Diffusion in Turbulent Pipe Flow Using a Stochastic Model.

Sakai, Yasuhiko; Nakamura, Ikuo; Tsunoda, Hiroyuki; Hanabusa, Kouta

doi:10.1299/jsmeb.39.667

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…Data from hot-wire anemometers described in this paper are finite or ideally infinite time curves. On the other hand, a representative of the analytical random curves is a mathematical theory of Brownian motion that has been treated widely with the development of the theory of stochastic differential equations of Ito or appears in fluid flows as an expression of random terms in some equations, such as fluid diffusion (23)(32) (33) or representation of turbulent velocity (34) . However, theories that discuss randomness of experimental curves in turbulent data directly are missing within the authors' knowledge.…”

Section: Fundamental Random Subjectsmentioning

confidence: 99%

Randomness Representation in Turbulent Flows with Kolmogorov Complexity (In Mixing Layer)

Ichimiya

Nakamura

2013

JFST

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Investigations of the definition and randomness of turbulence were reviewed. The Kolmogorov complexity measure of randomness was then introduced. Numerical and graphic data in the mixing layer formed downstream of a two-dimensional nozzle exit were compressed with the aid of a compression program. Approximated Kolmogorov complexity, AK, and normalized compression distance, NCD, were obtained. The AK indicated the regularity of the laminar flow and the randomness of the turbulent flow quantitatively. The NCD of the numerical value varied with data length. Between the same data, it approached zero, yet, between different data, it approached unity as the data length increased. The NCD of the numerical value in the natural transition process in the mixing layer increased monotonically downstream. Thus, the NCD appears to be the measure of the transition process. In the natural transition process in the mixing layer, the AK of the numerical value and the NCD of the graphic data did not change monotonously in the downstream direction. They therefore contain some uncertainty for measurement of the transition process.

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Section: Fundamental Random Subjectsmentioning

confidence: 99%

Randomness Representation in Turbulent Flows with Kolmogorov Complexity (In Mixing Layer)

Ichimiya

Nakamura

2013

JFST

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“…The chemical reaction treated here is a second-order irreversible reaction. The Lagrangian velocities of stochastic particles are modeled by a generalized Langevin equation (10), (11) expressed in the cylindrical coordinate system. This model is constructed to satisfy the consistency condition of a velocity field (12) and the thermodynamic constraint (13) .…”

Section: Journal Of Fluid Science and Technologymentioning

confidence: 99%

“…Assuming axisymmetricity, the following Langevin model for turbulent jets can be obtained (see Ref. (11) for the pipe flow):…”

Section: Generalized Langevin Model In Cylindrical Coordinate Systemmentioning

confidence: 99%

Numerical Simulation of Turbulent Reactive Jet in Liquid by the Semi-empirical PDF Method

Kubo

Sakai

Kazama

2006

JFST

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Turbulent reactive jet in liquid has been simulated by the "semi-empirical" Lagrangian probability density function (PDF) method, by which the velocity field consistent to the specified moments of the Eulerian PDF of velocity can be reproduced. The chemical reaction treated in this study is a second-order irreversible reaction, R + B → S, where a solution of species R is ejected from the nozzle into the main stream that includes species B. The Lagrangian velocities of the stochastic particles are modeled by a generalized Langevin equation in the cylindrical coordinate system. This model is constructed to satisfy the consistency condition of a velocity field and the thermodynamic constraint. For the molecular mixing of reactive scalar concentrations, the most fundamental IEM (interaction by exchange with the mean) was adopted. The simulation results are compared with the experimental data. It is found that the velocity field simulated by the present model satisfies the consistency condition up to the second-order moment and the thermodynamic constraint. The simulated reactive scalar concentration field shows almost the same distribution, on the whole, as the experimental data. Therefore, the models used in this study are useful for a turbulent reactive jet.

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“…Therefore, it is more reasonable to use the stochastic differential equation with to describe the real systems disturbed by random noises. For example, the stochastic logistic diffusion model has been widely used in the field of social life, application of stochastic logistic diffusion model has been used in the field of applied economics [1] [2] [3], biology [4] [5] [6] [7], power engineering [8] [9] [10] and so on. Very recently, considerable research results have been reported on the parameter estimation based on discrete observation.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for the Continuous Time Stochastic Logistic Diffusion Model

Zheng¹,

Shu²,

Kan³

et al. 2017

OJS

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In this paper, the parameter estimation problem is investigated for the continuous time stochastic logistic diffusion system. A new continuous process is built based on the likelihood ratio scheme, the Radon-Nikodym derivative and the explicit expressions of the error of estimation are given under this new continuous process. By using the random time transformations, law of large numbers for martingales, law of iterated logarithm and stationary distribution of solution, the consistency property are proved for the estimation error. Finally, a numerical simulation is presented to demonstrate the effectiveness of the proposed method in this paper.

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Diffusion in Turbulent Pipe Flow Using a Stochastic Model.

Cited by 5 publications

References 9 publications

Randomness Representation in Turbulent Flows with Kolmogorov Complexity (In Mixing Layer)

Randomness Representation in Turbulent Flows with Kolmogorov Complexity (In Mixing Layer)

Numerical Simulation of Turbulent Reactive Jet in Liquid by the Semi-empirical PDF Method

Parameter Estimation for the Continuous Time Stochastic Logistic Diffusion Model

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