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Fluids
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Stochastic Equations in Fluid Dynamics, 2nd Edition
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Stochastic Equations in Fluid Dynamics, 2nd Edition

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 4134

Special Issue Editor

Prof. Dr. Artur V. Dmitrenko

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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 transfer in single-phase fluids on the basis of stochastic equations.
  9. Equations and experiments. 
  10. Stochastic equations of the hydrodynamic theory of plasma.

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.

Published Papers (4 papers)

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11 pages, 2907 KiB  
Article
Numerical Simulation of Swept-Wing Laminar–Turbulent Flow in the Presence of Two-Dimensional Surface Reliefs
by Andrey V. Boiko, Stanislav V. Kirilovskiy and Tatiana V. Poplavskaya
Fluids 2024, 9(4), 95; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids9040095 - 19 Apr 2024
Viewed by 315
Abstract
Stochastization of boundary-layer flow has a dramatic effect on the aerodynamic characteristics of wings, nacelles, and other objects frequently encountered in practice, resulting in higher skin-friction drag and worse aerodynamic quality. A swept-wing boundary layer encountering a transition to turbulence in the presence [...] Read more.
Stochastization of boundary-layer flow has a dramatic effect on the aerodynamic characteristics of wings, nacelles, and other objects frequently encountered in practice, resulting in higher skin-friction drag and worse aerodynamic quality. A swept-wing boundary layer encountering a transition to turbulence in the presence of two-dimensional surface reliefs is considered. The relief has the form of strips of a rectangular cross-section oriented parallel to the leading edge and located at different distances from it. The computations are performed for the angle of attack of −5° and an incoming flow velocity of 30 m/s using the ANSYS Fluent 18.0 software together with the author’s LOTRAN 3 package for predicting the laminar–turbulent transition on the basis of the eN-method. New data on distributions of N factors of swept-wing cross-flow instability affected by the surface relief are presented. The data are of practical importance for engineering modeling of the transition. Also, the effectiveness of using the reliefs as a passive method of weakening the cross-flow instability up to 30% to delay the flow stochastization is shown. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics, 2nd Edition)
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29 pages, 2585 KiB  
Article
A Spectral/hp-Based Stabilized Solver with Emphasis on the Euler Equations
by Rakesh Ranjan, Lucia Catabriga and Guillermo Araya
Fluids 2024, 9(1), 18; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids9010018 - 08 Jan 2024
Viewed by 1314
Abstract
The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, [...] Read more.
The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/hp stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/hp framework. We introduce revised stabilization parameters, τsupg, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ: the first is described with entropy variables, and the other is the YZβ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L1 and L2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics, 2nd Edition)
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18 pages, 4506 KiB  
Article
Marangoni Bursting: Insight into the Role of the Thermocapillary Effect in an Oil Bath
by Michalina Ślemp and Andrzej Miniewicz
Fluids 2023, 8(9), 255; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids8090255 - 20 Sep 2023
Cited by 1 | Viewed by 1349
Abstract
Marangoni bursting describes the spontaneous spread of a droplet of a binary mixture of alcohol/water deposited on a bath of oil, followed by its fast spontaneous fragmentation into a large number of smaller droplets in a self-similar way. Several papers have aimed to [...] Read more.
Marangoni bursting describes the spontaneous spread of a droplet of a binary mixture of alcohol/water deposited on a bath of oil, followed by its fast spontaneous fragmentation into a large number of smaller droplets in a self-similar way. Several papers have aimed to describe the physical phenomena underlying this spectacular phenomenon, in which two opposite effects, solutal and thermal Marangoni stresses, play competitive roles. We performed investigations of the Marangoni bursting phenomenon, paying attention to the surface temperature changes during bursting and after it. Fragmentation instabilities were monitored using a thermal camera for various initial alcohol/water compositions and at different stages of the process. We uncovered the role of thermocapillary Marangoni flows within the more viscous oil phase that are responsible for outward and inward shrinking of the periphery circle at the final stage of the phenomenon, enabling a more comprehensive understanding of the thermal Marangoni effect. Simulations of the Marangoni thermocapillary effect in an oil bath by solving coupled Navier–Stokes and heat transport equations using the COMSOL Multiphysics software platform support our experimental observations. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics, 2nd Edition)
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37 pages, 1889 KiB  
Article
A Vaporization Model for Continuous Surface Force Approaches and Subcooled Configurations
by Charles Brissot, Léa Cailly-Brandstäter, Elie Hachem and Rudy Valette
Fluids 2023, 8(8), 233; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids8080233 - 19 Aug 2023
Viewed by 728
Abstract
The integration of phase change phenomena through an interface is a numerical challenge that requires proper attention. Solutions to properly ensure mass and energy conservation were developed for finite difference and finite volume methods, but not for Finite Element methods. We propose a [...] Read more.
The integration of phase change phenomena through an interface is a numerical challenge that requires proper attention. Solutions to properly ensure mass and energy conservation were developed for finite difference and finite volume methods, but not for Finite Element methods. We propose a Finite Element phase change model based on an Eulerian framework with a Continuous Surface Force (CSF) approach. It handles both momentum and energy conservation at the interface for anisotropic meshes in a light an efficient way. To do so, a model based on the Level Set method is developed. A thick interface is considered to fit with the CSF approach. To properly compute the energy conservation, heat fluxes are extended through this interface thanks to the resolution of a transport equation. A dedicated pseudo compressible Navier–Stokes solver is added to compute velocity jumps with a source term at the interface in the velocity divergence equation. Several 1D and 2D benchmarks are considered with increasing complexity to highlight the performances of each feature of the framework. This stresses the capacity of the model to properly tackle phase change problems. Full article
(This article belongs to the Special Issue Stochastic Equations in Fluid Dynamics, 2nd Edition)
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