Fluids

22 pages, 5156 KiB

Open AccessArticle

Analysis of the Aerodynamics in the Heating Section of an Anode Baking Furnace Using Non-Linear Finite Element Simulations

by Prajakta Nakate, Domenico Lahaye, Cornelis Vuik and Marco Talice

Fluids 2021, 6(1), 46; https://doi.org/10.3390/fluids6010046 - 19 Jan 2021

Cited by 4 | Viewed by 4011

Abstract

The emissions from the industrial furnaces impact the environment. Among the various factories, those having anode baking furnaces are working on reducing the pollutant emissions. The aerodynamics in the furnace influences the emissions due to the high dependence of combustion and radiation phenomena [...] Read more.

The emissions from the industrial furnaces impact the environment. Among the various factories, those having anode baking furnaces are working on reducing the pollutant emissions. The aerodynamics in the furnace influences the emissions due to the high dependence of combustion and radiation phenomena on the mixing characteristics. Therefore, this paper aims to establish the numerical simulation results for the three-dimensional turbulent flow in a single section of an anode baking furnace with a high rate of fuel injection. The stabilized non-linear finite element approach on the Reynolds-averaged Navier-Stokes (RANS) equation is used with COMSOLMultiphysics. The turbulent viscosity ratio is highly sensitive to the mesh for the standard k-

ϵ

model. The requirements of the Cartesian and refined mesh near the jet development region is explained. The comparison of meshes generated by two meshing tools namely cfMesh and COMSOL Multiphysics default Mesher is carried out. The high numerical diffusion in the flow models due to the coarser mesh leads to convergence but deficit the precision in the results. This paper shows that the mesh generated by cfMesh with flow aligned refinement combined with the non-linear finite element solver in COMSOL Multiphysics proves to provide accurate results of turbulent quantities. Full article

(This article belongs to the Special Issue Analytical and Computational Fluid Dynamics of Combustion and Fires [dedicated to Prof. Vitaly Bychkov (1968–2015) of Umea University, Sweden])

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8 pages, 202 KiB

Open AccessEditorial

Acknowledgment to Reviewers of Fluids in 2020

by Fluids Editorial Office

Fluids 2021, 6(1), 45; https://doi.org/10.3390/fluids6010045 - 18 Jan 2021

Viewed by 1675

Abstract

Peer review is the driving force of journal development, and reviewers are gatekeepers who ensure that Fluids maintains its standards for the high quality of its published papers [...] Full article

16 pages, 3520 KiB

Open AccessArticle

Some Observations on Shape Factors Influencing Aerodynamic Lift on Passenger Cars

by Jeff Howell, Steve Windsor and Martin Passmore

Fluids 2021, 6(1), 44; https://doi.org/10.3390/fluids6010044 - 18 Jan 2021

Cited by 5 | Viewed by 9236

Abstract

The car aerodynamicist developing passenger cars is primarily interested in reducing aerodynamic drag. Considerably less attention is paid to the lift characteristics except in the case of high-performance cars. Lift, however, can have an effect on both performance and stability, even at moderate [...] Read more.

The car aerodynamicist developing passenger cars is primarily interested in reducing aerodynamic drag. Considerably less attention is paid to the lift characteristics except in the case of high-performance cars. Lift, however, can have an effect on both performance and stability, even at moderate speeds. In this paper, the basic shape features which affect lift and the lift distribution, as determined from the axle loads, are examined from wind tunnel tests on various small-scale bodies representing passenger cars. In most cases, the effects of yaw are also considered. The front-end shape is found to have very little effect on overall lift, although it can influence the lift distribution. The shape of the rear end of the car, however, is shown to be highly influential on the lift. The add-on components and other features can have a significant effect on the lift characteristics of real passenger cars and are briefly discussed. The increase in lift at yaw is, surprisingly, almost independent of shape, as shown for the simple bodies. This characteristic is less pronounced on real passenger cars but lift increase at yaw is shown to rise with vehicle length. Full article

(This article belongs to the Special Issue Aerodynamics and Aeroacoustics of Vehicles)

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14 pages, 4457 KiB

Open AccessArticle

Heat Transfer Enhancement inside Rectangular Channel by Means of Vortex Generated by Perforated Concave Rectangular Winglets

by Syaiful, Monica Pranita Hendraswari, M.S.K. Tony S.U. and Maria F. Soetanto

Fluids 2021, 6(1), 43; https://doi.org/10.3390/fluids6010043 - 17 Jan 2021

Cited by 7 | Viewed by 2573

Abstract

Passive methods using vortex generators (VGs) to enhance heat transfer have been a concern of researchers in recent decades. This study is intended to investigate the strength of the vortex generated by VGs by trying to reduce the pressure drop in the flow. [...] Read more.

Passive methods using vortex generators (VGs) to enhance heat transfer have been a concern of researchers in recent decades. This study is intended to investigate the strength of the vortex generated by VGs by trying to reduce the pressure drop in the flow. The present work also takes into account the influence of the vortex intensity on the improvement of heat transfer, which can be indicated by the low value of the synergy angle. Experiments were carried out in the current investigation to validate the results of the numerical simulations in the Reynolds number range of 3102 to 16,132. The study results indicate that the observed heat transfer coefficients from the experimental and simulation results have a similar tendency with relatively small errors. A reduction in pressure drop is observed with the use of perforated concave rectangular winglets (PCRWs) against the nonperforated ones although there was a slight decrease in heat transfer improvements. Full article

(This article belongs to the Section Mathematical and Computational Fluid Mechanics)

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20 pages, 363 KiB

Open AccessArticle

On the Existence of Leray-Hopf Weak Solutions to the Navier-Stokes Equations

by Luigi C. Berselli and Stefano Spirito

Fluids 2021, 6(1), 42; https://doi.org/10.3390/fluids6010042 - 13 Jan 2021

Cited by 5 | Viewed by 4247

Abstract

We give a rather short and self-contained presentation of the global existence for Leray-Hopf weak solutions to the three dimensional incompressible Navier-Stokes equations, with constant density. We give a unified treatment in terms of the domains and the relative boundary conditions and in [...] Read more.

