. Warhaft
Keyword(s):  
Line Source ◽  
Cross Correlation ◽  
Thermal Field ◽  
Grid Turbulence ◽  
Inference Method ◽  
Thermal Fields ◽  
Downstream Distance ◽  
Scalar Variance ◽  
Rate Of Decay ◽  
Total Temperature

The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross-correlation coefficient ρ between the temperature fluctuations produced by the sources. The evolution of ρ as a function of downstream distance, for 0.075 < d/l < 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that ρ may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line-source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar-variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements.

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.

A scalar subgrid model with flow structure for large-eddy simulations of scalar variances

2000 ◽  
Vol 407 ◽  
pp. 315-349 ◽  
Author(s):  
P. FLOHR ◽  
J. C. VASSILICOS
Keyword(s):  
Flow Structure ◽  
Kinematic Model ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Inertial Range ◽  
Large Eddy Simulations ◽  
Tracer Particles ◽  
Particle Pairs ◽  
Large Eddy ◽  
Scalar Variance

A new model to simulate passive scalar fields in large-eddy simulations of turbulence is presented. The scalar field is described by clouds of tracer particles and the subgrid contribution of the tracer displacement is modelled by a kinematic model which obeys Kolmogorov's inertial-range scaling, is incompressible and incorporates turbulent-like flow structure of the turbulent small scales. This makes it possible to study the scalar variance field with inertial-range effects explicitly resolved by the kinematic subgrid field while the LES determines the value of the Lagrangian integral time scale TL. In this way, the modelling approach does not rely on unknown Lagrangian input parameters which determine the absolute value of the scalar variance.The mean separation of particle pairs displays a well-defined Richardson scaling in the inertial range, and we find that the Richardson constant GΔ ≈ 0.07 which is small compared to the value obtained from stochastic models with the same TL. The probability density function of the separation of particle pairs is found to be highly non-Gaussian in the inertial range of times and for long times becomes Gaussian. We compute the scalar variance field for an instantaneous line source and find good agreement with experimental data.

Investigation of internal intermittency by way of higher-order spectral moments

2021 ◽  
Vol 932 ◽  
Author(s):  
S. Lortie ◽  
L. Mydlarski
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Higher Order ◽  
Inertial Subrange ◽  
Grid Turbulence ◽  
Spectral Moments ◽  
Number Range ◽  
High Reynolds

The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$ . Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.

An algebraic model for the turbulent flux of a passive scalar

1989 ◽  
Vol 203 ◽  
pp. 77-101 ◽  
Author(s):  
Michael M. Rogers ◽  
Nagi N. Mansour ◽  
William C. Reynolds
Keyword(s):  
Stokes Equations ◽  
Transport Model ◽  
Time Derivative ◽  
Turbulent Channel Flow ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Flux Vector ◽  
Scalar Flux

The behaviour of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow has been studied using direct numerical simulations of the unsteady incompressible Navier-Stokes equations with 128 × 128 × 128 grid points. It is found that, for all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are approximately aligned with the scalar flux vector itself. In addition, the time derivative of the scalar flux is also approximately aligned with the flux vector for the developed fields (corresponding to roughly constant correlation coefficients). These alignments lead directly to a gradient transport model with a tensor turbulent diffusivity. The simulation results are used to fit a dimensionless model coefficient as a function of the turbulence Reynolds and Péclet numbers. The model is tested against two different passive-scalar fields in fully developed turbulent channel flow (also generated by direct numerical simulation) and is found to predict the scalar flux quite well throughout the entire channel.

Assessment of two-equation models of turbulent passive-scalar diffusion in channel flow

1992 ◽  
Vol 238 ◽  
pp. 405-433 ◽  
Author(s):  
Kiyosi Horiuti
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Eddy Diffusivity ◽  
Passive Scalar ◽  
Scalar Flux ◽  
Scalar Fluxes ◽  
Large Eddy ◽  
Scalar Variance ◽  
Flux Model ◽  
Kim Model

Models for the transport of passive scalar in turbulent flow were investigated using databases derived from numerical solutions of the Navier—Stokes equations for fully developed plane channel flow, these databases being generated using large-eddy and direct numerical simulation techniques. Their reliability has been established by comparison with the experimental measurements of Hishida. Nagano & Tagawa (1986). The present paper compares these simulations and calculations using the Nagano & Kim (1988) ‘two-equation’ model for the scalar variance (kθ) and scalar variance dissipation (εθ). This model accounts for the dependence of flow quantities on the Prandtl number by expressing eddy diffusivity in terms of the ratio of the timescales of velocity and scalar fluctuations. However, the statistical analysis by Yoshizawa (1988) showed that there was an inconsistency in the definition of the isotropic eddy diffusivity in the Nagano—Kim model, the implications of which are clearly demonstrated by the results of this paper where large-eddy simulation and direct numerical simulation (LES/DNS) databases are used to compute the quantities contained in both models. An extension of the Nagano-Kim model is proposed which resolves these inconsistencies, and a further development of this model is given in which the anisotropic scalar fluxes are calculated. Near a rigid surface, a third-order ‘anisotropic representation’ of scalar fluxes may be used as an alternative model for reducing the eddy diffusivity, instead of the conventional ‘damping functions’. This model is similar but distinct from the algebraic scalar flux model of Rogers, Mansour & Reynolds (1989). A third aspect of this paper is the use of the LES/DNS databases to evaluate certain coefficients (those for modelling the pressure-scalar gradient terms) of another model of a similar type, namely the algebraic scalar flux model of Launder (1975).

Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field

1999 ◽  
Vol 400 ◽  
pp. 163-197 ◽  
Author(s):  
LIAN-PING WANG ◽  
SHIYI CHEN ◽  
JAMES G. BRASSEUR
Keyword(s):  
Reynolds Number ◽  
Scalar Field ◽  
Velocity Field ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Experimental Results ◽  
Inertial Subrange ◽  
Scalar Dissipation ◽  
Scaling Exponent ◽  
Scaling Exponents

Using direct numerical simulations (DNS) and large-eddy simulations (LES) of velocity and passive scalar in isotropic turbulence (up to 5123 grid points), we examine directly and quantitatively the refined similarity hypotheses as applied to passive scalar fields (RSHP) with Prandtl number of order one. Unlike previous experimental investigations, exact energy and scalar dissipation rates were used and scaling exponents were quantified as a function of local Reynolds number. We first demonstrate that the forced DNS and LES scalar fields exhibit realistic inertial-range dynamics and that the statistical characteristics compare well with other numerical, theoretical and experimental studies. The Obukhov–Corrsin constant for the k−5/3 scalar variance spectrum obtained from the 5123 mesh is 0.87±0.10. Various statistics indicated that the scalar field is more intermittent than the velocity field. The joint probability distribution of locally-averaged energy dissipation εr and scalar dissipation χr is close to log-normal with a correlation coefficient of 0.25±0.01 between the logarithmic dissipations in the inertial subrange. The intermittency parameter for scalar dissipation is estimated to be in the range 0.43≈0.77, based on direct calculations of the variance of lnχr. The scaling exponents of the conditional scalar increment δrθ[mid ] χr,εr suggest a tendency to follow RSHP. Most significantly, the scaling exponent of δrθ[mid ] χr,εr over εr was shown to be approximately −⅙ in the inertial subrange, confirming a dynamical aspect of RSHP. In agreement with recent experimental results (Zhu et al. 1995; Stolovitzky et al. 1995), the probability distributions of the random variable βs = δrθ[mid ] χr,εr/ (χ1/2r ε−⅙rr1/3) were found to be nearly Gaussian. However, contrary to the experimental results, we find that the moments of βs are almost identical to those for the velocity field found in Part 1 of this study (Wang et al. 1996) and are insensitive to Reynolds number, large-scale forcing, and subgrid modelling.

Direct Numerical Simulation of Mixing of a Passive in Decaying Turbulence

1999 ◽  
Author(s):  
P. Deb ◽  
Pradip Majumdar
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Step Method ◽  
Fractional Step Method ◽  
Mixing Processes ◽  
Turbulent Reactive Flows ◽  
Decaying Turbulence

Abstract Research on turbulent mixing processes is of great interest to those working on turbulent-reactive flows. In this paper, a detailed study has been performed for the evolution of scalar fields of different initial integral scales in decaying, homogeneous and isotropic turbulence using DNS technique. Passive scalar mixing in a cubical decaying, homogeneous, isotropic turbulence field is considered. The three-dimensional incompressible Navier-Stokes equations together with scalar equation are solved using Fractional Step Method. The convective and diffusive terms in governing equations are discretised by Compact Finite Difference Scheme. The 32 × 32 × 32 uniform staggered grids are used. The present simulation is performed at Taylor Reynolds number of 28.83. In this paper, the evolution of scalar RMS and scalar dissipation rate for different integral length scales has been presented. The initial velocity vector and Probability Density Function (PDF) of scalar at different eddy turn over time have also been presented.

Experiments on density-gradient anisotropies and scalar dissipation of turbulence in a stably stratified fluid

1996 ◽  
Vol 322 ◽  
pp. 383-409 ◽  
Author(s):  
S. T. Thoroddsen ◽  
C. W. Van Atta
Keyword(s):  
Density Gradient ◽  
Correlation Method ◽  
Reynolds Numbers ◽  
Scalar Dissipation ◽  
Grid Turbulence ◽  
Mean Square ◽  
Induced Anisotropy ◽  
Scalar Variance ◽  
Variance Balance ◽  
The Mean

The anisotropic behaviour of density-gradient fluctuations in stably stratified grid turbulence and the consequences for simplified (isotropic) estimates of scalar dissipation rates χ were experimentally studied in a thermally stratified wind tunnel at moderate Reynolds numbers (Reλ ≃ 20). Strong stable stratifications were attained, with Brunt-Väisälä frequency N as high as 4 rad s−1. The correlation method was used to estimate the mean-square cross-stream and streamwise density gradients. Cross-stream gradients were measured using two cold wires. The mean-square vertical gradients were found to become larger than the streamwise gradients by as much as a factor of 2.2 for the largest dimensionless buoyancy times (Nt = 7). This corresponds to a 40% error in the scalar dissipation estimates based on ∂θ/∂x alone, and assuming the validity of the isotropic relations. Gradient spectral relations show that this buoyancy-induced anisotropy persists at all length scales. Better closure of the scalar variance balance was attained than in previously reported measurements by other researchers. This is attributed to our use of cold-wire temperature sensors having larger length-to-diameter ratio than used in the previous measurements.

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