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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 January 2020) | Viewed by 44394

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Dr. Mostafa Safdari Shadloo

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CORIA Lab., INSA Rouen/ CNRS (UMR 6614), Rouen, France
Interests: turbulence; computational fluid dynamics (CFD); multiphase flows; meshless methods; high performance computing (HPC)
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Special Issue Information

Dear Colleagues,

The existance of symmetry and its breacking in aero-/hydro-dynamics applications are some of the most important aspects of many engineering fields, such as mechanical, aurospace, chemical, and process engineering. For intance, the existence of breaking of symmetry at a critical Renolds number confirmed the existence of a bifurcation in expansion pipe flows. Such a symmetry breacking mechanism may cause the appearance of turbulence, which in retun increases the mixing and required pomping power for several process engineering design applications. In aerospace aplications, the receptivity of a symetric laminar flow to internal/external perturbations may cause the flow to transition, a dramatic change in the local drag coeeficient, and heat removal from the surface. The latter needs to be considered in the design step for choosing the proper materals that can also bear the unbalanced thermodynamic loads.

The applications of symmetry and its breacking are usually inter-disicplinary, and prior knowledge of them is crusial for many real-life applications. Therfore, the current Special Issue, Aero-/Hydro-dynamics and Symmetry, invites original and review works in the field for participation. The scope of this Special Issue contains, but is not limmited to, the state-of-the-art computational, theoritical, and experimental works dealing with symmetry and its breacking, which are in line with the aero-/hydro-dynamics applications. Recent advances in numerical, theoritical, and experimental methodologies, as well as finding new physics, new methodological developments, and their limmitations, lies within the scope of the current Special Issue. Potential topics dealing with the following subheadings are deemed suitable for publication, but are not limited to:

Mathematical models such as the symmetry method, homotopy perturbation method (HPM), homotopy analysis method (HAM), lie group, integral transform, and so on;
Equilibirium and out of equilibirium thermodynamics and fluid mechanics
Hydrodynamics for symmetric exclusion;
Hydrodynamics with multiple higher-form symmetries;
Ideal order and dissipative fluids with q-form symmetry;
Partial and fractional order differential equations;
Finite difference (FDM), finite volume (FVM), finite element (FEM), smoothed particle hydrodynamics (SPH), moving particle semi-implicit (MPS), lattice Boltzmann (LBM) methods, and so on;
multiphysics phenomena, such as non-Newtonian flows, multiphase flows, phase change, nanofluidic, magnetohydrodynamics (MHD), electrohydrodynamics (EHD), and so on;
Symmetry and its breackdown in transitional and turbulent flows.

Assc. Prof. Mostafa Safdari Shadloo
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. Symmetry 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 2400 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

magnetohydrodynamics
thermodynamics
fluid mechanics
Hydrodynamics

Published Papers (12 papers)

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Research

15 pages, 2508 KiB

Open AccessArticle

Investigation of Magneto Hydro-Dynamics Effects on a Polymer Chain Transfer in Micro-Channel Using Dissipative Particle Dynamics Method

by Ramin Zakeri, Moslem Sabouri, Akbar Maleki and Zahra Abdelmalek

Symmetry 2020, 12(3), 397; https://doi.org/10.3390/sym12030397 - 04 Mar 2020

Cited by 6 | Viewed by 2658

Abstract

In this paper, the effect of Magneto Hydro-Dynamics (MHD) on a polymer chain in the micro channel is studied by employing the Dissipative Particle Dynamics simulation (DPD) method. First, in a simple symmetric micro-channel, the results are evaluated and validated for different values of Hartmann (Ha) Number. The difference between the simulation and analytical solution is below 10%. Then, two types of polymer chain including short and long polymer chain are examined in the channel and the effective parameters such as Ha number, the harmony bond coefficient or spring constant (K), and the length of the polymer chain (N) are studied in the MHD flow. It is shown that by increasing harmony bond constant to 10 times with Ha = 20, the reduction of about 80% in radius of gyration squared, and half in polymer length compared to Ha = 1 would occur for both test cases. For short and long length of polymer, proper transfer of a polymer chain through MHD particles flow is observed with less perturbations (80%) and faster polymer transfer in the symmetric micro-channel. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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17 pages, 3615 KiB

Open AccessArticle

Impact of Nonlinear Thermal Radiation on the Time-Dependent Flow of Non-Newtonian Nanoliquid over a Permeable Shrinking Surface

by A. Zaib, Umair Khan, Ilyas Khan, El-Sayed M. Sherif, Kottakkaran Sooppy Nisar and Asiful H. Seikh