We give a rather short and self-contained presentation of the global existence for Leray-Hopf weak solutions to the three dimensional incompressible Navier-Stokes equations, with constant density. We give a unified treatment in terms of the domains and the relative boundary conditions and in terms of the approximation methods. More precisely, we consider the case of the whole space, the flat torus, and the case of a general bounded domain with a smooth boundary (the latter supplemented with homogeneous Dirichlet conditions). We consider as approximation schemes the Leray approximation method, the Faedo-Galerkin method, the semi-discretization in time and the approximation by adding a Smagorinsky-Ladyžhenskaya term. We mainly focus on developing a unified treatment especially in the compactness argument needed to show that approximations converge to the weak solutions. Full article

(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics, Volume II)

13 pages, 944 KiB

Open AccessArticle

Onset of Inertial Magnetoconvection in Rotating Fluid Spheres

by Radostin D. Simitev and Friedrich H. Busse

Fluids 2021, 6(1), 41; https://doi.org/10.3390/fluids6010041 - 13 Jan 2021

Cited by 4 | Viewed by 2847

Abstract

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied in this paper. Thermo-inertial convection is a distinctive flow regime on the border between rotating thermal convection and wave [...] Read more.

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied in this paper. Thermo-inertial convection is a distinctive flow regime on the border between rotating thermal convection and wave propagation. It occurs in astrophysical and geophysical contexts where self-sustained or external magnetic fields are commonly present. To investigate the onset of motion, a perturbation method is used here with an inviscid balance in the leading order and a buoyancy force acting against weak viscous dissipation in the next order of approximation. Analytical evaluation of constituent integral quantities is enabled by applying a Green’s function method for the exact solution of the heat equation following our earlier non-magnetic analysis. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained. In both cases, explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. It is found that an imposed azimuthal magnetic field exerts a stabilizing influence on the onset of inertial convection and as a consequence magneto-inertial convection with azimuthal wave number of unity is generally preferred. Full article

(This article belongs to the Special Issue Thermal Flows)

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22 pages, 2005 KiB

Open AccessEditor’s ChoiceArticle

Turbulent Bubble-Laden Channel Flow of Power-Law Fluids: A Direct Numerical Simulation Study

by Felix Bräuer, Elias Trautner, Josef Hasslberger, Paolo Cifani and Markus Klein

Fluids 2021, 6(1), 40; https://doi.org/10.3390/fluids6010040 - 12 Jan 2021

Cited by 17 | Viewed by 3116

Abstract

The influence of non-Newtonian fluid behavior on the flow statistics of turbulent bubble-laden downflow in a vertical channel is investigated. A Direct Numerical Simulation (DNS) study is conducted for power-law fluids with power-law indexes of 0.7 (shear-thinning), 1 (Newtonian) and 1.3 (shear-thickening) in [...] Read more.

The influence of non-Newtonian fluid behavior on the flow statistics of turbulent bubble-laden downflow in a vertical channel is investigated. A Direct Numerical Simulation (DNS) study is conducted for power-law fluids with power-law indexes of 0.7 (shear-thinning), 1 (Newtonian) and 1.3 (shear-thickening) in the liquid phase at a gas volume fraction of 6%. The flow is driven downward by a constant volumetric flow rate corresponding to a friction Reynolds number of

R e_{τ} \approx 127.3

. The Eötvös number is varied between

E o = 0.3125

and

E o = 3.75

in order to investigate the influence of quasi-spherical as well as wobbling bubbles and thus the interplay of the bubble deformability with the power-law behavior of the liquid bulk. The resulting first- and second-order fluid statistics, i.e., the gas fraction, mean velocity and velocity fluctuation profiles across the channel, show clear trends in reply to varying power-law indexes. In addition, it was observed that the bubble oscillations increase with decreasing power-law index. In the channel core, the bubbles significantly increase the dissipation rate, which, in contrast to its behavior at the wall, shows similar orders of magnitude for all power-law indexes. Full article

(This article belongs to the Special Issue Modelling of Reactive and Non-reactive Multiphase Flows)

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34 pages, 11340 KiB

Open AccessEditor’s ChoiceArticle

An Optimized-Parameter Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows

by Margaux Filippi, Irina I. Rypina, Alireza Hadjighasem and Thomas Peacock

Fluids 2021, 6(1), 39; https://doi.org/10.3390/fluids6010039 - 12 Jan 2021

Cited by 14 | Viewed by 4189

Abstract

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building [...] Read more.

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al. (2016), a new optimized-parameter spectral clustering approach is developed that automatically identifies optimal parameters within pre-defined ranges. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The optimized-parameter spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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18 pages, 2383 KiB

Open AccessArticle

Comparison of Rheological Behaviour of Bio-Based and Synthetic Epoxy Resins for Making Ecocomposites

by Samireh Vahid, Valentino Burattini, Saeed Afshinjavid and Arash Dashtkar

Fluids 2021, 6(1), 38; https://doi.org/10.3390/fluids6010038 - 12 Jan 2021

Cited by 5 | Viewed by 3063

Abstract

In this paper, the rheological behaviour of a petroleum-based epoxy (EL2 laminating epoxy) was compared with the Super Sap CLR clear bio-resin epoxy. The focus of the work was on the viscous and viscoelastic performance of these epoxy resins. Rheological tests were carried [...] Read more.

