Scalar passive

The Kolmogorov velocity field mixes packets of air with different passive scalars a passive scalar being one which does not exchange energy with the turbulent velocity flow. (Potential) temperature is such a passive scalar and the temperature fluctuations also follow the Kolmogorov law with a different proportionality constant... 

Via a passive scalar method [6] where or, denotes the volume fraction of the i-th phase, while T, represents the diffusivity coefiBcient of the tracer in the i-th phase. The transient form of the scalar transport equation was utilized to track the pulse of tracer through the computational domain. The exit age distribution was evaluated from the normalized concentration curve obtained via measurements at the reactor outlet at 1 second intervals. This was subsequently used to determine the mean residence time, tm and Peclet number, Pe [7]. 

The chemical species were treated as passive scalar tracers in the unsteady LBM equations. The reaction was simulated as being mass-transfer limited at low Re — 166, with diffusivities in the ratios DA DB Dc— 1 3 2. The concentration fields shown in Fig. 16 are different for each species due to the different diffusivities. The slow-diffusing species A is transported mainly by convection and regions of high or low concentration correspond to features of the flow field. A more uniform field is seen for the concentration of faster... 

RTD functions for combinations of ideal reactors can be constructed (Wen and Fan 1975) based on (1.6) and (1.7). For non-ideal reactors, the RTD function (see example in Fig. 1.4) can be measured experimentally using passive tracers (Levenspiel 1998 Fogler 1999), or extracted numerically from CFD simulations of time-dependent passive scalar mixing. 

The form of (1.15) is identical to the balance equation that is used in finite-volume CFD codes for passive scalar mixing.17 The principal difference between a zone model and a finite-volume CFD model is that in a zone model the grid can be chosen to optimize the capture of inhomogeneities in the scalar fields independent of the mean velocity and turbulence fields.18 Theoretically, this fact could be exploited to reduce the number of zones to the minimum required to resolve spatial gradients in the scalar fields, thereby greatly reducing the computational requirements. 

Because the random velocity field U(x, t) appears in (1.28), p. 16, a passive scalar field in a turbulent flow will be a random field that depends strongly on the velocity field (Warhaft 2000). Thus, turbulent scalar mixing can be described by a one-point joint velocity, composition PDF /u,< (V, i/r,x, t) defined by... 

For a passive scalar, the turbulent flow will be unaffected by the presence of the scalar. This implies that for wavenumbers above the scalar dissipation range, the characteristic time scale for scalar spectral transport should be equal to that for velocity spectral transport tst defined by (2.67), p. 42. Thus, by equating the scalar and velocity spectral transport time scales, we have23 t)... 

This chapter is devoted to methods for describing the turbulent transport of passive scalars. The basic transport equations resulting from Reynolds averaging have been derived in earlier chapters and contain unclosed terms that must be modeled. Thus the available models for these terms are the primary focus of this chapter. However, to begin the discussion, we first review transport models based on the direct numerical simulation of the Navier-Stokes equation, and other models that do not require one-point closures. The presentation of turbulent transport models in this chapter is not intended to be comprehensive. Instead, the emphasis is on the differences between particular classes of models, and how they relate to models for turbulent reacting flow. A more detailed discussion of turbulent-flow models can be found in Pope (2000). For practical advice on choosing appropriate models for particular flows, the reader may wish to consult Wilcox (1993). 

The filtered transport equation for an inert, passive scalar has the form... 

This is consistent with DNS data for passive scalar mixing in isotropic turbulence (Yeung 1996). 

For passive scalars, (A, V, ) will be independent of ip. For active scalars, e.g., temperature dependence in stratified flows, (A, V, ip) would also depend on the value of ip. 

Ui, the fluctuation field of a passive scalar molecular diffusion coefficient r is governed by... 

In the SR model, Cd = 3 is chosen to agree with passive scalar decay from isotropic initial conditions in the absence of turbulent mixing (i.e., pure diffusion). 

Anselmet, F., H. Djeridi, and L. Fulachier (1994). Joint statistics of a passive scalar and its dissipation in turbulent flows. Journal of Fluid Mechanics 280, 173-197. 

Bogucki, D., J. A. Domaradzki, and P. K. Yeung (1997). Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow. Journal of Fluid Mechanics 343, 111-130. 

Cai, X. D., E. E. O Brien, and F. Ladeinde (1996). Uniform mean scalar gradient in grid turbulence Asymptotic probability distribution of a passive scalar. Physics of Fluids 8, 2555-2557. 

Similarity states of passive scalar transport in isotropic turbulence. Physics of Fluids 6, 1036-1051. 

Eswaran, V. and S. B. Pope (1988). Direct numerical simulations of the turbulent mixing of a passive scalar. The Physics of Fluids 31, 506-520. 

The Fokker-Planck closure for turbulent molecular mixing Passive scalars. 

Improved Lagrangian mixing models for passive scalars in isotropic turbulence. 

Gonzalez, M. (2000). Study of the anisotropy of a passive scalar field at the level of dissipation. Physics of Fluids 12, 2302-2310. 

Hamba, F. (1987). Statistical analysis of chemically reacting passive scalars in turbulent shear flows. Journal of the Physical Society of Japan 56, 79-96. 

Kollmann, W. and J. Janicka (1982). The probability density function of a passive scalar in turbulent shear flows. The Physics of Fluids 25, 1755-1769. 

Convection of a passive scalar by a quasi-uniform random straining field. Journal of Fluid Mechanics 64, 737-762. 

Overholt, M. R. and S. B. Pope (1996). DNS of a passive scalar with imposed mean scalar gradient in isotropic turbulence. Physics of Fluids 8, 3128-3148. 

Rogers, M. M., P. Moin, and W. C. Reynolds (1986). The structure and modeling of the hydrodynamic and passive scalar fields in homogeneous turbulent shear flow. Report TF-25, Department of Mechanical Engineering, Stanford University. 

Warhaft, Z. (2000). Passive scalars in turbulent flows. Annual Reviews of Fluid Mechanics 32, 203-240. 

Livescu, D., F. A. Jaberi, and C.K. Madnia. 2000. Passive-scalar wake behind a line source in grid turbulence. J. Fluid Mechanics 416 117-49. 

Small errors in computation that may result in pockets of small negative temperature T can have disastrous effects here since temperature is an active scalar, and influences the flow directly (unlike passive scalars like dye concentration). To maintain positivity of temperature, a simple procedure used by Riley et al. [10] is followed, which merely involves setting any small negative temperature that may arise to zero at every time step. It has been shown [10] that one is still able to get superalgebraic convergence using this simple filter. 

The present study is to elaborate on the computational approaches to explore flame stabilization techniques in subsonic ramjets, and to control combustion both passively and actively. The primary focus is on statistical models of turbulent combustion, in particular, the Presumed Probability Density Function (PPDF) method and the Pressure-Coupled Joint Velocity-Scalar Probability Density Function (PC JVS PDF) method [23, 24]. 

Crimaldi, J. P., M. B. Wiley, and J. R. Koseff. The relationship between mean and instantaneous structure in turbulent passive scalar plumes. J. Turbul. 3(14), 1-24... 

A second bit of caginess in the introduction is our statement that (R ) is the primary complex scalar product space used in the study of a particle in three-space. Beware the passive voice We used it here to gloss over the fact that 7,2 (R3) is not the set of all states of the particle. The fact that we want /g3 2 = 1 is only part of the story. Because the only numbers we can measure physically are of the form, we cannot distinguish between... 

Figure 37 Evolution of a passive scalar inside the offset strip fin geometry.

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