Fluids, Volume 2, Issue 2 (June 2017) – 22 articles

An algorithm is derived for a hyperelastic incompressible solid coupled with a Newtonian fluid. It is based on a Eulerian formulation of the full system in which the main variables are the velocities. After a fully implicit discretization in time it is possible to eliminate the displacements and solve a variational equation for the velocities and pressures only. The stability of the method depends heavily on the use of characteristic-Galerkin discretization of the total derivatives. For comparison with previous works, the method is tested on a three-dimensional (3D) clamped beam in a pipe filled with a fluid. Convergence is studied numerically on an axisymmetric case. Full article

A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations. Full article

Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO₂ sequestration. The viscosity contrasts between heavy oil and water is several orders of magnitude larger than typical viscosity contrasts considered in the majority of the literature. We use the finite element method (FEM)-based COMSOL Multiphysics simulator to simulate miscible displacements in homogeneous porous media with very large viscosity contrasts. Our numerical model is suitable for a wide range of viscosity contrasts covering chromatographic separation as well as heavy oil recovery. We have successfully captured some interesting and previously unexplored dynamics of miscible blobs with very large viscosity contrasts in homogeneous porous media. We study the effect of viscosity contrast on the spreading and the degree of mixing of the blob. Spreading (variance of transversely averaged concentration) follows the power law $t^{3.34}$ for the blobs with viscosity $\sim \mathcal{O}\left({10}^2\right)$ and higher, while degree of mixing is found to vary non-monotonically with log-mobility ratio. Moreover, in the limit of very large viscosity contrast, the circular blob behaves like an erodible solid body and the degree of mixing approaches the viscosity-matched case. Full article

Computational fluid dynamics (CFD) can be seen as complementary tool alongside the visualization capabilities of cardiovascular magnetic resonance (CMR) and computed tomography (CT) imaging for decision-making. In this research CT images of three cases (i.e., a healthy heart pilot project and two patients with complex aortic disease) are used to validate and analyse the corresponding computational results. Three 3D domains of the thoracic aorta were tested under hemodynamic conditions. Under normal conditions, the flow inside the thoracic aorta is more streamlined. In the presence of ascending aortic aneurysm, large areas of blue separation zones (i.e., low velocities) are identified, as well as an internal geometry deformation of the aortic wall, respectively. This flow separation is characterized by the reversal of flow and sudden drop of the wall shear stress (WSS) in the aorta. Moreover, the aortic aneurysm simulations adversely affect the flow by increasing the pressure drop and flow inefficiency, due to the anatomical configuration of the ascending aorta. Altered hemodynamics led to a vortex formation and locally reversed the flow that eventually induced a low flow velocity and oscillating WSS in the thoracic aorta. Significant changes in the hemodynamic characteristics affect the normal blood circulation with strong turbulence occurrence, damaging the aortic wall, leading ultimately to the need of surgical intervention to avoid fatal events. Full article

Turbulence intensity profiles are compared for smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. The profile development in the transition from hydraulically smooth to fully rough flow displays a propagating sequence from the pipe wall towards the pipe axis. The scaling of turbulence intensity with Reynolds number shows that the smooth- and rough-wall level deviates with increasing Reynolds number. We quantify the correspondence between turbulence intensity and the friction factor. Full article

Magnetic drug targeting is a technique that involves the binding of medicine to magnetizable particles to allow for more specific transport to the target location. This has recently come to light as a method of drug delivery that reduces the disadvantages of conventional, systemic treatments. This study developed a mathematical model for tracking individual superparamagnetic nanoparticles in blood flow in the presence of an externally applied magnetic field. The model considers the magnetic attraction between the particles and the external magnet, influence of power law flow, diffusive interaction between the particles and blood, and random collisions with red blood cells. A stochastic system of differential equations is presented and solved numerically to simulate the paths taken by particles in a blood vessel. This study specifically focused on localized cancer treatment, in which a surface tumor is accessed through smaller blood vessels, which are more conducive to this delivery method due to slower flow velocities and smaller diameters. The probability of the particles reaching the tumor location is found to be directly dependent on ambient factors; thus, diffusion through Brownian motion and red blood cell collisions, different magnetic field and force models, blood viscosities, and release points are considered. Full article

Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant ${\mathbf{k}}_{\perp }$ cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases. Full article

Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4${\pi }^2$ . At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase. Full article

A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed. Full article

Miniaturized cells can be used in photo-electrochemistry to perform water splitting. The geometry, process variables and removal of oxygen bubbles in these cells need to be optimized. Bubbles tend to remain attached to the catalytic surface, thus blocking the reaction, and they therefore need to be dragged out of the cell. Computational Fluid Dynamics simulations have been carried out to assess the design of miniaturized cells and their results have been compared with experimental results. It has been found that low liquid inlet velocities (~0.1 m/s) favor the homogeneous distribution of the flow. Moderate velocities (0.5–1 m/s) favor preferred paths. High velocities (~2 m/s) lead to turbulent behavior of the flow, but avoid bubble coalescence and help to drag the bubbles. Gravity has a limited effect at this velocity. Finally, channeled cells have also been analyzed and they allow a good flow distribution, but part of the catalytic area could be lost. The here presented results can be used as guidelines for the optimum design of photocatalytic cells for the water splitting reaction for the production of solar fuels, such as H₂ or other CO₂ reduction products (i.e., CO, CH₄, among others). Full article

A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations using the conservation for energy and potential enstrophy is presented. Different mechanisms, such as vortical flows and emission of gravity waves, emerge from different conservation laws for total energy and potential enstrophy. The equations are constructed using exterior differential forms and self-adjoint operators, and result in the sum of two Nambu brackets—one for the vortical flow and one for the wave-mean flow interaction—and a Poisson bracket representing the interaction between divergence and geostrophic imbalance. The advantage of this approach is that the Hamiltonian and Nambu forms can here be written in a coordinate-independent form. Full article

In this work, the fluid mechanics performance of four different contraction wall shapes has been studied and compared side-by-side by computational simulation, and the effect of contraction cross-sectional shape on the flow uniformity at the contraction exit has been included as well. A different contraction wall shape could result in up to an extra 4% pressure drop of a closed-loop wind tunnel, and the contraction wall shape has a stronger influence on the pressure loss than the contraction cross-sectional shape. The first and the second derivatives from different wall shape equations could provide a hint for qualitatively comparing the flow uniformity at the contraction exits. A wind tunnel contraction with an octagonal shape provides not only better fluid mechanics performance than that with a circular or a square cross-sectional shape, but also lower manufacturing costs. Moreover, a smaller blockage ratio within the test section can be achieved by employing an octagonal cross-sectional shape instead of a circular cross-sectional shape under the same hydraulic diameter circumstance. A wind tunnel contraction with an octagonal cross-sectional shape is recommended to be a design candidate. Full article

Penetrative convection due to purely internal heating in a horizontal ferrofluid-saturated porous layer is examined by performing linear stability analysis. Four different types of heat supply functions are considered. The Darcy model is used to incorporate the effect of the porous medium. Numerical solutions are obtained by using the Chebyshev pseudospectral method, and the results are discussed for all three boundary conditions: when both boundaries are impermeable and conducting; when both boundaries are conducting with lower boundary impermeable and free upper boundary; and when both boundaries are impermeable with lower boundary conducting and upper with constant heat flux. The effect of the Langevin parameter, width of ferrofluid layer, permeability parameter, and nonlinearity of the fluid magnetization has been observed at the onset of penetrative convection for water- and ester-based ferrofluids. It is seen that the Langevin parameter, width of ferrofluid layer, and permeability parameter have stabilizing effects on the onset of convection, while the nonlinearity of the fluid magnetization advances the onset of convection. Full article

This paper presents a numerical study of high wavenumber coherent structure evolution in boundary layer transition flow using recently-developed high order Combined compact difference schemes with non-uniform grids in the wall-normal direction for efficient simulation of such flows. The study focuses on a simulation of an Adverse-Pressure-Gradient (APG) boundary layer transition induced by broadband disturbance corresponding to the experiment of Borodulin et al. (Journal of Turbulence, 2006, 7, pp. 1–30). The results support the experimental observation that although the coherent structures seen during transition to turbulence have asymmetric shapes and occur in a random pattern, their local evolutional behaviors are quite similar. Further calculated local wavelet spectra of these coherent structures are also very similar. The wavelet spectrum of the streamwise disturbance velocity demonstrates high wavenumber clusters at the tip and the rear parts of the Λ-vortex. Both parts are imbedded at the primary Λ-vortex stage and spatially coincide with the spike region and high shear layer. The tip part is associated with the later first ring-like vortex, while the rear part with the remainder of the Λ-vortex. These observations help to shed light on the generation of turbulence, which is dominated by high wavenumber coherent structures. Full article

McDougall, Groeskamp and Griffies (MGG) strongly criticise all aspects of Tailleux (2016) that challenge the current conventional wisdom about the use of neutral density concepts for studying and parameterising lateral ocean stirring and mixing. However, their claim that most of Tailleux (2016)’s results or conclusions are incorrect is easily shown to originate: (1) from mistakingly confusing Tailleux’s Eulerian arguments for Lagrangian ones; (2) from their irrational belief that only one particular kind of quasi-material surface is somehow endorsed by Nature and hence relevant to the description of stirring and mixing—namely the locally-defined neutral tangent planes—stating at one point: “why should the ocean care about human constructed density variables”? MGG appear to overlook the simple fact that solutions of the Navier–Stokes equations—which synthesise our ideas about how Nature works—never require the introduction of any form of quasi-material or quasi-neutral density variable. This implies that the empirical isopycnal/isentropic stirring property is necessarily an emergent property of the Navier–Stokes equations, and hence that all forms of isopycnal surfaces—both neutral and not—are necessarily all human constructs. To establish the relevance of any particular construct to the actual ocean, an explicit model of stirring is needed to elucidate the nature of the dynamical/energetics constraints on lateral stirring. Even in the simplest model of stirring, neutral stirring represents only one possible mode out of a continuum of stirring modes responsible for lateral stirring in the ocean, without any evidence that it should dominate over the other ones. To help clarify the issues involved, it is proposed to regard the rigorous study of ocean stirring and mixing as relying on at least five distinct stages, from defining a model of stirring to constructing physically-based mixing parameterisations in numerical ocean models. Full article

Tailleux has written about the concept of epineutral mixing and has attempted to justify it from an energetic viewpoint. However, Tailleux’s approach is incorrect because it ignores the unsteady nature of the density field during baroclinic motions, which in turn leads to incorrect conclusions. Tailleux also asserts that “adiabatic and isohaline parcel exchanges can only be meaningfully defined on material surfaces” that are functions of only Absolute Salinity and Conservative Temperature and are not separately a function of pressure. We disagree with this assertion because there is no physical reason why the ocean should care about a globally-defined function of Absolute Salinity and Conservative Temperature that we construct. Rather, in order to understand and justify the concept of epineutral mixing, we consider the known physical processes that occur at the in situ pressure of the mixing. The Tailleux paper begins with two incorrect equations that ignore the transience of the ocean. These errors echo throughout Tailleux, leading to sixteen conclusions, most of which we show are incorrect. (Comment on Tailleux, R. Neutrality Versus Materiality: A Thermodynamic Theory of Neutral Surfaces. Fluids 2016, 1, 32, doi:10.3390/fluids1040032.) Full article

In the present work, the flow field in a splitting-junction micro channel with a Y shape, which is the simplest geometry to be employed for heat and mass transfer in micro-devices such as micro-heat-exchangers and micro-mixers, is investigated experimentally using micro Particle Image Velocimetry (μPIV). The angular divergence in the Y splitting is changed, as well as the Reynolds number, in order to investigate the instantaneous and mean flow fields to determine which configurations are more suitable for practical applications. The results show that the flow configuration is strongly dependent on the Y shape angle, especially in the junction part, and that there is also a significant dependence on the Reynolds number. Full article

