Fluids

238 KiB

Open AccessArticle

On Thermomechanics of a Nonlinear Heat Conducting Suspension

by Mehrdad Massoudi and A. D. Kirwan

Fluids 2016, 1(2), 19; https://doi.org/10.3390/fluids1020019 - 18 Jun 2016

Cited by 8 | Viewed by 4064

In this short paper, we discuss and provide constitutive relations for the stress tensor and the heat flux vector for a nonlinear density-gradient dependent (Korteweg-type) fluid. Specifically, we attempt to present a unified thermo-mechanical approach to the two models given in papers of [...] Read more.

In this short paper, we discuss and provide constitutive relations for the stress tensor and the heat flux vector for a nonlinear density-gradient dependent (Korteweg-type) fluid. Specifically, we attempt to present a unified thermo-mechanical approach to the two models given in papers of Massoudi (International Journal of Non-Linear Mechanics, 2001, 36(1), pp. 25–37.) and Massoudi (Mathematical Methods in the Applied Sciences, 2006, 29(13), pp. 1599–1613.) where the entropy law is used and restrictions are also obtained on the constitutive parameters. In most thermomechanical studies of nonlinear fluids using the entropy law, the stress tensor is assumed to be nonlinear and the heat flux vector still has the form of the Fourier type, i.e., it is proportional to the temperature gradient. In this paper, we use a generalized (nonlinear) form for the heat flux vector. When our model is linearized we obtain constraints, due to the entropy inequality, which are in agreement with the earlier results. Full article

(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)

230 KiB

Open AccessArticle

Rendering the Navier–Stokes Equations for a Compressible Fluid into the Schrödinger Equation for Quantum Mechanics

by Peter Vadasz

Fluids 2016, 1(2), 18; https://doi.org/10.3390/fluids1020018 - 13 Jun 2016

Cited by 9 | Viewed by 5009

Abstract

The mass and momentum transfer phenomena in a compressible fluid represented by the Navier–Stokes equations are shown to convert into the Schrödinger equation for quantum mechanics. The complete Navier–Stokes equations render into an extended generalized version of Schrödinger equation. These results complement the [...] Read more.

The mass and momentum transfer phenomena in a compressible fluid represented by the Navier–Stokes equations are shown to convert into the Schrödinger equation for quantum mechanics. The complete Navier–Stokes equations render into an extended generalized version of Schrödinger equation. These results complement the Madelung’s (Zeitschrift für Physik 40 (3–4), pp. 322–326, 1926–1927) derivations that show how Schrödinger’s equation in quantum mechanics can be converted into the Euler equations for irrotational compressible flow. The theoretical results presented here join the classical Madelung paper to suggest the possibility that quantum effects at sub-atomic levels deal with a compressible fluid susceptible to wave propagation, rather than a particle. The link between such a fluid and the “quantum particle” is under current investigation. Full article

1837 KiB

Open AccessArticle

A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography

by David P. Marshall

Fluids 2016, 1(2), 17; https://doi.org/10.3390/fluids1020017 - 27 May 2016

Cited by 5 | Viewed by 5266

Abstract

An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for [...] Read more.

An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f and

f / H

contours, where f is the Coriolis parameter and H is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an

f / H

contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the

f / H

contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies. Full article

(This article belongs to the Collection Geophysical Fluid Dynamics)

► Show Figures

Graphical abstract

4277 KiB

Open AccessReview

Mathematical Modeling and Computer Simulations of Nanofluid Flow with Applications to Cooling and Lubrication

by Clement Kleinstreuer and Zelin Xu

Fluids 2016, 1(2), 16; https://doi.org/10.3390/fluids1020016 - 27 May 2016

Cited by 44 | Viewed by 9162

Abstract

There is a growing range of applications of nanoparticle-suspension flows with or without heat transfer. Examples include enhanced cooling of microsystems with low volume-fractions of nanoparticles in liquids, improved tribological performance with lubricants seeded with nanoparticles, optimal nanodrug delivery in the pulmonary as [...] Read more.

