Hiroyuki Tsunoda

Turbulent Plume Diffusion in a Pipe Flow by the PDF Method

This paper gives the new simulation results of the axisymmetric point source plume in a fully developed turbulent pipe flow by the Lagrangian Probability Density Function (PDF) method. The Lagrangian velocities of stochastic particles are modeled by a generalized Langevin equation expressed in the cylindrical coordinates. The generalized Langevin equation was originally suggested by Haworth and Pope [Phys. Fluids, 29–2, 387(1986)] and its cylindrical expression was derived by Sakai et al. [JSME Int. J., B39–4, 667(1996)]. For the molecular mixing of the scalar, two different models (i.e. the Dopazo’s deterministic model and the modified Curl’s model) are adopted. The simulated radial profiles of the mean concentration and concentration variance by two models show good agreements with the experimental data by Becker et al. [AIChE J., 15–5, 964(1966)]. It is also shown that the mixing process can be characterized well by the downstream variation of the scalar PDF profile.

Turbulent Diffusion in the Pipe Flow by the Stochastic Lagrangian Model

In this short paper, we present the results of the numerical simulations of the scalar diffusion fields in a fully developed turbulent pipe flow by using the Lagrangian stochastic process model. The model used here is a Generalized Langevin (GL) model expressed in the cylindrical coordinate system [l]. The GL equation was first proposed by Haworth & Pope [2] in order to model the joint PDF equation of the velocity, and then applied to simulate the velocity and scalar field with the scalar mixing model mainly for self-similar turbulent flows [3][4]. With regard to the velocity field, recently the relationship between stochastic Lagrangian models and second-moment closures has been in detail examined [5], and the extension of the GL model has been also made to include modelling of the near-wall turbulent flow [6]. However, to date, almost no applications of this technique to the scalar diffusion field in a wall turbulent flow and inner flow such as pipe flow have been made.

Stochastic characteristics of a point‐source plume diffusion field upstream of a sphere

This research aimed to clarify the disturbance generated by a sphere in a point‐source diffusing plume developing in grid‐generated turbulence. Of special concern is the effect of the distortion of the mean stream near the forward stagnation point on the diffusion. Some results from statistical processing of experimental data are given. It was found that, because of the strong distortion of the mean stream, molecular diffusion in the vicinity of the stagnation point is greatly accelerated. As a result, as the stagnation point is approached, the conditioned probability density function for near‐zero concentration shows a remarkable slump. This result is explained qualitatively with the help of the probability density function (PDF) budget equation. A new concept, smeariness, is defined and used to effectively explain the experimental results.

Fractal Feature of Sets of Isoconcentration Points of a Plume and the Effect of the Distortion of Flow due to a Sphere on It.

This paper gives a detailed investigation of the fractal feature of sets of isoconcentration points taken from data on an axisymmetric point source plume which is evolved in grid-generated turbulence and distorted by a sphere. The following points are clarified in this paper : (1) The fractal dimensions of sets of isoconcentration points, Df1, are valued at approximately 0.3, and are likely to be independent of the threshold level of a wide range of concentration : (2) Although there is no clear range of the -5/3 power law in the spectra of the turbulence and the concentration fluctuation, sets of isoconcentration points appear to be fractal-like, and the fractal dimension is close to the value of 0.36±0.05, found in high Reynolds number flows : (3) The distortion of flow due to a sphere has almost no effect on the magnitude of the fractal dimension of a set of isoconcentration points, but merely gives rise to the change of the boxsize range within which the fractality holds.

Distortion Effects of Flow due to a Sphere on the Structure of Axisymmetric Diffusing Plume.

This research aims to clarify the characteristics of the axisymmetric point-source plume which develops in the turbulent flow distorted by a sphere. Here reported are mainly results on the probability density function and the auto correlation function of the concentration field. The data are summarized by imagining a striation structure of a diffusing plume. The effects of the distortion of flow on the concentration detecting frequency and the molecular diffusion have been quantitatively estimated with a simple theory and compared with the experiment. The results obtained back up a conclusion : a striation structure exists in the plume, and the striae of the diffusing matter appear to slim and merge with each other principally due to the distortion of the mean flow and the molecular diffusion near the stagnation point. Some comments are also given on the limitation of resolution of the measuring probe.