Symmetry 2020, 12(2), 195; https://doi.org/10.3390/sym12020195 - 28 Jan 2020

Cited by 7 | Viewed by 1924

Abstract

Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial differential equations into nonlinear ordinary differential equations and then these ordinary differential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form

A < 0

. However, the unique result is obtained for flow in accelerating form

A \geq 0

. In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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12 pages, 1092 KiB

Open AccessArticle

Analytical Solution of Heat Conduction in a Symmetrical Cylinder Using the Solution Structure Theorem and Superposition Technique

by Rasool Kalbasi, Seyed Mohammadhadi Alaeddin, Mohammad Akbari and Masoud Afrand

Symmetry 2019, 11(12), 1522; https://doi.org/10.3390/sym11121522 - 16 Dec 2019

Cited by 5 | Viewed by 2960

Abstract

In this paper, non-Fourier heat conduction in a cylinder with non-homogeneous boundary conditions is analytically studied. A superposition approach combining with the solution structure theorems is used to get a solution for equation of hyperbolic heat conduction. In this solution, a complex origin problem is divided into, different, easier subproblems which can actually be integrated to take the solution of the first problem. The first problem is split into three sub-problems by setting the term of heat generation, the initial conditions, and the boundary condition with specified value in each sub-problem. This method provides a precise and convenient solution to the equation of non-Fourier heat conduction. The results show that at low times (t = 0.1) up to about r = 0.4, the contribution of T₁ and T₃ dominate compared to T₂ contributing little to the overall temperature. But at r > 0.4, all three temperature components will have the same role and less impact on the overall temperature (T). Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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Graphical abstract

18 pages, 441 KiB

Open AccessArticle

Large-Eddy Simulation of an Asymmetric Plane Diffuser: Comparison of Different Subgrid Scale Models

by Hui Tang, Yulong Lei, Xingzhong Li and Yao Fu

Symmetry 2019, 11(11), 1337; https://doi.org/10.3390/sym11111337 - 29 Oct 2019

Cited by 7 | Viewed by 3033

Abstract

Large-eddy simulation (LES) of separated turbulent flow through an asymmetric plane diffuser is investigated. The outcome of an actual LES depends on the quality of the subgrid-scale (SGS) model, as well as the accuracy of the numerical method used to solve the equations for the resolved scales. In this paper, we focus on the influence of SGS models for LES of the diffuser flow through using a high-order finite difference method to solve the equations for the resolved scales. Six resolutions are computed to investigate the influence of mesh resolution. Four existing SGS models, a new one-equation dynamic SGS model and a direct numerical simulation (DNS) are conducted in the diffuser flow. A series of computational analyses is performed to assess the performance of different SGS models on the coarse grids. By comparison with the experiment and DNS, the results produced by the new one-equation dynamic model give better agreement with experiment and DNS than the four other existing SGS models. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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17 pages, 4513 KiB

Open AccessArticle

MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

by Arshad Khan, Dolat Khan, Ilyas Khan, Muhammad Taj, Imran Ullah, Abdullah Mohammed Aldawsari, Phatiphat Thounthong and Kottakkaran Sooppy Nisar

Symmetry 2019, 11(10), 1295; https://doi.org/10.3390/sym11101295 - 15 Oct 2019

Cited by 20 | Viewed by 2584

Abstract

Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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16 pages, 7783 KiB

Open AccessArticle

Experimental Study on Plasma Flow Control of Symmetric Flying Wing Based on Two Kinds of Scaling Models

by Like Xie, Hua Liang, Menghu Han, Zhongguo Niu, Biao Wei, Zhi Su and Bingliang Tang

Symmetry 2019, 11(10), 1261; https://doi.org/10.3390/sym11101261 - 09 Oct 2019

Cited by 1 | Viewed by 2772

Abstract

The symmetric flying wing has a simple structure and a high lift-to-drag ratio. Due to its complicated surface design, the flow field flowing through its surface is also complex and variable, and the three-dimensional effect is obvious. In order to verify the effect of microsecond pulse plasma flow control on the symmetric flying wing, two different sizes of scaling models were selected. The discharge energy was analyzed, and the force and moment characteristics of the two flying wings and the particle image velocimetry (PIV) results on their surface flow field were compared to obtain the following conclusions. The microsecond pulse surface dielectric barrier discharge energy density is independent of the actuator length but increases with the actuation voltage. After actuation, the stall angle of attack of the small flying wing is delayed by 4°, the maximum lift coefficient is increased by 30.9%, and the drag coefficient can be reduced by 17.3%. After the large flying wing is actuated, the stall angle of attack is delayed by 4°, the maximum lift coefficient is increased by 15.1%, but the drag coefficient is increased. The test results of PIV in the flow field of different sections indicate that the stall separation on the surface of the symmetric flying wing starts first from the outer side, and then the separation area begins to appear on the inner side as the angle of attack increases. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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20 pages, 7038 KiB