In this paper, the rheological behaviour of a petroleum-based epoxy (EL2 laminating epoxy) was compared with the Super Sap CLR clear bio-resin epoxy. The focus of the work was on the viscous and viscoelastic performance of these epoxy resins. Rheological tests were carried out at 15, 30, and 60 min after the mixing of the pure epoxies and the hardeners at a constant temperature of 25 °C. The results obtained from the rheometer tests showed that the viscosity of both epoxy systems decreased with increasing shear rate, which is typical behaviour of a shear thinning fluid. Regarding the oscillatory rheology tests, the viscoelastic properties of both epoxy resins were studied within their linear viscoelastic region (LVER) by amplitude sweep test, which was also carried out 15, 30, and 60 min after mixing the epoxies with the hardeners. It was noticed that the petroleum-based epoxy possessed a more significant LVER relative to the bio-based resin. Finally, the storage modulus (G′), the loss modulus (G″), and the phase angle were extracted, and these parameters were investigated over low and high frequencies. From the test results, we observed that both epoxy resins showed a liquid-like viscoelastic behaviour due to their phase angle values, which were always between 45° and 90°, and by the general tendency of the G″ predominance over G′ at low and high frequencies. Full article

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18 pages, 7414 KiB

Open AccessArticle

Non-Modal Three-Dimensional Optimal Perturbation Growth in Thermally Stratified Mixing Layers

by Helena Vitoshkin and Alexander Gelfgat

Fluids 2021, 6(1), 37; https://doi.org/10.3390/fluids6010037 - 11 Jan 2021

Cited by 3 | Viewed by 2461

Abstract

A non-modal transient disturbances growth in a stably stratified mixing layer flow is studied numerically. The model accounts for a density gradient within a shear region, implying a heavier layer at the bottom. Numerical analysis of non-modal stability is followed by a full [...] Read more.

A non-modal transient disturbances growth in a stably stratified mixing layer flow is studied numerically. The model accounts for a density gradient within a shear region, implying a heavier layer at the bottom. Numerical analysis of non-modal stability is followed by a full three-dimensional direct numerical simulation (DNS) with the optimally perturbed base flow. It is found that the transient growth of two-dimensional disturbances diminishes with the strengthening of stratification, while three-dimensional disturbances cause significant non-modal growth, even for a strong, stable stratification. This non-modal growth is governed mainly by the Holmboe modes and does not necessarily weaken with the increase of the Richardson number. The optimal perturbation consists of two waves traveling in opposite directions. Compared to the two-dimensional transient growth, the three-dimensional growth is found to be larger, taking place at shorter times. The non-modal growth is observed in linearly stable regimes and, in slightly linearly supercritical regimes, is steeper than that defined by the most unstable eigenmode. The DNS analysis confirms the presence of the structures determined by the transient growth analysis. Full article

(This article belongs to the Special Issue Thermal Flows)

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26 pages, 42430 KiB

Open AccessArticle

Computational Study of Premixed Flame Propagation in Micro-Channels with Nonslip Walls: Effect of Wall Temperature

by Orlando J. Ugarte and V’yacheslav Akkerman

Fluids 2021, 6(1), 36; https://doi.org/10.3390/fluids6010036 - 11 Jan 2021

Cited by 5 | Viewed by 2491

Abstract

This investigation evaluates the propagation of premixed flames in narrow channels with isothermal walls. The study is based on the numerical solution of the set of fully-compressible, reacting flow equations that includes viscosity, diffusion, thermal conduction and Arrhenius chemical kinetics. Specifically, channels and [...] Read more.

This investigation evaluates the propagation of premixed flames in narrow channels with isothermal walls. The study is based on the numerical solution of the set of fully-compressible, reacting flow equations that includes viscosity, diffusion, thermal conduction and Arrhenius chemical kinetics. Specifically, channels and pipes with one extreme open and one extreme closed are considered such that a flame is sparked at the closed extreme and propagates towards the open one. The isothermal channel walls are kept at multiple constant temperatures in the range from

T_{w} = 300 K

to

1200 K

. The impact of these isothermal walls on the flame dynamics is studied for multiple radii of the channel (

R

) and for various thermal expansion ratios (

Θ

), which approximate the thermal behavior of different fuel mixtures in the system. The flame dynamics in isothermal channels is also compared to that with adiabatic walls, which were previously found to produce exponential flame acceleration at the initial stage of the burning process. The results show that the heat losses at the walls prevent strong acceleration and lead to much slower flame propagation in isothermal channels as compared to adiabatic ones. Four distinctive regimes of premixed burning in isothermal channels have been identified in the

Θ - T_{w} - R

space: (i) flame extinction; (ii) linear flame acceleration; (iii) steady or near-steady flame propagation; and (iv) flame oscillations. The physical processes in each of these regimes are discussed, and the corresponding regime diagrams are presented. Full article

(This article belongs to the Special Issue Analytical and Computational Fluid Dynamics of Combustion and Fires [dedicated to Prof. Vitaly Bychkov (1968–2015) of Umea University, Sweden])

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24 pages, 3163 KiB

Open AccessArticle

Coherent Streamwise Vortex Structure of a Three-Dimensional Wall Jet

by Lhendup Namgyal and Joseph W. Hall

Fluids 2021, 6(1), 35; https://doi.org/10.3390/fluids6010035 - 11 Jan 2021

Viewed by 2291

Abstract

The dynamics of the coherent structures in a turbulent three-dimensional wall jet with an exit Reynolds number of 250,000 were investigated using the Snapshot Proper Orthogonal Decomposition (POD). A low-dimensional reconstruction using the first 10 POD modes indicates that the turbulent flow is [...] Read more.