There is a growing range of applications of nanoparticle-suspension flows with or without heat transfer. Examples include enhanced cooling of microsystems with low volume-fractions of nanoparticles in liquids, improved tribological performance with lubricants seeded with nanoparticles, optimal nanodrug delivery in the pulmonary as well as the vascular systems to combat cancer, and spray-coating using plasma-jets with seeded nanoparticles. In order to implement theories that explain experimental evidence of nanoparticle-fluid dynamics and predict numerically optimum system performance, a description of the basic math modeling and computer simulation aspects is necessary. Thus, in this review article, the focus is on the fundamental understanding of the physics of nanofluid flow and heat transfer with summaries of microchannel-flow applications related to cooling and lubrication. Full article

(This article belongs to the Special Issue Fundamental Studies in Flow and Heat Transfer in Nanofluids)

► Show Figures

Figure 1

2926 KiB

Open AccessArticle

Modeling the Viscoelastic Behavior of Amorphous Shape Memory Polymers at an Elevated Temperature

by Fangda Cui, Swapnil Moon and I. Joga Rao

Fluids 2016, 1(2), 15; https://doi.org/10.3390/fluids1020015 - 13 May 2016

Cited by 8 | Viewed by 5389

Abstract

Shape memory polymers (SMPs) are soft active materials, their special property is the ability to hold a temporary shape and when exposed to a suitable trigger, they come back to their original shape. These external stimuli can be temperature, light or electro-magnetic fields. [...] Read more.

Shape memory polymers (SMPs) are soft active materials, their special property is the ability to hold a temporary shape and when exposed to a suitable trigger, they come back to their original shape. These external stimuli can be temperature, light or electro-magnetic fields. Amorphous SMPs are a class of thermally-activated SMPs that rely on glass transition to retain their temporary shape. Above the glass transition temperature (T > T_g), (amorphous SMPs exhibit finite deformation and viscoelastic behavior. In this work we develop a model to capture the viscoelastic behavior of the amorphous SMPs at elevated temperatures. The model uses an approach that was initially developed to study non-Newtonian viscoelastic fluids. We accomplish this by developing a multi-branch model based on the theory of multiple natural configurations using the maximization of the rate dissipation to determine the evolution of the natural configurations. We apply our model to study several different deformations at an elevated temperature T = 130 °C and show that this approach is able to capture the viscoelastic behavior of these polymers. The predictions of the theory are then compared with experimental results. Full article

(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)

► Show Figures

Figure 1

1211 KiB

Open AccessArticle

Natural Drag-Reducing Polymers: Discovery, Characterization and Potential Clinical Applications

by Joie N. Marhefka and Marina V. Kameneva

Fluids 2016, 1(2), 6; https://doi.org/10.3390/fluids1020006 - 6 May 2016

Cited by 9 | Viewed by 5110

Abstract

About seven decades ago, it was discovered that special long-chain soluble polymers added to fluid at nanomolar concentrations significantly reduce resistance to turbulent flow (Toms effect). These so-called drag-reducing polymers (DRPs) do not affect resistance to laminar flow. While the flow parameters associated [...] Read more.

About seven decades ago, it was discovered that special long-chain soluble polymers added to fluid at nanomolar concentrations significantly reduce resistance to turbulent flow (Toms effect). These so-called drag-reducing polymers (DRPs) do not affect resistance to laminar flow. While the flow parameters associated with the Toms effect do not occur in the cardiovascular system, many later studies demonstrated that intravenous injections of DRPs given to experimental animals produced significant hemodynamic effects, such as increasing tissue perfusion, suggesting potential clinical use of these polymers. Moreover, it was found that the specific viscoelastic properties of these polymers make them capable of modifying traffic of blood cells in microvessels and beneficially redistributing them in the blood capillary system—a phenomenon related to rheological properties of DRPs and not related to their specific chemistry. The domain of drag reducing polymers includes many organic and water-soluble, synthetic and natural long-chain molecules. The study presented here employed chemical and rheological methods, as well as macro and microfluidic tests, to characterize the DRP that we discovered in the Aloe vera plant, which was found to be a more powerful drag reducer and less fragile than many synthetic DRPs. The drag-reducing component of aloe gel was purified and chemically identified, which helped to standardize preparation and made this polymer a strong candidate for clinical use. Examples of successful testing of the aloe-derived DRP in animal models are described. Full article

(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)

► Show Figures

Figure 1

554 KiB

Open AccessReview

Review of CFD Guidelines for Dispersion Modeling

by Robert Meroney, Ryohji Ohba, Bernd Leitl, Hiroaki Kondo, David Grawe and Yoshihide Tominaga

Fluids 2016, 1(2), 14; https://doi.org/10.3390/fluids1020014 - 5 May 2016

Cited by 37 | Viewed by 10651

Abstract

This is the review of CFD (Computational Fluid Dynamics) guidelines for dispersion modeling in the USA, Japan and Germany. Most parts of this review are based on the short report of the special meeting on CFD Guidelines held at the International Symposium on [...] Read more.