Open AccessArticle

Hydrodynamic-Interaction Analysis of an Autonomous Underwater Hovering Vehicle and Ship with Wave Effects

by Chen-Wei Chen, Ying Chen and Qian-Wen Cai

Symmetry 2019, 11(10), 1213; https://doi.org/10.3390/sym11101213 - 29 Sep 2019

Cited by 15 | Viewed by 4030

Abstract

A new vertical axis-symmetrical dish-shaped autonomous underwater vehicle (AUV) with excellent maneuverability, known as the autonomous underwater hovering vehicle (AUH), is proposed. This study investigates an important working model of the AUH approaching a host ship in waves. The working model of AUH–Ship interactions deals with hydrodynamic interaction, seakeeping performance for communication, launch, and recovery near a free surface. The AUH is able to navigate and implement homing automation through acoustic positioning equipment, a depth sensor, a heading compass, and a Doppler velocity log (DVL) in the working area based on numerical analysis of AUH–Ship hydrodynamic performance in this study. The hydrodynamic-interaction performance of the AUH and ship near free surfaces is analyzed in the frequency and time domains using a potential-based surface-panel method based on a commercial computational fluid dynamics (CFD) solver (ANSYS-AQWA), i.e., a 3D panel code of seakeeping performance module in the ANSYS platform where the fluid is assumed to be irrotational, inviscid, and incompressible. The motion performance of the AUH approaching the host ship, with a dynamic positioning system in waves, is studied by estimating interactive response-amplitude operators (RAOs) of the AUH and host ship in 6-DOF that were estimated and analyzed at different wave amplitudes and frequencies. In the ship and AUH interaction simulations, the host ship is assumed to be a well-posed station keeping in waves with zero service speed. The AUH and ship interference effect is studied at different distances to appropriate recovery and launch positions for the AUH at the following sea and beam sea, i.e., wave-encounter angles 0° and 90°, respectively. In addition, the hydrodynamic interaction of the AUH and ship in yaw and roll at different AUH velocities is estimated. The AUH motion performance approaching the ship in long-crested irregular seas is analyzed in the time domain using the Pierson–Moskowitz wave spectrum model. Viscid hydrodynamic force on AUH motion in roll near a free surface was significant. A damping model was adopted to formulate the viscid effect to enhance the effectiveness of the ANSYS-AQWA inviscid potential-based solver. Numerical analysis of motion RAO of the AUH in roll with the damping effect was compared to the experimental data in wave-frequency range 0.2–1.0 Hz, resulting in the average error being reduced from 21.03% to 9.95% to verify the method’s accuracy. The proposed method conveniently and accurately predicted hydrodynamic-interaction characteristics and motion RAO for a dish-type AUH and host ship for the precise use of mounted sensors in waves. The results of these simulations can be used to analyze the homing automation and adaptive controllability to advance the AUV development and design. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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14 pages, 4558 KiB

Open AccessArticle

Computational Fluid Dynamics Study of Water Entry Impact Forces of an Airborne-Launched, Axisymmetric, Disk-Type Autonomous Underwater Hovering Vehicle

by Chen-Wei Chen and Yi-Fan Lu

Symmetry 2019, 11(9), 1100; https://doi.org/10.3390/sym11091100 - 02 Sep 2019

Cited by 11 | Viewed by 2744

Abstract

An autonomous underwater hovering vehicle (AUH) is a novel, dish-shaped, axisymmetric, multi-functional, ultra-mobile submersible in the autonomous underwater vehicle (AUV) family. Numerical studies of nonlinear, asymmetric water entry impact forces on symmetrical, airborne-launched AUVs from conventional single-arm cranes on a research vessel, or helicopters or planes, is significant for the fast and safe launching of low-speed AUVs into the target sea area in the overall design. Moreover, a single-arm crane is one of the important ways to launch AUVs with high expertise and security. However, AUVs are still subject to a huge load upon impact during water entry, causing damage to the body, malfunction of electronic components, and other serious accidents. This paper analyses the water entry impact forces of an airborne-launched AUH as a feasibility study for flight- or helicopter-launched AUHs in the future. The computational fluid dynamics (CFD) analysis software STAR-CCM+ solver was adopted to simulate AUH motions with different water entry speeds and immersion angles using overlapping grid technology and user-defined functions (UDFs). In the computational domain for a steady, incompressible, two-dimensional flow of water with identified boundary conditions, two components (two-phase flow) were modeled in the flow field: Liquid water and free surface air. The variations of stress and velocity versus time of the AUH and fluid structure deformation in the whole water entry process were obtained, which provides a reference for future structural designs of an AUH and appropriate working conditions for an airborne-launched AUH. This research will be conducive to smoothly carrying out the complex tasks of AUHs on the seabed. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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Graphical abstract