The dynamics of the coherent structures in a turbulent three-dimensional wall jet with an exit Reynolds number of 250,000 were investigated using the Snapshot Proper Orthogonal Decomposition (POD). A low-dimensional reconstruction using the first 10 POD modes indicates that the turbulent flow is dominated by streamwise vortex structures that grow in size and relative strength, and that are often accompanied by strong lateral sweeps of fluid across the wall. This causes an increase in the bulging and distortions of streamwise velocity contours as the flow evolves downstream. The instantaneous streamwise vorticity computed from the reconstructed instantaneous velocities has a high level of vorticity associated with these outer streamwise vortex structures, but often has a persistent pair of counter-rotating regions located close to the wall on either side of the jet centerline. A model of the coherent structures in the wall jet is presented. In this model, streamwise vortex structures are produced in the near-field by the breakdown of vortex rings formed at the jet outlet. Separate structures are associated with the near-wall streamwise vorticity. As the flow evolves downstream, the inner near-wall structures tilt outward, while the outer streamwise structures amalgamate to form larger streamwise asymmetric structures. In all cases, these streamwise vortex structures tend to cause large lateral velocity sweeps in the intermediate and far-field regions of the three-dimensional wall jet. Further, these structures meander laterally across the jet, causing a strongly intermittent jet flow. Full article

(This article belongs to the Special Issue Turbulent Flow)

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23 pages, 334 KiB

Open AccessArticle

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. II: Application to a Nuclear Reactor Thermal-Hydraulics Safety Benchmark

by Dan Gabriel Cacuci

Fluids 2021, 6(1), 34; https://doi.org/10.3390/fluids6010034 - 10 Jan 2021

Cited by 1 | Viewed by 1777

Abstract

Responses defined at critical points are particularly important for reactor safety analyses and licensing (e.g., the maximum fuel and/or clad temperature). The novel mathematical framework of the first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP) is applied in this work to [...] Read more.

Responses defined at critical points are particularly important for reactor safety analyses and licensing (e.g., the maximum fuel and/or clad temperature). The novel mathematical framework of the first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP) is applied in this work to develop a reactor safety thermal-hydraulics benchmark model which admits exact closed-form expressions for the adjoint functions and for the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) in physical systems characterized by imprecisely known parameters, external and internal boundaries. This benchmark model is designed for verifying the capabilities and accuracies of computational tools for modeling numerically thermal-hydraulics systems. The unique and extensive capabilities of the 1st-CASAM-CP methodology are demonstrated in this work by considering two responses of paramount importance in reactor safety, namely, (i) the maximum rod surface temperature, which occurs at the imprecisely known interface between the subsystem that models the heat conduction inside the heated rod and the subsystem modeling the heat convection process surrounding the rod; and (ii) the maximum temperature inside the heated rod, which has a critical point with two components, one located at a precisely known boundary of the subsystem that models the heat conduction inside the heated rod, while the other component depends on an imprecisely known boundary (i.e., the rod length). The exact analytical expressions developed in this work for the sensitivities of the maximum internal rod temperature and maximum rod surface temperature, as well as for the sensitivities of the locations where these respective maxima occur, provide exact benchmarks for verifying the accuracy of thermal-hydraulics computational tools. The sensitivities of such responses and of their critical points with respect to model parameters enable the quantification of uncertainties induced by uncertainties stemming from the system’s parameters and boundaries in the respective responses and their underlying critical points. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

24 pages, 413 KiB

Open AccessArticle

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. I: Mathematical Framework

by Dan Gabriel Cacuci

Fluids 2021, 6(1), 33; https://doi.org/10.3390/fluids6010033 - 10 Jan 2021

Cited by 1 | Viewed by 1804

Abstract

This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP), which enables the exact and efficient computation of the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) of coupled nonlinear models of physical systems [...] Read more.

This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP), which enables the exact and efficient computation of the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) of coupled nonlinear models of physical systems characterized by imprecisely known parameters underlying the models, boundaries, and interfaces between the coupled systems. Responses defined at critical points are important in many applications, including system optimization, safety analyses and licensing. For the design and licensing of nuclear reactors, such essentially important responses include the maximum temperatures of the fuel and cladding in hot channels. The 1st-CASAM-CP presented in this work makes it possible to determine, using a single large-scale “adjoint” computation, the first-order sensitivities of the magnitude of a response defined at a critical point of a function in the phase-space of the systems’ independent variables. In addition, the 1st-CASAM-CP enables the computation of the sensitivities of the location in phase-space of the critical point at which the respective response is located: one “adjoint” computation is required for each component of the respective critical point in the phase-space of independent variables. By enabling the exact and efficient computation of the sensitivities of responses and of their critical locations to imprecisely known model parameters, boundaries, and interfaces, the 1st-CASAM-CP significantly extends the practicality of analyzing crucially important responses for large-scale systems involving many uncertain parameters, interfaces, and boundaries. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

22 pages, 2890 KiB

Open AccessArticle

A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

by Kazuo Aoki, Marzia Bisi, Maria Groppi and Shingo Kosuge

Fluids 2021, 6(1), 32; https://doi.org/10.3390/fluids6010032 - 8 Jan 2021

Cited by 4 | Viewed by 2117

Abstract

The two-temperature Navier–Stokes equations derived from an ellipsoidal Bhatnagar-Gross-Krook (ES-BGK) model for a polyatomic gas (Phys. Rev. E102, 023104 (2020)) are considered in regimes where bulk viscosity is much greater than the shear viscosity. Possible existence of a shock-wave solution [...] Read more.

The two-temperature Navier–Stokes equations derived from an ellipsoidal Bhatnagar-Gross-Krook (ES-BGK) model for a polyatomic gas (Phys. Rev. E102, 023104 (2020)) are considered in regimes where bulk viscosity is much greater than the shear viscosity. Possible existence of a shock-wave solution for the steady version of these hydrodynamic equations is investigated resorting to the qualitative theory of dynamical systems. Stability properties of upstream and downstream equilibria are discussed for varying parameters. Full article

(This article belongs to the Special Issue Rarefied Gas Dynamics)

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18 pages, 1390 KiB

Open AccessArticle

Use of Nanoparticle Enhanced Phase Change Material for Cooling of Surface Acoustic Wave Sensor

by Mohammad Yaghoub Abdollahzadeh Jamalabadi

Fluids 2021, 6(1), 31; https://doi.org/10.3390/fluids6010031 - 8 Jan 2021

Cited by 8 | Viewed by 2936

Abstract

The use of resonators, filters, interdigital transducers (IDT) and stable sources in electronic industry is widespread today. One of the most used filters are the surface acoustic wave (SAW) type, which is mostly based on Rayleigh waves propagation on the surface. On the [...] Read more.

