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Fluids
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Stochastic Equations in Fluid Dynamics
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Stochastic Equations in Fluid Dynamics

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Mathematical and Computational Fluid Mechanics".

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 13739

Special Issue Editor

Prof. Dr. Artur V. Dmitrenko

E-Mail Website
Guest Editor
1. Department of Thermal Physics, National Research Nuclear University (MEPhI), Kashirskoye Shosse 31, Moscow 115409, Russia
2. Department of Thermal Engineering, Russian University of Transport (MIIT), Obraztsova Street 9, Moscow 127994, Russia
Interests: stochastic equations; measure theory; strange attractors; bifurcations; fractals; chaos; turbulence in nature and in technical devices; single-phase and multiphase flows; thermodynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent decades, solutions of stochastic equations for the study of processes in gases and liquids have been intensively studied. For an ideal and Newtonian fluid, we consider methods for solving the equation with random terms on the right side, as well as applications of these equations to various types of motion. The aim of the issue is to present the views of scientists on the methods of solving and prospects for applying stochastic equations (continuity, concentration, motion, energy and equations of state of matter) for studying processes in liquids and gases, as well as to demonstrate their results in the field of theory and numerical modeling of random processes. There are no restrictions on the length of articles.

This special issue will focus on the following areas:

  1. Theoretical solutions of stochastic equations for flows of an ideal fluid.
  2. Theoretical solutions of stochastic equations for Newtonian fluid flows.
  3. Numerical solution of stochastic equations for flows of an ideal fluid.
  4. Numerical solutions of stochastic equations for Newtonian fluid flows.
  5. Investigation of the generation of instabilities and bifurcations in liquids based on the Euler equation with a random term on the right side of the equation.
  6. Investigation of the onset of turbulence in a Newtonian fluid on the basis of on stochastic equations.
  7. Study of free and forced convection processes in liquids and gases in nature and in technical devices on the basis of stochastic equations.
  8. Study of the heat and mass trasfer in single-phase fluids on the basis of stochastic equations.
  9. Equations and experiment.

Prof. Dr. Artur V. Dmitrenko
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • stochastic equations
  • theory of measure
  • strange attractors
  • bifurcations
  • fractals
  • chaos
  • onset of turbulence
  • generation of instabilities
  • critical numbers in fluids
  • friction
  • heat and mass transfer

Published Papers (5 papers)