This is the review of CFD (Computational Fluid Dynamics) guidelines for dispersion modeling in the USA, Japan and Germany. Most parts of this review are based on the short report of the special meeting on CFD Guidelines held at the International Symposium on Computational Wind Engineering (CWE2014), University of Hamburg, June 2014. The objective of this meeting was to introduce and discuss the action program to make worldwide guidelines of CFD gas-dispersion modeling. The following six gas-dispersion guidelines including Verification and Validation (V&V) schemes are introduced by each author; (1) US CFD guidelines; (2) COST/ES1006; (3) German VDI (Verein Deutscher Ingenieure) guidelines; (4) Atomic Energy Society of Japan; (5) Japan Society of Atmospheric Environment; (6) Architectural Institute of Japan. All guidelines were summarized in the same format table shown in the main chapters in order to compare them with each other. In addition to the summary of guidelines, the overview of V&V schemes and many guidelines of CFD modeling in the USA are explained. Full article

► Show Figures

Figure 1

4808 KiB

Open AccessArticle

Fofonoff Negative Modes

by Joseph Pedlosky

Fluids 2016, 1(2), 13; https://doi.org/10.3390/fluids1020013 - 15 Apr 2016

Cited by 2 | Viewed by 3476

Abstract

The classic solution of Fofonoff to the problem of free inertial flow in a closed basin is extended to the case where the potential vorticity, q, is linearly proportional to the streamfunction, with a negative definite constant,

- K^{2}

. Such [...] Read more.

The classic solution of Fofonoff to the problem of free inertial flow in a closed basin is extended to the case where the potential vorticity, q, is linearly proportional to the streamfunction, with a negative definite constant,

- K^{2}

. Such a relation arises naturally in the presence of an eastward flow, instead of Fofonoff’s westward zonal flow on the β plane. The resulting solutions can be wavelike if

K^{2}

=

β L^{2} / U π^{2}

exceeds the critical value of 1 where U is the magnitude of the eastward flow and L is the characteristic meridional scale of the motion. Solutions are presented with various boundary conditions on the basin boundaries, and conditions for which the solutions suffer a resonance are also obtained. It is suggested that oceanic circulations with eastward flows naturally excite these Fofonoff negative modes. The possibility of resonance and instability adds additional physical complexity to the modes. Full article

(This article belongs to the Collection Geophysical Fluid Dynamics)

► Show Figures

Figure 1

3783 KiB

Open AccessArticle

Splash Dynamics of Paint on Dry, Wet, and Cooled Surfaces

by David Baron, Haiyan Su and Ashwin Vaidya

Fluids 2016, 1(2), 12; https://doi.org/10.3390/fluids1020012 - 14 Apr 2016

Cited by 1 | Viewed by 6102

Abstract

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington’s experiments has now [...] Read more.

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington’s experiments has now been clarified. One specific set of such recent studies, which motivates this paper, concerns the fluid dynamics behind Jackson Pollock’s drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors with watercolor paper. Specifically, we conduct experiments to analyze the settling patterns of droplets of watercolor paint on wet and frozen paper. Variations in paint viscosity, paper roughness, paper temperature, and the height of a released droplet are examined from time of impact, through its transient stages, until its final, dry state. Observable phenomena such as paint splashing, spreading, fingering, branching, rheological deposition, and fractal patterns are studied in detail and classified in terms of the control parameters. Full article

(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)

► Show Figures

Figure 1

4434 KiB

Open AccessArticle

Modeling the Viscosity of Concentrated Nanoemulsions and Nanosuspensions

by Rajinder Pal

Fluids 2016, 1(2), 11; https://doi.org/10.3390/fluids1020011 - 12 Apr 2016

Cited by 44 | Viewed by 7729

Abstract

The modeling of the viscous behavior of nanoemulsions and nanosuspensions is discussed. The influences of the viscosity ratio, solvation and aggregation of nanodroplets and nanoparticles on the relative viscosity of nanofluids are considered. The relative viscosity of a nanofluid is strongly affected by [...] Read more.