The use of resonators, filters, interdigital transducers (IDT) and stable sources in electronic industry is widespread today. One of the most used filters are the surface acoustic wave (SAW) type, which is mostly based on Rayleigh waves propagation on the surface. On the other hand, the use of Phase change materials (PCMs) is considered as a heat sink method in the field of thermal cooling of electronic circuits. Recent development in heat transfer is obtained by nanoparticle-enhanced PCM (NEPCM), which is a result of combining nanoparticles with PCMs. Increase of thermal conductivity of NEPCM in comparison with common PCM enhances the heat transfer rate. The aim of the current study is thermal management of SAW for the application of high frequency heating by phase change material. Melting of NEPCMs inside a rectangular cavity next to the SAW cell is used for the cooling purpose. Free convection heat transfer of a NEPCMs in an square cavity is modeled throughout the mass and momentum. Energy governing equations are solved by using the finite element method. Electrohydrodynamic (EHD) forces exist in natural convection heat transfer within the fluid part of the enclosure. The results also show that the NEPCM causes heat transfer improvement up to 10%. Full article

(This article belongs to the Special Issue Fluids in Magnetic/Electric Fields)

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23 pages, 14025 KiB

Open AccessEditor’s ChoiceArticle

The Zoo of Modes of Convection in Liquids Vibrated along the Direction of the Temperature Gradient

by Georgie Crewdson and Marcello Lappa

Fluids 2021, 6(1), 30; https://doi.org/10.3390/fluids6010030 - 8 Jan 2021

Cited by 16 | Viewed by 2902

Abstract

Thermovibrational flow can be seen as a variant of standard thermogravitational convection where steady gravity is replaced by a time-periodic acceleration. As in the parent phenomena, this type of thermal flow is extremely sensitive to the relative directions of the acceleration and the [...] Read more.

Thermovibrational flow can be seen as a variant of standard thermogravitational convection where steady gravity is replaced by a time-periodic acceleration. As in the parent phenomena, this type of thermal flow is extremely sensitive to the relative directions of the acceleration and the prevailing temperature gradient. Starting from the realization that the overwhelming majority of research has focused on circumstances where the directions of vibrations and of the imposed temperature difference are perpendicular, we concentrate on the companion case in which they are parallel. The increased complexity of this situation essentially stems from the properties that are inherited from the corresponding case with steady gravity, i.e., the standard Rayleigh–Bénard convection. The need to overcome a threshold to induce convection from an initial quiescent state, together with the opposite tendency of acceleration to damp fluid motion when its sign is reversed, causes a variety of possible solutions that can display synchronous, non-synchronous, time-periodic, and multi-frequency responses. Assuming a square cavity as a reference case and a fluid with Pr = 15, we tackle the problem in a numerical framework based on the solution of the governing time-dependent and non-linear equations considering different amplitudes and frequencies of the applied vibrations. The corresponding vibrational Rayleigh number spans the interval from Ra_ω = 10⁴ to Ra_ω = 10⁶. It is shown that a kaleidoscope of possible variants exist whose nature and variety calls for the simultaneous analysis of their temporal and spatial behavior, thermofluid-dynamic (TFD) distortions, and the Nusselt number, in synergy with existing theories on the effect of periodic accelerations on fluid systems. Full article

(This article belongs to the Special Issue Thermal Flows)

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13 pages, 2473 KiB

Open AccessEditor’s ChoiceArticle

Time-Dependent Motion of a Floating Circular Elastic Plate

by Michael H. Meylan

Fluids 2021, 6(1), 29; https://doi.org/10.3390/fluids6010029 - 8 Jan 2021

Cited by 21 | Viewed by 3443

Abstract

The motion of a circular elastic plate floating on the surface is investigated in the time-domain. The solution is found from the single frequency solutions, and the method to solve for the circular plate is given using the eigenfunction matching method. Simple plane [...] Read more.

The motion of a circular elastic plate floating on the surface is investigated in the time-domain. The solution is found from the single frequency solutions, and the method to solve for the circular plate is given using the eigenfunction matching method. Simple plane incident waves with a Gaussian profile in wavenumber space are considered, and a more complex focused wave group is considered. Results are given for a range of plate and incident wave parameters. Code is provided to show how to simulate the complex motion. Full article

(This article belongs to the Special Issue Mathematical and Numerical Modeling of Water Waves)

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19 pages, 1245 KiB

Open AccessArticle

On the Use of a Domain Decomposition Strategy in Obtaining Response Statistics in Non-Gaussian Seas

by Griet Decorte, Alessandro Toffoli, Geert Lombaert and Jaak Monbaliu

Fluids 2021, 6(1), 28; https://doi.org/10.3390/fluids6010028 - 7 Jan 2021

Cited by 3 | Viewed by 3280

Abstract

During recent years, thorough experimental and numerical investigations have led to an improved understanding of dynamic phenomena affecting the fatigue life and survivability of offshore structures, e.g., ringing and springing and extreme wave impacts. However, most of these efforts have focused on modeling [...] Read more.