Computational Fluid Dynamics (CFD) has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged Navier-Stokes (RANS) equations is applied, the turbulent scalar fluxes are generally estimated by assuming the standard gradient diffusion hypothesis (SGDH), which requires the definition of the turbulent Schmidt number, Sc_t (the ratio of momentum diffusivity to mass diffusivity in the turbulent flow). However, no universally-accepted values of this parameter have been established or, more importantly, methodologies for its computation have been provided. This paper firstly presents a review of previous studies about Sc_t in environmental flows, involving both water and air systems. Secondly, three case studies are presented where the key role of a correct parameterization of the turbulent Schmidt number is pointed out. These include: (1) transverse mixing in a shallow water flow; (2) tracer transport in a contact tank; and (3) sediment transport in suspension. An overall picture on the use of the Schmidt number in CFD emerges from the paper. Full article

The effect of varying wall flexibility on the deformation of an artery during steady and pulsatile flow of blood is investigated. The artery geometry is recreated from patient-derived data for a stenosed left coronary artery. Blood flow in the artery is modeled using power-law fluid. The fluid-structure interaction of blood flow on artery wall is simulated using ANSYS 16.2, and the resulting wall deformation is documented. A comparison of wall deformation using flexibility models like Rigid, Linear Elastic, Neo-hookean, Mooney-Rivlin and Holzapfel are obtained for teady flow in the artery. The maximum wall deformation in coronary flow onditions predicted by the Holzapfel model is only around 50% that predicted by the Neo-Hookean model. The flow-induced deformations reported here for patient-derived stenosed coronary artery with physiologically accurate model are the first of its kind. These results help immensely in the planning of angioplasty. Full article

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook’s equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook’s equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook’s equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly. Full article

Solving two-dimensional compressible turbulence problems up to a resolution of 16, 384², this paper investigates the characteristics of two promising computational approaches: (i) an implicit or numerical large eddy simulation (ILES) framework using an upwind-biased fifth-order weighted essentially non-oscillatory (WENO) reconstruction algorithm equipped with several Riemann solvers, and (ii) a central sixth-order reconstruction framework combined with various linear and nonlinear explicit low-pass spatial filtering processes. Our primary aim is to quantify the dissipative behavior, resolution characteristics, shock capturing ability and computational expenditure for each approach utilizing a systematic analysis with respect to its modeling parameters or parameterizations. The relative advantages and disadvantages of both approaches are addressed for solving a stratified Kelvin-Helmholtz instability shear layer problem as well as a canonical Riemann problem with the interaction of four shocks. The comparisons are both qualitative and quantitative, using visualizations of the spatial structure of the flow and energy spectra, respectively. We observe that the central scheme, with relaxation filtering, offers a competitive approach to ILES and is much more computationally efficient than WENO-based schemes. Full article

The majority of aerospace structural composites use thermoset resins for their processing flexibility, temperature capability, and environmental durability. In this study, the recovery behavior of Veriflex-E, an epoxy-based, thermosetting, thermally-triggered shape memory polymer (SMP) resin, is investigated in glassy (25 °C) and rubbery (130 °C) states, as a function of shape memory cycles, and as a means to evaluate its potential as a resin for a shape memory composite. At 25 °C, Veriflex-E exhibits a promising high elastic modulus and a positive, nonlinear strain rate sensitivity in monotonic loading. At 130 °C, the strain rate sensitivity in monotonic loading decreases. Stress relaxation after storage in the deformed temporary state and subsequent shape recovery is of particular interest, a challenge to measure, and has not been widely reported for SMPs. The current experimental program measures the influence of strain rate changes in the 10⁻⁴–10⁻² s⁻¹ range on the stress relaxation response of the material, as well as on the strain recovery behavior at both 25 °C and 130 °C. As expected, the post-relaxation strain is larger with faster loading. Unexpectedly, the total strain recovered after shape memory cycling is more similar to the low temperature deformation. Overall, the results suggest that, while being influenced by both the loading rate and the test temperature, Veriflex-E is a promising candidate for a shape memory composite which could enable adaptive structures. Full article