25 pages, 6061 KiB

Open AccessArticle

Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation

by Rahmat Ellahi, Sadiq M. Sait, N. Shehzad and N. Mobin

Symmetry 2019, 11(8), 1038; https://doi.org/10.3390/sym11081038 - 12 Aug 2019

Cited by 132 | Viewed by 5378

Abstract

The basic motivation of this investigation is to develop an innovative mathematical model for electro-osmotic flow of Couette–Poiseuille nanofluids. The power-law model is treated as the base fluid suspended with nano-sized particles of aluminum oxide (Al₂O₃). The uniform speed of the upper wall in the axial path generates flow, whereas the lower wall is kept fixed. An analytic solution for nonlinear flow dynamics is obtained. The ramifications of entropy generation, magnetic field, and a constant pressure gradient are appraised. Moreover, the physical features of most noteworthy substantial factors such as the electro-osmotic parameter, magnetic parameter, power law fluid parameter, skin friction, Nusselt number, Brinkman number, volume fraction, and concentration are adequately delineated through various graphs and tables. The convergence analysis of the obtained solutions has been discussed explicitly. Recurrence formulae in each case are also presented. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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13 pages, 1246 KiB

Open AccessArticle

The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

by M. Imran, D.L.C. Ching, Rabia Safdar, Ilyas Khan, M. A. Imran and K. S. Nisar

Symmetry 2019, 11(8), 962; https://doi.org/10.3390/sym11080962 - 01 Aug 2019

Cited by 4 | Viewed by 2879

Abstract

The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = [...] Read more.

Ω R t^{p}

with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtained solutions in the terms of the Modified Bessel’s equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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15 pages, 1980 KiB

Open AccessFeature PaperArticle

Two-Dimensional Advection–Diffusion Process with Memory and Concentrated Source

by Najma Ahmed, Nehad Ali Shah and Dumitru Vieru

Symmetry 2019, 11(7), 879; https://doi.org/10.3390/sym11070879 - 04 Jul 2019

Cited by 14 | Viewed by 2647

Abstract

Two-dimensional advection–diffusion processes with memory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studied model is a fractional differential equation with short-tail memory (a differential equation with Caputo–Fabrizio time-fractional derivatives). An analytical solution of the initial-boundary value problem has been determined by employing the Laplace transform and double sine-Fourier transforms. A numerical solution of the studied problem has been determined using finite difference approximations. Numerical simulations for both solutions have been carried out using the software Mathcad. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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16 pages, 6837 KiB

Open AccessArticle

Numerical Investigation of the Savonius Vertical Axis Wind Turbine and Evaluation of the Effect of the Overlap Parameter in Both Horizontal and Vertical Directions on Its Performance

by Mohammad Ebrahimpour, Rouzbeh Shafaghat, Rezvan Alamian and Mostafa Safdari Shadloo

Symmetry 2019, 11(6), 821; https://doi.org/10.3390/sym11060821 - 21 Jun 2019

Cited by 50 | Viewed by 10038

Abstract

Exploiting wind energy, which is a complex process in urban areas, requires turbines suitable for unfavorable weather conditions, in order to trap the wind from different directions; Savonius turbines are suitable for these conditions. In this paper, the effect of overlap ratios and the position of blades on a vertical axis wind turbine is comprehensively investigated and analyzed. For this purpose, two positive and negative overlap situations are first defined along the X-axis and examined at the different tip speed ratios of the blade, while maintaining the size of the external diameter of the rotor, to find the optimum point; then, the same procedure is done along the Y-axis. The finite volume method is used to solve the computational fluid dynamics. Two-dimensional numerical simulations are performed using URANS equations and the sliding mesh method. The turbulence model employed is a realizable K-ε model. According to the values of the dynamic torque and power coefficient, while investigating horizontal and vertical overlaps along the X- and Y-axis, the blades with overlap ratios of HOLR = +0.15 and VOLR = +0.1 show better performances when compared to other corresponding overlaps. Accordingly, the average C_m and C_p improvements are 16% and 7.5%, respectively, compared to the base with a zero overlap ratio. Full article

(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)

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