During recent years, thorough experimental and numerical investigations have led to an improved understanding of dynamic phenomena affecting the fatigue life and survivability of offshore structures, e.g., ringing and springing and extreme wave impacts. However, most of these efforts have focused on modeling either selected extreme events or sequences of highly nonlinear waves impacting offshore structures, possibly overestimating the actual load to be experienced by the structure. Overall, not much has been done regarding short-term statistics. Although clear non-Gaussian statistics and therefore higher probabilities of extreme waves have been observed in random seas due to wave–wave interaction phenomena, which can impact short-term statistics for the structural load, they have not been studied extensively regarding the assessment of the dynamic behavior of offshore structures. Computational fluid dynamics (CFD) models have shown their viability for studying wave–structure interaction phenomena. Despite the continuously increasing computational resources, these models remain too computationally demanding for applications to the large spatial domains and long periods of time necessary for studying short-term statistics of non-Gaussian seas. Higher-order spectral (HOS) models, on the other hand, have been proven to be efficient and adequate in studying non-Gaussian seas. We therefore propose a one-way domain decomposition strategy, which takes full advantage of the recent advances in CFD and of the computational benefits of HOS. When applying this domain decomposition strategy, it appeared to be possible to deduce response statistics regarding the impact of nonlinear wave–wave interactions. Full article

(This article belongs to the Special Issue Selected Papers from the 15th OpenFOAM Workshop)

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16 pages, 23821 KiB

Open AccessArticle

Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

by J. Barry Greenberg and David Katoshevski

Fluids 2021, 6(1), 27; https://doi.org/10.3390/fluids6010027 - 6 Jan 2021

Viewed by 2157

Abstract

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid [...] Read more.

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts. Full article

(This article belongs to the Special Issue Fluid Flow and Its Impact on Combustion)

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15 pages, 5287 KiB

Open AccessArticle

A Momentum-Conserving Scheme for Flow Simulation in 1D Channel with Obstacle and Contraction

by Putu Veri Swastika, Sri Redjeki Pudjaprasetya, Leo Hari Wiryanto and Revi Nurfathhiyah Hadiarti

Fluids 2021, 6(1), 26; https://doi.org/10.3390/fluids6010026 - 6 Jan 2021

Cited by 7 | Viewed by 3097

Abstract

We consider the extension of the momentum conservative staggered-grid (MCS) scheme for flow simulation in channels with varying depth and width. The scheme is formulated using the conservative properties of the Saint-Venant equations. The proposed scheme was successful in handling various steady flows [...] Read more.

We consider the extension of the momentum conservative staggered-grid (MCS) scheme for flow simulation in channels with varying depth and width. The scheme is formulated using the conservative properties of the Saint-Venant equations. The proposed scheme was successful in handling various steady flows and achieved results that are in complete accordance with the analytical steady solutions. Different choices of boundary conditions have created steady solutions according to the mass and energy conservations. This assessment has served as a validation of the proposed numerical scheme. Further, in a channel with a contraction and a nonuniform bed, we simulate two cases of dam break. The simulation results show a good agreement with existing experimental data. Moreover, our scheme, that uses a quasi-1-dimensional approach, has shown some fair agreement with existing 2-dimensional numerical results. This evaluation demonstrates the merits of the MCS scheme for various flow simulations in channels of varying width and bathymetry, suitable for river flow modeling. Full article

(This article belongs to the Special Issue Mathematical and Numerical Modeling of Water Waves)

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20 pages, 4720 KiB

Open AccessArticle

Efficiency Improvement of Miniaturized Heat Exchangers

by Iris Gerken, Thomas Wetzel and Jürgen J. Brandner

Fluids 2021, 6(1), 25; https://doi.org/10.3390/fluids6010025 - 6 Jan 2021

Cited by 4 | Viewed by 3307

Abstract

Micro heat exchangers have been revealed to be efficient devices for improved heat transfer due to short heat transfer distances and increased surface-to-volume ratios. Further augmentation of the heat transfer behaviour within microstructured devices can be achieved with heat transfer enhancement techniques, and [...] Read more.

Micro heat exchangers have been revealed to be efficient devices for improved heat transfer due to short heat transfer distances and increased surface-to-volume ratios. Further augmentation of the heat transfer behaviour within microstructured devices can be achieved with heat transfer enhancement techniques, and more precisely for this study, with passive enhancement techniques. Pin fin geometries influence the flow path and, therefore, were chosen as the option for further improvement of the heat transfer performance. The augmentation of heat transfer with micro heat exchangers was performed with the consideration of an improved heat transfer behaviour, and with additional pressure losses due to the change of flow path (pin fin geometries). To capture the impact of the heat transfer, as well as the impact of additional pressure losses, an assessment method should be considered. The overall exergy loss method can be applied to micro heat exchangers, and serves as a simple assessment for characterization. Experimental investigations with micro heat exchanger structures were performed to evaluate the assessment method and its importance. The heat transfer enhancement was experimentally investigated with microstructured pin fin geometries to understand the impact on pressure loss behaviour with air. Full article

(This article belongs to the Special Issue Recent Advances in Single and Multiphase Flows in Microchannels)

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17 pages, 3991 KiB

Open AccessArticle

On the Evaluation of Mesh Resolution for Large-Eddy Simulation of Internal Flows Using Openfoam

by Zahra Seifollahi Moghadam, François Guibault and André Garon

Fluids 2021, 6(1), 24; https://doi.org/10.3390/fluids6010024 - 5 Jan 2021

Cited by 11 | Viewed by 4504

Abstract

The central aim of this paper is to use OpenFOAM for the assessment of mesh resolution requirements for large-eddy simulation (LES) of flows similar to the ones which occur inside the draft-tube of hydraulic turbines at off-design operating conditions. The importance of this [...] Read more.