The modeling of the viscous behavior of nanoemulsions and nanosuspensions is discussed. The influences of the viscosity ratio, solvation and aggregation of nanodroplets and nanoparticles on the relative viscosity of nanofluids are considered. The relative viscosity of a nanofluid is strongly affected by solvation of nanoparticles. The scaling of the relative viscosity of nanoemulsions is successfully carried out using the volume fraction of the solvated nanodroplets. Four sets of experimental relative viscosity data of nanoemulsions consisting of different diameter nanodroplets (27.5 nm–205 nm) all collapse on a single unique curve when the data are scaled on the basis of the volume fraction of the solvated nanodroplets. A similar scaling is achieved using six sets of experimental relative viscosity data on nanosuspensions consisting of different diameter nanoparticles (29 nm–146 nm). A new modified version of the Oldroyd model is proposed to describe and predict the viscosity of nanofluids. The model takes into consideration the influences of the viscosity ratio, solvation and aggregation of nanoparticles/nanodroplets. The same model is applicable to both nanoemulsions and nanosuspensions as it includes the effect of the viscosity ratio (ratio of droplet viscosity to matrix viscosity) on the relative viscosity of nanofluids. More experimental work is needed on nanoemulsions to explore the effect of the viscosity ratio, especially at low values of the viscosity ratio. Full article

(This article belongs to the Special Issue Fundamental Studies in Flow and Heat Transfer in Nanofluids)

► Show Figures

Figure 1

223 KiB

Open AccessArticle

Semicompressible Ocean Thermodynamics and Boussinesq Energy Conservation

by William K. Dewar, Joseph Schoonover, Trevor McDougall and Rupert Klein

Fluids 2016, 1(2), 9; https://doi.org/10.3390/fluids1020009 - 8 Apr 2016

Cited by 5 | Viewed by 4407

Abstract

Equations more accurate than the Boussinesq set that still filter out sound were recently introduced. While these equations were shown to have a consistent potential energy, their thermodynamical behavior and associated implications were not fully analyzed. These shortcomings are remedied in the present [...] Read more.

Equations more accurate than the Boussinesq set that still filter out sound were recently introduced. While these equations were shown to have a consistent potential energy, their thermodynamical behavior and associated implications were not fully analyzed. These shortcomings are remedied in the present note that argues both sets are fully consistent from a thermodynamic perspective. It is further argued that both sets remain computationally competitive with the Boussinesq set. Full article

(This article belongs to the Collection Geophysical Fluid Dynamics)

8593 KiB

Open AccessArticle

Investigation of Slot-Burner Aerodynamics with Recessed-Type Nozzle Geometry

by Arafat Ahmed Bhuiyan, Md. Rezwanul Karim, James T. Hart, Peter J. Witt and Jamal Naser

Fluids 2016, 1(2), 10; https://doi.org/10.3390/fluids1020010 - 8 Apr 2016

Cited by 2 | Viewed by 4574

Abstract

The aerodynamics of fully turbulent jets supplied from rectangular slot-burners was modelled using the Reynolds Averaged Navier–Stokes (RANS) model. Three different turbulent models were considered, such as standard k-ε, RNG k-ε and Reynolds stress turbulence models. The recessed-type nozzle geometry was investigated to [...] Read more.

The aerodynamics of fully turbulent jets supplied from rectangular slot-burners was modelled using the Reynolds Averaged Navier–Stokes (RANS) model. Three different turbulent models were considered, such as standard k-ε, RNG k-ε and Reynolds stress turbulence models. The recessed-type nozzle geometry was investigated to determine the effect of burner geometry on jet development. The slot-burner was based on physical models, which were designed to be representative of typical burner geometries found in tangentially-fired coal boilers. The study was validated against the physical models. The detailed flow field obtained from the simulations was used to explain the aerodynamic development of jets in such burners. It was found that the addition of a recess section to the nozzle geometry introduced significant changes to the flow due to complex pressure and mixing fields being set up inside the recess, which altered the jets once they exited into the open atmosphere. Full article

(This article belongs to the Special Issue Computational Fluid Dynamics)

► Show Figures

Figure 1

1363 KiB

Open AccessArticle

On the Flows of Fluids Defined through Implicit Constitutive Relations between the Stress and the Symmetric Part of the Velocity Gradient

by Kumbakonam R. Rajagopal

Fluids 2016, 1(2), 5; https://doi.org/10.3390/fluids1020005 - 24 Mar 2016

Cited by 3 | Viewed by 4285

Abstract

Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is [...] Read more.

Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is only recently purely algebraic relationships between the stress and the displacement gradient (or the velocity gradient) have been introduced to describe the response of non-linear fluids and solids. Such models can describe phenomena that the classical theory, wherein the stress is expressed explicitly in terms of kinematical variables, is incapable of describing, and they also present a sensible way to approach important practical problems, such as the flows of colloids and suspensions and the turbulent flows of fluids, and that of the fracture of solids. In this paper we review this new class of algebraic implicit constitutive relations that can be used to describe the response of fluids. Full article

(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Fluids, Volume 1, Issue 2 (June 2016) – 13 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI