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A novel method for prediction of particle dispersion in a planar jet using ODT model
Abstract
The One Dimensional Turbulence (ODT) model was used to study a particle laden flow in a planar jet. As an outgrowth of the LEM (Linear Eddy Model) model, the ODT model maintains a distinction among the turbulence, molecular diffusion and chemical reaction scales. Additionally, the turbulent mixing process is only considered in one-dimension, where eddy events are stochastically represented, which allows for representation of a large range of time and length scales with relatively small computing requirements. In this study, the particle and fluid time scales are split by advancing the fluid phase independently of the particle phase. When an eddy was judged to occur, it is assumed that the eddy will always exist at this area. Therefore locations of the eddy occurrences in the fluid phase are recorded after each fluid advancement step. After the fluid phase has advanced, particles are tracked through the established flow field, interacting with the eddy occurrences. When a particle encounters an eddy, its motion is affected by the eddy velocity, which is a combination of the local gas flow field and turbulent mixing. With this method, eddy effects on the particle motion are considered. Different intensities of eddy effects on particle motion were compared. Particle dispersion rate is proportional to eddy effects. This suggests that turbulent eddies always have a positive effect on particle dispersion. Besides that, particle diameter has an important influence on particle-eddy interactions. Small particles are not sensitive to eddy effects, whereas medium particles are very sensitive to eddy effects. According to Budilarto's observation, a medium eddy shape factor is selected. Based on this eddy shape factor, the final results shows that particle diameter always has a negative effect on particle dispersion, causing large particles to concentrate at center of the jet while small particles disperse to the edge. A 2-way The ability of this ODT model to capture these dispersion effects provides motivation for applying it to particle-gas chemical processes, such as coal combustion and gasification where particle clustering and dispersion has been observed.
... These two quantities are closely related, but there are situations where a clear distinction is important, such as in particle-laden flows where particle-eddy interaction is important. In these cases, τ −1 e is interpreted as an eddy frequency governing eddy sampling and the eddy turnover time is calculated using an adjustable constant of proportionality [122]. 8 More recent formulations that employ the " vector " formulation and solve several components of velocity use the kinetic energy from all velocity components in determining the eddy velocity and time scale [59]. ...
... The same statement holds true for both the particle sizes studied here. This contradicts the earlier observations (using ODT model but with a different particle-eddy interaction model [122]) that only small particle dispersion is not sensitive to the γ. For both particle sizes, a bimodal distribution is observed in the number density distribution. ...
... The ODT model was first proposed with only the streamwise component of velocity [58], and was later extended to a velocity vector formulation with kernel transformations to allow for intercomponent energy transfer [3, 122]. When energy transfer is enabled between the velocity components, mass is necessarily conserved but mass flux may not be. ...
... This applies to all ψ except ψ = 1 (continuity), since (25) is in weak form. The Lagrangian form of the continuity equation can be obtained by substituting (24) into (18) to obtain ...
... These two quantities are closely related, but there are situations where a clear distinction is important, such as in particle-laden flows where particle-eddy interaction is important. In these cases, τ −1 e is interpreted as an eddy frequency governing eddy sampling and the eddy turnover time is calculated using an adjustable constant of proportionality [24]. 8 More recent formulations that employ the "vector" formulation and solve several components of velocity use the kinetic energy from all velocity components in determining the eddy velocity and time scale [25]. ...
... The ODT model was first proposed with only the streamwise component of velocity [1], and was later extended to a velocity vector formulation with kernel transformations to allow for inter-component energy transfer [13,24]. When energy transfer is enabled between the velocity components, mass is necessarily conserved but mass flux may not be. ...
Stably stratified turbulent flows are common in geophysics and astrophysics, and frequently exhibit layered structures in which large regions of nearly constant fluid density are separated by sharp density gradients. Experiments have demonstrated that, under suitable conditions, the stirring of a stably stratified fluid generates these layer structures. In this paper, a stochastic one-dimensional model is used to study layer formation in stably stratified turbulence. The results support mixing length arguments previously proposed to describe layers in steady state.
One-dimensional turbulence, a stochastic simulation of turbulent flow evolution based on application of a mixing-length-type hypothesis to individual turbulent eddies, is used to predict transverse profiles of single-point statistics up to third order for two time-developing planar free shear flows, a mixing layer and a wake. Comparison of computed results to statistics obtained from direct numerical simulations of these flows indicates that the model, despite its simplicity, captures important features of turbulent free shear flow structure. Implications concerning the possible universality of some aspects of turbulent shear flow are discussed.
The results of an experimental investigation into the development of a turbulent plane jet issuing into a parallel moving airstream are described. On the basis of a simple dimensional argument, it is shown that the results for the spread of jets with different ratios of jet nozzle to free-stream velocity can be collapsed into a single universal curve provided the effective origins of the various sets of data can be shifted. Evidence is found of a change in structure of the jet from a self-preserving plane jet flow near the origin of the flow towards a selfpreserving wake type of flow far downstream from the origin. This change of structure is compared with a prediction based on a simple application of Town-send's large-eddy hypothesis. It is shown that the hypothesis does not account for the way in which the jet structure changes and possible reasons for this are briefly discussed. Finally, some comments are made on the usefulness of the various theories of jet spreading.
Measurements and simulations indicate that the particle-pair radial distribution function in isotropic turbulence is a power law in a range of length scales below the Kolmogorov scale for Stokes number St<1. In this range, the exponent is proportional to St1St2 for unlike particles (1 and 2) in a bidispersion, hence St2 for a monodispersion. Here, this result is derived from a model of particle response to random advection. The analysis generalizes a geometrical interpretation of clustering to polydispersions and suggests an economical Monte Carlo simulation method.