The central aim of this paper is to use OpenFOAM for the assessment of mesh resolution requirements for large-eddy simulation (LES) of flows similar to the ones which occur inside the draft-tube of hydraulic turbines at off-design operating conditions. The importance of this study is related to the fact that hydraulic turbines often need to be operated over an extended range of operating conditions, which makes the investigation of fluctuating stresses crucial. Scale-resolving simulation (SRS) approaches, such as LES and detached-eddy simulation (DES), have received more interests in the recent decade for understanding and mitigating unsteady operational behavior of hydro turbines. This interest is due to their ability to resolve a larger part of turbulent flows. However, verification studies in LES are very challenging, since errors in numerical discretization, but also subgrid-scale (SGS) models, are both influenced by grid resolution. A comprehensive examination of the literature shows that SRS for different operating conditions of hydraulic turbines is still quite limited and that there is no consensus on mesh resolution requirement for SRS studies. Therefore, the goal of this research is to develop a reliable framework for the validation and verification of SRS, especially LES, so that it can be applied for the investigation of flow phenomena inside hydraulic turbine draft-tube and runner at their off-design operating conditions. Two academic test cases are considered in this research, a turbulent channel flow and a case of sudden expansion. The sudden expansion test case resembles the flow inside the draft-tube of hydraulic turbines at part load. In this study, we concentrate on these academic test cases, but it is expected that hydraulic turbine flow simulations will eventually benefit from the results of the current research. The results show that two-point autocorrelation is more sensitive to mesh resolution than energy spectra. In addition, for the case of sudden expansion, the mesh resolution has a tremendous effect on the results, and, so far, we have not capture an asymptotic converging behavior in the results of Root Mean Square (RMS) of velocity fluctuations and two-point autocorrelation. This case, which represents complex flow behavior, needs further mesh resolution studies. Full article

(This article belongs to the Special Issue Selected Papers from the 15th OpenFOAM Workshop)

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17 pages, 2273 KiB

Open AccessArticle

Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios

by Mohamed El Ouafa, Stephane Vincent and Vincent Le Chenadec

Fluids 2021, 6(1), 23; https://doi.org/10.3390/fluids6010023 - 5 Jan 2021

Cited by 8 | Viewed by 3157

Abstract

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such [...] Read more.

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods. Full article

(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)

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21 pages, 3488 KiB

Open AccessArticle

Numerical Investigation of Thermally Developing and Fully Developed Electro-Osmotic Flow in Channels with Rounded Corners

by Nicola Suzzi and Marco Lorenzini

Fluids 2021, 6(1), 22; https://doi.org/10.3390/fluids6010022 - 4 Jan 2021

Cited by 4 | Viewed by 2912

Abstract

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as [...] Read more.

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as microchannels with cross sections of almost arbitrary shape can easily be integrated on the chips. It is therefore important to assess how the geometry of the channel influences the heat transfer performance. In this paper, the thermal entry region and the fully developed electro-osmotic flow in a microchannel of rectangular cross section with smoothed corners is investigated for uniform wall temperature. For the fully developed region, correlations for the Poiseuille and Nusselt numbers considering the aspect ratio and nondimensional smoothing radius are given, which can be used for practical design purposes. For thermally developing flow, it is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it also shortens the thermal entry length. It is also found that Joule heating in the fluid may cause a reversal of the heat flux, and that the thermal entry length has a linear dependence on the Reynolds number and the hydraulic diameter and on the logarithm of the nondimensional Joule heating. Full article

(This article belongs to the Special Issue Recent Advances in Single and Multiphase Flows in Microchannels)

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11 pages, 22333 KiB

Open AccessArticle

Ultra-Lean Gaseous Flames in Terrestrial Gravity Conditions

by Ivan Yakovenko, Alexey Kiverin and Ksenia Melnikova

Fluids 2021, 6(1), 21; https://doi.org/10.3390/fluids6010021 - 3 Jan 2021

Cited by 10 | Viewed by 2524

Abstract

Development of the combustion process in the gaseous mixtures of near-limit composition is of great interest for fundamental aspects of combustion theory and fire-safety applications. The dynamics of ultra-lean gaseous flames in near-limit mixtures is governed by many effects, such as buoyancy, preferential [...] Read more.

Development of the combustion process in the gaseous mixtures of near-limit composition is of great interest for fundamental aspects of combustion theory and fire-safety applications. The dynamics of ultra-lean gaseous flames in near-limit mixtures is governed by many effects, such as buoyancy, preferential diffusion, radiation, and instability development. Though ultra-lean combustion was extensively studied in microgravity conditions, the influence of gravity on the ultra-lean flame structure and stability is still poorly understood. The paper is devoted to deepening the knowledge of ultra-lean flame dynamics in hydrogen-air mixtures under terrestrial gravity conditions. The spatial structures of the flame developing under the effect of buoyancy forces are investigated employing detailed numerical analysis. Different modes of near-limit flame evolution are observed depending on the mixture concentration. In particular, we registered and described three distinct spatial structures: individual kernels tending to extinguish in leanest compounds, complex multi-kernel structures in marginal compositions, and stable cap-shaped flames in more chemically active mixtures. We apply the flame-bubble analogy to interpret flame dynamics. On this basis, the diagram in the Re-Fr plane is developed. That allows classifying the emerging flame structures and determine flame stability. Additionally, different ignition modes are studied, and the mechanisms determining the impact of ignition mode on the flammability limits are distinguished. Obtained results provide useful insights into the processes of flame quenching and development in near-limit hydrogen-air mixtures under real gravity conditions and can be applied in the design of contemporary fire-safety systems. Full article

(This article belongs to the Special Issue Analytical and Computational Fluid Dynamics of Combustion and Fires [dedicated to Prof. Vitaly Bychkov (1968–2015) of Umea University, Sweden])

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17 pages, 549 KiB

Open AccessArticle

Low-Speed DSMC Simulations of Hotwire Anemometers at High-Altitude Conditions

by Christopher A. Roseman and Brian M. Argrow

Fluids 2021, 6(1), 20; https://doi.org/10.3390/fluids6010020 - 2 Jan 2021

Cited by 4 | Viewed by 2708

Abstract

Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast [...] Read more.

Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast time responses are achieved by the wires having small diameters (1–5

μ

m). Hotwire instruments are currently being used to make in-situ measurements of high-altitude turbulence (20–40 km). At these altitudes, hotwires experience Knudsen number values that lie in the transition-regime between slip-flow and free-molecular flow. This article expands the current knowledge of hotwire anemometers by investigating their behavior in the transition-regime. Challenges involved with simulating hotwires at high Knudsen number and low Reynolds number conditions are discussed. The ability of the DSMC method to simulate hotwires from the free-molecular to slip-flow regimes is demonstrated. Dependence of heat transfer on surface accommodation coefficient is explored and discussed. Simulation results of Nusselt number dependence on Reynolds number show good agreement with experimental data. Magnitude discrepancies are attributed to differences between simulation and experimental conditions, while discrepancies in trend are attributed to finite simulation domain size. Full article

(This article belongs to the Special Issue Rarefied Gas Dynamics)

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14 pages, 3918 KiB

Open AccessCase Report

Bidimensional Ray Tracing Model for the Underwater Noise Propagation Prediction

by Emmanuele D’Andrea, Maurizio Arena, Massimo Viscardi and Tommaso Coppola

Fluids 2021, 6(1), 19; https://doi.org/10.3390/fluids6010019 - 1 Jan 2021

Cited by 2 | Viewed by 2656

Abstract

An increasing attention has recently been paid to the effect of the underwater noise field generated by ship activities on the marine environment. Although this problem is widely discussed in international treaties and conventions, it has not yet found a consolidated technical-scientific treatment [...] Read more.

An increasing attention has recently been paid to the effect of the underwater noise field generated by ship activities on the marine environment. Although this problem is widely discussed in international treaties and conventions, it has not yet found a consolidated technical-scientific treatment capable of quantifying the level of underwater noise emissions produced by naval systems. As part of a national research collaboration, a novel code has been developed to predict noise propagation according to the Ray Tracing approach. Such optical geometry-based technique allows for calculating the Transmission Loss (TL) trend in its respective contributions: geometrical loss (due to the distance between the source and receiver), dissipation loss (due to the characteristics of the propagation environment), and reflection loss (due to the surfaces that delimit the field). The simulation requires as input parameters the source info as spatial position, frequency, and sound pressure level (SPL) as well as the sea properties like seabed depth, the speed of sound profile, the layers thickness the water column is divided into, the sea salinity, temperature, and pH. The simulation code provides the SPL spatial distribution useful as a fast industrial tool in the future studies addressed to identify the emission limits for the protection of marine wildlife. Full article

(This article belongs to the Special Issue Models and Applications of Acoustic for Fluids)

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12 pages, 488 KiB

Open AccessArticle

Stability Analysis for an Interface with a Continuous Internal Structure

by Mikhail Modestov

Fluids 2021, 6(1), 18; https://doi.org/10.3390/fluids6010018 - 1 Jan 2021

Cited by 2 | Viewed by 1919

Abstract

A general method for solving a linear stability problem of an interface with a continuous internal structure is described. Such interfaces or fronts are commonly found in various branches of physics, such as combustion and plasma physics. It extends simplified analysis of an [...] Read more.

A general method for solving a linear stability problem of an interface with a continuous internal structure is described. Such interfaces or fronts are commonly found in various branches of physics, such as combustion and plasma physics. It extends simplified analysis of an infinitely thin discontinuous front by means of numerical integration along the steady-state solution. Two examples are presented to demonstrate the application of the method for 1D pulsating instability in magnetic deflagration and 2D Darrieus–Landau instability in a laser ablation wave. Full article

(This article belongs to the Special Issue Analytical and Computational Fluid Dynamics of Combustion and Fires [dedicated to Prof. Vitaly Bychkov (1968–2015) of Umea University, Sweden])

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18 pages, 994 KiB

Open AccessArticle

The Half-Range Moment Method in Harmonically Oscillating Rarefied Gas Flows

by Giorgos Tatsios, Alexandros Tsimpoukis and Dimitris Valougeorgis

Fluids 2021, 6(1), 17; https://doi.org/10.3390/fluids6010017 - 1 Jan 2021

Cited by 3 | Viewed by 1950

Abstract

The formulation of the half-range moment method (HRMM), well defined in steady rarefied gas flows, is extended to linear oscillatory rarefied gas flows, driven by oscillating boundaries. The oscillatory Stokes (also known as Stokes second problem) and the oscillatory Couette flows, as representative [...] Read more.

The formulation of the half-range moment method (HRMM), well defined in steady rarefied gas flows, is extended to linear oscillatory rarefied gas flows, driven by oscillating boundaries. The oscillatory Stokes (also known as Stokes second problem) and the oscillatory Couette flows, as representative ones for harmonically oscillating half-space and finite-medium flow setups respectively, are solved. The moment equations are derived from the linearized time-dependent BGK kinetic equation, operating accordingly over the positive and negative halves of the molecular velocity space. Moreover, the boundary conditions of the “positive” and “negative” moment equations are accordingly constructed from the half-range moments of the boundary conditions of the outgoing distribution function, assuming purely diffuse reflection. The oscillatory Stokes flow is characterized by the oscillation parameter, while the oscillatory Couette flow by the oscillation and rarefaction parameters. HRMM results for the amplitude and phase of the velocity and shear stress in a wide range of the flow parameters are presented and compared with corresponding results, obtained by the discrete velocity method (DVM). In the oscillatory Stokes flow the so-called penetration depth is also computed. When the oscillation frequency is lower than the collision frequency excellent agreement is observed, while when it is about the same or larger some differences are present. Overall, it is demonstrated that the HRMM can be applied to linear oscillatory rarefied gas flows, providing accurate results in a very wide range of the involved flow parameters. Since the computational effort is negligible, it is worthwhile to consider the efficient implementation of the HRMM to stationary and transient multidimensional rarefied gas flows. Full article

(This article belongs to the Special Issue Rarefied Gas Dynamics)

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