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Research

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16 pages, 3556 KiB  
Article
Application of an Integral Turbulence Model to Close the Model of an Anisotropic Porous Body as Applied to Rod Structures
by Maksim N. Vlasov and Igor G. Merinov
Fluids 2022, 7(2), 77; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7020077 - 14 Feb 2022
Cited by 4 | Viewed by 1932
Abstract
In practice, often devices are ordered rod structures consisting of a large number of rods. Heat exchangers, fuel assemblies of nuclear reactors, and their cores in the case of using caseless assemblies are examples of such devices. Simulation of heat and mass transfer [...] Read more.
In practice, often devices are ordered rod structures consisting of a large number of rods. Heat exchangers, fuel assemblies of nuclear reactors, and their cores in the case of using caseless assemblies are examples of such devices. Simulation of heat and mass transfer processes in such devices in porous-body approximation can significantly reduce the required resources compared to computational fluid dynamics (CFD) approaches. The paper describes an integral turbulence model developed for defining anisotropic model parameters of a porous body. The parameters of the integral turbulence model were determined by numerical simulations for assemblies of smooth rods, assemblies with spacer grids, and wire-wrapped fuel assemblies. The results of modeling the flow of a liquid metal coolant in an experimental fuel assembly with local blocking of its flow section in anisotropic porous-body approximation using an integral turbulence model are described. The possibility of using the model of an anisotropic porous body with the integral model of turbulence to describe thermal-hydraulic processes during fluid flow in rod structures is confirmed. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics)
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6 pages, 1270 KiB  
Article
Application of Direct Numerical Simulation to Determine the Correlation Describing Friction Losses during the Transverse Flow of Fluid in Hexagonal Array Pin Bundles
by Yury E. Shvetsov, Yury S. Khomyakov, Mikhail V. Bayaskhalanov and Regina P. Dichina
Fluids 2022, 7(1), 22; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7010022 - 03 Jan 2022
Viewed by 1053
Abstract
This paper presents the results of a numerical simulation to determine the hydraulic resistance for a transverse flow through the bundle of hexagonal rods. The calculations were carried out using the precision CFD code CONV-3D, intended for direct numerical simulation of the flow [...] Read more.
This paper presents the results of a numerical simulation to determine the hydraulic resistance for a transverse flow through the bundle of hexagonal rods. The calculations were carried out using the precision CFD code CONV-3D, intended for direct numerical simulation of the flow of an incompressible fluid (DNS-approximation) in the parts of fast reactors cooled by liquid metal. The obtained dependencies of the pressure drop and the coefficient of anisotropy of friction on the Reynolds number can be used in the thermal-hydraulic codes that require modeling of the flow in similar structures and, in particular, in the inter-wrapper space of the reactor core. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics)
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10 pages, 287 KiB  
Article
Analytical Estimates of Critical Taylor Number for Motion between Rotating Coaxial Cylinders Based on Theory of Stochastic Equations and Equivalence of Measures
by Artur V. Dmitrenko
Fluids 2021, 6(9), 306; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6090306 - 30 Aug 2021
Cited by 5 | Viewed by 1652
Abstract
The purpose of this article was to present the solution for the critical Taylor number in the case of the motion between rotating coaxial cylinders based on the theory of stochastic equations of continuum laws and the equivalence of measures between random and [...] Read more.
The purpose of this article was to present the solution for the critical Taylor number in the case of the motion between rotating coaxial cylinders based on the theory of stochastic equations of continuum laws and the equivalence of measures between random and deterministic motions. Analytical solutions are currently of special value, as the solutions obtained by modern numerical methods require verification. At present, in the scientific literature, there are no mathematical relationships connecting the critical Taylor number with the parameters of the initial disturbances in the flow. The result of the solution shows a satisfactory correspondence of the obtained analytical dependence for the critical Taylor number to the experimental data. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics)
11 pages, 801 KiB  
Article
On the Use of Probability-Based Methods for Estimating the Aerodynamic Boundary-Layer Thickness
by Andrey V. Boiko, Kirill V. Demyanko, Yuri M. Nechepurenko and Grigory V. Zasko
Fluids 2021, 6(8), 267; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6080267 - 28 Jul 2021
Cited by 1 | Viewed by 1309
Abstract
In this paper, known probabilistic methods for estimating the thickness of the boundary layer of a two-dimensional laminar flow of viscous incompressible fluid are extended to three-dimensional laminar flows of a viscous compressible medium. Their applicability to the problems of boundary-layer stability is [...] Read more.
In this paper, known probabilistic methods for estimating the thickness of the boundary layer of a two-dimensional laminar flow of viscous incompressible fluid are extended to three-dimensional laminar flows of a viscous compressible medium. Their applicability to the problems of boundary-layer stability is studied with the LOTRAN3 software package, which allows us to compute the position of laminar-turbulent transition in three-dimensional aerodynamic configurations. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics)
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Review

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11 pages, 1042 KiB  
Review
Euler’s Equation of Continuity: Additional Terms of High Order of Smallness—An Overview
by Vladislav M. Ovsyannikov
Fluids 2021, 6(4), 162; https://doi.org/10.3390/fluids6040162 - 17 Apr 2021
Cited by 1 | Viewed by 6785
Abstract
Professor N.E. Zhukovsky was a famous Russian mechanic and engineer. In 1876 he defended his master’s thesis at Moscow University. At a careful reading of N.E. Zhukovsky’s master’s thesis in 1997, V.A. Bubnov—a professor at the Moscow City Pedagogical University—discovered terms of the [...] Read more.
Professor N.E. Zhukovsky was a famous Russian mechanic and engineer. In 1876 he defended his master’s thesis at Moscow University. At a careful reading of N.E. Zhukovsky’s master’s thesis in 1997, V.A. Bubnov—a professor at the Moscow City Pedagogical University—discovered terms of the second order of smallness in the continuity equation for an incompressible fluid. Zhukovsky calculated them, but did not use the amount of substance in the balance. Ten years later, the author found high-order terms in Euler’s derivation of the 1752 continuity equation for an incompressible fluid. The physical meaning of the additional terms became clear after the derivation in 2006 of the continuity equation with terms of high order of smallness for a compressible gas. The higher order terms of the smallness of the continuity equation penetrate into the inhomogeneous part of the wave equation and lead to the generation of self-oscillations, vibrations, sound, and the initial stage of turbulent pulsations. The stochastic approach ensured success in modeling turbulent flows. The use of high-order terms of smallness of the Euler continuity equation makes it possible to transfer the description of some part of the motions from the stochastic part of the equation to the deterministic part. The article contains a review of works with the derivation of the inhomogeneous wave equation. These works use additional terms of a high order of smallness in the continuity equation. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics)
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